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Volume 1, Number 1--2, May, 1968Hans Freudenthal Why to teach mathematics so as to be useful . . . . . . . . . . . . . . . . . 3--8 A. Z. Krygovska Processus de la mathématisation dans l'enseignement. (French) [The process of mathematicizing education] . . . . . . . 9--16 J. M. Hammersley On the enfeeblement of mathematical skills by modern mathematics and by similar soft intellectual trash in schools and universities . . . . . . . . 17--17 H. B. Griffiths Pure mathematicians as teachers of applied mathematicians . . . . . . . . . 18--23 H. O. Pollak On some of the problems of teaching applications of mathematics . . . . . . 24--30 André Revuz Les pi\`eges de l'enseignement des mathématiques. (French) [The pitfalls of teaching mathematics] . . . . . . . . . 31--36 W. Servais Comment enseigner la mathématique pour qu'elle soit utile?. (French) [How can we teach mathematics to be useful?] . . 37--54 Jean Tavernier The thinking of a physicist about mathematics . . . . . . . . . . . . . . 55--60 Anonymous Panel discussion . . . . . . . . . . . . 61--79 A. Delessert Quelques observations na\"\ives en marge de deux enquêtes sur l'enseignement mathématique. (French) [Some observations made in the margins of two surveys on mathematical education] . . . . . . . . 80--88 Charles Pisot Enseignement des mathématiques pour physiciens. (French) [Teaching mathematics for physicists] . . . . . . 89--92 Matts Håstad Mathematics and engineers . . . . . . . 93--97 R. C. Lyness Applied mathematics in English schools 98--104 Gail Young The computer and the calculus . . . . . 105--110 R. J. Walker Student use of a computer . . . . . . . 111--117 Maurice Glaymann Initiation au calcul numérique et usage des machines \`a calculer. (French) [Introduction to numerical calculation and use of calculating machines] . . . . 118--125 Murray S. Klamkin On the teaching of mathematics so as to be useful . . . . . . . . . . . . . . . 126--160 H. Behnke Wandlungen in der Auswahl der Stoffe für den Unterricht. (German) [Changes in the choice of subjects for teaching] . . . . 161--165 T. J. Fletcher A heuristic approach to matrices . . . . 166--180 Hans-Georg Steiner Examples of exercises in mathematization on the secondary school level . . . . . 181--201 Arthur Engel Systematic use of applications in mathematics teaching . . . . . . . . . . 202--221 André Roumanet Une expérience d'enseignement de mathématique avec des enfants de 11 \`a 13 ans. (French) [A mathematics-teaching experiment with 11-to-13-year-old children] . . . . . . . . . . . . . . . 222--236 A. Brailly Un exemple d'exploitation d'une `situation'. (French) [An example of exploitation of a `situation'] . . . . . 237--243 Anonymous Propositions on the teaching of mathematics . . . . . . . . . . . . . . 244--244 Anonymous Final recommendations of the participants about the coordination of the teaching of mathematics and physics 245--246
Joseph M. Scandura and Joan Barksdale and John H. Durnin and Robert Mcgee An unexpected relationship between failure and subsequent mathematics learning . . . . . . . . . . . . . . . . 247--251 Keith Hirst and Norman Biggs Undergraduate projects in mathematics 252--261 Jacques Fort Expérimentation d'un enseignement des mathématiques en classe de sixi\`eme des lycées et coll\`eges. (French) [Experimentation in teaching of mathematics in sixth grade of high schools and colleges] . . . . . . . . . 262--273 Emma Castelnuovo Les transformations affines dans le 1er cycle de l'école secondaire. (French) [Affine transformations in the first cycle of secondary school] . . . . . . . 274--288 Hans-Georg Steiner Examples of exercises in mathematization 289--299 Arnold Kirsch An analysis of commercial arithmetic . . 300--311 Burt A. Kaufman and Hans-G. Steiner The CSMP approach to a content-oriented, highly individualized mathematics education . . . . . . . . . . . . . . . 312--326 Hans Freudenthal L'intégration apr\`es coup ou \`a la source. (French) [Integration after the fact or at the source] . . . . . . . . . 327--337 Hans Freudenthal The concept of integration at the Varna Congress . . . . . . . . . . . . . . . . 338--339 Emma Castelnuovo L'intégration centrée autour des mathématiques du 1er cycle de l'enseignement secondaire. (French) [Integration centered on the mathematics of the first cycle of secondary education] . . . . . . . . . . . . . . . 340--342 P. M. Van Hiele Quelques aspects didactiques du développement de la pensée des enfants dans les mathématiques et la physique. (French) [Some didactic aspects of the development of children's thinking in mathematics and physics] . . . . . . . . 343--346 Howard F. Fehr Contemporary mathematics and its intervention in the sciences . . . . . . 347--351 A. Z. Krygovska Préparation des ma\^\itres \`a l'enseignement intégré des sciences. (French) [Preparing Teachers for Integrated Science Education] . . . . . 352--364
André Delessert Connections between the reform of mathematical instruction and the further training of teachers . . . . . . . . . . 365--377 Lina Mancini Proia An experiment in teaching geometry . . . 378--385 A. Hollinger Sur l'initiation \`a la géométrie. (French) [On initiation to geometry] . . 386--393 P. G. J. Vredenduin The conclusive force of Venn diagrams, and the implication . . . . . . . . . . 394--401 J. Van Dormolen The uselessness of Venn diagrams . . . . 402--407 Hans Freudenthal Braces and Venn diagrams . . . . . . . . 408--414 J. Bastier Games and relations . . . . . . . . . . 415--421 Jaroslav \vSedivý Teaching of elements of logic by means of finite graphs . . . . . . . . . . . . 422--439 Hans-Joachim Vollrath Some algebraic aspects in analysis teaching . . . . . . . . . . . . . . . . 440--444 Hans-G. Steiner and Burt A. Kaufman Checker games in operational systems as media for an inductive approach to teaching algebra . . . . . . . . . . . . 445--483
Patrick Suppes and Elizabeth F. Loftus and Max Jerman Problem-solving on a computer-based teletype . . . . . . . . . . . . . . . . 1--15 E. Fischbein and Ileana Pampu and I. M\^\inzat Initiation aux probabilités \`a l'école élémentaire. (French) [Initiation in Probability in Elementary School] . . . 16--31 Hans Freudenthal A teachers course colloquium on sets and logic . . . . . . . . . . . . . . . . . 32--58 Floyd R. Vest A catalog of models for the operations of addition and subtraction of whole numbers . . . . . . . . . . . . . . . . 59--68 Maurice Glaymann Initiation to vector spaces . . . . . . 69--79 Anonymous ICMI report on mathematical contests in secondary education (olympiads) I . . . 80--114 M. Bruckheimer and N. Gowar Apparent conflicts in maths education 115--122 Erich Wittmann The development of self-reliant thinking in mathematics teaching . . . . . . . . 123--133
Hans Freudenthal Allocution du premier congr\`es international de l'enseignement mathématique, Lyon, 24--31 août 1969. (French) [Address to the First International Congress of Mathematical Education, Lyon, 24--31 August 1969] . . 135--138 Bent Christiansen Induction and deduction in the learning of mathematics and in mathematical instruction . . . . . . . . . . . . . . 139--159 W. Servais Logique et enseignement mathématique. (French) [Logic and Mathematical Education] . . . . . . . . . . . . . . . 160--179 J. V. Armitage The relation between abstract and `concrete' mathematics at school . . . . 180--188 R. Gauthier Essai d'individualisation de l'enseignement. (French) [Testing the Individualization of Education] . . . . 189--200 G. G. Maslova Le développement des idées et des concepts mathématiques fondamentaux dans l'enseignement des enfants de 7 \`a 15 ans. (French) [The development of fundamental mathematical ideas and concepts in the teaching of children aged 7 to 15] . . . . . . . . . . . . . 201--211 A. Roumanet Une classe de mathématique: Motivations et méthodes. (French) [A class of mathematics: Motivations and methods] 212--231 E. G. Begle The role of research in the improvement of mathematics education . . . . . . . . 232--244 A. Delessert De quelques probl\`emes touchant \`a la formation des ma\^\itres de mathématiques. (French) [Some problems affecting the training of mathematics teachers] . . . . . . . . . . . . . . . 245--256 Arthur Engel The relevance of modern fields of applied mathematics for mathematical education . . . . . . . . . . . . . . . 257--269 André Revuz Les premiers pas en analyse. (French) [The first steps in analysis] . . . . . 270--278 A. Markouchevitch Certains probl\`emes de l'enseignement des mathématiques \`a l'école. (French) [Some problems of teaching mathematics at school] . . . . . . . . . . . . . . . 279--289 E. Fischbein Enseignement mathématique et développement intellectuel. (French) [Mathematical education and intellectual development] 290--306 Emma Castelnuovo Différentes représentations utilisant la notion de barycentre. (French) [Different representations using the notion of barycenter] . . . . . . . . . 307--332 Frédérique Papy Minicomputer . . . . . . . . . . . . . . 333--345 Bryan Thwaites The role of the computer in school mathematics . . . . . . . . . . . . . . 346--359 Zofia Krygowska Le texte mathématique dans l'enseignement. (French) [Mathematical text in teaching] . . . . . . . . . . . 360--370 Hans-Georg Steiner Magnitudes and rational numbers --- A didactical analysis . . . . . . . . . . 371--392 H. O. Pollak How can we teach applications of mathematics? . . . . . . . . . . . . . . 393--404 Paul C. Rosenbloom Vectors and symmetry . . . . . . . . . . 405--414
Ferenc Genzwein The system and the organization of further training for the mathematics teachers of the secondary schools in Budapest . . . . . . . . . . . . . . . . 419--429 E. Georgescu-Buz\=au and N. Matei and Gr. B\=anescu The importance of appropriate problems in the teaching of mathematics . . . . . 430--437 Max Jerman A counting model for simple addition . . 438--445 Richard S. Long and Nancy S. Meltzer and Peter J. Hilton Research in mathematics education . . . 446--468 E. E. Biggs Communication on primary education in mathematics . . . . . . . . . . . . . . 469--475 Bert K. Waits Relative effectiveness of two different television techniques and one large lecture technique for teaching large enrollment college mathematics courses 476--477 John C. Egsgard Some ideas in geometry that can be taught from K--6 . . . . . . . . . . . . 478--495 Bruce R. Vogeli Sweep away all cows, ghosts, dragons and devils . . . . . . . . . . . . . . . . . 496--500
David A. Smith A calculus-with-computer experiment . . 1--11 Z. P. Dién\`es Les six étapes de l'apprentissage des structures. (French) [The six stages of learning structures] . . . . . . . . . . 12--42 Lina Mancini Proia Une expérience dans un lycée classique. (French) [An experience in a classical high school] . . . . . . . . . . . . . . 43--62 Thomas C. O'Brien Some notes on multiplication of whole numbers . . . . . . . . . . . . . . . . 63--67 A. D. Semu\vsin Study of geometry in the fourth grade 68--83 Maurice Glaymann A geometry on the cube . . . . . . . . . 84--94 William E. Lamon and Lloyd F. Scott An investigation of structure in elementary school mathematics: Isomorphism . . . . . . . . . . . . . . 95--110 J. N. Kapur Combinatorial analysis and school mathematics . . . . . . . . . . . . . . 111--127 Anonymous XIth International Olympiad Bucharest, 5--20 July 1969 . . . . . . . . . . . . 128--129
Anonymous XIIth International Olympiad Budapest--Keszthely, 10--24 June 1970 131--132 G. D. Balk Application of heuristic methods to the study of mathematics at school . . . . . 133--146 M. A. Grabovskij and P. M. Kotel'nikov The use of kinematic models in the study of trigonometric functions . . . . . . . 147--160 E. G. Jakuba Experiments on improving the teaching process . . . . . . . . . . . . . . . . 161--169 N. M. Roganovskij Axiomatic approach to the teaching of solid geometry in grade IX . . . . . . . 170--179 S. I. Veksler Developing the capabilities of the pupil 180--183 Geoffrey Giles Switch boards and logic . . . . . . . . 184--191 K. Orlov Experimental verification of the use of the mathematical balance in secondary teaching . . . . . . . . . . . . . . . . 192--205 Alexander Graham and Graham A. Read A television programme on finite differences . . . . . . . . . . . . . . 206--219 Floyd R. Vest A catalog of models for multiplication and division of whole numbers . . . . . 220--228 Joseph M. Scandura A research basis for teacher education 229--243 Murray S. Klamkin On the ideal role of an industrial mathematician and its educational implications . . . . . . . . . . . . . . 244--269 M. A. Touyarot Inquiry into the meanings of `relation' 270--276
Burt Kaufman Background . . . . . . . . . . . . . . . 277--280 Anonymous The CSMP development of geometry . . . . 281--285 Anonymous Geometry conference recommendations . . 286--287 Friedrich Bachmann $n$-Gons . . . . . . . . . . . . . . . . 288--309 H. S. M. Coxeter Inversive geometry . . . . . . . . . . . 310--321 Robert B. Davis The problem of relating mathematics to the possibilities and needs of schools and children . . . . . . . . . . . . . . 322--336 Zoltan P. Dién\`es An example of the passage from the concrete to the manipulation of formal systems . . . . . . . . . . . . . . . . 337--352 Arthur Engel Geometrical activities for the upper elementary school . . . . . . . . . . . 353--394 T. J. Fletcher The teaching of geometry present problems and future aims . . . . . . . . 395--412 Hans Freudenthal Geometry between the devil and the deep sea . . . . . . . . . . . . . . . . . . 413--435 Peter Hilton Topology in the high school . . . . . . 436--453 M. A. Jeeves Some experiments on structured learning 454--476 Paul J. Kelly Topology and transformations in high school geometry . . . . . . . . . . . . 477--481 Victor Klee The use of research problems in high school geometry . . . . . . . . . . . . 482--489 Howard Levi Geometric algebra for the High School Program . . . . . . . . . . . . . . . . 490--500
Karl Menger The geometry relevant to modern education . . . . . . . . . . . . . . . 1--17 G. Papy A first introduction to the notion of topological space . . . . . . . . . . . 18--30 Günter Pickert The introduction of metric by the use of conics . . . . . . . . . . . . . . . . . 31--47 André Revuz The position of geometry in mathematical education . . . . . . . . . . . . . . . 48--52 Thomas G. Room The geometry and algebra of reflections (and of $ 2 \times 2 $ matrices) . . . . 53--75 Seymour Schuster On the teaching of geometry a potpourri 76--86 Hans-Georg Steiner A foundation of Euclidean geometry by means of congruence mappings . . . . . . 87--90 Marshall Stone Learning and teaching axiomatic geometry 91--103 Herbert E. Vaughan The development of Euclidean geometry in terms of translations . . . . . . . . . 104--110 Mario Villa A logical approach to the teaching of geometry at the secondary level . . . . 111--134 John Williams Problems and possibilities in the assessment and investigation of mathematics learning . . . . . . . . . . 135--149 Hans Zassenhaus Genetic development of the congruence axioms . . . . . . . . . . . . . . . . . 150--152
H. Brian Griffiths Mathematical insight and mathematical curricula . . . . . . . . . . . . . . . 153--165 William E. Lamon and Leslie E. Huber The learning of the vector space structure by sixth grade students . . . 166--181 Lucie Libois Mathematics in the Decroly School . . . 182--186 J. E. Phythian Mathematical kujitegemea in Tanzania . . 187--200 Thomas C. O'Brien and Bernard J. Shapiro and Norma C. Reali Logical thinking-language and context 201--219 E. G. Begle Time devoted to instruction and student achievement . . . . . . . . . . . . . . 220--224 Jacques Chayé Apprentissage de la déduction. (French) [Learning Deduction] . . . . . . . . . . 225--231 Magdeleine Motte En marge de l'apprentissage de la déduction. (French) [On the margin of learning deduction] . . . . . . . . . . 232--242 Erich Wittmann Complementary attitudes in problem solving . . . . . . . . . . . . . . . . 243--251 J. E. Baker and M. Bruckheimer and H. G. Flegg A pedagogic approach to morphisms . . . 252--263 E. Fischbein and Ileana B\uarbat and I. M\^\inzat Intuitions primaires et intuitions secondaires dans l'initiation aux probabilités. (French) [Primary and secondary intuitions in initiation in probabilities] . . . . . . . . . . . . . 264--280
A. Revuz La notion de continuité dans l'enseignement du second degré. (French) [The notion of continuity in secondary education] . . . . . . . . . . . . . . . 281--298 K. E. Hirst Derivatives and tangents . . . . . . . . 299--305 Max Jerman and Raymond Rees Predicting the relative difficulty of verbal arithmetic problems . . . . . . . 306--323 Philip S. Marcus Comments on variable-free calculus . . . 324--330 Joseph M. Scandura and Robert McGee An exploratory investigation of basic mathematical abilities of kindergarten children . . . . . . . . . . . . . . . . 331--345 T. Varga Logic and probability in the lower grades . . . . . . . . . . . . . . . . . 346--357 Hugh Thurston What exactly is $ d y / d x $? . . . . . 358--367 Josette Adda Quelques études pour contribuer \`a l'observation du comportement mathématique des non-mathématiciens. (French) [Some studies contributing to the observation of mathematical behavior of non-mathematicians] . . . . . . . . . 368--392 A. F. Monna Set-theory in 1888 . . . . . . . . . . . 393--397 Anonymous XIIIth International Olympiad Bratislava--Zilina, 7--20 July 1971 . . 398--399
Thomas C. O'Brien Logical thinking in adolescents . . . . 401--428 Adele Goldberg and Patrick Suppes A computer-assisted instruction program for exercises on finding axioms . . . . 429--449 Théo Bernet and André Delessert Un inventaire des notions impliquées dans un enseignement général de mathématique \`a l'école secondaire. (French) [An inventory of the notions involved in a general education of mathematics in secondary school] . . . . . . . . . . . 450--465 Jan Konior Essai de détermination des causes d'échecs des él\`eves dans la recherche de démonstrations. (French) [Test to determine the causes of failure of students in the search for demonstrations] . . . . . . . . . . . . 466--483 H. Freudenthal The `empirical law of large numbers' or `The stability of frequencies' . . . . . 484--490 Anonymous Probl\`emes de la pensée logique dans l'enseignement des mathématiques. (French) [Problems of Logical Thinking in Mathematics Education] . . . . . . . 491--500
William E. Hartnett The CF/PMM approach to learning Mathematics . . . . . . . . . . . . . . 1--22 Héléna Siwek Logique formelle et raisonnement naturel des él\`eves dans l'enseignement de la mathématique. (French) [Formal logic and natural reasoning of pupils in the teaching of mathematics] . . . . . . . . 23--37 A. Z. Krygovska and Maria Ciosek Quelques remarques sur le comportement des él\`eves concernant les probl\`emes mathématiques. (French) [Some remarks on the behavior of pupils concerning mathematical problems] . . . . . . . . . 39--48 Burt Kaufman and Lennart Råde Relations and probability . . . . . . . 49--64 Jean Galtier Around a game . . . . . . . . . . . . . 65--70 Thomas C. O'Brien Logical thinking in college students . . 71--79 Hartmut Wallrabenstein Development and signification of a geometry test . . . . . . . . . . . . . 81--89 Hartmut Wallrabenstein Experiments in teaching intuitive topology in the 5th and 6th grades . . . 91--108 Max Jerman Problem length as a structural variable in verbal arithmetic problems . . . . . 109--123 Erich Wittmann The concept of grouping in Jean Piaget's psychology --- formalization and applications . . . . . . . . . . . . . . 125--146 Floyd Vest Using models of operations and equations 147--155 A. G. Howson Charles Godfrey (1873--1924) and the reform of mathematical education . . . . 157--180
Max Jerman Problem length as a structural variable in verbal arithmetic problems . . . . . 109--123 Erich Wittmann The concept of grouping in Jean Piaget's psychology --- Formalization and applications . . . . . . . . . . . . . . 125--146 Floyd Vest Using models of operations and equations 147--155 A. G. Howson Charles Godfrey (1873--1924) and the reform of mathematical education . . . . 157--180 Bernard J. Shapiro and Thomas C. O'Brien Quasi-Child Logics . . . . . . . . . . . 181--184 Robert A. Bagnato Teaching college mathematics by question-and-answer . . . . . . . . . . 185--192 Lyman Holden The march of the discoverer . . . . . . 193--205 Une Équipe de l'I.R.E.M. de Strasbourg Sur l'assimilation des programmes de 6\`eme--5\`eme. (French) [On the assimilation of programs of 6th--5th] 207--242
Detlef Laugwitz Motivations and Linear Algebra . . . . . 243--254 Joseph B. Harkin and Gerald R. Rising Some psychological and pedagogical aspects of mathematical symbolism . . . 255--260 H. Freudenthal The crux of course design in probability 261--277 Zalman Usiskin Some corresponding properties of real numbers and implications for teaching 279--290 Barnabas B. Hughes Heuristic teaching in mathematics . . . 291--299 Richard J. Shumway and Frank K. Lester Negative instances and the acquisition of the mathematical concepts of commutativity and associativity . . . . 301--315 Max E. Jerman and Sanford Mirman Linguistic and computational variables in problem solving in elementary mathematics . . . . . . . . . . . . . . 317--362 Amy C. King Plan Ahead . . . . . . . . . . . . . . . 363--370 Barbara W. Searle and Paul Lorton, Jr. and Patrick Suppes Structural variables affecting CaI performance on arithmetic word problems of disadvantaged and deaf students . . . 371--384 Anonymous XIVth International Olympiad Warsaw--Toru\'n, 7--18 July 1972 . . . . 385--386 Anonymous XVth International Olympiad Moscow, 4--17 July 1973 . . . . . . . . . . . . 387--388 Anonymous International symposium on `The Role of Geometry in present-day Mathematics Teaching' scheduled to be held in Bielefeld (West Germany) from September 16 to 20, 1974 . . . . . . . . . . . . . 389--389 Anonymous A call for resource materials . . . . . 390--390
H. Freudenthal Soviet research on teaching algebra at the lower grades of the elementary school . . . . . . . . . . . . . . . . . 391--412 P. M. Van Hiele System separation and transfer . . . . . 413--417 Ramesh Kapadia A critical examination of Piaget--Inhelder's view on topology . . 419--424 T. Roman Les olympiades mathématiques en Roumanie. (French) [The mathematical olympiads in Romania] . . . . . . . . . . . . . . . . 425--440 Une Équipe de l'Irem de Strasbourg Sur l'acquisition des structures numériques en fin de $ 3^{\hbox {\` e}me} $. (French) [On the acquisition of the numerical structures at the end of the third [grade]] . . . . . . . . . . . . . 441--459 J. B. Harkin Transformation and tesselation on the geoboard . . . . . . . . . . . . . . . . 461--465 Emma Castelnuovo and Daniela Gori-Giorgi and Claudio Gori-Giorgi Les graphes de flux dans l'enseignement secondaire. (French) [Flow Graphs in Secondary Education] . . . . . . . . . . 467--492 Lars C. Jansson Structural and linguistic variables that contribute to difficulty in the judgment of simple verbal deductive arguments . . 493--505
Arthur Engel The probabilistic abacus . . . . . . . . 1--22 Thomas C. O'Brien Deformation and the four card problem 23--39 Perla Nesher and Eva Teubal Verbal cues as an interfering factor in verbal problem solving . . . . . . . . . 41--51 Erich Wittmann Natural numbers and groupings . . . . . 53--75 J. D. Gray Criticism in the mathematics class . . . 77--86 R. M. Cater and H. W. Johnstone, Jr. A computer language for teaching introductory logic . . . . . . . . . . . 87--91 Mario Barra The cycloid . . . . . . . . . . . . . . 93--98 H. P. Hahn A model of the symmetric group $ S_4 $ used as a means of teaching fundamental algebraic concepts . . . . . . . . . . . 99--111 J. B. Harkin Introducing the geoboard . . . . . . . . 113--118 J. Vy\vsín An experience of the Czechoslovakian experimental center . . . . . . . . . . 119--123 Anonymous Errata . . . . . . . . . . . . . . . . . 125--125
Hans Freudenthal Pupils' achievements internationally compared --- The IEA . . . . . . . . . . 127--186 Dietger Heitele An epistemological view on fundamental stochastic ideas . . . . . . . . . . . . 187--205 James J. Roberge Development of comprehension of logical connectives in symbolic or verbal form 207--212 H. N. Jahnke and H. Steinbring and D. Vogel Zahlbegriff und Rechenfertigkeit --- zur Problematik der Entwicklung wissenschaftlicher Begriffe. (German) [Numerical concepts and rendering skills --- on the problem of the development of scientific terms] . . . . . . . . . . . 213--252 Anonymous Announcement . . . . . . . . . . . . . . 253--257
H. J. L. Kamps and J. H. Van Lint A comparison of a classical calculus test with a similar multiple choice test 259--271 A. G. Howson University courses for future teachers 273--292 D. E. Mackenzie and J. D. Gray and S. J. Prokhovnik Large-group lecturing in mathematics . . 293--309 Josette Adda L'incompréhension en mathématiques et les malentendus. (French) [Misunderstandings in mathematics and the misunderstood] 311--326 D. Anxolabéh\`ere and G. Périquet Approche des mod\`eles mathématiques de l'évolution des populations par la simulation d'expériences sur ordinateur. (French) [Approach of mathematical models of population evolution by simulation with computer experiments] 327--338 Shlomo Vinner The naive platonic approach as a teaching strategy in arithmetics . . . . 339--350 John Niman Graph theory in the elementary school 351--373 Joseph M. Scandura How does mathematics learning take place? . . . . . . . . . . . . . . . . . 375--385 Anonymous Errata . . . . . . . . . . . . . . . . . 387--388
Maurice Glaymann Les probabilités \`a l'école élémentaire. (French) [Probabilities in elementary school] . . . . . . . . . . . . . . . . 389--393 Floyd Vest Teaching problem solving as viewed through a theory of models . . . . . . . 395--408 Ramesh Kapadia Set-theory and logic in school . . . . . 409--413 Mich\`ele Artigue and Jacqueline Viennot Quelques reflexions sur l'enseignement de la numération aux enfants de 7, 8 ou 9 ans. (French) [Some reflections on the teaching of numeration to children of 7, 8 or 9 years] . . . . . . . . . . . . . 415--428 Pierre Buisson Évaluation-sondage dans le premier cycle (12--16 ans). (French) [Assessment survey in the first cycle (12--16 years)] . . . . . . . . . . . . . . . . 429--445 Adele Goldberg and Patrick Suppes Computer-assisted instruction in elementary logic at the university level 447--474 M. Otte Book Review: \booktitleDie didaktischen systeme von V. V. Davidov/D. B. Elkonin einerseits und L. V. Zankov andererseits 475--497 Anonymous XVIth International Mathematical Olympiad . . . . . . . . . . . . . . . . 499--500 Anonymous XVIIth International Mathematical Olympiad . . . . . . . . . . . . . . . . 501--502
Josette Adda Difficultés liées \`a la présentation des questions mathématiques. (French) [Difficulties in presenting mathematical questions] . . . . . . . . . . . . . . . 3--22 A. W. Bell A study of pupils' proof --- explanations in mathematical situations 23--40 Alan J. Bishop Decision-making, the intervening variable . . . . . . . . . . . . . . . . 41--47 Régine Douady Une expérience \`a Montrouge. (French) [An experiment at Montrouge] . . . . . . 49--58 Arthur Engel Why does the probabilistic abacus work? 59--69 T. J. Fletcher Nomograms and the foundations of geometry . . . . . . . . . . . . . . . . 71--82 Maurice Glaymann Ou le premier n'est pas toujours premier \ldots. (French) [Or the first is not always first \ldots] . . . . . . . . . . 83--88 Thomas C. O'Brien Three informal essays . . . . . . . . . 89--108 H. O. Pollak What industry wants a mathematician to know and how we want them to know it . . 109--112 A. Revuz Stratégies pour une approche de $ \mathbb {Z} $. (French) [Strategies for an approach to $ \mathbb {Z} $] . . . . . . 113--120 Jaroslav \vSedivý A note on the role of parameters in mathematics teaching . . . . . . . . . . 121--126 W. Servais Problématique dans l'apprentissage de la mathématique. (French) [Problems in the learning of mathematics] . . . . . . . . 127--137 Hans Georg Steiner Finite geometries and non-measurable voting bodies . . . . . . . . . . . . . 139--146 Stefan Turnau On a class-room incident . . . . . . . . 147--155 P. M. Van Hiele Wie kann man im Mathematikunterricht den Denkstufen Rechnung tragen?. (German) [How can one in mathematics teaching teach thought levels?] . . . . . . . . . 157--169 Tamás Varga On primary school teachers' mathematics 171--177 Erich Wittmann Mathematizing around convexity . . . . . 179--184
Hans Freudenthal Preface . . . . . . . . . . . . . . . . 189--190 Anonymous Foreword . . . . . . . . . . . . . . . . 191--192 Anonymous Mathematics education . . . . . . . . . 193--258 Anonymous Learning to teach . . . . . . . . . . . 332--350 Anonymous Curriculum development --- A strategy 351--363 Anonymous Publications . . . . . . . . . . . . . . 364--367
Pearla Nesher Three determinants of difficulty in verbal arithmetic problems . . . . . . . 369--388 Menahem Finegold and Shmuel Avital Enquiry, discovery and research: Terminology and meaning . . . . . . . . 389--397 Shmuel Avital and Rodney T. Hansen Mathematical induction in the classroom 399--411 Shlomo Vinner The naive concept of definition in mathematics . . . . . . . . . . . . . . 413--429 H. J. Vollrath The place of geometry in mathematics teaching: An analysis of recent developments . . . . . . . . . . . . . . 431--442 Emma Castelnuovo and Daniela and Claudio Gori-Giorgi La géométrie projective \`a l'école. (French) [Projection geometry at school] 443--463 G. Walther Balancierte Graphen --- ein Thema für die didaktische Diskussion zum Geometrieunterricht. (German) [Balanced graphs --- a topic for didactic discussion on teaching of geometry] . . 465--495 Claude Comiti and Marie-Rose Guillermard and Alain Solano Approche des statistiques en classe de sixi\`eme: Analyse de résultats sportifs. (French) [Approach to statistics in sixth grade: Analysis of sporting results] . . . . . . . . . . . . . . . . 497--521 G. F. Peaker A commentary from IEA on Dr. Freudenthal's article in: Educational Studies in Mathematics, vol. 6, no. 2 523--527 H. Freudenthal Rejoinder . . . . . . . . . . . . . . . 529--533 Anonymous Erratum . . . . . . . . . . . . . . . . 535--535
Hans Freudenthal Creativity . . . . . . . . . . . . . . . 1--1 Hans Freudenthal Bastiaan's experiments on Archimedes' principle . . . . . . . . . . . . . . . 3--16 Shlomo Vinner The concept of exponentiation at the undergraduate level and the definitional approach . . . . . . . . . . . . . . . . 17--26 J. Van Dormolen Learning to understand what giving a proof really means . . . . . . . . . . . 27--34 János Surány ``I have lost the thread completely \ldots'' . . . . . . . . . . . . . . . . 35--39 Emma Castelnuovo L'enseignement des mathématiques. (French) [The teaching of mathematics] 41--50 R. Duval and F. Pluvinage Démarches individuelles de réponse en mathématique. (French) [Individual responses in mathematics] . . . . . . . 51--116
F. Goffree Johan --- a teacher training freshman studying mathematics and didactics . . . 117--152 E. Fischbein Image and concept in learning mathematics . . . . . . . . . . . . . . 153--165 Shlomo Libeskind A problem solving approach to teaching mathematics . . . . . . . . . . . . . . 167--179 Claude Comiti Approche du nombre par des enfants de 6 \`a 7 ans. (French) [Number Approach by Children aged 6--7] . . . . . . . . . . 181--198 Ramesh Kapadia Curriculum development: Practice and theory . . . . . . . . . . . . . . . . . 199--210 Hans-Joachim Vollrath The understanding of similarity and shape in classifying tasks . . . . . . . 211--224 Murad E. Jurdak Structural and linguistic variables in selected inference patterns for bilinguals in grades six to ten . . . . 225--238 Anonymous Announcements . . . . . . . . . . . . . 239--240
Jacques Nimier Mathématique et affectivité. (French) [Mathematics and affectivity] . . . . . 241--250 Pearla Nesher and Tamar Katriel A semantic analysis of addition and subtraction word problems in arithmetic 251--269 Dieter Lunkenbein Rationalising teaching interventions --- A working model of a process of research in mathematics teaching . . . . . . . . 271--293 J. Michael Shaughnessy Misconceptions of probability: An experiment with a small-group, activity-based, model building approach to introductory probability at the college level . . . . . . . . . . . . . 295--316 Adolf Af Ekenstam On children's quantitative understanding of numbers . . . . . . . . . . . . . . . 317--332 J. Grossel Recherche sur les difficultés occasionnées chez les étudiants par les notations avec indices et par le signe `$ \Sigma $' en mathématiques. (French) [Research on the difficulties experienced by students in notation with indices and by the sign `$ \Sigma $' in mathematics] . . . . . . . 333--357 Robert B. Wenger and Charles R. Rhyner A problem-oriented mathematical optimization course . . . . . . . . . . 359--368
H. Freudenthal Teacher training --- An experimental philosophy . . . . . . . . . . . . . . . 369--376 Iowo-Team Eleven minutes group work --- A transcript . . . . . . . . . . . . . . . 377--389 Nathan Hoffman The teaching and learning of basic number facts . . . . . . . . . . . . . . 391--398 K. Bognár and T. Nemetz On the teaching of probability at secondary level . . . . . . . . . . . . 399--404 Thomas C. O'Brien Implications of Piagetian research for teachers of teachers and teachers of children . . . . . . . . . . . . . . . . 405--412 Nitsa Hadar Children's conditional reasoning . . . . 413--438 Uwe Beck Auslaufvorgänge aus Wasserbehältern --- eine anwendungsorientierte Einführung in die Analysis. (German) [Outflow processes from water reservoirs --- an application-oriented introduction to analysis] . . . . . . . . . . . . . . . 439--460 Frank Swetz The `open-door' policy and the reform of mathematics education in the People's Republic of China . . . . . . . . . . . 461--478 Norbert Knoche On the indicative value of the classical goodness criteria of reliability and validity . . . . . . . . . . . . . . . . 479--508 Anonymous XVIIIth International Mathematical Olympiad (IMO) . . . . . . . . . . . . . 509--510 Anonymous XIXth International Mathematical Olympiad (IMO) . . . . . . . . . . . . . 511--512
Hans Freudenthal Address to the First Conference of I.G.P.M.E. (International Group for the Psychology of Mathematical Education), at Utrecht 29 August 1977 . . . . . . . 1--5 A. Abele The usage of graphs in solving mathematical problems . . . . . . . . . 7--15 Annie Bessot and Claude Comiti Une étude sur l'approche du nombre par l'él\`eve du cours préparatoire. (French) [A study of the pupil's approach in the preparatory course] . . . . . . . . . . 17--39 C. Laborde Relations arithmétiques --- aspect statique --- aspect dynamique. (French) [Arithmetical relations --- static aspect --- dynamic aspect] . . . . . . . 41--50 Leen Streefland Some observational results concerning the mental constitution of the concept of fraction . . . . . . . . . . . . . . 51--73 Hans Ter Heege Testing the maturity for learning the algorithm of multiplication . . . . . . 75--83 Anonymous Five plus four minutes class instruction --- a transcript . . . . . . . . . . . . 85--95 N. Hadar and L. Henkin Children's conditional reasoning. Part II: Towards a reliable test of conditional reasoning ability . . . . . 97--114 N. Hadar Children's conditional reasoning. Part III: A design for research on children's learning of conditional reasoning and research findings . . . . . . . . . . . 115--140 Anonymous Announcements . . . . . . . . . . . . . 141--142
Hans Freudenthal Change in mathematics education since the late 1950's --- ideas and realisation . . . . . . . . . . . . . . 143--145 A. L. Blakers Change in mathematics education since the late 1950's --- ideas and realisation Australia . . . . . . . . . 147--158 S. M. Sharfunddin Change in mathematics education since the late 1950's --- ideas and realisation Bangladesh . . . . . . . . . 159--170 A. Revuz Change in mathematics education since the late 1950's --- ideas and realisation France . . . . . . . . . . . 171--181 A. G. Howson Change in mathematics education since the late 1950's --- ideas and realisation Great Britain . . . . . . . 183--223 Mária Halmos and Tamás Varga Change in mathematics education since the late 1950's --- ideas and realisation Hungary . . . . . . . . . . 225--244 J. N. Kapur Change in mathematical education since the late 1950's --- ideas and realisation India . . . . . . . . . . . 245--253 Badiollah Rostami Change in mathematics education since the late 1950's --- Ideas and realisation Iran . . . . . . . . . . . . 255--260
Hans Freudenthal Change in mathematics education since the late 1950's --- Ideas and realisation The Netherlands . . . . . . 261--270 R. Ogbonna Ohuche Change in mathematics education since the late 1950's --- Ideas and realisation Nigeria . . . . . . . . . . 271--281 Aniela Ehrenfeucht Change in mathematics education since the late 1950's --- Ideas and realisation Poland . . . . . . . . . . . 283--295 A. Williams Change in mathematics education since the late 1950's --- Ideas and realisation Sierra Leone . . . . . . . . 297--302 A. J. Gunawardena Changes in mathematics education since the late 1950's --- Ideas and realisation Sri Lanka . . . . . . . . . 303--316 M. El Sawi Change in mathematics education since the late 1950's --- Ideas and realisation Sudan . . . . . . . . . . . 317--330 Orasri Purakam Change in mathematics education since the late 1950's --- Ideas and realisation Thailand . . . . . . . . . . 331--337 James T. Fey Change in mathematics education since the late 1950's --- Ideas and realisation U.S.A. . . . . . . . . . . . 339--353 B. J. Wilson Change in mathematics education since the late 1950's --- Ideas and realisation West Indies . . . . . . . . 355--379
A. Vidal-Madjar Teaching mathematics and statistics to adults who are keen on psychology . . . 381--390 Stephen I. Brown and Gerald R. Rising One third Cherokee: Problem solving, teaching, and intuition . . . . . . . . 391--409 I. D. MacDonald Insight and intuition in mathematics . . 411--420 Brian Griffiths Some comments on Macdonald's paper . . . 421--427 Shmuel Avital and Shlomo Libeskind Mathematical induction in the classroom: Didactical and mathematical issues . . . 429--438 M. Vandewiele and W. D'Hondt Quelques difficultés en mathématique et leur perception par les él\`eves en classe de troisi\`eme dans l'enseignement secondaire \`a Dakar. (French) [Some difficulties in mathematics and their perception by pupils in third grade in secondary education in Dakar] . . . . . . . . . . 439--460 Dominique Pastre Observation du mathématicien: Aide \`a l'enseignement et \`a la démonstration automatique de théor\`emes. (French) [Observation of the mathematician: Aid for teaching and the automatic demonstration of theorems] . . . . . . . 461--502 Hans Freudenthal Acknowledgment . . . . . . . . . . . . . 503--504 Anonymous Tribute . . . . . . . . . . . . . . . . 504--504 Anonymous XXth International mathematical Olympiad (IMO) . . . . . . . . . . . . . . . . . 505--506
Alan Bishop Editorial statement . . . . . . . . . . 1--1 E. Fischbein and D. Tirosh and P. Hess The intuition of infinity . . . . . . . 3--40 Adolf A. F. Ekenstam and Margita Nilsson A new approach to the assessment of children's mathematical competence . . . 41--66 Hans Freudenthal Rings and string . . . . . . . . . . . . 67--70 B. V. Gnedenko and Z. Khalil The mathematical education of engineers 71--83 David S. Fielker Strategies for teaching geometry to younger children . . . . . . . . . . . . 85--133
Alan J. Bishop Visualising and mathematics in a pre-technological culture . . . . . . . 135--146 Emma Castelnuovo and Daniela Gori-Giorgi and Claudio Gori-Giorgi Le lancement des projectiles. (French) [The launch of projectiles] . . . . . . 147--159 J. L. Austin and A. G. Howson Language and mathematical education . . 161--197 M. Vandewiele and W. D'Hondt La perception de quelques difficultés en mathématiques par les professeurs en classe de troisi\`eme dans l'enseignement secondaire au Sénégal. (French) [The perception of some difficulties in mathematics by third-grade teachers in secondary education in Senegal] . . . . . . . . . 199--225 Johnston Anderson Objective testing in elementary analysis 227--243 F. Lowenthal and R. Severs Langage, jeu et activité mathématique. (French) [Language, game and mathematical activity] . . . . . . . . . 245--262 Gérard Vergnaud The acquisition of arithmetical concepts 263--274
Hans Freudenthal Ways to report on empirical research in education . . . . . . . . . . . . . . . 275--303 M. A. (Ken) Clements Sex differences in mathematical performance: An historical perspective 305--322 E. Castelnuovo and D. Gori-Giorgi and C. Gori-Giorgi Coniques et gravitation universelle. (French) [Conics and universal gravitation] . . . . . . . . . . . . . . 323--359 A. W. Bell The learning of process aspects of mathematics . . . . . . . . . . . . . . 361--387
Elizabeth Fennema Women and girls in mathematics --- Equity in mathematics education . . . . 389--401 Jan Van Den Brink and Leen Streefland Young children (6--8)-ratio and proportion . . . . . . . . . . . . . . . 403--420 M. Sueur and J.-P. Lamarche and P. Marthe Locutions inductrices et distractrices: `de plus que', `de moins que'. (French) [Inductive and distracting dispositions: `more than',`less than'] . . . . . . . . 421--434 Frank Swetz and Ying-King Yu Mathematical olympiads in the People's Republic of China . . . . . . . . . . . 435--442 F. Pluvinage Loto-questionnaires (pour l'évaluation et l'auto-contrôle en mathématiques). (French) [Loto-questionnaires (for evaluation and self-checking in mathematics)] . . . . . . . . . . . . . 443--485
M. A. (Ken) Clements Analyzing children's errors on written mathematical tasks . . . . . . . . . . . 1--21 Heinrich Bauersfeld Hidden dimensions in the so-called reality of a mathematics classroom . . . 23--41 Leone Burton The teaching of mathematics to young children using a problem solving approach . . . . . . . . . . . . . . . . 43--58 Peter Bender and Alfred Schreiber The principle of operative concept formation in geometry teaching . . . . . 59--90 N. Balacheff Une étude, \`a l'aide de graphes, de démonstrations mathématiques formulées par des él\`eves. (French) [A study, using graphs, of mathematical demonstrations formulated by pupils] . . . . . . . . . 91--111 David N. Burghes Mathematical modelling: A positive direction for the teaching of applications of mathematics at school 113--131 Anonymous Announcements . . . . . . . . . . . . . 133--135
David Kent and Keith Hedger Growing tall . . . . . . . . . . . . . . 137--179 Ruma Falk and Raphael Falk and Iris Levin A potential for learning probability in young children . . . . . . . . . . . . . 181--204 Michael C. Mitchelmor Three-dimensional geometrical drawing in three cultures . . . . . . . . . . . . . 205--216 Gerald Noelting The development of proportional reasoning and the ratio concept. Part I --- Differentiation of stages . . . . . 217--253 Anonymous Announcements . . . . . . . . . . . . . 255--256
Alan J. Bishop Spatial abilities and mathematics education --- A review . . . . . . . . . 257--269 David Tall The notion of infinite measuring number and its relevance in the intuition of infinity . . . . . . . . . . . . . . . . 271--284 A. G. Howson Socialist mathematics education: Does it exist? . . . . . . . . . . . . . . . . . 285--299 Claude Comiti Les premi\`eres acquisitions de la notion de nombre par l'enfant. (French) [The first acquisitions of the notion of number by the child] . . . . . . . . . . 301--318 Ivan Watson Investigating errors of beginning mathematicians . . . . . . . . . . . . . 319--329 Gerald Noelting The development of proportional reasoning and the ratio concept. Part II --- problem-structure at successive stages; problem-solving strategies and the mechanism of adaptive restructuring 331--363
William H. Brock and Michael H. Price Squared paper in the nineteenth century: Instrument of science and engineering, and symbol of reform in mathematical education . . . . . . . . . . . . . . . 365--381 Erich Wittmann `Discrete analysis' --- An approach to fundamental ideas of analysis . . . . . 383--392 Stefan Turnau The mathematical textbook for young students . . . . . . . . . . . . . . . . 393--410 Gilah Leder Bright girls, mathematics and fear of success . . . . . . . . . . . . . . . . 411--422 Diane Resek and William H. Rupley Combatting `mathophobia' with a conceptual approach toward mathematics 423--441 Ramesh Kapadia Developments in statistical education 443--461 Jerry P. Becker 1978 Mathematics olympiads in the People's Republic of China . . . . . . . 463--478 Helen Adi and Robert Karplus and Anton E. Lawson Conditional logic abilities on the four-card problem: Assessment of behavioral and reasoning performances 479--496 Anonymous Notice . . . . . . . . . . . . . . . . . 497--497
P. L. Galbraith Aspects of proving: A clinical investigation of process . . . . . . . . 1--28 Lesley R. Booth Child-methods in secondary mathematics 29--41 S. L. Kemme References of speech acts as characteristics of mathematical classroom conversation . . . . . . . . . 43--58 Raymond A. Zepp Relationships between mathematics achievement and various English language proficiencies . . . . . . . . . . . . . 59--70 Klaus Hasemann On difficulties with fractions . . . . . 71--87 F. Royoux Sur l'enseignement de la relation transitive \`a l'école élémentaire. (French) [On the teaching of the transitive relation in the elementary school] . . . . . . . . . . . . . . . . 89--111 Claude Janvier Use of situations in mathematics education . . . . . . . . . . . . . . . 113--122 Bryan Lang and Peter Ruane Geometry in English secondary schools 123--132
Hans Freudenthal Major problems of mathematics education 133--150 David Tall and Shlomo Vinner Concept image and concept definition in mathematics with particular reference to limits and continuity . . . . . . . . . 151--169 Ron Hoz The effects of rigidity on school geometry learning . . . . . . . . . . . 171--190 A. Pollatsek and S. Lima and A. D. Well Concept or computation: Students' understanding of the mean . . . . . . . 191--204 K. Hart Hierarchies in mathematics education . . 205--218 M. Holcombe The role of automata and machine theory in school and college mathematics syllabuses . . . . . . . . . . . . . . . 219--234 Richard Lesh Applied mathematical problem solving . . 235--264 Anonymous Preliminary announcement . . . . . . . . 265--265 Anonymous Cultural contexts of science and mathematics education . . . . . . . . . 266--266
Glen Lean and M. A. (Ken) Clements Spatial ability, visual imagery, and mathematical performance . . . . . . . . 267--299 Dietmar Küchemann Cognitive demand of secondary school mathematics items . . . . . . . . . . . 301--316 Carolyn Kieran Concepts associated with the equality symbol . . . . . . . . . . . . . . . . . 317--326 Julia Matthews An investigation into subtraction . . . 327--338 John Head Personality and the learning of mathematics . . . . . . . . . . . . . . 339--350 Stieg Mellin-Olsen Instrumentalism as an educational concept . . . . . . . . . . . . . . . . 351--367 Keith Austin Busprongs . . . . . . . . . . . . . . . 369--371 K. E. Hirst Undergraduate investigations in mathematics . . . . . . . . . . . . . . 373--387 Erich Wittmann The complementary roles of intuitive and reflective thinking in mathematics teaching . . . . . . . . . . . . . . . . 389--397
Alan Bell and Malcolm Swan and Glenda Taylor Choice of operation in verbal problems with decimal numbers . . . . . . . . . . 399--420 James A. Levin Estimation techniques for arithmetic: Everyday math and mathematics instruction . . . . . . . . . . . . . . 421--434 N. Hadar and R. Hadass The road to solving a combinatorial problem is strewn with pitfalls . . . . 435--443 David F. Lancy The indigenous mathematics project: An overview . . . . . . . . . . . . . . . . 445--453 Paulus Gerdes Changing mathematics education in Mozambique . . . . . . . . . . . . . . . 455--477 Sam O. Ale Difficulties facing mathematics teachers in developing countries --- A case study of Nigeria . . . . . . . . . . . . . . . 479--489 E. Fischbein and D. Tirosh and U. Melamed Is it possible to measure the intuitive acceptance of a mathematical statement? 491--512 Anonymous Announcement . . . . . . . . . . . . . . 513--513
Jenz Holger Lorenz On some psychological aspects of mathematics achievement assessment and classroom interaction . . . . . . . . . 1--19 Josette Adda L'observation de classes et le paradoxe de l'observateur. (French) [Class Observation and Observer Paradox] . . . 21--32 Nadine Bednarz and Bernadette Janvier The understanding of numeration in primary school . . . . . . . . . . . . . 33--57 A. Bessot and C. Comiti Appropriation des propriétés ordinales du nombre par l'él\`eve du cours préparatoire. (French) [Appropriation of the ordinal properties of number by the pupil in the preparatory course] . . . . 59--88 P. L. Galbraith The mathematical vitality of secondary mathematics graduates and prospective teachers: A comparative study . . . . . 89--112 Erich Wittmann Book review . . . . . . . . . . . . . . 113--116 Anonymous Announcement . . . . . . . . . . . . . . 117--118
Ian Darke A review of research related to the topological primacy thesis . . . . . . . 119--142 Twila Slesnick Algorithmic skill vs. conceptual understanding . . . . . . . . . . . . . 143--154 Mich\`ele Artigue and Jacqueline Robinet Numération a l'école élémentaire. (French) 155--175 P. Teule-Sensacq and G. Vinrich Résolution de probl\`emes de division au cycle élémentaire dans deux types de situations didactiques. (French) [Solving division problems at the elementary cycle in two types of teaching situations] . . . . . . . . . . 177--203 Raymond A. Zepp Bilinguals' understanding of logical connectives in English and Sesotho . . . 205--221 Peter Hilton and Hans Freudenthal and W. Dörfler Book review . . . . . . . . . . . . . . 223--232
Leen Streefland Subtracting fractions with different denominators . . . . . . . . . . . . . . 233--255 Christine Keitel Curriculum variables, theory and goals: A comment on Begle's Critical Variables in Mathematics Education . . . . . . . . 257--267 Peter L. Jones Learning mathematics in a second language: A problem with more and less 269--287 Graciela Bicco Les premi\`eres acquisitions de la notion de fonction linéaire chez l'enfant de 7 \`a 11 ans. (French) [The first acquisitions of the notion of linear function in the child of 7 to 11 years] 289--327 James Hiebert and Thomas P. Carpenter Piagetian tasks as readiness measures in mathematics instruction: A critical review . . . . . . . . . . . . . . . . . 329--345 Dieter Lunkenbein Book review . . . . . . . . . . . . . . 347--348
Celia Hoyles The pupil's view of mathematics learning 349--372 P. Nesher and J. G. Greeno and M. S. Riley The development of semantic categories for addition and subtraction . . . . . . 373--394 Hans Freudenthal Fiabilité, validité et pertinence --- crit\`eres de la recherche sur l'enseignement de la mathématique. (French) [Reliability, Validity, and Relevance --- Criteria for Research in Mathematics Education] . . . . . . . . . 395--408 Bernard Dumont L'influence du `décor' et du langage dans des épreuves de type `logique' portant apparemment sur l'implication. (French) [The influence of `decor' and language in `logic' type tests apparently involving implication] . . . . . . . . . 409--429 Donald R. Kerr, Jr. and Frank K. Lester, Jr. A new look at the professional training of secondary school mathematics teachers 431--441 Hans Freudenthal and N. Knoche and Ian Stewart and Frank J. Swetz Book reviews . . . . . . . . . . . . . . 443--448 Anonymous Announcement . . . . . . . . . . . . . . 449--449
A. Orton Students' understanding of integration 1--18 Saburoh Minato Some mathematical attitudinal data on eighth grade students in Japan measured by a semantic differential . . . . . . . 19--38 Frank J. Swetz and Albert Y. Chi Mathematics entrance examinations in Chinese institutions of higher education 39--54 T. P. Carpenter and J. Hiebert and J. M. Moser The effect of instruction on children's solutions of addition and subtraction word problems . . . . . . . . . . . . . 55--72 I. F. Svenson and J. A. Lawrence and S. G. Willis Distance university students' processing of mathematics exercises . . . . . . . . 73--85 Hans Niels Jahnke Technology and education: The example of the computer . . . . . . . . . . . . . . 87--100 M. Borovcnik and R. Fischer and G. Glaeser Book reviews . . . . . . . . . . . . . . 101--105 Anonymous Announcement . . . . . . . . . . . . . . 107--107
Leslie P. Steffe Children's algorithms as schemes . . . . 109--125 Miriam A. D. Wolters The part--whole schema and artithmetical problems . . . . . . . . . . . . . . . . 127--138 Julia Matthews A subtraction experiment with six and seven year old children . . . . . . . . 139--154 Gerard Audibert Processus de recherche d'un probl\`eme de géometrie chez l'él\`eve de l'enseignement secondaire. (French) [Process of research of a geometry problem in secondary-education pupils] 155--181 Randall J. Souviney Mathematics achievement, language and cognitive development: Classroom practices in Papua New Guinea . . . . . 183--212 G. Glaeser and Joop Van Dormolen Book Review . . . . . . . . . . . . . . 213--215
Robert Karplus and Steven Pulos and Elizabeth K. Stage Early adolescents' proportional reasoning on `rate' problems . . . . . . 219--233 A. Orton Students' understanding of differentiation . . . . . . . . . . . . 235--250 Spyros P. Kalomitsines Two methods for solving problems . . . . 251--274 G. Trelinski Spontaneous mathematization of situations outside mathematics . . . . . 275--284 Wilhelm Schipper The topological primacy thesis: Genetic and didactic aspects . . . . . . . . . . 285--296 H. B. Griffiths Simplification and complexity in mathematics education . . . . . . . . . 297--317 Richard Lesh and G. Walther Book Reviews . . . . . . . . . . . . . . 319--322 Anonymous Announcement . . . . . . . . . . . . . . 323--323 Anonymous Announcement . . . . . . . . . . . . . . 324--324
Lloyd Dawe Bilingualism and mathematical reasoning in English as a second language . . . . 325--353 Philip Clarkson Types of errors made by Papua New Guinean students . . . . . . . . . . . . 355--367 Adolf Afekenstam and Karl Greger Some aspects of children's ability to solve mathematical problems . . . . . . 369--384 Raymond Duval L'obstacle du dédoublement des objets mathématiques. (French) [The obstacle of the duplication of mathematical objects] 385--414 Zemira R. Mevarech A deep structure model of students' statistical misconceptions . . . . . . . 415--429 G. Schrage and Curtis McKnight Book reviews . . . . . . . . . . . . . . 431--433 Anonymous Announcement . . . . . . . . . . . . . . 434--434
E. Fischbein and A. Gazit Does the teaching of probability improve probabilistic intuitions? . . . . . . . 1--24 Erich Wittmann Teaching units as the integrating core of mathematics education . . . . . . . . 25--36 Jean-Guy Dubois Une systématique des configurations combinatoires simples. (French) [A system of simple combinatorial configurations] . . . . . . . . . . . . 37--57 A. Edwards Computational estimation for numeracy 59--73 A. G. Howson Seventy five years of the International Commission on Mathematical Instruction 75--93 Siegbert Schmidt and T. J. Fletcher Book reviews . . . . . . . . . . . . . . 95--102 Anonymous Announcements . . . . . . . . . . . . . 103--104
Alba Gonzalez Thompson The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice . . . . . . . . . . . . . . . . 105--127 Alan Bell and Efraim Fischbein and Brian Greer Choice of operation in verbal arithmetic problems: the effects of number size, problem structure and context . . . . . 129--147 Paulus Gerdes The first mathematics olympiads in Mozambique . . . . . . . . . . . . . . . 149--172 Paul Ernest Mathematical induction: A pedagogical discussion . . . . . . . . . . . . . . . 173--189 Anonymous Conic sections in the sky and on the earth . . . . . . . . . . . . . . . . . 191--210 Anonymous Announcement . . . . . . . . . . . . . . 211--211
M. A. (Ken) Clements Terence Tao . . . . . . . . . . . . . . 213--238 F. J. Van Den Brink Numbers in contextual frameworks . . . . 239--257 Victor Byers and Stanley Erlwanger Content and form in mathematics . . . . 259--275 John Mason and David Pimm Generic examples: Seeing the general in the particular . . . . . . . . . . . . . 277--289 H. B. Griffiths and R. R. McLone A critical analysis of university examinations in mathematics . . . . . . 291--311 Saburoh Minato and Shyoichi Yanase On the relationship between students attitudes towards school mathematics and their levels of intelligence . . . . . . 313--320 Erkki Pehkonen and C. A. Brown Book reviews . . . . . . . . . . . . . . 321--323
Leen Streefland Search for the roots of ratio: Some thoughts on the long term learning process (towards \ldots a theory) . . . 327--348 Anne S. Hawkins and Ramesh Kapadia Children's conceptions of probability --- A psychological and pedagogical review . . . . . . . . . . . . . . . . . 349--377 Zbigniew Semadeni A principle of concretization permanence for the formation of arithmetical concepts . . . . . . . . . . . . . . . . 379--395 Paul Ernest The CXC mathematics examination: A Caribbean innovation in assessment . . . 397--412 P. Clarkson and G. C. Leder Causal attributions for success and failure in mathematics: A cross cultural perspective . . . . . . . . . . . . . . 413--422 H. B. Griffiths and R. R. McLone A critical analysis of university examinations in mathematics . . . . . . 423--442 Heinrich Winter and Alan J. Bishop Book reviews . . . . . . . . . . . . . . 443--446 Anonymous Preliminary announcement . . . . . . . . 447--447
Anonymous Editorial announcement . . . . . . . . . iv--iv Jeremy Kilpatrick Reflection and recursion . . . . . . . . 1--26 Nurit Zehavi and Maxim Bruckheimer and Ruth Ben-Zvi Qualitative evaluation of mathematical activity and its relation to effective guidance . . . . . . . . . . . . . . . . 27--40 Barbara Rabijewska and Mieczys\law Tr\kad A mathematical camp for bright pupils 41--57 Uri Fidelman Hemispheric basis for schools in mathematics . . . . . . . . . . . . . . 59--74 Leen Streefland Search for the roots of ratio: Some thoughts on the long term learning process (towards \ldots a theory) . . . 75--94 M. Otte and W. Zawadowski Creativity . . . . . . . . . . . . . . . 95--97 E. B. C. Thornton Between behaviour and neurology . . . . 98--101 A. W. Bell Book review . . . . . . . . . . . . . . 103--110
Paul Cobb Two children's anticipations, beliefs, and motivations . . . . . . . . . . . . 111--126 Dudley Blane A longitudinal study of children's school mobility and attainment in mathematics . . . . . . . . . . . . . . 127--142 Renan Samurçay Signification et fonctionnement du concept de variable informatique chez des él\`eves debutants. (French) [Meaning and functioning of the computer variable concept in early students] . . . . . . . 143--161 Rolf Hedren The hand-held calculator at the intermediate level . . . . . . . . . . . 163--179 Françoise Tourniaire and Steven Pulos Proportional reasoning: A review of the literature . . . . . . . . . . . . . . . 181--204 Celia Hoyles What is the point of group discussion in mathematics? . . . . . . . . . . . . . . 205--214 Safder Alladina Second language teaching through maths --- learning maths through a second language . . . . . . . . . . . . . . . . 215--219 A. Rogerson MISP --- the Mathematics in Society Project . . . . . . . . . . . . . . . . 220--221 Zalman Usiskin Didactical Phenomenology of Mathematical Structures . . . . . . . . . . . . . . . 223--228 Anonymous Announcement . . . . . . . . . . . . . . 229--229
David Clarke The impact of secondary schooling and secondary mathematics on student mathematical behaviour . . . . . . . . . 231--257 Victor Byers and Stanley Erlwanger Memory in mathematical understanding . . 259--281 Sylvette Maury Influence de la question dans une épreuve relative \`a la notion d'indépendance. (French) [Influence of the question in a test relating to the notion of independence] . . . . . . . . . . . . . 283--301 Fennema Elizabeth Explaining sex-related differences in mathematics: Theoretical models . . . . 303--303 Elizabeth Fennema and Herbert Walberg and Cora Marrett Introduction . . . . . . . . . . . . . . 303--304 Gilah Leder Sex-related differences in mathematics: An overview . . . . . . . . . . . . . . 304--309 Elizabeth Fennema and Penelope L. Peterson Autonomous learning behavior: A possible explanation of sex-related differences in mathematics . . . . . . . . . . . . . 309--311 Jacquelynne Eccles Model of students' mathematics enrollment decisions . . . . . . . . . . 311--314 David R. Maines Preliminary notes on a theory of informal barriers for women in mathematics . . . . . . . . . . . . . . 314--320 Uri Leron A direct approach to indirect proofs . . 321--325 E. Ch. Wittmann and Douglas Quadling and G. Törner and J. H. Van Lint Book reviews . . . . . . . . . . . . . . 327--334
Alan Bishop Editorial statement . . . . . . . . . . 335--335 Ole Skovsmose Mathematical education versus critical education . . . . . . . . . . . . . . . 337--354 Jack A. Hope Unravelling the mysteries of expert mental calculation . . . . . . . . . . . 355--374 Hans Ter Heege The acquisition of basic multiplication skills . . . . . . . . . . . . . . . . . 375--388 D. Ben-Haim and G. Lappan and R. T. Houang Visualizing rectangular solids made of small cubes: Analyzing and effecting students' performance . . . . . . . . . 389--409 Paul Ernest The number line as a teaching aid . . . 411--424 T. Patronis Convexity and shortest road . . . . . . 425--430 Kathryn Crawford Book Review . . . . . . . . . . . . . . 431--433 Anonymous Announcement . . . . . . . . . . . . . . 434--434
J. W. McQualter Becoming a mathematics teacher: The use of personal construct theory . . . . . . 1--14 B. Denvir and M. Brown Understanding of number concepts in low attaining 7--9 year olds: Part I. Development of descriptive framework and diagnostic instrument . . . . . . . . . 15--36 Paul Cobb Concrete can be abstract: A case study 37--48 Robert P. Hunting Rachel's schemes for constructing fraction knowledge . . . . . . . . . . . 49--66 Pearla Nesher and Irit Peled Shifts in reasoning . . . . . . . . . . 67--79 Henry Markovits The curious effect of using drawings in conditional reasoning problems . . . . . 81--87 Jerry P. Becker Book Review . . . . . . . . . . . . . . 89--96
G. Lemoyne and C. Tremblay Addition and multiplication: Problem-solving and interpretation of relevant data . . . . . . . . . . . . . 97--123 Raffa\vella Borasi On the nature of problems . . . . . . . 125--141 B. Denvir and M. Brown Understanding of number concepts in low attaining 7--9 year olds: Part II. The teaching studies . . . . . . . . . . . . 143--164 M. E. A. El Tom Aspects of mathematics education in some third world universities . . . . . . . . 165--191 Peter E. Langford Arithmetical word problems: Thinking in the head versus thinking on the table 193--199 Mary S. Riley Comments on Langford's article . . . . . 200--202 Peter E. Langford Reply to Riley . . . . . . . . . . . . . 203--204 Paul Ernest Computer gaming for the practice of transformation geometry skills . . . . . 205--207 Anonymous Announcement . . . . . . . . . . . . . . 209--209 Anonymous Announcement . . . . . . . . . . . . . . 210--210
Anonymous Guest editorial . . . . . . . . . . . . 211--212 Yvonne Larsson Governmental policies on the education of gifted and talented children: A world view . . . . . . . . . . . . . . . . . . 213--219 Barry V. Kissane Selection of mathematically talented students . . . . . . . . . . . . . . . . 221--241 Harald Wagner and Bernd Zimmermann Identification and fostering of mathematically gifted students . . . . . 243--260 Nerida F. Ellerton Children's made-up mathematics problems --- a new perspective on talented mathematicians . . . . . . . . . . . . . 261--271 Pieter Span and Ruth Overtoom-Corsmit Information processing by intellectually gifted pupils solving mathematical problems . . . . . . . . . . . . . . . . 273--295 Norma C. Presmeg Visualisation and mathematical giftedness . . . . . . . . . . . . . . . 297--311 Billy Tao Parental involvement in gifted education 313--321 Hans Freudenthal and Konrad Jacobs and Paulo Abrantes Book reviews . . . . . . . . . . . . . . 323--333
Richard Noss Constructing a conceptual framework for elementary algebra through Logo programming . . . . . . . . . . . . . . 335--357 J. Robinet Les réels: Quels mod\`eles en ont les él\`eves?. (French) [Reals: What models do students have?] . . . . . . . . . . . 359--386 Hans-Joachim Vollrath Search strategies as indicators of functional thinking . . . . . . . . . . 387--400 Françoise Tourniaire Proportions in elementary school . . . . 401--412 P. L. Galbraith The use of mathematical strategies: factors and features affecting performance . . . . . . . . . . . . . . 413--441 Detlef D. Spalt and Leone Burton and Erhard Scholz Book review . . . . . . . . . . . . . . 443--452 Anonymous Announcement . . . . . . . . . . . . . . 453--453
R. Zepp and J. Monin and C. L. Lei Common logical errors in English and Chinese . . . . . . . . . . . . . . . . 1--17 Françoise Boschet Fonctions du code symbolique dans le discours mathématique. (French) [Functions of symbolic code in mathematical discourse] . . . . . . . . 19--34 F. K. S. Leung The secondary school mathematics curriculum in China . . . . . . . . . . 35--57 Derek W. Haylock A framework for assessing mathematical creativity in school children . . . . . 59--74 Eon Harper Ghosts of Diophantus . . . . . . . . . . 75--90 Mansour G. A. Hussein Private tutoring a hidden educational problem . . . . . . . . . . . . . . . . 91--96 H. N. Jahnke and Ole Skovsmose Book review . . . . . . . . . . . . . . 97--105 Anonymous Announcements . . . . . . . . . . . . . 107--108
Paul Cobb An investigation of young children's academic arithmetic contexts . . . . . . 109--124 A. Treffers Integrated column arithmetic according to progressive schematisation . . . . . 125--145 Nicolas Balacheff Processus de preuve et situations de validation. (French) [Proof Process and Validation Situations] . . . . . . . . . 147--176 Ian Isaacs Using problem solving teaching styles to prepare candidates for the CXC basic proficiency examinations . . . . . . . . 177--190 Rachel Griffiths A tale of 804.573 horses: Arithmetic teaching in Victoria 1860--1914 . . . . 191--207 Josette Adda and Anna Sierpi\'nska Book reviews . . . . . . . . . . . . . . 209--221
Josette Adda Guest editorial . . . . . . . . . . . . 223--227 Hassler Whitney Coming alive in school math and beyond 229--242 Kenneth Ruthven Ability stereotyping in mathematics . . 243--253 Gilah C. Leder Teacher student interaction: A case study . . . . . . . . . . . . . . . . . 255--271 Stella Baruk The reality and potential of correcting pupils' work in mathematics . . . . . . 273--303 Leone Burton From failure to success: Changing the experience of adult learners of mathematics . . . . . . . . . . . . . . 305--316 Rijkje Dekker Roos and José, two children in a mixed ability group . . . . . . . . . . . . . 317--324 B. F. Sherman A cautionary note . . . . . . . . . . . 325--326 Gilah C. Leder Response to `a cautionary note' . . . . 327--328 Colette Laborde and Lucia Grugnetti Book reviews . . . . . . . . . . . . . . 329--337
Helen Watson Learning to apply numbers to nature . . 339--357 A. T. Olson and T. E. Kieren and S. Ludwig Linking logo, levels and language in mathematics . . . . . . . . . . . . . . 359--370 Anna Sierpi\'nska Humanities students and epistemological obstacles related to limits . . . . . . 371--397 Nina Kay Buchanan Factors contributing to mathematical problem-solving performance: An exploratory study . . . . . . . . . . . 399--415 David S. Fielker A calculator, a tape recorder, and thou 417--437 A. B. Pollitt and J. W. Searl and A. S. El Sheikh Factors affecting girls' learning of mathematics in Sudan . . . . . . . . . . 439--444 Neil Straker Videodisc technology and mathematics education . . . . . . . . . . . . . . . 445--450 Peter Damerow Die Entstehung des Mathematiklehrerberufs im 19. Jahrhundert. Studien u. Materialien zum Prozeß d. Professionalisierung in Preußen (1810--1870). (German) [The emergence of the mathematics teacher's profession in the 19th century. Studies and materials for the process of professionalisation in Prussia (1810--1870)] . . . . . . . . 451--453 Anonymous Announcement . . . . . . . . . . . . . . 454--454 Anonymous Announcement . . . . . . . . . . . . . . 455--455
Anonymous Editorial . . . . . . . . . . . . . . . 1--1 Paulus Gerdes On possible uses of traditional Angolan sand drawings in the mathematics classroom . . . . . . . . . . . . . . . 3--22 Ole Skovsmose Mathematics as part of technology . . . 23--41 Rene Baldy De l'espace du dessin \`a celui de l'objet. Une activité de mises en correspondances entre des dessins en perspective cavali\`ere et des objects réels. (French) [From the space of the drawing to that of the object. An activity of mappings between cavalier perspective drawings and real objects] 43--57 Jill Adler Newspaper-based mathematics for adults in South Africa . . . . . . . . . . . . 59--78 Bernard Parzysz ``Knowing'' vs ``seeing''. Problems of the plane representation of space geometry figures . . . . . . . . . . . . 79--92 Shudao Xu and Biao Huang Current status of secondary school mathematics curriculum development in China . . . . . . . . . . . . . . . . . 93--104 Josette Adda and N. Balacheff and Erich Wittmann Book Review . . . . . . . . . . . . . . 105--114
Anonymous Publisher's announcement . . . . . . . . 115--115 A. J. B. Editorial . . . . . . . . . . . . . . . 117--118 Beth Graham Mathematical education and Aboriginal children . . . . . . . . . . . . . . . . 119--135 Paulus Gerdes On culture, geometrical thinking and mathematics education . . . . . . . . . 137--162 Norma C. Presmeg School mathematics in culture-conflict situations . . . . . . . . . . . . . . . 163--177 Alan J. Bishop Mathematics education in its cultural context . . . . . . . . . . . . . . . . 179--191 Marc Swadener and R. Soedjadi Values, mathematics education, and the task of developing pupils' personalities: an Indonesian perspective 193--208 K. C. Cheung Outcomes of schooling: Mathematics achievement and attitudes towards mathematics learning in Hong Kong . . . 209--219 Thomas S. Popkewitz Institutional issues in the study of school mathematics: Curriculum research 221--249 Richard Noss The computer as a cultural influence in mathematical learning . . . . . . . . . 251--268 T. J. Fletcher and K. M. Hart Book review . . . . . . . . . . . . . . 269--275 M. Artigue and M. F. Costeroy and Detlef D. Spalt Book review . . . . . . . . . . . . . . 277--286
Alan J. Bishop Editorial . . . . . . . . . . . . . . . 287--287 Anna Zofia Krygowska \`A la mémoire de Tam\`as Varga. (French) [In memory of Tam\`as Varga] . . . . . . 289--290 Anonymous Mathematics education in Hungary today 291--298 Nadine Bednarz and Bernadette Janvier A constructivist approach to numeration in primary school: Results of a three year intervention with the same group of children . . . . . . . . . . . . . . . . 299--331 James Hiebert A theory of developing competence with written mathematical symbols . . . . . . 333--355 Marie-Paule Lecoutre and Jean-Luc Durand Jugements probabilistes et mod\`eles cognitifs: Étude d'une situation aléatoire. (French) [Probabilistic judgments and cognitive models: Study of a random situation] . . . . . . . . . . 357--368 Arthur J. Baroody Mental-addition development of children classified as mentally handicapped . . . 369--388 Luciana Bazzini The new government programs for Italian primary schools . . . . . . . . . . . . 389--393 Cathy W. Hall and Cynthia Hoff Gender differences in mathematical performance . . . . . . . . . . . . . . 395--401 Richard Noss and Régine Douady Book review . . . . . . . . . . . . . . 403--417 Anonymous Announcement . . . . . . . . . . . . . . 418--418
Anonymous Publisher's announcement . . . . . . . . iii--iii Alan J. Bishop Editorial . . . . . . . . . . . . . . . 419--419 Stefan Turnau Anna Sophia Krygowska . . . . . . . . . 420--422 Zofia Krygowska Composants de l'activité mathématique qui devraient jouer le rôle essentiel dans la mathématique pour tous. (French) [Components of mathematical activity that should play the essential role in mathematics for all] . . . . . . . . . . 423--433 G. S. Kaeley Sex differences in the learning of post-secondary mathematics in a neo-literate society . . . . . . . . . . 435--457 S. E. B. Pirie and R. L. E. Schwarzenberger Mathematical discussion and mathematical understanding . . . . . . . . . . . . . 459--470 Fou-Lai Lin Societal differences and their influences on children's mathematics understanding . . . . . . . . . . . . . 471--497 Brian Greer and George Booker Book reviews . . . . . . . . . . . . . . 499--510 Anonymous Call for proposals . . . . . . . . . . . 511--511 Anonymous Announcement . . . . . . . . . . . . . . 512--512
Joel Hillel and Carolyn Kieran and Jean-Luc Gurtner Solving structured geometric tasks on the computer: The role of feedback in generating strategies . . . . . . . . . 1--39 Lesley Lee and David Wheeler The arithmetic connection . . . . . . . 41--54 A. L. Mesquita Sur une situation d'éveil \`a la déduction en géométrie. (French) [On a situation of awakening in deduction in geometry] . . 55--77 Dina Tirosh and Anna O. Graeber Preservice elementary teachers' explicit beliefs about multiplication and division . . . . . . . . . . . . . . . . 79--96 K. C. Cheung Gender differences in the junior secondary (grade 7) mathematics curriculum in Hong Kong . . . . . . . . 97--103 John K. Backhouse Better mathematics for low attainers . . 105--110 Nitsa Movshovitz-Hadar Book Review . . . . . . . . . . . . . . 111--119
David Ben-Chaim and Glenda Lappan and Richard T. Houang Adolescents' ability to communicate spatial information: Analyzing and effecting students' performance . . . . 121--146 Kaye Stacey Finding and using patterns in linear generalising problems . . . . . . . . . 147--164 Johnston Anderson Sex-related differences on objective tests among undergraduates . . . . . . . 165--177 B. Capponi and N. Balacheff Tableur et calcul algébrique. (French) [Spreadsheet and algebraic computation] 179--210 Stephen Lerman Constructivism, mathematics and mathematics education . . . . . . . . . 211--223 Gila Hanna Mathematics achievement of girls and boys in grade eight: results from twenty countries . . . . . . . . . . . . . . . 225--232
Kenneth Ruthven Guest editorial . . . . . . . . . . . . 233--235 James T. Fey Technology and mathematics education: A survey of recent developments and important problems . . . . . . . . . . . 237--272 Sara Hennessy and Tim O'Shea and Rick Evertsz and Ann Floyd An intelligent tutoring system approach to teaching primary mathematics . . . . 273--292 Claire Dupuis and Dominique Guin Gestion des relations entre variables dans un environnement de programmation logo. (French) [Managing relationships between variables in a Logo programming environment] . . . . . . . . . . . . . . 293--316 Rosamund Sutherland Providing a computer based framework for algebraic thinking . . . . . . . . . . . 317--344 Alan J. Bishop Editorial . . . . . . . . . . . . . . . 345--345
Raffaella Borasi and Barbara J. Rose Journal writing and mathematics instruction . . . . . . . . . . . . . . 347--365 Julie Anghileri An investigation of young children's understanding of multiplication . . . . 367--385 Regine Douady and Marie-Jeanne Perrin-Glorian Un processus d'apprentissage du concept d'aire de surface plane. (French) [A learning process for the concept of the area of a flat surface] . . . . . . . . 387--424 Janet L. McDonald Accuracy and stability of cognitive structures and retention of geometric content . . . . . . . . . . . . . . . . 425--448 Kenneth Ruthven An exploratory approach to advanced mathematics . . . . . . . . . . . . . . 449--467 Anonymous Book review . . . . . . . . . . . . . . 469--474 Anonymous Publisher's notice . . . . . . . . . . . 481--481
W. Dörfler Editorial . . . . . . . . . . . . . . . 1--2 Yves Chevallard On mathematics education and culture: Critical afterthoughts . . . . . . . . . 3--27 A. Gagatsis and T. Patronis Using geometrical models in a process of reflective thinking in learning and teaching mathematics . . . . . . . . . . 29--54 Elizabeth Fennema and Penelope L. Peterson and Thomas P. Carpenter and Cheryl A. Lubinski Teachers' attributions and beliefs about girls, boys, and mathematics . . . . . . 55--69 Nancy C. Whitman and Morris K. Lai Similarities and differences in teachers' beliefs about effective teaching of mathematics: Japan and Hawai'i . . . . . . . . . . . . . . . . 71--81 Madis Lepik Algebraic word problems: Role of linguistic and structural variables . . 83--90 David Pimm Problems of representation in the teaching and learning of mathematics . . 91--99 Anonymous Announcement . . . . . . . . . . . . . . 101--107
Ole Skovsmose Mathematical education and democracy . . 109--128 Brian Hudson Global perspectives in the mathematics classroom . . . . . . . . . . . . . . . 129--136 P. L. Galbraith and N. J. Clatworthy Beyond Standard Models --- Meeting the Challenge of Modelling . . . . . . . . . 137--163 Glendon A. Lean and McKenzie A. Clements and Gina Del Campo Linguistic and pedagogical factors affecting children's understanding of arithmetic word problems: A comparative study . . . . . . . . . . . . . . . . . 165--191 N. Balacheff ICME-6 report of the international group psychology of mathematics education . . 193--197
Michal Yerushalmy and Daniel Chazan Overcoming visual obstacles with the aid of the supposer . . . . . . . . . . . . 199--219 Pamela Liebeck Scores and foreits --- An intuitive model for integer arithmetic . . . . . . 221--239 Carol A. Thornton Solution strategies: Subtraction number facts . . . . . . . . . . . . . . . . . 241--263 Nitsa Movshovitz-Hadar and Rina Hadass Preservice education of math teachers using paradoxes . . . . . . . . . . . . 265--287 Gordon Burt Doing critical cultural and ideological technology . . . . . . . . . . . . . . . 289--298
Peter L. Galbraith and D. Chant Factors shaping community attitudes to school mathematics: Implications for future curriculum change . . . . . . . . 299--318 Gurcharn S. Kaeley The influence of socio-economic status, entry style and instructional variables on the learning of mathematics in a neo-literate society . . . . . . . . . . 319--350 Lawal O. Adetula Language factor: Does it affect children's performance on word problems? 351--365 Gary Ernest Davis and Robert Paul Hunting Spontaneous partitioning: Pre-schoolers and discrete items . . . . . . . . . . . 367--374 Malcolm Simmons and Peter Cope Fragile knowledge of angle in turtle geometry . . . . . . . . . . . . . . . . 375--382 Luciana Bazzini The IEA study of mathematics II: Contexts and outcomes of school mathematics . . . . . . . . . . . . . . 383--390 Anonymous Announcement . . . . . . . . . . . . . . 391--392 Anonymous Call for papers . . . . . . . . . . . . 393--393
David F. Robitaille Achievement comparisons between the first and second IEA studies of mathematics . . . . . . . . . . . . . . 395--414 David Ben-Chaim and Barbara Fresko and Miriam Carmeli Comparison of teacher and pupil perceptions of the learning environment in mathematics classes . . . . . . . . . 415--429 Kenneth Ruthven The influence of graphic calculator use on translation from graphic to symbolic forms . . . . . . . . . . . . . . . . . 431--450 Barend Vlaardingerbroek and Lawrence Ros Educational transition rates and upper secondary students' arithmetical ability in five developing countries . . . . . . 451--460 Jeanne Connors When mathematics meets anthropology: The need for interdisciplinary dialogue . . 461--469 Yusuf Aydin Mathematics teacher preparation in Turkey today . . . . . . . . . . . . . . 471--478 E. Fischbein and Gila Hanna Book reviews . . . . . . . . . . . . . . 479--489
Charalampos Toumasis The epos of Euclidean geometry in Greek secondary education (1836--1985): Pressure for change and resistance . . . 491--508 Ng Li Fung Lin The effect of superfluous information on children's solution of story arithmetic problems . . . . . . . . . . . . . . . . 509--520 Ruhama Even Subject matter knowledge for teaching and the case of functions . . . . . . . 521--544 Diana Wearne Acquiring meaning for decimal fraction symbols: A one year follow-up . . . . . 545--564 Anna O. Graeber and Dina Tirosh Insights fourth and fifth graders bring to multiplication and division with decimals . . . . . . . . . . . . . . . . 565--588 Keith Porteous What do children really believe? . . . . 589--598 Anonymous In memoriam: Hans Freudenthal . . . . . 599--601
Anna Sfard On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin . . . . . . . . . . . . . . . 1--36 Werner Blum and Mogens Niss Applied mathematical problem solving, modelling, applications, and links to other subjects --- State, trends and issues in mathematics instruction . . . 37--68 Beatriz Silva D'Ambrosio The modern mathematics reform movement in Brazil and its consequences for Brazilian mathematics education . . . . 69--85 Jens Holger Lorenz and John P. Pace Book review . . . . . . . . . . . . . . 87--103 Anonymous Announcement . . . . . . . . . . . . . . 104--105
Nick Taylor Independence and interdependence: Analytical vectors for defining the mathematics curriculum of schools in a democratic society . . . . . . . . . . . 107--123 David Tall and Michael Thomas Encouraging versatile thinking in algebra using the computer . . . . . . . 125--147 Moncef Zaki and François Pluvinage Démarches de résolution et de simulation face au probl\`eme de la ruine d'un joueur. (French) [Solving and simulating the problem of the ruin of a player] . . 149--181 Werner Blum and Arnold Kirsch Preformal proving: Examples and reflections . . . . . . . . . . . . . . 183--203 Zhu Ziqiang and Eula Ewing Monroe Mathematics education in China today: Four problem areas . . . . . . . . . . . 205--208 Anonymous Announcement . . . . . . . . . . . . . . 209--209
E. Luis and A. Moreno and Guillermina Waldegg The conceptual evolution of actual mathematical infinity . . . . . . . . . 211--231 Raymond Duval Structure du raisonnement déductif et apprentissage de la démonstration. (French) [Structure of deductive reasoning and learning of demonstration] 233--261 Helga Jungwirth Interaction and gender --- Findings of a microethnographical approach to classroom discourse . . . . . . . . . . 263--284 Rina Zazkis and Uri Leron Capturing congruence with a turtle . . . 285--295 Warren J. Atkins and Gilah C. Leder and Peter J. O'Halloran and Graham H. Pollard and Peter Taylor Measuring risk taking . . . . . . . . . 297--308
Martin A. Simon and Deborah Schifter Towards a constructivist perspective: An intervention study of mathematics teacher development . . . . . . . . . . 309--331 Adrian Treffers Meeting innumeracy at primary school . . 333--352 Barbara J. Reys and Robert E. Reys and Alfinio Flores Peñafiel Estimation performance and strategy use of Mexican 5th and 8th grade student sample . . . . . . . . . . . . . . . . . 353--375 Muhammad Maqsud and Chaudhry M. Khalique Relationships of some socio-personal factors to mathematics achievement of secondary school and university students in Bophuthatswana . . . . . . . . . . . 377--390 David Pimm Book review . . . . . . . . . . . . . . 391--405 Anonymous Seventh International Congress on Mathematical Education . . . . . . . . . 407--407
Hans-Georg Weigand Iteration sequences and their representations . . . . . . . . . . . . 411--437 Astrid Pettersson Pupils' mathematical performance in grades 3 and 6. A longitudinal study . . 439--450 Lyn D. English Young children's combinatoric strategies 451--474 Tony Brown Hermeneutics and mathematical activity 475--480 Roy D. Pea and A. J. Sandy Dawson Book review . . . . . . . . . . . . . . 481--501
Heinz Steinbring The concept of chance in everyday teaching: Aspects of a social epistemology of mathematical knowledge 503--522 Efraim Fischbein and Maria Sainati Nello and Maria Sciolis Marino Factors affecting probabilistic judgements in children and adolescents 523--549 Edward M. Gray An analysis of diverging approaches to simple arithmetic: Preference and its consequences . . . . . . . . . . . . . . 551--574 Bernard Parzysz Representation of space and students' conceptions at high school level . . . . 575--593 Gail S. Gliner Factors contributing to success in mathematical estimation in preservice teachers: Types of problems and previous mathematical experience . . . . . . . . 595--606
Colette Laborde Guest editorial . . . . . . . . . . . . 1--4 Gilbert Arsac and Nicolas Balacheff and Michel Mante Teacher's role and reproducibility of didactical situations . . . . . . . . . 5--29 Celia Hoyles and Richard Noss A pedagogy for mathematical microworlds 31--57 F. Bellemain and B. Capponi Spécificité de l'organisation d'une séquence d'enseignement lors de l'utilisation de l'ordinateur. (French) [Specificity of the organization of a teaching sequence when using the computer] . . . . . . . . . . . . . . . 59--97 Paul Cobb and Erna Yackel and Terry Wood Interaction and learning in mathematics classroom situations . . . . . . . . . . 99--122
Bogdan J. Nowecki Anna Zofia Krygowska . . . . . . . . . . 123--137 Jean-Pierre Levain La résolution de probl\`emes multiplicatifs \`a la fin du cycle primaire. (French) [Resolution of multiplicative problems at the end of the primary cycle] . . . . . . . . . . . 139--161 Caryl Cox and John T. Mouw Disruption of the representativeness heuristic: Can we be perturbed into using correct probabilistic reasoning? 163--178 Martin Cooper Three-dimensional symmetry . . . . . . . 179--202 David F. Robitaille and J. Stuart Donn The Third International Mathematics and Science Study (TIMSS): A brief introduction . . . . . . . . . . . . . . 203--210 Anonymous Call for papers . . . . . . . . . . . . 211--211
Beatriz S. D'Ambrosio and Tânia Maria Mendonça Campos Pre-service teachers' representations of children's understanding of mathematical concepts: conflicts and conflict resolution . . . . . . . . . . . . . . . 213--230 Janice Ann Singer and Lauren B. Resnick Representations of proportional relationships: Are children part--part or part--whole reasoners? . . . . . . . 231--246 Daniel Breidenbach and Ed Dubinsky and Julie Hawks and Devilyna Nichols Development of the process conception of function . . . . . . . . . . . . . . . . 247--285 Wang Lin Quan Chinese advancements in mathematics education . . . . . . . . . . . . . . . 287--298 Elfriede Wenzelburger Guttenberger In-service high school mathematics teacher training in Mexico . . . . . . . 299--306 Norma C. Presmeg The body in the mind: The bodily basis of meaning, imagination and reason . . . 307--314
W. Dörfler Editorial . . . . . . . . . . . . . . . 315--315 Maggy Schneider \`A propos de l'apprentissage du taux de variation instantané. (French) [On learning about the instantaneous rate of change] . . . . . . . . . . . . . . . . 317--350 Tamara Lemerise and Claude Dessurealt and Lucille Marcotte Élaboration d'un environnement logo favorable au développement d'habiletés en manipulation procédurale. (French) [Elaboration of an enabling Logo environment for the development of procedural manipulation skills] . . . . 351--382 Gilah C. Leder Mathematics before formal schooling . . 383--396 Gary Davis and Kristine Pepper Mathematical problem solving by pre-school children . . . . . . . . . . 397--415 Philip C. Clarkson Language and mathematics: A comparison of bilingual and monolingual students of mathematics . . . . . . . . . . . . . . 417--429 Anonymous Announcements . . . . . . . . . . . . . 431--441
Ernst von Glasersfeld Guest editorial . . . . . . . . . . . . 443--444 Leslie P. Steffe and Heide G. Wiegel On reforming practice in mathematics education . . . . . . . . . . . . . . . 445--465 Heinrich Bauersfeld Classroom cultures from a social constructivist's perspective . . . . . . 467--481 Paul Cobb and Terry Wood and Erna Yackel and Marcela Perlwitz A follow-up assessment of a second-grade problem-centered mathematics project . . 483--504 Susan Pirie and Thomas Kieren Creating constructivist environments and constructing creative mathematics . . . 505--528 Grayson H. Wheatley The role of reflection in mathematics learning . . . . . . . . . . . . . . . . 529--541 Jack Lochhead Knocking down the building blocks of learning: Constructivism and the ventures program . . . . . . . . . . . . 543--552 Anonymous Announcement . . . . . . . . . . . . . . 553--555
Anonymous Publisher's notice . . . . . . . . . . . iii--iii Marie-Paule Lecoutre Cognitive models and problem spaces in ``purely random'' situations . . . . . . 557--568 Peter L. Galbraith and Marjorie C. Carss and Richard D. Grice and Lovie Endean and Merle C. Warry Towards numeracy for the third millennium: A study of the future of mathematics and mathematics education 569--593 Norma C. Presmeg Prototypes, metaphors, metonymies and imaginative rationality in high school mathematics . . . . . . . . . . . . . . 595--610 Aparna B. Ganguli The effect on students' attitudes of the computer as a teaching aid . . . . . . . 611--618 Theo Wubbels Book review . . . . . . . . . . . . . . 619--624 Anonymous Announcement . . . . . . . . . . . . . . 625--629
W. Dörfler Editorial . . . . . . . . . . . . . . . v--v Alan Bell Guest editorial . . . . . . . . . . . . 1--4 Alan Bell Principles for the design of teaching 5--34 Jan Van Den Brink Different aspects in designing mathematics education: Three examples from the Freudenthal Institute . . . . . 35--64 Konrad Krainer Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction . . . . . . . . 65--93 Rosamund Sutherland Connecting theory and practice: Results from the teaching of Logo . . . . . . . 95--113 Alan Bell Some experiments in diagnostic teaching 115--137
Anonymous Announcement . . . . . . . . . . . . . . i--i Efraim Fischbein The theory of figural concepts . . . . . 139--162 Malcolm Simmons and Peter Cope Angle and rotation: Effects of different types of feedback on the quality of response . . . . . . . . . . . . . . . . 163--176 Chronis Kynigos Children's inductive thinking during intrinsic and Euclidean Geometrical activities in a computer programming environment . . . . . . . . . . . . . . 177--197 Anne Sinclair and Nora Scheuer Understanding the written number system: 6 Year-olds in Argentina and Switzerland 199--221 Winifred A. Mallam Impact of school-type and sex of the teacher on female students' attitudes toward mathematics in Nigerian secondary schools . . . . . . . . . . . . . . . . 223--229 Tommy Dreyfus Book review . . . . . . . . . . . . . . 231--234
Stefan Turnau Mathematics education research in Poland 235--238 Agnieszka Demby L'usage de la compensation additionner--soustraire et multiplier--diviser par les él\`eves de onze ans. (French) [Use of compensation to add--subtract and multiply--divide by eleven-year-old students] . . . . . . . 239--249 Jan Konior Research into the construction of mathematical texts . . . . . . . . . . . 251--256 Irena Trzcieniecka-Schneider Some remarks on creating mathematical concepts . . . . . . . . . . . . . . . . 257--264 Aleksandra Urba\'nska On the numerical competence of six-years-old children . . . . . . . . . 265--275 István Lénárt Alternative models on the drawing ball 277--312 Irith Shillor and Bridget Egan The King Alfred's College Maths Game: Problem solving and mathematical activity . . . . . . . . . . . . . . . . 313--317 Laurie D. Edwards Book review . . . . . . . . . . . . . . 319--327
Gila Hanna and H. Niels Jahnke Guest editorial . . . . . . . . . . . . 329--331 Philip J. Davis Visual theorems . . . . . . . . . . . . 333--344 Man-Keung Siu Proof and pedagogy in ancient China: Examples from Liu Hui's commentary on Jiu Zhang Suan Shu . . . . . . . . . . . 345--357 Daniel Chazan High school geometry students' justification for their views of empirical evidence and mathematical proof . . . . . . . . . . . . . . . . . 359--387 Reuben Hersh Proving is convincing and explaining . . 389--399 Jean Dhombres Is one proof enough? Travels with a mathematician of the baroque period . . 401--419 Gila Hanna and Hans Niels Jahnke Proof and application . . . . . . . . . 421--438
W. Dörfler Editorial . . . . . . . . . . . . . . . v--vi Josette Adda Une lumi\`ere s'est éteinte. H. Freudenthal --- Homo Universalis. (French) [A light is extinguished: H. Freudenthal --- universal man] . . . . . 9--19 Fred Goffree HF: Working on mathematics education . . 21--49 Henk J. M. Bos `The bond with reality is cut' --- Freudenthal on the foundations of geometry around 1900 . . . . . . . . . . 51--58 W. T. Van Est Hans Freudenthal (17 September 1905--13 October 1990) . . . . . . . . . . . . . 59--69 Hans Freudenthal Thoughts on teaching mechanics didactical phenomenology of the concept of force . . . . . . . . . . . . . . . . 71--87 A. Treffers Wiskobas and Freudenthal realistic mathematics education . . . . . . . . . 89--108 L. Streefland The design of a mathematics course. A theoretical reflection . . . . . . . . . 109--135 J. De Lange Between end and beginning . . . . . . . 137--160 Christine Keitel Hans Freudenthal: Revisiting mathematics education China lecturers . . . . . . . 161--164 Leen Streefland Editorial: The legacy of Freudenthal . . viii-7
Patrick W. Thompson Quantitative reasoning, complexity, and additive structures . . . . . . . . . . 165--208 Gabriele Kaiser-Messmer Results of an empirical study into gender differences in attitudes towards mathematics . . . . . . . . . . . . . . 209--233 David J. Clarke and Andrew Waywood and Max Stephens Probing the structure of mathematical writing . . . . . . . . . . . . . . . . 235--250 Gurcharn S. Kaeley Explaining mathematics achievement of mature internal and external students at the University of Papua New Guinea . . . 251--260 David Pimm Book review . . . . . . . . . . . . . . 261--277 Anonymous Call for papers . . . . . . . . . . . . 279--279
David William Carraher Lines of thought: A ratio and operator model of rational number . . . . . . . . 281--305 Jacob Perrenet and Wim Groen A hint is not always a help . . . . . . 307--329 Martin A. Simon and Deborah Schifter Toward a constructivist perspective: The impact of a mathematics teacher inservice program on students . . . . . 331--340 Jo Boaler Encouraging the transfer of `school' mathematics to the `real world' through the integration of process and content, context and culture . . . . . . . . . . 341--373 Roberta Mura Images of mathematics held by university teachers of mathematical sciences . . . 375--385
Pearla Nesher and Sara Hershkovitz The role of schemes in two-step problems: Analysis and research findings 1--23 Robert J. Wright A study of the numerical development of 5-year-olds and 6-year-olds . . . . . . 25--44 Gilli Shama and Tommy Dreyfus Visual, algebraic and mixed strategies in visually presented linear programming problems . . . . . . . . . . . . . . . . 45--70 Martin A. Simon Learning mathematics and learning to teach: Learning cycles in mathematics teacher education . . . . . . . . . . . 71--94 M. C. Batanero and J. D. Godino and H. G. Steiner and E. Wenzelburger The training of researchers in mathematics education --- Results from an international survey . . . . . . . . 95--102 Hans-Georg Steiner Elfriede Wenzelburger 1947--1993 . . . . 103--103 Anonymous Announcement . . . . . . . . . . . . . . 104--104
Paul Cobb Guest editorial . . . . . . . . . . . . 105--109 Leslie P. Steffe and Heide G. Wiegel Cognitive play and mathematical learning in computer microworlds . . . . . . . . 111--134 Jere Confrey and Erick Smith Exponential functions, rates of change, and the multiplicative unit . . . . . . 135--164 Susan Pirie and Thomas Kieren Growth in mathematical understanding: How can we characterise it and how can we represent it? . . . . . . . . . . . . 165--190 Anna Sfard and Liora Linchevski The gains and the pitfalls of reification --- The case of algebra . . 191--228 Patrick W. Thompson Images of rate and operational understanding of the fundamental theorem of calculus . . . . . . . . . . . . . . 229--274 Jörg Voigt Negotiation of mathematical meaning and learning mathematics . . . . . . . . . . 275--298
Michael Otte Mathematical knowledge and the problem of proof . . . . . . . . . . . . . . . . 299--321 Ian Thompson Young children's idiosyncratic written algorithms for addition . . . . . . . . 323--345 João P. Ponte and João F. Matos and Henrique M. Guimarães and Leonor C. Leal and Ana P. Canavarro Teachers' and students' views and attitudes towards a new mathematics curriculum: A case study . . . . . . . . 347--365 Margaret Morton and Barbara Reilly and Elizabeth Robinson and Sharleen Forbes A comparative study of two nationwide examinations: Maths with calculus and maths with statistics . . . . . . . . . 367--387 Roy Sayers Gender differences in mathematics education in Zambia . . . . . . . . . . 389--403 Gary G. Bitter and Mary M. Hatfield Training elementary mathematics teachers using interactive multimedia . . . . . . 405--409
María Luz Callejo Les représentations graphiques dans la résolution de probl\`emes: Une expérience d'entra\^\inement d'étudiants dans un club mathématique. (French) [Graphical Representations in Problem Solving: An Experience of Student Engagement in a Mathematical Club] . . . . . . . . . . . 1--33 Ole Skovsmose Towards a critical mathematics education 35--57 Nicolas Herscovics and Liora Linchevski A cognitive gap between arithmetic and algebra . . . . . . . . . . . . . . . . 59--78 Tony Brown Creating and knowing mathematics through language and experience . . . . . . . . 79--100 Kenneth Ruthven and Robert Coe A structural analysis of students' epistemic views . . . . . . . . . . . . 101--109 Gurcharn S. Kaeley Erratum: \booktitleExplaining mathematics achievement of mature internal and external students at the University of Papua New Guinea [Short Communication], \booktitleEducational Studies in Mathematics \bf 25, pp. 251--260 . . . . . . . . . . . . . . . . 111--111 Brian Hudson Announcement . . . . . . . . . . . . . . 113--114 Anonymous Announcement . . . . . . . . . . . . . . 115--116
W. Dörfler Editorial . . . . . . . . . . . . . . . iii--iii Jacques C. Bergeron In memoriam Nicolas Herscovics 1935--1994 . . . . . . . . . . . . . . . v--vi Graham A. Jones and Carol A. Thornton and Ian J. Putt A model for nurturing and assessing multidigit number sense among first grade children . . . . . . . . . . . . . 117--143 Jane-Jane Lo and Grayson H. Wheatley Learning opportunities and negotiating social norms in mathematics class discussion . . . . . . . . . . . . . . . 145--164 Christine De Block-Docq Modalités de la pensée mathématique d'él\`eves de douze ans devant des probl\`emes de pavages. (French) [Modalities of Mathematical Thinking of Twelve-Year-Old Pupils in Tiling Problems] . . . . . . . . . . . . . . . 165--189 Helen A. Khoury and Rina Zazkis On fractions and non-standard representations: Pre-service teachers' concepts . . . . . . . . . . . . . . . . 191--204 Antonio R. Quesada and Mary E. Maxwell The effects of using graphing calculators to enhance college students' performance in precalculus . . . . . . . 205--215
Rainer Bromme and Heinz Steinbring Interactive development of subject matter in the mathematics classroom . . 217--248 Robert C. Moore Making the transition to formal proof 249--266 Ed Dubinsky and Jennie Dautermann and Uri Leron and Rina Zazkis On learning fundamental concepts of group theory . . . . . . . . . . . . . . 267--305 A. J. Dawson Book review . . . . . . . . . . . . . . 307--315 Anonymous Announcement . . . . . . . . . . . . . . 316--316
Leone Burton Guest editorial . . . . . . . . . . . . 317--319 Andrew Waywood Informal writing-to-learn as a dimension of a student profile . . . . . . . . . . 321--340 Marja Van Den Heuvel-Panhuizen Improvement of (didactical) assessment by improvement of problems: An attempt with respect to percentage . . . . . . . 341--372 Chris Haines and John Izard Assessing mathematical communications about projects and investigations . . . 373--386 Will Morony and Kevin Olssen Support for informal assessment in mathematics in the context of standards referenced reporting . . . . . . . . . . 387--399 Josep M. Fortuny and Joaquim Giménez and Claudi Alsina Integrated assessment on mathematics 12--16 . . . . . . . . . . . . . . . . . 401--412 Howard Tanner and Sonia Jones Using peer and self-assessment to develop modelling skills with students aged 11 to 16: A socio-constructive view 413--431 Kenneth Ruthven Better judgement: Rethinking assessment in mathematics education . . . . . . . . 433--450 Anonymous Announcement . . . . . . . . . . . . . . 451--451 Anonymous Call for papers . . . . . . . . . . . . 452--452
W. Dörfler Editorial . . . . . . . . . . . . . . . v--v Ma Tzu-Lin Yang and Paul Cobb A cross-cultural investigation into the development of place-value concepts of children in Taiwan and the United States 1--33 Edward A. Silver and Shukkwan S. Leung and Jinfa Cai Generating multiple solutions for a problem: A comparison of the responses of U.S. and Japanese students . . . . . 35--54 Siegbert Smidt and Werner Weiser Semantic structures of one-step word problems involving multiplication or division . . . . . . . . . . . . . . . . 55--72 Aline Robert Analyse des discours non strictement mathématiques accompagnant des cours de mathématiques. (French) [Analysis of non-strictly mathematical discourses accompanying mathematics courses] . . . 73--86 G. Hanna Book review . . . . . . . . . . . . . . 87--90 Anonymous The International Commission on Mathematical Instruction . . . . . . . . 91--98 Anonymous Announcement . . . . . . . . . . . . . . 99--99
Adalira Sáenz-Ludlow Ann's fraction schemes . . . . . . . . . 101--132 Richard J. Phillips and Daniel Pead and John Gillespie Evolving strategies for using interactive video resources in mathematics classrooms . . . . . . . . . 133--154 Cândida Moreira and Richard Noss Understanding teachers' attitudes to change in a Logomathematics environment 155--176 K. Jennifer Campbell and Kevin F. Collis and Jane M. Watson Visual processing during mathematical problem solving . . . . . . . . . . . . 177--194
Gilah Leder Guest editorial . . . . . . . . . . . . 195--198 Lindsay Anne Tartre and Elizabeth Fennema Mathematics achievement and gender: A longitudinal study of selected cognitive and affective variables [grades 6--12] 199--217 Helen J. Forgasz Gender and the relationship between affective beliefs and perceptions of grade 7 mathematics classroom learning environments . . . . . . . . . . . . . . 219--239 Monique Boekaerts and Gerard Seegers and Harriet Vermeer Solving math problems: Where and why does the solution process go astray? . . 241--262 James K. Taole and Marlies Zonneveld and Lebohang Letsie-Taole Gender interaction in mathematics classrooms: Reflection and transformation . . . . . . . . . . . . . 263--274 Leone Burton Moving towards a feminist epistemology of mathematics . . . . . . . . . . . . . 275--291 Bill Atweh and Tom Cooper The construction of gender, social class and mathematics in the classroom . . . . 293--310 Claudie Solar An inclusive pedagogy in mathematics education . . . . . . . . . . . . . . . 311--333
Celia Hoyles and Marilyn Nickson Stieg Mellin--Olsen . . . . . . . . . . 335--336 Regis Gras and Andre Totohasina Conceptions d'él\`eves sur la notion de probabilité conditionnelle révélées par une méthode d'analyse des données: Implication --- similarité --- corrélation. (French) [Student concepts on the idea of conditional probability revealed by a method of data analysis: Implication --- similarity --- correlation] . . . . . . 337--363 Elizabeth Warren and Lyn English Facility with plane shapes: A multifaceted skill . . . . . . . . . . . 365--383 Roberta Mura Images of mathematics held by university teachers of mathematics education . . . 385--399 Nira Hativa and Dorit Cohen Self learning of negative number concepts by lower division elementary students through solving computer-provided numerical problems . . 401--431 Anonymous Announcement . . . . . . . . . . . . . . 433--433
Ruhama Even and Dina Tirosh Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter . . 1--20 John Berry and Ken Houston Students using posters as a means of communication and assessment . . . . . . 21--27 Efraim Fischbein and Ruth Jehiam and Dorit Cohen The concept of irrational numbers in high-school students and prospective teachers . . . . . . . . . . . . . . . . 29--44 Klaus Hasemann and Helen Mansfield Concept mapping in research on mathematical knowledge development: Background, methods, findings and conclusions . . . . . . . . . . . . . . 45--72 Frank Swetz To know and to teach: Mathematical pedagogy from a historical context . . . 73--88 Anonymous Announcement . . . . . . . . . . . . . . 89--92
Tommy Dreyfus Guest editorial . . . . . . . . . . . . 93--95 David Pimm The advance party . . . . . . . . . . . 97--122 John Selden and Annie Selden Unpacking the logic of mathematical statements . . . . . . . . . . . . . . . 123--151 Uri Leron and Orit Hazzan and Rina Zazkis Learning group isomorphism: A crossroads of many concepts . . . . . . . . . . . . 153--174 Jean-luc Dorier Meta level in the teaching of unifying and generalizing concepts in mathematics 175--197 Renuka Vithal and Iben Christiansen and Ole Skovsmose Project work in university mathematics education . . . . . . . . . . . . . . . 199--223
T. A. Triandafillidis Circumventing visual limitations in teaching the geometry of shapes . . . . 225--235 Alistair McIntosh and Nobuhiko Nohda and Barbara J. Reys and Robert E. Reys Mental computation performance in Australia, Japan and the United States 237--258 Baruch Schwarz and Tommy Dreyfus New actions upon old objects: A new ontological perspective on functions . . 259--291 T. Nunes Book review . . . . . . . . . . . . . . 293--294 Anonymous Erratum . . . . . . . . . . . . . . . . 295--295
W. Dörfler Editorial . . . . . . . . . . . . . . . iii--iii F. K. S. Leung The mathematics classroom in Beijing, Hong Kong and London . . . . . . . . . . 297--325 Tim Rowland Hedges in mathematics talk: Linguistic pointers to uncertainty . . . . . . . . 327--353 Erich Ch. Wittmann Mathematics education as a `design science' . . . . . . . . . . . . . . . . 355--374
Kenneth Ruthven Editorial . . . . . . . . . . . . . . . 1--2 Anonymous Announcement . . . . . . . . . . . . . . 3--4 Anne Pitkethly and Robert Hunting A review of recent research in the area of initial fraction concepts . . . . . . 5--38 Liora Linchevski and Nicolas Herscovics Crossing the cognitive gap between arithmetic and algebra: Operating on the unknown in the context of equations . . 39--65 Grayson H. Wheatley and Anne Reynolds The construction of abstract units in geometric and numeric settings . . . . . 67--83 Terry Wood Events in learning mathematics: Insights from research in classrooms . . . . . . 85--105 Anonymous Erratum . . . . . . . . . . . . . . . . 107--107
Rosa Maria Bottino and Fulvia Furinghetti The emerging of teachers' conceptions of new subjects inserted in mathematics programs: the case of informatics . . . 109--134 Lyn D. English and Patrick V. Sharry Analogical reasoning and the development of algebraic abstraction . . . . . . . . 135--157 Ted Hodgson Students' ability to visualize set expressions: An initial investigation 159--178 Joe Relich Gender, self-concept and teachers of mathematics: Effects on attitudes to teaching and learning . . . . . . . . . 179--195 Martin A. Simon Beyond inductive and deductive reasoning: The search for a sense of knowing . . . . . . . . . . . . . . . . 197--210 Anonymous Announcement . . . . . . . . . . . . . . 211--211
Paul Cobb and Joy W. Whitenack A method for conducting longitudinal analyses of classroom videorecordings and transcripts . . . . . . . . . . . . 213--228 Merrilyn Goos and Peter Galbraith Do it this way! Metacognitive strategies in collaborative mathematical problem solving . . . . . . . . . . . . . . . . 229--260 Gerard Sensevy Fabrication de probl\`emes de fraction par des éléves \`a la fin de l'enseignement élémentaire. (French) [Manufacturing of fraction problems by pupils at the end of elementary education] . . . . . . . . . . . . . . . 261--288 Woo-Hyung Whang The influence of English--Korean bilingualism in solving mathematics word problems . . . . . . . . . . . . . . . . 289--312
Douglas H. Clements and Michael T. Battista and Julie Sarama and Sudha Swaminathan Development of turn and turn measurement concepts in a computer-based instructional unit . . . . . . . . . . . 313--337 Sara Hershkovitz and Pearla Nesher The role of schemes in designing computerized environments . . . . . . . 339--366 Antoine Dagher Apprentissage dans un environnement informatique: possibilité nature transfert des acquis. (French) [Learning in a computer environment: native opportunity for transferring acquired knowledge] . . . . . . . . . . . . . . . 367--398 Heather McLeay and David Piggins The mental manipulation of $2$-D representations of knots as deformable structures . . . . . . . . . . . . . . . 399--414 Anonymous Call for papers . . . . . . . . . . . . 415--415
Stephen Lerman Guest editorial . . . . . . . . . . . . 1--9 Maria G. Bartolini Bussi Mathematical discussion and perspective drawing in primary school . . . . . . . 11--41 Kathryn Crawford Vygotskian approaches in human development in the information era . . . 43--62 Catherine A. Brown and Mary Kay Stein and Ellice Ann Forman Assisting teachers and students to reform the mathematics classroom . . . . 63--93 Robyn Zevenbergen Constructivism as a liberal bourgeois discourse . . . . . . . . . . . . . . . 95--113 Tony Brown The phenomenology of the mathematics classroom . . . . . . . . . . . . . . . 115--150 Peter Charles Taylor Mythmaking and mythbreaking in the mathematics classroom . . . . . . . . . 151--173 Joanna O. Masingila and Susana Davidenko and Ewa Prus-Wisniowska Mathematics learning and practice in and out of school: A framework for connecting these experiences . . . . . . 175--200 Bill Barton Making sense of ethnomathematics: Ethnomathematics is making sense . . . . 201--233
Anonymous Publisher's note . . . . . . . . . . . . iii--iii Annette Baturo and Rod Nason Student teachers' subject matter knowledge within the domain of area measurement . . . . . . . . . . . . . . 235--268 Kazuhiko Nunokawa Applying Lakatos' theory to the theory of mathematical problem solving . . . . 269--293 Douglas R. Franks A situational study of the meanings of personal excellence for secondary mathematics teachers and students . . . 295--317 Marcelo C. Borba and Jere Confrey A student's construction of transformations of functions in a multiple representational environment 319--337 David Wheeler Book review . . . . . . . . . . . . . . 339--348
Glenda Anthony Active learning in a constructivist framework . . . . . . . . . . . . . . . 349--369 Bob Burn What are the fundamental concepts of group theory? . . . . . . . . . . . . . 371--377 Xin Ma The effects of cooperative homework on mathematics achievement of Chinese high school students . . . . . . . . . . . . 379--387 Paul Dowling A sociological analysis of school mathematics texts . . . . . . . . . . . 389--415
Theo Wubbels and Fred Korthagen and Harrie Broekman Preparing teachers for realistic mathematics education . . . . . . . . . 1--28 Zvia Markovits and Rina Hershkowitz Relative and absolute thinking in visual estimation processes . . . . . . . . . . 29--47 Heinz Steinbring Epistemological investigation of classroom interaction in elementary mathematics teaching . . . . . . . . . . 49--92
Graham A. Jones and Cynthia W. Langrall and Carol A. Thornton and A. Timothy Mogill A framework for assessing and nurturing young children's thinking in probability 101--125 Sylvine Schmidt and Nadine Bednarz Raisonnements arithmétiques et algébriques dans un contexte de résolution de probl\`emes: difficultés rencontrées par les futurs enseignants. (French) [Arithmetic and algebraic reactions in a context of problem solving: difficulties encountered by future teachers] . . . . 127--155 Junichi Hasegawa Concept formation of triangles and quadrilaterals in the second grade . . . 157--179 Carmen Batanero and Virginia Navarro-Pelayo and Juan D. Godino Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils . . . . . . . . 181--199
Olive Chapman Metaphors in the Teaching of Mathematical Problem Solving . . . . . . 201--228 Zemira R. Mevarech and Bracha Kramarsky From verbal descriptions to graphic representations: Stability and change in students' alternative conceptions . . . 229--263 Uri Leron and Orit Hazzan The World According to Johnny; A Coping Perspective in Mathematics Education . . 265--292
Mollie MacGregor and Kaye Stacey Students' understanding of algebraic notation: 11--15 . . . . . . . . . . . . 1--19 Gilbert Arsac and Michel Mante Situations d'initiation au raisonnement déductif. (French) [Situations of initiation to deductive reasoning] . . . 21--43 Agnieszka Demby Algebraic procedures used by 13-to-15-year-olds . . . . . . . . . . . 45--70 Wim Haeck and Nan Yeld and Jurie Conradie and Neill Robertson and Adrienne Shall A developmental approach to mathematics testing for university admissions and course placement . . . . . . . . . . . . 71--91
Ricardo Nemirovsky and Tracy Noble On Mathematical Visualization and the Place Where We Live . . . . . . . . . . 99--131 Mich\`ele Artigue Le logiciel `Derive' comme révélateur de phenom\`enes didactiques liés \`a l'utilisation d'environnements informatiques pour l'apprentissage. (French) [The Derive software as a developer of didactic phenomena related to the use of computing environments for learning] . . . . . . . . . . . . . . . 133--169 Uri Wilensky What is Normal Anyway? Therapy for Epistemological Anxiety . . . . . . . . 171--202 Richard Noss and Lulu Healy and Celia Hoyles The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic . . . . . . . . . . . . . . . . 203--233
Jill Adler A Participatory--Inquiry Approach And The Mediation Of Mathematical Knowledge In A Multilingual Classroom . . . . . . 235--258 David Slavit An Alternate Route to the Reification of Function . . . . . . . . . . . . . . . . 259--281 Randall P. Dahlberg and David L. Housman Facilitating Learning Events Through Example Generation . . . . . . . . . . . 283--299 Leslie Aspinwall and Kenneth L. Shaw and Norma C. Presmeg Uncontrollable Mental Imagery: Graphical Connections Between A Function And Its Derivative . . . . . . . . . . . . . . . 301--317 Sudhir K. Goel and Michael S. Robillard The Equation: $ - 2 = ( - 8)^{1 / 3} = ( - 8)^{2 / 6} = [( - 8)^2]^{1 / 6} = 2 $ 319--320 Dina Tirosh and Ruhama Even To Define or Not to Define: The Case of $ ( - 8)^{1 / 3} $ . . . . . . . . . . . 321--330
Iben Maj Christiansen When Negotiation of Meaning is also Negotiation of Task . . . . . . . . . . 1--25 Efraim Fischbein and Aline Grossman Schemata and Intuitions in Combinatorial Reasoning . . . . . . . . . . . . . . . 27--47 James P. Byrnes and Li Hong and Shaoying Xing Gender Differences on the Math Subtest of the Scholastic Aptitude Test may be Culture-Specific . . . . . . . . . . . . 49--66 Lucie DeBlois Trois él\`eves en difficulté devant des situations de réunion et de complément d'ensembles. (French) [Three students in difficulty in situations of union and complement of sets] . . . . . . . . . . 67--96
Shlomo Vinner The Pseudo-Conceptual and the Pseudo-Analytical Thought Processes in Mathematics Learning . . . . . . . . . . 97--129 Renuka Vithal and Ole Skovsmose The End of Innocence: A Critique of `Ethnomathematics' . . . . . . . . . . . 131--157 Susan E. B. Pirie and Lyndon Martin The Equation, the Whole Equation and Nothing But the Equation! One Approach to the Teaching of Linear Equations . . 159--181
Lyn D. English The Development of Fifth-Grade Children's Problem-Posing Abilities . . 183--217 Maria Alessandra Mariotti and Efraim Fischbein Defining in Classroom Activities . . . . 219--248 Ed Dubinsky and Jennie Dautermann and Uri Leron and Rina Zazkis A Reaction to Burn's ``What Are The Fundamental Concepts of Group Theory?'' 249--253 John Fauvel and Jan van Maanen The role of the history of mathematics in the teaching and learning of mathematics: Discussion Document for an ICMI Study (1997--2000) . . . . . . . . 255--259
Moyra Ruffell and John Mason and Barbara Allen Studying attitude to mathematics . . . . 1--18 Barry Cooper Assessing National Curriculum Mathematics in England: Exploring Children's Interpretation of Key Stage 2 Tests in Clinical Interviews . . . . . . 19--49 Dina Tirosh and Ruhama Even and Naomi Robinson Simplifying Algebraic Expressions: Teacher Awareness and Teaching Approaches . . . . . . . . . . . . . . . 51--64 Dirk De Bock and Lieven Verschaffel and Dirk Janssens The Predominance of the Linear Model in Secondary School Students' Solutions of Word Problems Involving Length and Area of Similar Plane Figures . . . . . . . . 65--83 Terezinha Nunes and Constanza Moreno The signed algorithm and its bugs . . . 85--92 Ian Stevenson Radical Constructivism. Ernst von Glasersfeld . . . . . . . . . . . . . . 93--104
Kay Owens and Bob Perry and John Conroy and Noel Geoghegan and Peter Howe Responsiveness and Affective Processes in the Interactive Construction of Understanding in Mathematics . . . . . . 105--127 Sylvie Coppé Composantes Privées et Publiques du Travail de l'Él\`eve en Situation de Devoir Surveillé de Mathématiques. (French) [Private and Public Components of Student Work in Supervised Mathematics] . . . . . . . . . . . . . . 129--151 Adalira Sáenz-Ludlow and Catherine Walgamuth Third Graders' Interpretations of Equality and the Equal Symbol . . . . . 153--187 George N. Philippou and Constantinos Christou The Effects of a Preparatory Mathematics Program in Changing Prospective Teachers' Attitudes Towards Mathematics 189--206
Núria Gorgorió Exploring the Functionality of Visual and Non-Visual Strategies in Solving Rotation Problems . . . . . . . . . . . 207--231 César Sáenz Castro Teaching Probability for Conceptual Change: La Enseñanza de la Probabilidad por Cambio Conceptual . . . . . . . . . 233--254 Gilli Shama Understanding Periodicity as a Process with a Gestalt Structure . . . . . . . . 255--281 Jacinthe Giroux and Gis\`ele Lemoyne Coordination of Knowledge of Numeration and Arithmetic Operations on First Grade Students . . . . . . . . . . . . . . . . 283--301 Rijkje Dekker and Marianne Elshout-Mohr A Process Model for Interaction and Mathematical Level Raising . . . . . . . 303--314
Anonymous Editorial . . . . . . . . . . . . . . . VII--VII Christoph Selter Building on Children's Mathematics --- a Teaching Experiment in Grade Three . . . 1--27 Mal Shield and Peter Galbraith The Analysis of Student Expository Writing in Mathematics . . . . . . . . . 29--52 Karen Newstead Aspects of Children's Mathematics Anxiety . . . . . . . . . . . . . . . . 53--71 Rina Zazkis Odds and Ends of Odds and Evens: An Inquiry Into Students' Understanding of Even and Odd Numbers . . . . . . . . . . 73--89 Anonymous ICMI Study on the Teaching and Learning of Mathematics At University Level . . . 91--103
Kenneth Ruthven Advice to Prospective Authors . . . . . III--IV Stefano Pozzi and Richard Noss and Celia Hoyles Tools in practice, mathematics in use 105--122 Mary E. Brenner Meaning and Money . . . . . . . . . . . 123--155 Gloria A. Stillman and Peter L. Galbraith Applying mathematics with real world connections: metacognitive characteristics of secondary students 157--194 Gila Hanna Book Review: Akihori Kanamori (Guest editor), \booktitleProof and Progress in Mathematics Synthese: An International Journal for Epistemology, Methodology and Philosophy of Science . . . . . . . 197--200
Mohan Chinnappan Schemas and mental models in geometry problem solving . . . . . . . . . . . . 201--217 Tracy Goodson-Espy The roles of reification and reflective abstraction in the development of abstract thought: Transitions from arithmetic to algebra . . . . . . . . . 219--245 David Ben-Chaim and James T. Fey and William M. Fitzgerald and Catherine Benedetto and Jane Miller Proportional Reasoning among 7th Grade Students with Different Curricular Experiences . . . . . . . . . . . . . . 247--273 Peter Galbraith and Chris Haines Disentangling the Nexus: Attitudes to Mathematics and Technology in a Computer Learning Environment . . . . . . . . . . 275--290 Anonymous Book Review . . . . . . . . . . . . . . 291--298 Anonymous Corrigendum . . . . . . . . . . . . . . 299--299
Anonymous Advice to Prospective Authors . . . . . 1--6 Efraim Fischbein and Madlen Baltsan The Mathematical Concept of set and the `Collection' Model . . . . . . . . . . . 1--22 Anonymous Editorial . . . . . . . . . . . . . . . 7--8 Anonymous An appreciation of Efraim Fischbein, 1920--1998 . . . . . . . . . . . . . . . 9--10 Uwe Gellert Prospective elementary teachers' comprehension of mathematics instruction 23--43 Cynthia Nicol Learning to Teach Mathematics: Questioning, Listening, and Responding 45--66 Yudariah bt. Mohammad Yusof and David Tall Changing Attitudes to University Mathematics Through Problem Solving . . 67--82 O. A. Adedayo Differential effectiveness by gender of instructional methods on achievement in mathematics at tertiary level . . . . . 83--91 Anonymous A Call for Papers . . . . . . . . . . . 93--94
Kenneth Ruthven Advice to Prospective Authors . . . . . i--iv David Williamson Shaffer and James J. Kaput Mathematics and Virtual Culture: an Evolutionary Perspective on Technology and Mathematics Education . . . . . . . 97--119 Leone Burton The Practices of Mathematicians: What do They Tell us About Coming to Know Mathematics? . . . . . . . . . . . . . . 121--143 Jane M. Watson and Jonathan B. Moritz The Beginning of Statistical Inference: Comparing two Data Sets . . . . . . . . 145--168 Judit N. Moschkovich Students' use of the $x$-intercept as an instance of a transitional conception 169--197
Elizabeth Smith Senger Reflective Reform in Mathematics: The Recursive Nature of Teacher Change . . . 199--221 M. Kathleen Heid and Glendon W. Blume and Rose Mary Zbiek and Barbara S. Edwards Factors that influence teachers learning to do interviews to understand students' mathematical understandings . . . . . . 223--249 David Slavit The role of operation sense in transitions from arithmetic to algebraic thought . . . . . . . . . . . . . . . . 251--274 Dimitris Chassapis The mediation of tools in the development of formal mathematical concepts: The compass and the circle as an example . . . . . . . . . . . . . . . 275--293 Anonymous Book Review . . . . . . . . . . . . . . 295--299
Dina Tirosh Forms of Mathematical Knowledge: Learning and Teaching with Understanding 1--9 Efraim Fischbein Intuitions and Schemata in Mathematical Reasoning . . . . . . . . . . . . . . . 11--50 Dina Tirosh and Ruth Stavy Intuitive rules: A way to explain and predict students' reasoning . . . . . . 51--66 Paul Ernest Forms of Knowledge in Mathematics and Mathematics Education: Philosophical and Rhetorical Perspectives . . . . . . . . 67--83 Tommy Dreyfus Why Johnny Can't Prove . . . . . . . . . 85--109 Eddie Gray and Marcia Pinto and Demetra Pitta and David Tall Knowledge construction and diverging thinking in elementary & advanced mathematics . . . . . . . . . . . . . . 111--133 John Mason and Mary Spence Beyond mere knowledge of mathematics: The importance of knowing-to act in the moment . . . . . . . . . . . . . . . . . 135--161 Thomas J. Cooney Conceptualizing Teachers' Ways of Knowing . . . . . . . . . . . . . . . . 163--187 Anna Graeber Forms of Knowing Mathematics: What Preservice Teachers Should Learn . . . . 189--208 Pessia Tsamir The Transition from Comparison of Finite to the Comparison of Infinite Sets: Teaching Prospective Teachers . . . . . 209--234 Ruhama Even Integrating academic and practical knowledge in a teacher leaders' development program . . . . . . . . . . 235--252
Carlo Dapueto and Laura Parenti Contributions and Obstacles of Contexts in the Development of Mathematical Knowledge . . . . . . . . . . . . . . . 1--21 Anonymous Guest Editorial . . . . . . . . . . . . 5--8 Jeff Evans Building Bridges: Reflections on the problem of transfer of learning in mathematics . . . . . . . . . . . . . . 23--44 Rafael E. Núñez and Laurie D. Edwards and João Filipe Matos Embodied cognition as grounding for situatedness and context in mathematics education . . . . . . . . . . . . . . . 45--65 Maria G. Bartolini Bussi and Mara Boni and Franca Ferri and Rossella Garuti Early approach to theoretical thinking: gears in primary school . . . . . . . . 67--87 Nadia Douek Argumentation and Conceptualization in Context: a Case Study on Sunshadows in Primary School . . . . . . . . . . . . . 89--110 Koeno Gravemeijer and Michiel Doorman Context Problems in Realistic Mathematics Education: A Calculus Course as an Example . . . . . . . . . . . . . 111--129 Liora Linchevski and Julian Williams Using Intuition From Everyday Life in `Filling' the gap in Children's Extension of Their Number Concept to Include the Negative Numbers . . . . . . 131--147 Rina Hershkowitz and Baruch Schwarz The emergent perspective in rich learning environments: Some roles of tools and activities in the construction of sociomathematical norms . . . . . . . 149--166 Susan Molyneux-Hodgson and Teresa Rojano and Rosamund Sutherland and Sonia Ursini Mathematical Modelling: the Interaction of Culture and Practice . . . . . . . . 167--183 Michal Yerushalmy and Shoshana Gilead Structures of Constant Rate Word Problems: A functional approach analysis 185--203 Tine Wedege To know or not to know --- mathematics, that is a question of context . . . . . 205--227 Corinne Hahn Proportionnalité et pourcentage chez des apprentis vendeurs. Réflexion sur la relation mathématiques/réalité dans une formation `en alternance'. (French) [Proportionality and percentage among apprentice sellers. Reflection on the mathematical reality relationship in an `alternating' formation] . . . . . . . . 229--249
Kenneth Ruthven Advice to Prospective Authors . . . . . v--vi Mogens Niss Aspects of the Nature and State of Research in Mathematics Education . . . 1--24 Richard Noss and Stefano Pozzi and Celia Hoyles Touching epistemologies: meanings of average and variation in nursing practice . . . . . . . . . . . . . . . . 25--51 Tony Brown and Frank Eade and Dave Wilson Semantic Innovation: Arithmetical and Algebraic Metaphors Within Narratives of Learning . . . . . . . . . . . . . . . . 53--70 Orit Hazzan Reducing Abstraction Level When Learning Abstract Algebra Concepts . . . . . . . 71--90 Barbara Allen Book Review: Keitel, C. (ed.), \booktitleSocial Justice and Mathematics Education . . . . . . . . . . . . . . . 91--92 Lyn English Book Review: Larochelle, M., Bednarz, N. and Garrison, J. (eds.), \booktitleConstructivism and Education 93--99
Kenneth Ruthven Advice to Prospective Authors . . . . . iii--iv Dagmar Neuman Early learning and awareness of division: A phenomenographic approach 101--128 Per Frostad Deaf children's use of cognitive strategies in simple arithmetic problems 129--153 Murad Jurdak and Iman Shahin An Ethnographic Study of the Computational Strategies of a Group of Young Street Vendors in Beirut . . . . . 155--172 Liora Linchevski and Drora Livneh Structure sense: The relationship between algebraic and numerical contexts 173--196 Rina Zazkis Intuitive rules in number theory: Example of `The more of A, the more of B' rule implementation . . . . . . . . . 197--209
Kenneth Ruthven Advice to Prospective Authors . . . . . iii--iv Anonymous Acknowledgements . . . . . . . . . . . . v--v Alice F. Artzt and Eleanor Armour-Thomas A Cognitive Model for Examining Teachers' Instructional Practice in Mathematics: A Guide for Facilitating Teacher Reflection . . . . . . . . . . . 211--235 Marilyn P. Carlson The Mathematical Behavior of Six Successful Mathematics Graduate Students: Influences Leading to Mathematical Success . . . . . . . . . . 237--258 Jo Boaler Participation, Knowledge and Beliefs: A Community Perspective on Mathematics Learning . . . . . . . . . . . . . . . . 259--281 Catherine Houdement and Alain Kuzniak Un exemple de cadre conceptuel pour létude de l'enseignement de la géométrie en formation des ma\^\itres. (French) [An example of a conceptual framework for the study of teaching of geometry in teacher training] . . . . . . . . . . . 283--312
Kenneth Ruthven Editorial . . . . . . . . . . . . . . . vii--vii Guida de Abreu Relationships between macro and micro socio-cultural contexts: implications for the study of interactions in the mathematics classroom . . . . . . . . . 1--29 Douglas H. Clements and Barbara A. Burns Students' Development of Strategies for Turn and Angle Measure . . . . . . . . . 31--45 Mikio Miyazaki Levels of Proof in Lower Secondary School Mathematics . . . . . . . . . . . 47--68 Anne Watson Mathematics Teachers Acting as Informal Assessors: Practices, Problems and Recommendations . . . . . . . . . . . . 69--91 Candia Morgan Book Review: \booktitleLanguage in Use in Mathematics Classrooms: Developing Approaches to a Research Domain, H. Steinbring, M. G. Bartolini Bussi and A. Sierpi\'nska . . . . . . . . . . . . . . 93--99
Lillie R. Albert Outside-In--Inside-Out: Seventh-Grade Students' Mathematical Thought Processes 109--141 Helen M. Doerr and Roxana Zangor Creating Meaning for and with the Graphing Calculator . . . . . . . . . . 143--163 Johan Lithner Mathematical Reasoning in School Tasks 165--190 Joachim Tiedemann Gender-related beliefs of teachers in elementary school mathematics . . . . . 191--207
Michael C. Mitchelmore and Paul White Development of angle concepts by progressive abstraction and generalisation . . . . . . . . . . . . . 209--238 Luc Trouche La parabole du gaucher et de la casserole \`a bec verseur: \`etude des processus d'apprentissage dans un environnement de calculatrices symboliques. (French) [The parabola of the left-handed and spout-casserole: study of learning processes in an environment of symbolic calculators] . . 239--264 Alan T. Graham and Michael O. J. Thomas Building a versatile understanding of algebraic variables with a graphic calculator . . . . . . . . . . . . . . . 265--282 Anne M. Raymond and Marylin Leinenbach Collaborative action research on the learning and teaching of algebra: a story of one mathematics teacher's development . . . . . . . . . . . . . . 283--307 Anonymous Book Review . . . . . . . . . . . . . . 309--310 Anonymous One hundred years of \em L'enseignement mathématique. (French) [One hundred years of Mathematical Education] . . . . . . . 311--312
Kenneth Ruthven Advise to Prospective Authors . . . . . v--vi Kenneth Ruthven Editorial . . . . . . . . . . . . . . . vii--vii Azita Manouchehri and Terry Goodman Implementing Mathematics Reform: The Challenge Within . . . . . . . . . . . . 1--34 Patricia A. Forster and Peter C. Taylor A multiple-perspective analysis of learning in the presence of technology 35--59 Donald Macnab Raising standards in mathematics education: values, vision, and TIMSS . . 61--80 Peter Huckstep and Tim Rowland `Creative mathematics' --- real or rhetoric? . . . . . . . . . . . . . . . 81--100 Alex Lawson Book Review: Liping Ma, \booktitleKnowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States . . . . . 101--106
Pedro Cobo and Josep M. Fortuny Social interactions and cognitive effects in contexts of area-comparison problem solving . . . . . . . . . . . . 115--140 A. Chronaki Teaching maths through theme-based resources: Pedagogic style, `theme' and `maths' in lessons . . . . . . . . . . . 141--163 Mary K. Porter and Joanna O. Masingila Examining the effects of writing on conceptual and procedural knowledge in calculus . . . . . . . . . . . . . . . . 165--177 Frank Monaghan What difference does it make? Children's views of the differences between some quadrilaterals . . . . . . . . . . . . . 179--196 Rodney E. McNair Working in the Mathematics Frame: Maximizing the Potential to Learn From Students' Mathematics Classroom Discussions . . . . . . . . . . . . . . 197--209 Christoph Selter Book Review: Verschaffel, L., Greer, B., and de Corte, E., \booktitleMaking Sense of Word Problems . . . . . . . . . . . . 211--213 Anonymous Discussion Document for the Twelfth ICMI Study . . . . . . . . . . . . . . . . . 215--224
Anonymous Advice to Prospective Authors . . . . . iii--iv Jurie Conradie and John Frith Comprehension tests in mathematics . . . 225--235 Luis Radford Signs and meanings in students' emergent algebraic thinking: A semiotic analysis 237--268 Cathy Arsenault and Gis\`ele Lemoyne Une introduction non classique aux algorithmes d'addition et de soustraction. (French) [An unconventional introduction to addition and subtraction algorithms] . . . . . . 269--296 Anonymous Announcement . . . . . . . . . . . . . . 297--297 Anonymous Volume contents . . . . . . . . . . . . 299--300
Jean-baptiste Lagrange L'intégration d'instruments informatiques dans l'enseignement: Une approche par les techniques. (French) [Integrating IT tools into teaching: An approach through technology] . . . . . . . . . . . . . . 1--30 Paul Andrews and Gillian Hatch A comparison of Hungarian and English teachers' conceptions of mathematics and its teaching . . . . . . . . . . . . . . 31--64 Susan H. Picker and John S. Berry Investigating pupils' images of mathematicians . . . . . . . . . . . . . 65--94 Klaus-D. Graf and Frederick K. S. Leung The Thirteenth ICMI Study on Mathematics Education in Different Cultural Traditions . . . . . . . . . . . . . . . 95--116 Anonymous Instructions for Authors . . . . . . . . 117--124
Michal Yerushalmy Problem solving strategies and mathematical resources: A longitudinal view on problem solving in a function based approach to algebra . . . . . . . 125--147 Inés María Gómez-Chacón Affective influences in the knowledge of mathematics . . . . . . . . . . . . . . 149--168 Elena Nardi Mathematics Undergraduates' Responses to Semantic Abbreviations, `Geometric' Images and Multi-Level Abstractions in Group Theory . . . . . . . . . . . . . . 169--189 Kathy Charles and Rod Nason Young children's partitioning strategies 191--221
Anonymous Editorial . . . . . . . . . . . . . . . 223--224 Patricia A. Forster Katie thought she couldn't do it but now she knows she can . . . . . . . . . . . 225--242 Mamokgethi Setati and Jill Adler Between languages and discourses: Language practices in primary multilingual mathematics classrooms in South Africa . . . . . . . . . . . . . . 243--269 Parmjit Singh Understanding the concepts of proportion and ratio constructed by two grade six students . . . . . . . . . . . . . . . . 271--292 Louis van Schalkwijk and Theo Bergen and Arnoud van Rooij Learning to prove by investigations: a promising approach in Dutch secondary education . . . . . . . . . . . . . . . 293--311 Barbara M. Moskal and Maria E. Magone Making Sense of What Students Know: Examining the Referents, Relationships and Modes Students Displayed in Response to a Decimal Task . . . . . . . . . . . 313--335 Anonymous Volume contents . . . . . . . . . . . . 337--338
Keith Jones and Ángel Gutiérrez and Maria Alessandra Mariotti Guest Editorial . . . . . . . . . . . . 1--3 Gila Hanna Proof, Explanation and Exploration: An Overview . . . . . . . . . . . . . . . . 5--23 Maria Alessandra Mariotti Introduction to Proof: The Mediation of a Dynamic Software Environment . . . . . 25--53 Keith Jones Providing a Foundation for Deductive Reasoning: Students' Interpretations when Using Dynamic Geometry Software and Their Evolving Mathematical Explanations 55--85 Ramón Marrades and Ángel Gutiérrez Proofs produced by secondary school students learning geometry in a dynamic computer environment . . . . . . . . . . 87--125 Nurit Hadas and Rina Hershkowitz and Baruch B. Schwarz The role of contradiction and uncertainty in promoting the need to prove in Dynamic Geometry environments 127--150 Colette Laborde Dynamic Geometry Environments as a Source of Rich Learning Contexts for the Complex Activity of Proving . . . . . . 151--161 Anonymous Instructions for Authors . . . . . . . . 163--170
Janet Aunley and Dave Pratt Introducing a special issue on constructing meanings from data . . . . 1--13 Brian Greer Understanding probabilistic thinking: The legacy of Efraim Fischbein . . . . . 15--33 Dani Ben-Zvi and Abraham Arcavi Junior high school students' construction of global views of data and data representations . . . . . . . . . . 35--65 Ricardo Nemirovsky and Cornelia Tierney Children creating ways to represent changing situations: On the development of homogeneous spaces . . . . . . . . . 67--102 Kay McClain and Paul Cobb Supporting Students' Ability to Reason about Data . . . . . . . . . . . . . . . 103--129 Janet Ainley and Dave Pratt and Elena Nardi Normalising: Children's activity to construct meanings for trend . . . . . . 131--146 Anonymous Instructions for Authors . . . . . . . . 147--154
Carolyn Kieran and Ellice Forman and Anna Sfard Guest Editorial: Learning discourse: Sociocultural approaches to research in mathematics education . . . . . . . . . 1--12 Anna Sfard There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning . . . . . . . . . 13--57 Bert van Oers Educational forms of initiation in mathematical culture . . . . . . . . . . 59--85 Stephen Lerman Cultural, Discursive Psychology: A Sociocultural Approach to Studying the Teaching and Learning of Mathematics . . 87--113 Ellice Forman and Ellen Ansell The multiple voices of a mathematics classroom community . . . . . . . . . . 115--142 M. C. O'Connor ``Can any fraction be turned into a decimal?'' A case study of a mathematical group discussion . . . . . 143--185 Carolyn Kieran The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges . . . . . . . . . . . . . . . . 187--228 Vicki Zack and Barbara Graves Making mathematical meaning through dialogue: ``Once you think of it, the $Z$ minus three seems pretty weird'' . . 229--271 Celia Hoyles From describing to designing mathematical activity: the next step in developing a social approach to research in mathematics education? . . . . . . . 273--286 Falk Seeger Research on Discourse in the Mathematics Classroom: A Commentary . . . . . . . . 287--297 Anonymous Instructions for Authors . . . . . . . . 299--306
Anna Sierpinska Editorial . . . . . . . . . . . . . . . 1--5 Núria Gorgorió and Núria Planas Teaching Mathematics in Multilingual Classrooms . . . . . . . . . . . . . . . 7--33 Frederick K. S. Leung In Search of an East Asian Identity in Mathematics Education . . . . . . . . . 35--51 Ronald Keijzer and Jan Terwel Audrey's acquisition of fractions: A case study into the learning of formal mathematics . . . . . . . . . . . . . . 53--73 Steven R. Williams and Kathy M. C. Ivey Affective Assessment and Mathematics Classroom Engagement: A Case Study . . . 75--100 Jeremy Kilpatrick Understanding mathematical literacy: The contribution of research . . . . . . . . 101--116 Anonymous Instructions for Authors . . . . . . . . 117--124
Paulo Abrantes Mathematical competence for all: Options, implications and obstacles . . 125--143 Christoph Selter Addition and Subtraction of Three-digit Numbers: German Elementary Children's Success, Methods and Strategies . . . . 145--173 Patricia S. Moyer Are We Having Fun Yet? How Teachers Use Manipulatives to Teach Mathematics . . . 175--197 Kaye Stacey and Sue Helme and Shona Archer and Caroline Condon The effect of epistemic fidelity and accessibility on teaching with physical materials: A comparison of two models for teaching decimal numeration . . . . 199--221 Iris Gulikers and Klaske Blom `A historical angle', a survey of recent literature on the use and value of history in geometrical education . . . . 223--258
Luciana Bazzini From Grounding Metaphors to Technological Devices: A Call for Legitimacy in School Mathematics . . . . 259--271 Amina Benbachir and Moncef Zaki Production d'exemples et de contre-exemples en analyse: étude de cas en premi\`ere d'université. (French) [Production of examples and counterexamples in analysis: first-year university case study] . . . . . . . . . 273--295 Murad Jurdak and Iman Shahin Problem solving activity in the workplace and the school: The case of constructing solids . . . . . . . . . . 297--315 Esther Kapa A Metacognitive Support during the Process of Problem Solving in a Computerized Environment . . . . . . . . 317--336 Jane M. Watson Longitudinal Development of Inferential Reasoning by School Students . . . . . . 337--372 Anonymous Volume contents . . . . . . . . . . . . 373--374
Erich Ch. Wittmann Developing mathematics education in a systemic process . . . . . . . . . . . . 1--20 Richard Noss For a learnable mathematics in the digital cultures . . . . . . . . . . . . 21--46 Jane M. Watson and Jonathan B. Moritz Development of reasoning associated with pictographs: Representing, interpreting, and predicting . . . . . . . . . . . . . 47--81 Angel M. Recio and Juan D. Godino Institutional and personal meanings of mathematical proof . . . . . . . . . . . 83--99 Keith Weber Student difficulty in constructing proofs: The need for strategic knowledge 101--119 Anonymous Instructions for Authors . . . . . . . . 121--128
David Tall and Dina Tirosh Infinity --- The never-ending struggle 129--136 Israel Kleiner History of the Infinitely Small and the Infinitely Large in Calculus . . . . . . 137--174 Hans Niels Jahnke Cantor's Cardinal and Ordinal Infinities: an Epistemological and Didactic View . . . . . . . . . . . . . 175--197 David Tall Natural and Formal Infinities . . . . . 199--238 John Monaghan Young Peoples' Ideas of Infinity . . . . 239--257 Joanna Mamona-Downs Letting the Intuitive bear on the Formal; A Didactical Approach for the Understanding of the Limit of a Sequence 259--288 Pessia Tsamir When `The Same' is not perceived as such: The case of infinite sets . . . . 289--307 Efraim Fischbein Tacit Models and Infinity . . . . . . . 309--329 Anonymous Contents of Volume 48 . . . . . . . . . 331--331
Barry Cooper and Tony Harries Children's Responses to Contrasting `Realistic' Mathematics Problems: Just how realistic are children ready to be? 1--23 Markku S. Hannula Attitude towards mathematics: emotions, expectations and values . . . . . . . . 25--46 Kenneth Ruthven and Sara Hennessy A practitioner model of the use of computer-based tools and resources to support mathematics teaching and learning . . . . . . . . . . . . . . . . 47--88 Bernard Sarrazy Les hétérogénéités dans l'enseignement des mathématiques. (French) [Heterogeneities in the teaching of mathematics] . . . . 89--117 Orit Zaslavsky and Hagit Sela and Uri Leron Being sloppy about slope: The effect of changing the scale . . . . . . . . . . . 119--140 Anonymous Technical instructions for authors . . . 141--148
Julia Anghileri and Meindert Beishuizen and Kees van Putten From Informal Strategies to Structured Procedures: mind the gap! . . . . . . . 149--170 Aurora Gallardo The extension of the natural-number domain to the integers in the transition from arithmetic to algebra . . . . . . . 171--192 Merrilyn Goos and Peter Galbraith and Peter Renshaw Socially mediated metacognition: creating collaborative zones of proximal development in small group problem solving . . . . . . . . . . . . . . . . 193--223 Bracha Kramarski and Zemira R. Mevarech and Marsel Arami The effects of metacognitive instruction on solving mathematical authentic tasks 225--250 Willy Mwakapenda The status and context of change in mathematics education in Malawi . . . . 251--281
Patricio G. Herbst Establishing a custom of proving in American school geometry: evolution of the two-column proof in the early twentieth century . . . . . . . . . . . 283--312 Jo Towers and Brent Davis Structuring Occasions . . . . . . . . . 313--340 Joëlle Vlassis The balance model: Hindrance or support for the solving of linear equations with one unknown . . . . . . . . . . . . . . 341--359 Sharon B. Walen and Steven R. Williams A Matter of Time: Emotional Responses to Timed Mathematics Tests . . . . . . . . 361--378 Rina Zazkis and Peter Liljedahk Generalization of patterns: the tension between algebraic thinking and algebraic notation . . . . . . . . . . . . . . . . 379--402 Anonymous Contents of Volume 49 . . . . . . . . . 403--404
Anna Sierpinska Editorial . . . . . . . . . . . . . . . i--ii Jennifer S. Thom and Susan E. B. Pirie Problems, perseverance, and mathematical residue . . . . . . . . . . . . . . . . 1--28 John Threlfall Flexible Mental Calculation . . . . . . 29--47 Joachim Tiedemann Teachers' Gender Stereotypes as Determinants of Teacher Perceptions in Elementary School Mathematics . . . . . 49--62 M. Klein Teaching mathematics in/for new times: A poststructuralist analysis of the productive quality of the pedagogic process . . . . . . . . . . . . . . . . 63--78 Stuart Rowlands and Robert Carson Where would formal, academic mathematics stand in a curriculum informed by ethnomathematics? A critical review of ethnomathematics . . . . . . . . . . . . 79--102 Pentecost M. Nkhoma What successful black South African students consider as factors of their success . . . . . . . . . . . . . . . . 103--113 Anonymous Technical instructions for authors . . . 115--122
Gila Hanna and Nathan Sidoli The story of ESM . . . . . . . . . . . . 123--156 Leone Burton Recognising commonalities and reconciling differences in mathematics education . . . . . . . . . . . . . . . 157--175 A. H. Herzig Where have all the students gone? Participation of doctoral students in authentic mathematical activity as a necessary condition for persistence toward the PH.D. . . . . . . . . . . . . 177--212 Lucie DeBlois and Hassan Squalli Implication de l'analyse de productions d'él\`eves dans la formation des ma\^\itres du primaire. (French) [Involvement of the analysis of pupil productions in the training of primary-school teachers] . . . . . . . . 212--237 Claudi Alsina Too much is not enough Teaching maths through useful applications with local and global perspectives . . . . . . . . 239--250
Anonymous Reflections on Educational Studies in Mathematics . . . . . . . . . . . . . . 251--257 Teresa Assude and Jean-Michel Gelis La dialectique ancien--nouveau dans l'intégration de Cabri --- géom\`etre \`a l'école primaire. (French) [The old--new dialectic in the integration of Cabri --- geometry in primary school] . . . . 259--287 Cynthia Nicol Where's the Math? Prospective Teachers Visit the Workplace . . . . . . . . . . 289--309 Dirk De Bock and Wim Van Dooren and Dirk Janssens and Lieven Verschaffel Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students' errors . . . . . . . . . . . . 311--334 Frank Uhlig The Role of Proof in Comprehending and Teaching Elementary Linear Algebra . . . 335--346 Anonymous Volume contents . . . . . . . . . . . . 347--348
Anonymous Advice to prospective authors . . . . . 1--2 Jo Boaler Exploring the nature of mathematical activity: using theory, research and `working hypotheses' to broaden conceptions of mathematics knowing . . . 3--21 Stephen Lerman and Guorong Xu and Anna Tsatsaroni Developing theories of mathematics education research: the ESM story . . . 23--40 Derek Foxman and Meindert Beishuizen Mental Calculation Methods Used By 11-Year-Olds in Different Attainment Bands: a reanalysis of data from the 1987 APU survey in the UK . . . . . . . 41--69 Barbara Jaworski Sensitivity and Challenge in University Mathematics Tutorial Teaching . . . . . 71--94 Jean-Marie Kraemer Évaluer pour mieux comprendre les enfants et améliorer sa pratique. (French) [Evaluate to better understand children and improve their practice] . . . . . . 95--116 Ronnie Karsenty What do adults remember from their high school mathematics? The case of linear functions . . . . . . . . . . . . . . . 117--144 Kenneth Ruthven Book Review: Barbin, E., Duval, R., Giorgiutti, I., Houdebine, J. and Laborde, C. (Eds.), \booktitleProduire et lire des textes de démonstration, Paris: Ellipses, 2001 . . . . . . . . . 145--147 Werner Blum ICMI Study 14: Applications and modelling in mathematics education --- Discussion document . . . . . . . . . . 149--171 Mich\`ele Artigue Information about the ICMI Awards . . . 173--174 Anonymous Technical instructions for authors . . . 175--182
R. P. Burn Some comments on the ``Role of proof in comprehending and teaching elementary linear algebra' by F. Uhlig . . . . . . 183--184 Jean-Luc Dorier and Aline Robert and Marc Rogalski Some comments on `The role of proof in comprehending and teaching elementary linear algebra' by F. Uhlig . . . . . . 185--192 Celia Hoyles and Dietmar Küchemann Students' understandings of logical implication . . . . . . . . . . . . . . 193--223 J. M. Watson Inferential reasoning and the influence of cognitive conflict . . . . . . . . . 225--256 L. Saldanha and P. Thompson Conceptions of sample and their relationship to statistical inference 257--270 Pessia Tsamir Book Review: \booktitleLearning and Teaching Number Theory: Research in Cognition and Instruction by S. R. Campbell and R. Zazkis (eds.) . . . . . 271--286 P. S. Clarkson Teaching/learning: Finding new ways to meaning . . . . . . . . . . . . . . . . 287--290 Anonymous Volume contents . . . . . . . . . . . . 291--292
Anonymous Advice to prospective authors . . . . . 1--2 I. Bloch Teaching functions in a graphic milieu: What forms of knowledge enable students to conjecture and prove? . . . . . . . . 3--28 J. Lithner Students' mathematical reasoning in university textbook exercises . . . . . 29--55 Patricia A. Forster and Peter C. Taylor An investigation of communicative competence in an upper-secondary class where using graphics calculators was routine . . . . . . . . . . . . . . . . 57--77 N. Sinclair and M. Schiralli A constructive response to `Where mathematics comes from' . . . . . . . . 79--91 Anonymous Technical instructions for authors . . . 93--100
Z. Magajna and J. Monaghan Advanced Mathematical Thinking in a Technological Workplace . . . . . . . . 101--122 Luis Radford On the epistemological limits of language: Mathematical knowledge and social practice during the Renaissance 123--150 P. Nesher and S. Hershkovitz and J. Novotna Situation model, Text Base and what else? Factors affecting Problem Solving 151--176 M. Kordaki The effect of tools of a computer microworld on students' strategies regarding the concept of conservation of area . . . . . . . . . . . . . . . . . . 177--209 B. Burn Book Review . . . . . . . . . . . . . . 211--214
A. Arcavi The role of visual representations in the learning of mathematics . . . . . . 215--241 S. Crespo Learning to pose mathematical problems: Exploring changes in preservice teachers' practices . . . . . . . . . . 243--270 C. Winslòw Semiotic and discursive variables in cas-based didactical engineering . . . . 271--288 M. P. Sinclair Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials . . 289--317 M. Raman Key Ideas: What are they and how can they help us understand how people view proof? . . . . . . . . . . . . . . . . . 319--325 S. Adam and W. Alangui and B. Barton A Comment on: Rowlands & Carson, ``Where would formal, academic mathematics stand in a curriculum informed by ethnomathematics? A critical review'' 327--335 Anonymous Volume contents . . . . . . . . . . . . 337--338
Anonymous Advice to prospective authors . . . . . 1--2 Anna Sierpinska Editorial . . . . . . . . . . . . . . . 3--4 V. Durand-Guerrier Which notion of implication is the right one? From logical considerations to a didactic perspective . . . . . . . . . . 5--34 R. Barwell Patterns of attention in the interaction of a primary school mathematics student with English as an additional language 35--59 Lou Edward Matthews Babies overboard! The complexities of incorporation culturally relevant teaching into mathematics instruction 61--82 Anonymous Technical instructions for authors . . . 83--90
Michael N. Fried and Miriam Amit Some reflections on mathematics classroom notebooks and their relationship to the public and private nature of student practices . . . . . . 91--112 Wim Van Dooren and Dirk De Bock and Fien Depaepe and Dirk Janssens and Lieven Verschaffel The Illusion of Linearity: Expanding the evidence towards probabilistic reasoning 113--138 David Housman and Mary Porter Proof schemes and learning strategies of above-average mathematics students . . . 139--158 David Pimm and David Wagner Investigation, mathematics education and genre: An essay review of Candia Morgan's \booktitleWriting Mathematically: the Discourse of Investigation . . . . . . . . . . . . . 159--178
S. J. Pape and C. V. Bell and \.IE. Yetkin Developing Mathematical Thinking and Self-Regulated Learning: A Teaching Experiment in a Seventh-Grade Mathematics Classroom . . . . . . . . . 179--202 M. Otte Complementarity, sets and numbers . . . 203--228 M. Sajka A secondary school student's understanding of the concept of function --- a case study . . . . . . . . . . . . 229--254 Ricardo Cantoral and Rosa M. Farfáan Mathematics Education: A Vision of Its Evolution . . . . . . . . . . . . . . . 255--270 Frank Uhlig Author's Response to the Comments on `The Role of Proof in \ldots Teaching \ldots Elementary Linear Algebra', by Frank Uhlig, this Journal, vol. \bf 50.3 (2002), p. 335--346 . . . . . . . . . . 271--274 Anonymous Volume contents . . . . . . . . . . . . 275--276
Norma Presmeg and Marja van den Heuvel-Panhuizen Leen Streefland's Legacy . . . . . . . . 1--4 Willibald Dörfler Introduction: A focus on experiences --- My experience with Leen . . . . . . . . 5--7 Marja Van Den Heuvel-Panhuizen The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage . . . . . . . . . . . . . 9--35 L. Streefland Learning from history for teaching in the future . . . . . . . . . . . . . . . 37--62 Barbara A. Van Amerom Focusing on informal strategies when linking arithmetic to early algebra . . 63--75 Ed Elbers Classroom interaction as reflection: Learning and teaching mathematics in a community of inquiry . . . . . . . . . . 77--99 Erna Yackel and Michelle Stephan and Chris Rasmussen and Diana Underwood Didactising: Continuing the work of Leen Streefland . . . . . . . . . . . . . . . 101--126 Norma Presmeg Creativity, Mathematizing, and Didactizing: Leen Streefland's work continues . . . . . . . . . . . . . . . 127--137
Deborah Loewenberg Ball and Ruhama Even Preface . . . . . . . . . . . . . . . . 139--146 Willi Dörfler Mathematics and mathematics education: Content and people, relation and difference . . . . . . . . . . . . . . . 147--170 Gerald A. Goldin Developing complex understandings: On the relation of mathematics education research to mathematics . . . . . . . . 171--202 Maria G. Bartolini Bussi and Luciana Bazzini Research, practice and theory in didactics of mathematics: Towards dialogue between different fields . . . 203--223 Lyn D. English Reconciling theory, research, and practice: A models and modelling perspective . . . . . . . . . . . . . . 225--248 Barbara Jaworski Research Practice into/influencing Mathematics Teaching and Learning Development: Towards a Theoretical framework based on co-learning partnerships . . . . . . . . . . . . . . 249--282 Ruhama Even and Baruch B. Schwarz Implications of competing interpretations of practice for research and theory in mathematics education . . 283--313 Anonymous Volume contents . . . . . . . . . . . . 315--316
Anonymous Advice to prospective authors . . . . . 1--2 R. A. Bruce and J. Threlfall One, Two, Three and Counting . . . . . . 3--26 David K. Pugalee A Comparison of Verbal and Written Descriptions of Students' Problem Solving Processes . . . . . . . . . . . 27--47 Judit N. Moschkovich Appropriating Mathematical Practices: A Case Study of Learning to Use and Explore Functions Through Interaction with a Tutor . . . . . . . . . . . . . . 49--80 Margot Berger The functional use of a mathematical sign . . . . . . . . . . . . . . . . . . 81--102 Ma\lgorzata Przenioslo Images of the limit of function formed in the course of mathematical studies at the university . . . . . . . . . . . . . 103--132 Andreas J. Stylianides and Gabriel J. Stylianides and George N. Philippou Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts . . . . . . 133--162 Uwe Gellert Didactic material confronted with the concept of mathematical literacy . . . . 163--179 Luc Trouche Environnements informatisés et mathématiques: quels usages pour quels apprentissages?. (French) [Computerized and mathematical environments: what uses for what learning?] . . . . . . . . . . 181--197 Raymond Bjuland Student teachers' reflections on their learning process through collaborative problem solving in geometry . . . . . . 199--225 Jeppe Skott The Forced Autonomy of Mathematics Teachers . . . . . . . . . . . . . . . . 227--257 Elizabeth de Freitas Plotting intersections along the political axis: The interior voice of dissenting mathematics teachers . . . . 259--274 Anonymous Technical instructions for authors . . . 275--280
Anonymous Advice to prospective authors . . . . . 1--2 Carol Murphy How Do Children Come to Use a Taught Mental Calculation Strategy? . . . . . . 3--18 Anastasia Steffen Morrone and Shelly S. Harkness and Beatriz D'Ambrosio and Richard Caulfield Patterns of Instructional Discourse that Promote the Perception of Mastery Goals in a Social Constructivist Mathematics Course . . . . . . . . . . . . . . . . . 19--38 Rijkje Dekker and Marianne Elshout-Mohr Teacher Interventions Aimed at Mathematical Level Raising During Collaborative Learning . . . . . . . . . 39--65 Dominic Peressini and Hilda Borko and Lew Romagnano and Eric Knuth and Christine Willis A Conceptual Framework for Learning to Teach Secondary Mathematics: A Situative Perspective . . . . . . . . . . . . . . 67--96 Robyn Zevenbergen Technologizing Numeracy: Intergenerational Differences in Working Mathematically in New Times . . . . . . 97--117 W. Stephen Wilson and Daniel Q. Naiman K--12 Calculator Usage and College Grades . . . . . . . . . . . . . . . . . 119--122 Anonymous Technical instructions for authors . . . 123--128
Bettina Dahl Analysing Cognitive Learning Processes through Group Interviews of Successful High School Pupils: Development and Use of a Model . . . . . . . . . . . . . . . 129--155 Andreas Ryve Can collaborative concept mapping create mathematically productive discourses? 157--177 Wim Van Dooren and Dirk De Bock and Dave Weyers and Lieven Verschaffel The predictive power of intuitive rules: A critical analysis of the impact of `more A--more B' and `same A--same B' 179--207 Keith Weber and Lara Alcock Semantic and Syntactic Proof Productions 209--234 Joanna Mamona-Downs and Martin Downs Realization of Techniques in Problem Solving: The Construction of Bijections for Enumeration Tasks . . . . . . . . . 235--253 Vilma Mesa Characterizing Practices Associated with Functions in Middle School Textbooks: An Empirical Approach . . . . . . . . . . . 255--286 Colleen M. Vale and Gilah C. Leder Student Views of Computer-Based Mathematics in the Middle Years: Does Gender Make a Difference? . . . . . . . 287--312 Afzal Ahmed and Alison Clark-Jeavons and Adrian Oldknow How Can Teaching Aids Improve the Quality of Mathematics Education . . . . 313--328 Stuart Rowlands and Robert Carson Our response to Adam, Alangui and Barton's ``A Comment on Rowlands & Carson `Where would Formal, Academic Mathematics stand in a Curriculum informed by Ethnomathematics? A Critical Review'\,'' . . . . . . . . . . . . . . 329--342 Paul Cooper and Ray d'Inverno Those who can, teach: addressing the crisis in mathematics in UK schools and universities . . . . . . . . . . . . . . 343--357 Anonymous Discussion Document: The Fifteenth ICMI Study: The Professional Education and Development of Teachers of Mathematics: The International Commission on Mathematical Instruction . . . . . . . . 359--372 Anonymous Announcement: The International Commission on Mathematical Instruction: The ICMI Felix Klein and Hans Freudenthal Medals for 2003 . . . . . . 373--377 Anonymous Volume Contents . . . . . . . . . . . . 379--380
Lara Alcock and Adrian Simpson Convergence of sequences and series: Interactions between visual reasoning and the learner's beliefs about their own role . . . . . . . . . . . . . . . . 1--32 Corine Castela Institutions influencing mathematics students' private work: A factor of academic achievement . . . . . . . . . . 33--63 Diana F. Steele and Debra I. Johanning A schematic--theoretic view of problem solving and development of algebraic thinking . . . . . . . . . . . . . . . . 65--90 Varda Talmon and Michal Yerushalmy Understanding dynamic behavior: Parent--Child relations in dynamic geometry environments . . . . . . . . . 91--119 Jane M. Watson and Ben A. Kelly Statistical variation in a chance setting: A two-year study . . . . . . . 121--144 Harry B. Tunis Letter to the Editor . . . . . . . . . . 145--146 P. Herbst Announcement . . . . . . . . . . . . . . 147--148 Anonymous Instructions for Authors . . . . . . . . 149--155
Constantinos Christou and Maria Eliophotou-Menon and George Philippou Teachers' concerns regarding the adoption of a new mathematics curriculum: An application of CBAM . . . 157--176 Mellony Graven Investigating mathematics teacher learning within an in-service community of practice: The centrality of confidence . . . . . . . . . . . . . . . 177--211 Susan M. Brookhart and Marissa Andolina and Megan Zuza and Rosalie Furman Minute math: An action research study of student self-assessment . . . . . . . . 213--227 Philippe R. Richard L'inférence figurale: Un pas de raisonnement discursivo-graphique. (French) [The figurative inference: A step of discursive-graphic reasoning] 229--263 Wolff-Michael Roth and Yew Jin Lee Interpreting unfamiliar graphs: A generative, activity theoretic model . . 265--290 Jorge M. López and Ana Helvia Quintero and Wanda Velázquez A reaction to ``Mathematics education: A vision of its evolution'' by Ricardo Cantoral and Rosa M. Farfán . . . . . . . 291--294 Diana Coben Book Review . . . . . . . . . . . . . . 295--300
Anna Sierpinska Breaking the Silence and Revealing the Backstage . . . . . . . . . . . . . . . 301--301 Ricardo Nemirovsky and Marcelo Borba and Cara Dimattia and Ferdinando Arzarello and Ornella Robutti and Marty Schnepp and Daniel Chazan and Chris Rasmussen and Jennifer Olszewski and Kevin Dost and James L. Johnson and Marcelo C. Borba and Nilce Fatima Scheffer PME Special Issue: Bodily Activity and Imagination in Mathematics Learning . . 303--321 Cara Dimattia Instructions for Opening, Reading and Viewing the Videopapers on the Attached CD . . . . . . . . . . . . . . . . . . . 323--324
Gareth Q. Witten Designing a Mathematics Course for Chemistry and Geology Students . . . . . 1--19 Helen M. G. Watt Attitudes to the Use of Alternative Assessment Methods in Mathematics: A Study with Secondary Mathematics Teachers in Sydney, Australia . . . . . 21--44 Marilyn P. Carlson and Irene Bloom The Cyclic Nature of Problem Solving: An Emergent Multidimensional Problem-Solving Framework . . . . . . . 45--75 Lara Alcock and Adrian Simpson Convergence of Sequences and Series 2: Interactions Between Nonvisual Reasoning and the Learner's Beliefs about their own Role . . . . . . . . . . . . . . . . 77--100 Orit Hazzan and Rina Zazkis Reducing Abstraction: The Case of School Mathematics . . . . . . . . . . . . . . 101--119 Janet Duffin and Adrian Simpson Cognitive Empathy and the Transition to Independent Graduate Study in Mathematics . . . . . . . . . . . . . . 121--135 Anna Sierpinska and Marie Sheldon Technical Instructions for Authors . . . 137--143
Miriam Amit and Michael N. Fried Authority and Authority Relations in Mathematics Education: A View from an 8th Grade Classroom . . . . . . . . . . 145--168 Kathryn C. Irwin and Murray S. Britt The Algebraic Nature of Students' Numerical Manipulation in the New Zealand Numeracy Project . . . . . . . . 169--188 Bob Speiser and Chuck Walter and Tiffini Glaze Getting at the Mathematics: Sara's Journal . . . . . . . . . . . . . . . . 189--207 Anne Watson and Els De Geest Principled Teaching for Deep Progress: Improving Mathematical Learning Beyond Methods and Materials . . . . . . . . . 209--234 Johann Engelbrecht and Ansie Harding Teaching Undergraduate Mathematics on the Internet. Part 1: Technologies and Taxonomy . . . . . . . . . . . . . . . . 235--252 Johann Engelbrecht and Ansie Harding Teaching Undergraduate Mathematics on the Internet. Part 2 . . . . . . . . . . 253--276 Nathan Sidoli Reviel Netz, The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History . . . . . . . . . . . . . . . . 277--282
Kathryn C. Irwin and R. John Irwin Assessing Development in Numeracy of Students from Different Socio-Economic Areas: A Rasch Analysis of Three Fundamental Tasks . . . . . . . . . . . 283--298 Gabriela Buendía and Francisco Cordero Prediction and the Periodical Aspect as Generators of Knowledge in a Social Practice Framework . . . . . . . . . . . 299--333 Ed Dubinsky and Kirk Weller and Michael A. Mcdonald and Anne Brown Some Historical Issues and Paradoxes Regarding the Concept of Infinity: An APOS-Based Analysis: Part 1 . . . . . . 335--359 Natasha M. Speer Issues of Methods and Theory in the Study of Mathematics Teachers' Professed and Attributed Beliefs . . . . . . . . . 361--391 Anna Sfard What Could be More Practical than Good Research? . . . . . . . . . . . . . . . 393--413 W. Stephen Wilson Short Response to Tunis's Letter to the Editor on Technology in College . . . . 415--420 Mich\`ele Artigue ICMI: The International Commission on Mathematical Instruction, ICMI Awards Committee . . . . . . . . . . . . . . . 421--421
Colette Laborde and Marie-Jeanne Perrin-Glorian Introduction Teaching Situations as Object of Research: Empirical Studies within Theoretical Perspectives . . . . 1--12 Guy Brousseau and Patrick Gibel Didactical Handling of Students' Reasoning Processes in Problem Solving Situations . . . . . . . . . . . . . . . 13--58 Annick Flückiger Macro-Situation and Numerical Knowledge Building: The Role of Pupils' Didactic Memory in Classroom Interactions . . . . 59--84 Patricia Sadovsky and Carmen Sessa The Adidactic Interaction with the Procedures of Peers in the Transition from Arithmetic to Algebra: A Milieu for the Emergence of New Questions . . . . . 85--112 Magali Hersant and Marie-Jeanne Perrin-Glorian Characterization of an Ordinary Teaching Practice with the Help of the Theory of Didactic Situations . . . . . . . . . . 113--151 Gérard Sensevy and Maria-Luisa Schubauer-Leoni and Alain Mercier and Florence Ligozat and Gérard Perrot An Attempt to Model the Teacher's Action in the Mathematics Class . . . . . . . . 153--181 Teresa Assude Time Management in the Work Economy of a Class, a Case Study: Integration of Cabri in Primary School Mathematics Teaching . . . . . . . . . . . . . . . . 183--203 Claire Margolinas and Lalina Coulange and Annie Bessot What Can the Teacher Learn in the Classroom? . . . . . . . . . . . . . . . 205--234 Joaquim Barbé and Marianna Bosch and Lorena Espinoza and Josep Gascón Didactic Restrictions on the Teacher's Practice: The Case of Limits of Functions in Spanish High Schools . . . 235--268 Aline Robert and Janine Rogalski A Cross-Analysis of the Mathematics Teacher's Activity. An Example in a French 10th-Grade Class . . . . . . . . 269--298 Maria G. Bartolini Bussi When Classroom Situation is the Unit of Analysis: The Potential Impact on Research in Mathematics Education . . . 299--311 Heinz Steinbring Analyzing Mathematical Teaching--Learning Situations --- the Interplay of Communicational and Epistemological Constraints . . . . . . 313--324
Anonymous Advice to Prospective Authors . . . . . 1--2 Juan D. Godino and Carmen Batanero and Rafael Roa An Onto-Semiotic Analysis of Combinatorial Problems and the Solving Processes by University Students . . . . 3--36 Bryan Moseley Students' Early Mathematical Representation Knowledge: The Effects of Emphasizing Single or Multiple Perspectives of the Rational Number Domain in Problem Solving . . . . . . . 37--69 Ma\lgorzata Przenioslo Introducing the Concept of Convergence of a Sequence in Secondary School . . . 71--93 Tami S. Martin and Sharon M. Soucy McCrone and Michelle L. Wallace Bower and Jaguthsing Dindyal The Interplay of Teacher and Student Actions in the Teaching and Learning of Geometric Proof . . . . . . . . . . . . 95--124 Edward J. Barbeau and Peter J. Taylor ICMI Study 16: Challenging Mathematics in and Beyond the Classroom: Discussion Document . . . . . . . . . . . . . . . . 125--139
Viviane Durand-Guerrier and Gilbert Arsac An Epistemological and Didactic Study of a Specific Calculus Reasoning Rule . . . 149--172 Barbro Grevholm and Lars-Erik Persson and Peter Wall A Dynamic Model for Education of Doctoral Students and Guidance of Supervisors in Research Groups . . . . . 173--197 Frederick Koon Shing Leung Some Characteristics of East Asian Mathematics Classrooms Based on Data from the TIMSS 1999 Video Study . . . . 199--215 Masakazu Okazaki and Masataka Koyama Characteristics of 5th Graders' Logical Development Through Learning Division with Decimals . . . . . . . . . . . . . 217--251 Ed Dubinsky and Kirk Weller and Michael A. McDonald and Anne Brown Some Historical Issues and Paradoxes Regarding the Concept of Infinity: An APOS Analysis: Part 2 . . . . . . . . . 253--266 Celia Hoyles and Jean-baptiste Lagrange 17th ICMI Study Digital Technologies and Mathematics Teaching and Learning: Rethinking the Domain --- Short Announcement . . . . . . . . . . . . . . 267--268
Bob Burn The Vice: Some Historically Inspired and Proof-Generated Steps to Limits of Sequences . . . . . . . . . . . . . . . 269--295 Orit Zaslavsky Seizing the Opportunity to Create Uncertainty in Learning Mathematics . . 297--321 Carla Fiori and Luciana Zuccheri An Experimental Research on Error Patterns in Written Subtraction . . . . 323--331 Arthur Bakker and Michael H. G. Hoffmann Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution . . . . . . . . . . . . . . 333--358 Jill Adler and Deborah Ball and Konrad Krainer and Fou-Lai Lin and Jarmila Novotna Reflections on an Emerging Field: Researching Mathematics Teacher Education . . . . . . . . . . . . . . . 359--381 Kenneth Ruthven Alternative Interpretation of the Dataset on K--12 Calculator Usage and College Grades as Analysed by Wilson and Naiman (2003, 2004) . . . . . . . . . . 383--387
Adalira Sáenz--Ludlow and Norma Presmeg Guest Editorial Semiotic Perspectives on Learning Mathematics and Communicating Mathematically . . . . . . . . . . . . . 1--10 Michael Otte Mathematical Epistemology from a Peircean Semiotic Point of View . . . . 11--38 Luis Radford The Anthropology of Meaning . . . . . . 39--65 Paul Ernest A Semiotic Perspective of Mathematical Activity: The Case of Number . . . . . . 67--101 Raymond Duval A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics . . . . . . . . . . . . . . 103--131 Heinz Steinbring What Makes a Sign a Mathematical Sign? --- An Epistemological Perspective on Mathematical Interaction . . . . . . . . 133--162 Norma Presmeg Semiotics and the ``Connections'' Standard: Significance of Semiotics for Teachers of Mathematics . . . . . . . . 163--182 Adalira Sáenz-Ludlow Classroom Interpreting Games with an Illustration . . . . . . . . . . . . . . 183--218 Candia Morgan What does Social Semiotics have to Offer Mathematics Education Research? . . . . 219--245 Sigmund Ongstad Mathematics and Mathematics Education as Triadic Communication? A Semiotic Framework Exemplified . . . . . . . . . 247--277 Michael H. G. Hoffmann What Is a ``Semiotic Perspective'', and What Could It Be? Some Comments on the Contributions to This Special Issue . . 279--291
Brent Davis and Elaine Simmt Mathematics-for-Teaching: an Ongoing Investigation of the Mathematics that Teachers (Need to) Know . . . . . . . . 293--319 S. Philemon Ntenza Investigating Forms of Children's Writing in Grade 7 Mathematics Classrooms . . . . . . . . . . . . . . . 321--345 Adrian Simpson and Nada Stehlíková Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring . . . . . . . . . . . . 347--371 Yvette Solomon Deficit or Difference? The Role of Students' Epistemologies of Mathematics in their Interactions with Proof . . . . 373--393 Analía Bergé Convergence of Numerical Sequences --- a Commentary on \booktitleThe Vice: Some Historically Inspired and Proof Generated Steps to Limits of Sequences'' by R. P. Burn . . . . . . . . . . . . . 395--402 R. P. Burn Further Reflections on ``The Vice'' . . 403--407 Anonymous Contents of Volume 61 . . . . . . . . . 409--410
Tommy Dreyfus E, S, and M as in ESM-- an Editorial . . 1--2 Helen M. Doerr Examining the Tasks of Teaching When Using Students' Mathematical Thinking 3--24 Santiago Cueto and Cecilia Ramirez and Juan Leon Opportunities to Learn and Achievement in Mathematics in a Sample of Sixth Grade Students in Lima, Peru . . . . . . 25--55 Rijkje Dekker and Marianne Elshout-Mohr and Terry Wood How Children Regulate their Own Collaborative Learning . . . . . . . . . 57--79 Peter Sullivan and Steve Tobias and Andrea McDonough Perhaps the Decision of Some Students not to Engage in Learning Mathematics in School is Deliberate . . . . . . . . . . 81--99 Robyn Zevenbergen Search of a Pedagogy of Conflict and Dialogue for Mathematics Education . . . 101--104
Uri Leron and Orit Hazzan The Rationality Debate: Application of Cognitive Psychology to Mathematics Education . . . . . . . . . . . . . . . 105--126 May Hamdan Equivalent Structures on Sets: Equivalence Classes, Partitions and Fiber Structures of Functions . . . . . 127--147 Arthur Bakker and Koeno P. E. Gravemeijer An Historical Phenomenology of Mean and Median . . . . . . . . . . . . . . . . . 149--168 Elizabeth Warren Comparative Mathematical Language in the Elementary School: A Longitudinal Study 169--189 Andreas Ryve Making Explicit the Analysis of Students' Mathematical Discourses --- Revisiting a Newly Developed Methodological Framework . . . . . . . . 191--209 Olive Chapman Classroom Practices for Context of Mathematics Word Problems . . . . . . . 211--230 Anonymous ICMI Awards the 2005 Felix Klein and Hans Freudenthal Medals . . . . . . . . 231--231
John Monaghan and Mehmet Fatih Ozmantar Abstraction and Consolidation . . . . . 233--258 Giorgio T. Bagni Some Cognitive Difficulties Related to the Representations of two Major Concepts of Set Theory . . . . . . . . . 259--280 Bárbara M. Brizuela Young Children's Notations For Fractions 281--305 Lucie Deblois Influence des interprétations des productions des él\`eves sur les stratégies d'intervention en classe de mathématiques. (French) [Influence of interpretations of students' productions on strategies of intervention in a mathematics class] . . . . . . . . . . . 307--329 C. C. Nicol and S. M. Crespo Learning to Teach with Mathematics Textbooks: How Preservice Teachers Interpret and Use Curriculum Materials 331--355
Susan B. Empson and Debra Junk and Higinio Dominguez and Erin Turner Fractions as the Coordination of Multiplicatively Related Quantities: A Cross-Sectional Study of Children's Thinking . . . . . . . . . . . . . . . . 1--28 Sandra Crespo Elementary Teacher Talk in Mathematics Study Groups . . . . . . . . . . . . . . 29--56 Gwendolyn M. Lloyd Preservice Teachers' Stories Of Mathematics Classrooms: Explorations Of Practice Through Fictional Accounts . . 57--87 Rose Mary Zbiek and AnnaMarie Conner Beyond Motivation: Exploring Mathematical Modeling as A Context for Deepening Students' Understandings of Curricular Mathematics . . . . . . . . . 89--112
Rosetta Zan and Laurinda Brown and Jeff Evans and Markku S. Hannula Affect in Mathematics Education: An Introduction . . . . . . . . . . . . . . 113--121 Peter Op't Eynde and Markku S. Hannula The Case Study of Frank . . . . . . . . 123--129 Valerie A. DeBellis and Gerald A. Goldin Affect and Meta-Affect in Mathematical Problem Solving: a Representational Perspective . . . . . . . . . . . . . . 131--147 Marja-Liisa Malmivuori Affect and Self-Regulation . . . . . . . 149--164 Markku S. Hannula Motivation in Mathematics: Goals Reflected in Emotions . . . . . . . . . 165--178 Laurinda Brown and David A. Reid Embodied Cognition: Somatic Markers, Purposes and Emotional Orientations . . 179--192 Peter Op 't Eynde and Erik De Corte and Lieven Verschaffel ``Accepting Emotional Complexity'': A Socio-Constructivist Perspective on the Role of Emotions in the Mathematics Classroom . . . . . . . . . . . . . . . 193--207 Jeff Evans and Candia Morgan and Anna Tsatsaroni Discursive Positioning and Emotion in School Mathematics Practices . . . . . . 209--226 Melissa Rodd Commentary: Mathematics, Emotion and Special Needs . . . . . . . . . . . . . 227--234
Michal Tabach and Rina Hershkowitz and Baruch Schwarz Constructing and Consolidating of Algebraic Knowledge within Dyadic Processes: A Case Study . . . . . . . . 235--258 Cecile Ouvrier-Buffet Exploring Mathematical Definition Construction Processes . . . . . . . . . 259--282 Murad Eid Jurdak Contrasting Perspectives and Performance of High School Students on Problem Solving in Real World, Situated, and School Contexts . . . . . . . . . . . . 283--301 Lyn D. English Mathematical Modeling in the Primary School: Children's Construction of a Consumer Guide . . . . . . . . . . . . . 303--323 Magnus Österholm Characterizing Reading Comprehension of Mathematical Texts . . . . . . . . . . . 325--346 Peter Gates Going Beyond Belief Systems: Exploring a Model for the Social Influence on Mathematics Teacher Beliefs . . . . . . 347--369
Mercedes García and Victoria Sánchez and Isabel Escudero Learning Through Reflection in Mathematics Teacher Education . . . . . 1--17 Laurie O. Cavey and Joy W. Whitenack and Louann Lovin Investigating Teachers' Mathematics Teaching Understanding: A Case for Coordinating Perspectives . . . . . . . 19--43 Hanan Innabi and Omar El Sheikh The Change in Mathematics Teachers' Perceptions of Critical Thinking after 15 Years of Educational Reform in Jordan 45--68 Douglas P. Newton and Lynn D. Newton Could Elementary Mathematics Textbooks Help Give Attention to Reasons in the Classroom? . . . . . . . . . . . . . . . 69--84 Zhongjun Cao and Alan Bishop and Helen Forgasz Perceived Parental Influence on Mathematics Learning: A Comparison Among Students in China and Australia . . . . 85--106 Gila Hanna Book review . . . . . . . . . . . . . . 107--111
Richard Barwell and Bill Barton and Mamokgethi Setati Multilingual issues in mathematics education: introduction . . . . . . . . 113--119 Judit Moschkovich Using Two Languages When Learning Mathematics . . . . . . . . . . . . . . 121--144 Siôn Wyn Evans Differential Performance of Items in Mathematics Assessment Materials For 7-Year-Old Pupils in English-Medium and Welsh-Medium Versions . . . . . . . . . 145--168 Mercy Kazima Malawian Students' Meanings For Probability Vocabulary . . . . . . . . . 169--189 Philip C. Clarkson Australian Vietnamese Students Learning Mathematics: High Ability Bilinguals and Their Use of Their Languages . . . . . . 191--215 Jackeline Rodrigues Mendes Numeracy and Literacy in a Bilingual Context: Indigenous Teachers Education in Brazil . . . . . . . . . . . . . . . 217--230 Charoula Stathopoulou and Fragiskos Kalabasis Language and Culture in Mathematics Education: Reflections on Observing a Romany Class in a Greek School . . . . . 231--238 Candia Morgan Who is not multilingual now? . . . . . . 239--242 Eric Gutstein Multiple language use and mathematics: Politicizing the discussion . . . . . . 243--246
Kalifa Traoré and Caroline Lajoie and Roberta Mura Quelques erreurs pouvant être liées \`a une difficulté \`a concevoir un ensemble comme un objet distinct de ses éléments chez des étudiants et des étudiantes Universitaires. (French) [Some errors that can be related to a difficulty in conceiving a set as an object distinct from its elements in university students] . . . . . . . . . . . . . . . 247--264 Michael Shayer and Mundher Adhami Fostering Cognitive Development Through the Context of Mathematics: Results of the CAME Project . . . . . . . . . . . . 265--291 Charalambos Y. Charalambous and Demetra Pitta-Pantazi Drawing on a Theoretical Model to Study Students' Understandings of Fractions 293--316 Julian Williams and Geoff Wake Black Boxes in Workplace Mathematics . . 317--343 Julian Williams and Geoff Wake Metaphors and Models in Translation Between College and Workplace Mathematics . . . . . . . . . . . . . . 345--371 Brent Davis Book review . . . . . . . . . . . . . . 373--379
Andreas J. Stylianides The Notion of Proof in the Context of Elementary School Mathematics . . . . . 1--20 Jane M. Watson The Role of Cognitive Conflict in Developing Students' Understanding of Average . . . . . . . . . . . . . . . . 21--47 Natasa Sirotic and Andrina Zazkis Irrational Numbers: The Gap between Formal and Intuitive Knowledge . . . . . 49--76 Amal Alajmi and Robert Reys Reasonable and Reasonableness of Answers: Kuwaiti Middle School Teachers' Perspectives . . . . . . . . . . . . . . 77--94 Kim Beswick Teachers' Beliefs That Matter in Secondary Mathematics Classrooms . . . . 95--120 Norma Presmeg Book review: Pattern and beauty in mathematics and music . . . . . . . . . 121--124
William Hook and Wayne Bishop and John Hook A Quality Math Curriculum in Support of Effective Teaching For Elementary Schools . . . . . . . . . . . . . . . . 125--148 Robert Adjiage and François Pluvinage An Experiment in Teaching Ratio and Proportion . . . . . . . . . . . . . . . 149--175 Betina Zolkower and Sam Shreyar A Teacher's Mediation of a Thinking-Aloud Discussion in a 6th Grade Mathematics Classroom . . . . . . . . . 177--202 Janet G. Walter and Hope Gerson Teachers' Personal Agency: Making Sense of Slope Through Additive Structures . . 203--233 Shelly Sheats Harkness and Beatriz D'Ambrosio and Anastasia S. Morrone Preservice Elementary Teachers' Voices Describe How Their Teacher Motivated Them to do Mathematics . . . . . . . . . 235--254
Pessia Tsamir When Intuition Beats Logic: Prospective Teachers' Awareness of their Same Sides--Same Angles Solutions . . . . . . 255--279 Ferdinand D. Rivera Accounting for Students' Schemes in the Development of a Graphical Process for Solving Polynomial Inequalities in Instrumented Activity . . . . . . . . . 281--307 Monique Pijls and Rijkje Dekker and Bernadette Van Hout-Wolters Reconstruction of a Collaborative Mathematical Learning Process . . . . . 309--329 Zahra Gooya Mathematics teachers' beliefs about a new reform in high school geometry in Iran . . . . . . . . . . . . . . . . . . 331--347 Boris Koichu and Guershon Harel Triadic interaction in clinical task-based interviews with mathematics teachers . . . . . . . . . . . . . . . . 349--365 Richard Noss and Arthur Bakker and Celia Hoyles and Phillip Kent Situating graphs as workplace knowledge 367--384 Gail E. FitzSimons Book review . . . . . . . . . . . . . . 385--392
Tommy Dreyfus Editorial: Review Articles . . . . . . . 1--1 Matthew Inglis and Juan Pablo Mejia-Ramos and Adrian Simpson Modelling mathematical argumentation: the importance of qualification . . . . 3--21 Bettina Pedemonte How can the relationship between argumentation and proof be analysed? . . 23--41 John K. Lannin and David D. Barker and Brian E. Townsend How students view the general nature of their errors . . . . . . . . . . . . . . 43--59 Lianghuo Fan and Yan Zhu Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks 61--75 Tang Jing The popularization of China's higher education and its influence on university mathematics education . . . . 77--82 Vassiliki Farmaki and Theodorus Paschos Employing genetic `moments' in the history of mathematics in classroom activities . . . . . . . . . . . . . . . 83--106
Luis Radford and Fulvia Furinghetti and Victor Katz Introduction The topos of meaning or the encounter between past and present . . . 107--110 Abraham Arcavi and Masami Isoda Learning to listen: from historical sources to classroom practice . . . . . 111--129 Fulvia Furinghetti Teacher education through the history of mathematics . . . . . . . . . . . . . . 131--143 Luis Radford and Luis Puig Syntax and Meaning as Sensuous, Visual, Historical forms of Algebraic Thinking 145--164 Yannis Thomaidis and Constantinos Tzanakis The notion of historical ``parallelism'' revisited: historical evolution and students' conception of the order relation on the number line . . . . . . 165--183 Victor J. Katz and Bill Barton Stages in the History of Algebra with Implications for Teaching . . . . . . . 185--201 Michael N. Fried Didactics and History of Mathematics: Knowledge and Self-Knowledge . . . . . . 203--223 Evelyne Barbin On the argument of simplicity in Elements and schoolbooks of Geometry . . 225--242 Michael Otte Mathematical history, philosophy and education . . . . . . . . . . . . . . . 243--255 Jens Hòyrup The roles of Mesopotamian bronze age mathematics tool for state formation and administration --- carrier of teachers' professional intellectual autonomy . . . 257--271
Ron Tzur Fine grain assessment of students' mathematical understanding: participatory and anticipatory stagesin learning a new mathematical conception 273--291 Per Nilsson Different ways in which students handle chance encounters in the explorative setting of a dice game . . . . . . . . . 293--315 Rossana Falcade and Colette Laborde and Maria Alessandra Mariotti Approaching functions: Cabri tools as instruments of semiotic mediation . . . 317--333 John Threlfall and Peter Pool and Matthew Homer and Bronwen Swinnerton Implicit aspects of paper and pencil mathematics assessment that come to light through the use of the computer 335--348 Roza Leikin and Anat Levav-Waynberg Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks . . . . . . 349--371 Raimo Kaasila Mathematical biography and key rhetoric 373--384
Giorgio T. Bagni Richard Rorty (1931--2007) and his legacy for mathematics educators . . . . 1--2 Rosana Nogueira de Lima and David Tall Procedural embodiment and magic in linear equations . . . . . . . . . . . . 3--18 Anne Birgitte Fyhn A climbing class' reinvention of angles 19--35 Torulf Palm Impact of authenticity on sense making in word problem solving . . . . . . . . 37--58 Kai-Lin Yang and Fou-Lai Lin A model of reading comprehension of geometry proof . . . . . . . . . . . . . 59--76 Kamuran Tarim and Fikri Akdeniz The effects of cooperative learning on Turkish elementary students' mathematics achievement and attitude towards mathematics using TAI and STAD methods 77--91
Uwe Gellert Routines and collective orientations in mathematics teachers' professional development . . . . . . . . . . . . . . 93--110 Raimo Kaasila and Markku S. Hannula and Anu Laine and Erkki Pehkonen Socio-emotional orientations and teacher change . . . . . . . . . . . . . . . . . 111--123 Charalambos Y. Charalambous and George N. Philippou and Leonidas Kyriakides Tracing the development of preservice teachers' efficacy beliefs in teaching mathematics during fieldwork . . . . . . 125--142 David Wagner and Beth Herbel-Eisenmann ``Just don't'': The suppression and invitation of dialogue in the mathematics classroom . . . . . . . . . 143--157 Konstantinos A. Sdrolias and Triandafillos A. Triandafillidis The transition to secondary school geometry: can there be a ``chain of school mathematics''? . . . . . . . . . 159--169 Elizabeth Warren and Tom Cooper Generalising the pattern rule for visual growth patterns: Actions that support 8-year olds' thinking . . . . . . . . . 171--185
Matthew Inglis and Adrian Simpson Conditional inference and advanced mathematical study . . . . . . . . . . . 187--204 Sean Larsen and Michelle Zandieh Proofs and refutations in the undergraduate mathematics classroom . . 205--216 Analía Bergé The completeness property of the set of real numbers in the transition from calculus to analysis . . . . . . . . . . 217--235 Ghislaine Gueudet Investigating the secondary--tertiary transition . . . . . . . . . . . . . . . 237--254 Johan Lithner A research framework for creative and imitative reasoning . . . . . . . . . . 255--276
Zbigniew Semadeni Deep intuition as a level in the development of the concept image . . . . 1--17 Erhan Bingolbali and John Monaghan Concept image revisited . . . . . . . . 19--35 Cecilia Agudelo-Valderrama The power of Colombian mathematics teachers' conceptions of social/institutional factors of teaching 37--54 M. Pari\`es and A. Robert and J. Rogalski Analyses de séances en classe et stabilité des pratiques d'enseignants de mathématiques expérimentés du second degré. (French) [Analyzes of classroom sessions and stability of the practices of experimental-mathematics teachers of the second level] . . . . . . . . . . . . . 55--80
Richard Lesh and Stephen Hegedus Introduction: Building on the vision of Jim Kaput (1942--2005) . . . . . . . . . 81--83 Celia Hoyles and Richard Noss Next steps in implementing Kaput's research programme . . . . . . . . . . . 85--97 Luis Moreno-Armella and Stephen J. Hegedus and James J. Kaput From static to dynamic mathematics: historical and representational perspectives . . . . . . . . . . . . . . 99--111 Richard Lesh and James A. Middleton and Elizabeth Caylor and Shweta Gupta A science need: Designing tasks to engage students in modeling complex data 113--130 Roberta Y. Schorr and Gerald A. Goldin Students' expression of affect in an inner-city simcalc classroom . . . . . . 131--148 J. Roschelle and D. Tatar and N. Shechtman and J. Knudsen The role of scaling up research in designing for and evaluating robustness 149--170 Stephen J. Hegedus and William R. Penuel Studying new forms of participation and identity in mathematics classrooms with integrated communication and representational infrastructures . . . . 171--183 David Tall James J. Kaput (1942--2005) imagineer and futurologist of mathematics education . . . . . . . . . . . . . . . 185--193
Rina Zazkis and Egan J. Chernoff What makes a counterexample exemplary? 195--208 Bárbara M. Brizuela and Gabrielle A. Cayton The roles of punctuation marks while learning about written numbers . . . . . 209--225 Tony Brown Lacan, subjectivity and the task of mathematics education research . . . . . 227--245 Keith Weber and Carolyn Maher and Arthur Powell and Hollylynne Stohl Lee Learning opportunities from group discussions: warrants become the objects of debate . . . . . . . . . . . . . . . 247--261 Enis Dogan and Kikumi Tatsuoka An international comparison using a diagnostic testing model: Turkish students' profile of mathematical skills on TIMSS-R . . . . . . . . . . . . . . . 263--272
Christian Greiffenhagen and Wes Sharrock School mathematics and its everyday other? Revisiting Lave's `Cognition in Practice' . . . . . . . . . . . . . . . 1--21 David W. Carraher Beyond `blaming the victim' and `standing in awe of noble savages': a response to ``Revisiting Lave's `cognition in practice''' . . . . . . . 23--32 Vicenç Font and Ángel Contreras The problem of the particular and its relation to the general in mathematics education . . . . . . . . . . . . . . . 33--52 Michal Tabach and Abraham Arcavi and Rina Hershkowitz Transitions among different symbolic generalizations by algebra beginners in a computer intensive environment . . . . 53--71 Giorgio T. Bagni Centenary birth anniversary of E. W. Beth (1908--1964) . . . . . . . . . . . 73--76
Liz Bills and Anne Watson Editorial introduction . . . . . . . . . 77--79 Pessia Tsamir and Dina Tirosh and Esther Levenson Intuitive nonexamples: the case of triangles . . . . . . . . . . . . . . . 81--95 Anne Watson and Steve Shipman Using learner generated examples to introduce new concepts . . . . . . . . . 97--109 Lara Alcock and Matthew Inglis Doctoral students' use of examples in evaluating and proving conjectures . . . 111--129 Rina Zazkis and Roza Leikin Exemplifying definitions: a case of a square . . . . . . . . . . . . . . . . . 131--148 Tim Rowland The purpose, design and use of examples in the teaching of elementary mathematics . . . . . . . . . . . . . . 149--163 Iris Zodik and Orit Zaslavsky Characteristics of teachers' choice of examples in and for the mathematics classroom . . . . . . . . . . . . . . . 165--182 Paul Goldenberg and John Mason Shedding light on and with example spaces . . . . . . . . . . . . . . . . . 183--194
Tommy Dreyfus Editorial . . . . . . . . . . . . . . . 195--196 Ivy Kidron Abstraction and consolidation of the limit procept by means of instrumented schemes: the complementary role of three different frameworks . . . . . . . . . . 197--216 Kyeong Hah Roh Students' images and their understanding of definitions of the limit of a sequence . . . . . . . . . . . . . . . . 217--233 Michal Ayalon and Ruhama Even Deductive reasoning: in the eye of the beholder . . . . . . . . . . . . . . . . 235--247 Tony Brown Signifying ``students'', ``teachers'' and ``mathematics'': a reading of a special issue . . . . . . . . . . . . . 249--263 Norma Presmeg and Luis Radford On semiotics and subjectivity: a response to Tony Brown's ``Signifying `students', `teachers', and `mathematics': a reading of a special issue'' . . . . . . . . . . . . . . . . 265--276 Rudolf Sträßer Review of the proceedings of the 2001, 2003 and 2005 French summer schools in Didactics of Mathematics . . . . . . . . 277--281 Keith Jones and Joanna Mamona-Downs Brian Griffiths (1927--2008) --- his pioneering contributions to mathematics and education . . . . . . . . . . . . . 283--286
Norma Presmeg Editorial . . . . . . . . . . . . . . . 1--3 Demetra Pitta-Pantazi and Constantinos Christou Cognitive styles, dynamic geometry and measurement performance . . . . . . . . 5--26 Dor Abrahamson Embodied design: constructing means for constructing meaning . . . . . . . . . . 27--47 Melissa Gresalfi and Taylor Martin and Victoria Hand and James Greeno Constructing competence: an analysis of student participation in the activity systems of mathematics classrooms . . . 49--70 Fulvia Furinghetti and Francesca Morselli Every unsuccessful problem solver is unsuccessful in his or her own way: affective and cognitive factors in proving . . . . . . . . . . . . . . . . 71--90
L. Radford and L. Edwards and F. Arzarello Introduction: beyond words . . . . . . . 91--95 Ferdinando Arzarello and Domingo Paola and Ornella Robutti and Cristina Sabena Gestures as semiotic resources in the mathematics classroom . . . . . . . . . 97--109 Luis Radford Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings . . . . . . . . . 111--126 Laurie D. Edwards Gestures and conceptual integration in mathematical talk . . . . . . . . . . . 127--141 Michela Maschietto and Maria G. Bartolini Bussi Working with artefacts: gestures, drawings and speech in the construction of the mathematical meaning of the visual pyramid . . . . . . . . . . . . . 143--157 Ricardo Nemirovsky and Francesca Ferrara Mathematical imagination and embodied cognition . . . . . . . . . . . . . . . 159--174 Wolff-Michael Roth and Jennifer S. Thom Bodily experience and mathematical conceptions: from classical views to a phenomenological reconceptualization . . 175--189 Anna Sfard What's all the fuss about gestures? A commentary . . . . . . . . . . . . . . . 191--200 Julian Williams Embodied multi-modal communication from the perspective of activity theory . . . 201--210 James Kaput Building intellectual infrastructure to expose and understand ever-increasing complexity . . . . . . . . . . . . . . . 211--215
Patrick Barmby and Tony Harries and Steve Higgins and Jennifer Suggate The array representation and primary children's understanding and reasoning in multiplication . . . . . . . . . . . 217--241 Shelly Sheats Harkness Social constructivism and the Believing Game: a mathematics teacher's practice and its implications . . . . . . . . . . 243--258 Donna Kotsopoulos and Michelle Cordy Investigating imagination as a cognitive space for learning mathematics . . . . . 259--274 Michael Weiss and Patricio Herbst and Chialing Chen Teachers' perspectives on ``authentic mathematics'' and the two-column proof form . . . . . . . . . . . . . . . . . . 275--293 Gaywalee Yamskulna Book Review: \booktitleThe beautiful Monster . . . . . . . . . . . . . . . . 295--298
Joke Torbeyns and Bert De Smedt and Pol Ghesqui\`ere and Lieven Verschaffel Acquisition and use of shortcut strategies by traditionally schooled children . . . . . . . . . . . . . . . . 1--17 Elsa Malisani and Filippo Spagnolo From arithmetical thought to algebraic thought: The role of the ``variable'' 19--41 Máire Ní Ríordáin and John O'Donoghue The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish . . . . . . 43--64 Jean-Baptiste Lagrange and Emel Ozdemir Erdogan Teachers' emergent goals in spreadsheet-based lessons: analyzing the complexity of technology integration . . 65--84 Ramesh Kapadia Book review: mathematics classrooms in twelve countries . . . . . . . . . . . . 85--93
Gail FitzSimons Call for book reviewers . . . . . . . . 95--95 Paul Andrews Comparative studies of mathematics teachers' observable learning objectives: validating low inference codes . . . . . . . . . . . . . . . . . 97--122 César Sáenz The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA) . . . . 123--143 Amanda Jansen Prospective elementary teachers' motivation to participate in whole-class discussions during mathematics content courses for teachers . . . . . . . . . . 145--160 Charalambos Y. Charalambous and Areti Panaoura and George Philippou Using the history of mathematics to induce changes in preservice teachers' beliefs and attitudes: insights from evaluating a teacher education program 161--180 Jacob Perrenet and Ruurd Taconis Mathematical enculturation from the students' perspective: shifts in problem-solving beliefs and behaviour during the bachelor programme . . . . . 181--198
Ghislaine Gueudet and Luc Trouche Towards new documentation systems for mathematics teachers? . . . . . . . . . 199--218 Amir H. Asghari Experiencing equivalence but organizing order . . . . . . . . . . . . . . . . . 219--234 Uffe Thomas Jankvist A categorization of the ``whys'' and ``hows'' of using history in mathematics education . . . . . . . . . . . . . . . 235--261 Uri Leron and Orit Hazzan Intuitive vs analytical thinking: four perspectives . . . . . . . . . . . . . . 263--278 Kenneth Ruthven and Rosemary Deaney and Sara Hennessy Using graphing software to teach about algebraic forms: a study of technology-supported practice in secondary-school mathematics . . . . . . 279--297 Robyn Pierce and Lynda Ball Perceptions that may affect teachers' intention to use technology in secondary mathematics classes . . . . . . . . . . 299--317
David Wagner and Beth Herbel-Eisenmann Re-mythologizing mathematics through attention to classroom positioning . . . 1--15 Tobin White Encrypted objects and decryption processes: problem-solving with functions in a learning environment based on cryptography . . . . . . . . . 17--37 Marilena Pantziara and Athanasios Gagatsis and Iliada Elia Using diagrams as tools for the solution of non-routine mathematical problems . . 39--60 Núria Gorgorió and Guida de Abreu Social representations as mediators of practice in mathematics classrooms with immigrant students . . . . . . . . . . . 61--76 Tiruwork Mulat and Abraham Arcavi Success in mathematics within a challenged minority: the case of students of Ethiopian origin in Israel (SEO) . . . . . . . . . . . . . . . . . 77--92 Maria Lorelei Fernandez and Evrim Erbilgin Examining the supervision of mathematics student teachers through analysis of conference communications . . . . . . . 93--110 María Luz Callejo and Antoni Vila Approach to mathematical problem solving and students' belief systems: two case studies . . . . . . . . . . . . . . . . 111--126 Doug M. Clarke and Anne Roche Students' fraction comparison strategies as a window into robust understanding and possible pointers for instruction 127--138
Mariana Montiel and Miguel R. Wilhelmi and Draga Vidakovic and Iwan Elstak Using the onto-semiotic approach to identify and analyze mathematical meaning when transiting between different coordinate systems in a multivariate context . . . . . . . . . . 139--160 Jeanne Tunks and Kirk Weller Changing practice, changing minds, from arithmetical to algebraic thinking: an application of the concerns-based adoption model (CBAM) . . . . . . . . . 161--183 Matthew Inglis and Adrian Simpson Conditional inference and advanced mathematical study: further evidence . . 185--198 Takeshi Miyakawa and Carl Winslòw Didactical designs for students' proportional reasoning: an ``open approach'' lesson and a ``fundamental situation'' . . . . . . . . . . . . . . 199--218 Barbara Jaworski and Despina Potari Bridging the macro- and micro-divide: using an activity theory model to capture sociocultural complexity in mathematics teaching and its development 219--236 Andreas J. Stylianides and Gabriel J. Stylianides Proof constructions and evaluations . . 237--253 Richard Barwell Researchers' descriptions and the construction of mathematical thinking 255--269
Kaye Stacey and Jill Vincent Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks . . . . . . . . . . . . . . . 271--288 Denna L. Wheeler and Diane Montgomery Community college students' views on learning mathematics in terms of their epistemological beliefs: a Q method study . . . . . . . . . . . . . . . . . 289--306 Paul Ngee-Kiong Lau and Parmjit Singh and Tee-Yong Hwa Constructing mathematics in an interactive classroom context . . . . . 307--324 Kamuran Tarim The effects of cooperative learning on preschoolers' mathematics problem-solving ability . . . . . . . . 325--340 Nadia Hardy Students' perceptions of institutional practices: the case of limits of functions in college level Calculus courses . . . . . . . . . . . . . . . . 341--358 Kalifa Traoré and Nadine Bednarz Mathématiques de la vie quotidienne au Burkina Faso: une analyse de la pratique sociale de comptage et de vente de mangues. (French) [Mathematics of everyday life in Burkina Faso: an analysis of the social practice of counting and selling mangoes] . . . . . 359--378 Bracha Kramarski and Tali Revach The challenge of self-regulated learning in mathematics teachers' professional training . . . . . . . . . . . . . . . . 379--399
Norma Presmeg Editorial . . . . . . . . . . . . . . . 1--2 Maria Trigueros and Rafael Martínez-Planell Geometrical representations in the learning of two-variable functions . . . 3--19 Sam Shreyar and Betina Zolkower and Silvia Pérez Thinking aloud together: A teacher's semiotic mediation of a whole-class conversation about percents . . . . . . 21--53 Laura Black and Julian Williams and Paul Hernandez-Martinez and Pauline Davis and Maria Pampaka and Geoff Wake Developing a `leading identity': the relationship between students' mathematical identities and their career and higher education aspirations . . . . 55--72 Bruno D'Amore Obituary: Giorgio Tomaso Bagni (1958--2009) . . . . . . . . . . . . . . 73--74 Giorgio T. Bagni Mathematics and positive sciences: a reflection following Heidegger . . . . . 75--85 Kenneth Ruthven Book review: Summing up mathematics teacher education . . . . . . . . . . . 87--97 Margaret Anne Walshaw Book review: Teacher-centredness and student-centredness under interrogation 99--103
Jaehoon Yim Children's strategies for division by fractions in the context of the area of a rectangle . . . . . . . . . . . . . . 105--120 Esther Levenson Fifth-grade students' use and preferences for mathematically and practically based explanations . . . . . 121--142 David S. Bolden and Tony V. Harries and Douglas P. Newton Pre-service primary teachers' conceptions of creativity in mathematics 143--157 Atara Shriki Working like real mathematicians: developing prospective teachers' awareness of mathematical creativity through generating new concepts . . . . 159--179 Roger G. Brown Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested? . . . . . . 181--203 Luis Rico Book review: \booktitleThe first century of the International Commission on Mathematical Instruction . . . . . . . . 205--210 George Brian Greer and Swapna Mukhopadhyay Book Review: \booktitleThe language of mathematics: Telling mathematical tales. Bill Barton. 2008 . . . . . . . . . . . 211--215
Pessia Tsamir and Dina Tirosh and Michal Tabach and Esther Levenson Multiple solution methods and multiple outcomes --- is it a task for kindergarten children? . . . . . . . . . 217--231 Pnina S. Klein and Esther Adi-Japha and Simcha Hakak-Benizri Mathematical thinking of kindergarten boys and girls: similar achievement, different contributing processes . . . . 233--246 Raimo Kaasila and Erkki Pehkonen and Anu Hellinen Finnish pre-service teachers' and upper secondary students' understanding of division and reasoning strategies used 247--261 Kyeong Hah Roh An empirical study of students' understanding of a logical structure in the definition of limit via the $ \varepsilon $-strip activity . . . . . . 263--279 Eirini Geraniou The transitional stages in the PhD degree in mathematics in terms of students' motivation . . . . . . . . . . 281--296 F. D. Rivera Visual templates in pattern generalization activity . . . . . . . . 297--328
Ronnie Karsenty Nonprofessional mathematics tutoring for low-achieving students in secondary schools: A case study . . . . . . . . . 1--21 Bert van Oers Emergent mathematical thinking in the context of play . . . . . . . . . . . . 23--37 David Wagner and Brent Davis Feeling number: grounding number sense in a sense of quantity . . . . . . . . . 39--51 Uffe Thomas Jankvist An empirical study of using history as a `goal' . . . . . . . . . . . . . . . . . 53--74 Ivy Kidron and Tommy Dreyfus Justification enlightenment and combining constructions of knowledge . . 75--93
Martin Carlsen Appropriating geometric series as a cultural tool: a study of student collaborative learning . . . . . . . . . 95--116 Ji-Won Son and Sharon L. Senk How reform curricula in the USA and Korea present multiplication and division of fractions . . . . . . . . . 117--142 Günhan Caglayan and John Olive Eighth grade students' representations of linear equations based on a cups and tiles model . . . . . . . . . . . . . . 143--162 Hagar Gal and Liora Linchevski To see or not to see: analyzing difficulties in geometry from the perspective of visual perception . . . . 163--183 Michael Meyer Abduction --- A logical view for investigating and initiating processes of discovering mathematical coherences 185--205
Ruhama Even and Tova Kvatinsky What mathematics do teachers with contrasting teaching approaches address in probability lessons? . . . . . . . . 207--222 Nathalie Sinclair and Shiva Gol Tabaghi Drawing space: mathematicians' kinetic conceptions of eigenvectors . . . . . . 223--240 Per Nilsson and Andreas Ryve Focal event, contextualization, and effective communication in the mathematics classroom . . . . . . . . . 241--258 Karin Usadi Katz and Mikhail G. Katz Zooming in on infinitesimal $ 1 - .9 \ldots {} $ in a post-triumvirate era 259--273 Chrissavgi Triantafillou and Despina Potari Mathematical practices in a technological workplace: the role of tools . . . . . . . . . . . . . . . . . 275--294
Charalambos Y. Charalambous and George N. Philippou Teachers' concerns and efficacy beliefs about implementing a mathematics curriculum reform: integrating two lines of inquiry . . . . . . . . . . . . . . . 1--21 Beth Herbel-Eisenmann and David Wagner and Viviana Cortes Lexical bundle analysis in mathematics classroom discourse: the significance of stance . . . . . . . . . . . . . . . . . 23--42 Beth Herbel-Eisenmann and David Wagner Appraising lexical bundles in mathematics classroom discourse: obligation and choice . . . . . . . . . 43--63 Gila Ron and Tommy Dreyfus and Rina Hershkowitz Partially correct constructs illuminate students' inconsistent answers . . . . . 65--87 Jesper Boesen and Johan Lithner and Torulf Palm The relation between types of assessment tasks and the mathematical reasoning students use . . . . . . . . . . . . . . 89--105 Uldarico Malaspina and Vicenç Font The role of intuition in the solving of optimization problems . . . . . . . . . 107--130
Vicenç Font and Janete Bolite and Jorge Acevedo Metaphors in mathematics classrooms: analyzing the dynamic process of teaching and learning of graph functions 131--152 Kim Beswick and Anne Watson and Els De Geest Comparing theoretical perspectives in describing mathematics departments: complexity and activity . . . . . . . . 153--170 Åse Hansson Instructional responsibility in mathematics education: modelling classroom teaching using Swedish data 171--189 Marios Pittalis and Constantinos Christou Types of reasoning in 3D geometry thinking and their relation with spatial ability . . . . . . . . . . . . . . . . 191--212 Paul Drijvers and Michiel Doorman and Peter Boon and Helen Reed and Koeno Gravemeijer The teacher and the tool: instrumental orchestrations in the technology-rich mathematics classroom . . . . . . . . . 213--234 Robert Ely Book review: Theories of mathematics education: Seeking new frontiers . . . . 235--240
Eva Thanheiser Investigating further preservice teachers' conceptions of multidigit whole numbers: refining a framework . . 241--251 Maria Kaisari and Tasos Patronis So we decided to call ``straight line'' (\ldots ): Mathematics students' interaction and negotiation of meaning in constructing a model of elliptic geometry . . . . . . . . . . . . . . . . 253--269 Kirsti Hemmi Three styles characterising mathematicians' pedagogical perspectives on proof . . . . . . . . . . . . . . . . 271--291 Christine M. Phelps Factors that pre-service elementary teachers perceive as affecting their motivational profiles in mathematics . . 293--309 Mehmet Bekdemir The pre-service teachers' mathematics anxiety related to depth of negative experiences in mathematics classroom while they were students . . . . . . . . 311--328 Tony Brown Truth and the renewal of knowledge: the case of mathematics education . . . . . 329--343 Denise Silva Vilela Discussing a philosophical background for the ethnomathematical program . . . 345--358
Norma Presmeg Editorial . . . . . . . . . . . . . . . 1--2 Deborah Moore-Russo and AnnaMarie Conner and Kristina I. Rugg Can slope be negative in 3-space? Studying concept image of slope through collective definition construction . . . 3--21 Yifat Ben-David Kolikant and Orit Broza The effect of using a video clip presenting a contextual story on low-achieving students' mathematical discourse . . . . . . . . . . . . . . . 23--47 Aaron Weinberg and Emilie Wiesner Understanding mathematics textbooks through reader-oriented theory . . . . . 49--63 Xuhua Sun ``Variation problems'' and their roles in the topic of fraction division in Chinese mathematics textbook examples 65--85 Robyn Jorgensen Zevenbergen Young workers and their dispositions towards mathematics: tensions of a mathematical habitus in the retail industry . . . . . . . . . . . . . . . . 87--100 Luis Radford Book Review: \booktitleClassroom Interaction: Why is it Good, Really? Baruch Schwarz, Tommy Dreyfus and Rina Hershkowitz (Eds.) (2009) Transformation of knowledge through classroom interaction . . . . . . . . . . . . . . 101--115 Julie Gainsburg Book Review: Hoyles, C., Noss, R., Kent, P., & Bakker. A. (2010). \booktitleImproving mathematics at work: The need for techno-mathematical literacies . . . . . . . . . . . . . . . 117--122
Kyeong-Hwa Lee and Bharath Sriraman Conjecturing via reconceived classical analogy . . . . . . . . . . . . . . . . 123--140 Mourat A. Tchoshanov Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics . . . . . . . 141--164 Cécile Ouvrier-Buffet A mathematical experience involving defining processes: in-action definitions and zero-definitions . . . . 165--182 Agida Gabil Manizade and Marguerite M. Mason Using Delphi methodology to design assessments of teachers' pedagogical content knowledge . . . . . . . . . . . 183--207 Alexandre Pais Criticisms and contradictions of ethnomathematics . . . . . . . . . . . . 209--230 Kathleen Nolan Book review: Pausing to relate and participate . . . . . . . . . . . . . . 231--235 Karin Brodie Book review: \booktitleMathematical relationships in education: identities and participation, edited by Laura Black, Heather Mendick, & Yvette Solomon (2009) . . . . . . . . . . . . . . . . . 237--241 Gail FitzSimons Book Review: \booktitleMathematics education where people really matter. Brian Greer, Swapna Mukhopadhyay, Arthur B. Powell & Sharon Nelson--Barber (Eds.) (2009). Culturally responsive mathematics education . . . . . . . . . 243--246
Rina Zazkis and Dov Zazkis The significance of mathematical knowledge in teaching elementary methods courses: perspectives of mathematics teacher educators . . . . . . . . . . . 247--263 Despina A. Stylianou An examination of middle school students' representation practices in mathematical problem solving through the lens of expert work: towards an organizing scheme . . . . . . . . . . . 265--280 Bettina Pedemonte and David Reid The role of abduction in proving processes . . . . . . . . . . . . . . . 281--303 Higinio Domínguez Using what matters to students in bilingual mathematics problems . . . . . 305--328 Keith Weber and Juan Pablo Mejia-Ramos Why and how mathematicians read proofs: an exploratory study . . . . . . . . . . 329--344 José Domingo Villarroel and Margarita Miñón and Teresa Nuño The origin of counting: A study of the early meaning of `one', `two' and `three' among Basque- and Spanish-speaking children . . . . . . . 345--361 Tony Wing Book Review: Purifying the dialect of the tribe. Anna Sfard (2008). \booktitleThinking as communicating: Human development, the growth of discourses, and mathematizing . . . . . 363--369
Paola Iannone and Matthew Inglis and Juan Pablo Mejía-Ramos and Adrian Simpson and Keith Weber Does generating examples aid proof production? . . . . . . . . . . . . . . 1--14 Egan J. Chernoff and Rina Zazkis From personal to conventional probabilities: from sample set to sample space . . . . . . . . . . . . . . . . . 15--33 Troels Lange and Tamsin Meaney I actually started to scream: emotional and mathematical trauma from doing school mathematics homework . . . . . . 35--51 Carla van de Sande A description and characterization of student activity in an open, online, mathematics help forum . . . . . . . . . 53--78 Gert Schubring Conceptions for relating the evolution of mathematical concepts to mathematics learning --- epistemology, history, and semiotics interacting . . . . . . . . . 79--104 George Kospentaris and Panagiotis Spyrou and Dionyssios Lappas Exploring students' strategies in area conservation geometrical tasks . . . . . 105--127 Alain Kuzniak and Jean-Claude Rauscher How do teachers' approaches to geometric work relate to geometry students' learning difficulties? . . . . . . . . . 129--147
Luis Radford and Gert Schubring and Falk Seeger Signifying and meaning-making in mathematical thinking, teaching, and learning . . . . . . . . . . . . . . . . 149--156 Lulu Healy and Solange Hassan Ahmad Ali Fernandes The role of gestures in the mathematical practices of those who do not see with their eyes . . . . . . . . . . . . . . . 157--174 Harun Zurina and Julian Williams Gesturing for oneself . . . . . . . . . 175--188 Ferdinando Arzarello and Cristina Sabena Semiotic and theoretic control in argumentation and proof activities . . . 189--206 Falk Seeger On meaning making in mathematics education: social, emotional, semiotic 207--226 Luis Radford and Wolff-Michael Roth Intercorporeality and ethical commitment: an activity perspective on classroom interaction . . . . . . . . . 227--245 Juan D. Godino and Vicenç Font and Miguel R. Wilhelmi and Orlando Lurduy Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects . . . . . . . . . . 247--265 Jennifer S. Thom and Wolff-Michael Roth Radical embodiment and semiotics: toward a theory of mathematics in the flesh . . 267--284 George Santi Objectification and semiotic function 285--311 Michael Friedrich Otte Evolution, learning, and semiotics from a Peircean point of view . . . . . . . . 313--329 Gert Schubring On how $n$ and $i$ turned out to become indices in mathematical sequences and formulae . . . . . . . . . . . . . . . . 331--350 Tony Brown and David Heywood Geometry, subjectivity and the seduction of language: the regulation of spatial perception . . . . . . . . . . . . . . . 351--367 Stephen John Hegedus and Luis Moreno-Armella The emergence of mathematical structures 369--388 Michael N. Fried Signs for you and signs for me: the double aspect of semiotic perspectives 389--397
Megan Wawro and George F. Sweeney and Jeffrey M. Rabin Subspace in linear algebra: investigating students' concept images and interactions with the formal definition . . . . . . . . . . . . . . . 1--19 Michelle H. Wilkerson-Jerde and Uri J. Wilensky How do mathematicians learn math?: resources and acts for constructing and understanding mathematics . . . . . . . 21--43 Mary Q. Foote and Tonya Gau Bartell Pathways to equity in mathematics education: how life experiences impact researcher positionality . . . . . . . . 45--68 Maurício Rosa and Stephen Lerman Researching online mathematics education: opening a space for virtual learner identities . . . . . . . . . . . 69--90 Sarah Bansilal Assessment reform in South Africa: opening up or closing spaces for teachers? . . . . . . . . . . . . . . . 91--107 Ivy Kidron Tacit models, treasured intuitions and the discrete --- continuous interplay 109--126 Kaye Stacey Book Review: A journey through the world of technology in mathematics education. Celia Hoyles and Jean-Baptiste Lagrange (Eds.) (2010). \booktitleMathematics education and technology --- Rethinking the terrain . . . . . . . . . . . . . . 127--134
Margaret Sinclair and Ami Mamolo and Walter J. Whiteley Designing spatial visual tasks for research: the case of the filling task 135--163 Iuliana Radu and Keith Weber Refinements in mathematics undergraduate students' reasoning on completed infinite iterative processes . . . . . . 165--180 Iuliana Radu and Keith Weber Erratum to: Refinements in mathematics undergraduate students' reasoning on completed infinite iterative processes 181--182 Hagar Gal From Another Perspective --- training teachers to cope with problematic learning situations in geometry . . . . 183--203 Jenq-Jong Tsay and April B. Judd and Shandy Hauk and Mark K. Davis Case study of a college mathematics instructor: patterns of classroom discourse . . . . . . . . . . . . . . . 205--229 H. Bahadir Yanik Prospective middle school mathematics teachers' preconceptions of geometric translations . . . . . . . . . . . . . . 231--260 Rik Pinxten and Karen François Politics in an Indian canyon? Some thoughts on the implications of ethnomathematics . . . . . . . . . . . . 261--273
Anna Sierpinska and Georgeana Bobos and Andreea Pruncut Teaching absolute value inequalities to mature students . . . . . . . . . . . . 275--305 Elise Lockwood Student connections among counting problems: an exploration using actor-oriented transfer . . . . . . . . 307--322 Janet G. Walter and Tara Barros Students build mathematical theory: semantic warrants in argumentation . . . 323--342 Magali Hersant Correspondance entre él\`eves: conditions d'une activité mathématique \flqq créative \frqq et problématisée \`a la fin du lycée. (French) [Correspondence between pupils: conditions of a `creative' and problematized mathematical activity at the end of the secondary school] . . . . 343--370 Caroline Yoon and Michael O. J. Thomas and Tommy Dreyfus Grounded blends and mathematical gesture spaces: developing mathematical understandings via gestures . . . . . . 371--393 Andrew Brantlinger Rethinking critical mathematics: a comparative analysis of critical, reform, and traditional geometry instructional texts . . . . . . . . . . 395--411
Norma Presmeg Editorial . . . . . . . . . . . . . . . 1--2 Juan Pablo Mejia-Ramos and Evan Fuller and Keith Weber and Kathryn Rhoads and Aron Samkoff An assessment model for proof comprehension in undergraduate mathematics . . . . . . . . . . . . . . 3--18 Naomi Prusak and Rina Hershkowitz and Baruch B. Schwarz From visual reasoning to logical necessity through argumentative design 19--40 Alfredo Bautista and Wolff-Michael Roth Conceptualizing sound as a form of incarnate mathematical consciousness . . 41--59 Marilena Pantziara and George Philippou Levels of students' ``conception'' of fractions . . . . . . . . . . . . . . . 61--83 Vilma Mesa and Brett Griffiths Textbook mediation of teaching: an example from tertiary mathematics instructors . . . . . . . . . . . . . . 85--107 Leigh N. Wood Practice and conceptions: communicating mathematics in the workplace . . . . . . 109--125 Kim Beswick Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice . . . . . . . . . . . . . . . . 127--147 Victoria Hand Book Review: Adding depth to portraits of mathematical inquiry. Karin Brodie (2010). \booktitleTeaching mathematical reasoning in secondary school classrooms 149--155
Elena Nardi and Irene Biza and Theodossios Zachariades `Warrant' revisited: Integrating mathematics teachers' pedagogical and epistemological considerations into Toulmin's model for argumentation . . . 157--173 Lisa Anne Kasmer and Ok-Kyeong Kim The nature of student predictions and learning opportunities in middle school algebra . . . . . . . . . . . . . . . . 175--191 Chronoula Voutsina Procedural and conceptual changes in young children's problem solving . . . . 193--214 Stanis\law Schukajlow and Dominik Leiss and Reinhard Pekrun and Werner Blum and Marcel Müller and Rudolf Messner Teaching methods for modelling problems and students' task-specific enjoyment, value, interest and self-efficacy expectations . . . . . . . . . . . . . . 215--237 Amal Hussain Alajmi How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait 239--261 Yuichi Handa Teasing out repetition from rote: an essay on two versions of will . . . . . 263--272 Sebastian Kuntze Pedagogical content beliefs: global, content domain-related and situation-specific components . . . . . 273--292 Joy A. Oslund Mathematics-for-teaching: what can be learned from the ethnopoetics of teachers' stories? . . . . . . . . . . . 293--309 Megan Che and Elaine Wiegert and Karen Threlkeld Problem solving strategies of girls and boys in single-sex mathematics classrooms . . . . . . . . . . . . . . . 311--326
Lieven Verschaffel and Peter Bryant and Joke Torbeyns Introduction . . . . . . . . . . . . . . 327--334 Greet Peters and Bert De Smedt and Joke Torbeyns and Pol Ghesqui\`ere and Lieven Verschaffel Children's use of subtraction by addition on large single-digit subtractions . . . . . . . . . . . . . . 335--349 Marjolijn Peltenburg and Marja van den Heuvel-Panhuizen and Alexander Robitzsch Special education students' use of indirect addition in solving subtraction problems up to 100--- A proof of the didactical potential of an ignored procedure . . . . . . . . . . . . . . . 351--369 Terezinha Nunes and Peter Bryant and Deborah Evans and Daniel Bell and Rossana Barros Teaching children how to include the inversion principle in their reasoning about quantitative relations . . . . . . 371--388 Christoph Selter and Susanne Prediger and Marcus Nührenbörger and Stephan Hußmann Taking away and determining the difference --- a longitudinal perspective on two models of subtraction and the inverse relation to addition . . 389--408 Katherine M. Robinson and Jo-Anne LeFevre The inverse relation between multiplication and division: Concepts, procedures, and a cognitive framework 409--428 Brian Greer Inversion in mathematical thinking and learning . . . . . . . . . . . . . . . . 429--438 Gerard Vergnaud Commentary 1 . . . . . . . . . . . . . . 439--445 Michael Schneider Commentary 2: knowledge integration in mathematics learning: the case of inversion . . . . . . . . . . . . . . . 447--453
Tony Brown and Margaret Walshaw Mathematics education and contemporary theory: guest editorial . . . . . . . . 1--8 Alexandre Pais and Paola Valero Researching research: mathematics education in the Political . . . . . . . 9--24 Mary Klein How inconvenient assumptions affect preservice teachers' uptake of new interactional patterns in mathematics: analysis and aspiration through a bifocal lens . . . . . . . . . . . . . . 25--40 David W. Stinson and Erika C. Bullock Critical postmodern theory in mathematics education research: a praxis of uncertainty . . . . . . . . . . . . . 41--55 Julian Williams Use and exchange value in mathematics education: contemporary CHAT meets Bourdieu's sociology . . . . . . . . . . 57--72 Sverker Lundin Hating school, loving mathematics: On the ideological function of critique and reform in mathematics education . . . . 73--85 Gelsa Knijnik Differentially positioned language games: ethnomathematics from a philosophical perspective . . . . . . . 87--100 Luis Radford Education and the illusions of emancipation . . . . . . . . . . . . . . 101--118 Ole Skovsmose Symbolic power, robotting, and surveilling . . . . . . . . . . . . . . 119--132 Elizabeth de Freitas and Nathalie Sinclair Diagram, gesture, agency: theorizing embodiment in the mathematics classroom 133--152 David Wagner Opening mathematics texts: resisting the seduction . . . . . . . . . . . . . . . 153--169 Yvette Solomon Finding a voice? Narrating the female self in mathematics . . . . . . . . . . 171--183 Margaret Walshaw and Tony Brown Affective productions of mathematical experience . . . . . . . . . . . . . . . 185--199 Kathleen Nolan Dispositions in the field: viewing mathematics teacher education through the lens of Bourdieu's social field theory . . . . . . . . . . . . . . . . . 201--215 Laurinda Brown and Alf Coles Developing ``deliberate analysis'' for learning mathematics and for mathematics teacher education: how the enactive approach to cognition frames reflection 217--231 Victoria Hand Seeing culture and power in mathematical learning: toward a model of equitable instruction . . . . . . . . . . . . . . 233--247 Melissa Sommerfeld Gresalfi and Jacqueline Barnes and Dionne Cross When does an opportunity become an opportunity? Unpacking classroom practice through the lens of ecological psychology . . . . . . . . . . . . . . . 249--267 Nigel Calder The layering of mathematical interpretations through digital media 269--285
Michal Yerushalmy and Osama Swidan Signifying the accumulation graph in a dynamic and multi-representation environment . . . . . . . . . . . . . . 287--306 Kai-Lin Yang Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof 307--326 Tinne Hoff Kjeldsen and Morten Blomhòj Beyond motivation: history as a method for learning meta-discursive rules in mathematics . . . . . . . . . . . . . . 327--349 Rakhi Banerjee and K. Subramaniam Evolution of a teaching approach for beginning algebra . . . . . . . . . . . 351--367 Mary Mueller and Dina Yankelewitz and Carolyn Maher A framework for analyzing the collaborative construction of arguments and its interplay with agency . . . . . 369--387 Vida Manfreda Kolar and Tatjana Hodnik \vCade\vz Analysis of factors influencing the understanding of the concept of infinity 389--412 Maria Manuela David and Vanessa Sena Tomaz The role of visual representations for structuring classroom mathematical activity . . . . . . . . . . . . . . . . 413--431 Elisabetta Robotti Natural language as a tool for analyzing the proving process: the case of plane geometry proof . . . . . . . . . . . . . 433--450 Wolff-Michael Roth Re/writing the subject: a contribution to post-structuralist theory in mathematics education . . . . . . . . . 451--473 Tony Brown Subjectivity and cultural adjustment in mathematics education: a response to Wolff--Michael Roth . . . . . . . . . . 475--490
Andreas Ryve and Per Nilsson and John Mason Establishing mathematics for teaching within classroom interactions in teacher education . . . . . . . . . . . . . . . 1--14 Lyn D. English Data modelling with first-grade students 15--30 Sarah Crafter Parental cultural models and resources for understanding mathematical achievement in culturally diverse school settings . . . . . . . . . . . . . . . . 31--46 Csaba Csíkos and Judit Szitányi and Rita Kelemen The effects of using drawings in developing young children's mathematical word problem solving: A design experiment with third-grade Hungarian students . . . . . . . . . . . . . . . . 47--65 Kathleen Michelle Clark History of mathematics: illuminating understanding of school mathematics concepts for prospective mathematics teachers . . . . . . . . . . . . . . . . 67--84 Sandra Herbert and Robyn Pierce Revealing educationally critical aspects of rate . . . . . . . . . . . . . . . . 85--101 Åse Hansson The meaning of mathematics instruction in multilingual classrooms: analyzing the importance of responsibility for learning . . . . . . . . . . . . . . . . 103--125 Marco Shappeck and Gwendolyn Johnson and Ali Shalaih Book review: Understanding culture and social identity as the key to success in mathematics. Na'ilah Suad Nasir and Paul Cobb (Eds.) (2007). \booktitleImproving access to mathematics: diversity and equity in the classroom . . . . . . . . 127--132 Elizabeth de Freitas Book Review: Teacher identity: Harsh lessons learned from the micro-management of teachers and teacher education: A review of Tony Brown and Olwen McNamara's \booktitleBecoming a mathematics teacher: Identity and identifications (2011) . . . . . . . . . 133--137
Dave Hewitt Young students learning formal algebraic notation and solving linear equations: are commonly experienced difficulties avoidable? . . . . . . . . . . . . . . . 139--159 Ami Mamolo and Rina Zazkis Stuck on convention: a story of derivative relationships . . . . . . . . 161--177 Philip Vahey and Ken Rafanan and Charles Patton and Karen Swan and Mark van 't Hooft and Annette Kratcoski and Tina Stanford A cross-disciplinary approach to teaching data literacy and proportionality . . . . . . . . . . . . 179--205 Ruma Falk and Patricia Yudilevich-Assouline and Adily Elstein Children's concept of probability as inferred from their binary choices --- revisited . . . . . . . . . . . . . . . 207--233 Rafael Martínez-Planell and Ana Carmen Gonzalez and Gladys DiCristina and Vanessa Acevedo Students' conception of infinite series 235--249 Susan Joan Courey and Endre Balogh and Jody Rebecca Siker and Jae Paik Academic music: music instruction to engage third-grade students in learning basic fraction concepts . . . . . . . . 251--278 Jean-François Maheux and Jérôme Proulx and Elaine Simmt Book Review: A review of the book by SungWon Hwang and Wolff--Michael Roth (2011). \booktitleScientific & mathematical bodies: the interface of culture and mind . . . . . . . . . . . . 279--285
Codruta Temple and Helen M. Doerr Developing fluency in the mathematical register through conversation in a tenth-grade classroom . . . . . . . . . 287--306 Cindy S. Ticknor Situated learning in an abstract algebra classroom . . . . . . . . . . . . . . . 307--323 Timothy Patrick Fukawa-Connelly A case study of one instructor's lecture-based teaching of proof in abstract algebra: making sense of her pedagogical moves . . . . . . . . . . . 325--345 Nava Almog and Bat-Sheva Ilany Absolute value inequalities: high school students' solutions and misconceptions 347--364 Rafael Martínez-Planell and María Trigueros Gaisman Students' understanding of the general notion of a function of two variables 365--384 Anna Llewellyn Unpacking understanding: the (re)search for the Holy Grail of mathematics education . . . . . . . . . . . . . . . 385--399 Margaret Walshaw Book Review: Interpreting how students come to understand mathematics in the digital environment. Nigel Calder (2011). \booktitleProcessing mathematics through digital technologies: The primary years . . . . . . . . . . . . . 401--405 Rina Hershkowitz and Barbara Jaworski Book Review: a dialog in the footsteps of the book \booktitle``A journey in mathematics education research --- insights from the work of Paul Cobb; Erna Yackel, Koeno Gravemeijer and Anna Sfard (Eds.); (2011) . . . . . . . . . . 407--420
Norma Presmeg Editorial . . . . . . . . . . . . . . . 1--3 Theodossios Zachariades and Constantinos Christou and Demetra Pitta-Pantazi Reflective, systemic and analytic thinking in real numbers . . . . . . . . 5--22 Paul Drijvers and Juan D. Godino and Vicenç Font and Luc Trouche One episode, two lenses . . . . . . . . 23--49 Christof Schreiber Semiotic processes in chat-based problem-solving situations . . . . . . . 51--73 Martin Griffiths Intuiting the fundamental theorem of arithmetic . . . . . . . . . . . . . . . 75--96 Vicenç Font and Juan D. Godino and Jesús Gallardo The emergence of objects from mathematical practices . . . . . . . . . 97--124 Dan Battey ``Good'' mathematics teaching for students of color and those in poverty: the importance of relational interactions within instruction . . . . 125--144 Siew Yee Lim and Elaine Chapman Development of a short form of the attitudes toward mathematics inventory 145--164 Robert George Stein Review of \booktitleRewriting the history of school mathematics in North America 1607--1861 by Nerida Ellerton and M. A. (Ken) Clements (2012). The central role of cyphering books . . . . 165--167
Michael C. Wittmann and Virginia J. Flood and Katrina E. Black Algebraic manipulation as motion within a landscape . . . . . . . . . . . . . . 169--181 Malcolm Shield and Shelley Dole Assessing the potential of mathematics textbooks to promote deep learning . . . 183--199 Xianwei Y. Van Harpen and Bharath Sriraman Creativity and mathematical problem posing: an analysis of high school students' mathematical problem posing in China and the USA . . . . . . . . . . . 201--221 Debbie Bautista Verzosa and Joanne Mulligan Learning to solve addition and subtraction word problems in English as an imported language . . . . . . . . . . 223--244 Brent Davis and Moshe Renert Profound understanding of emergent mathematics: broadening the construct of teachers' disciplinary knowledge . . . . 245--265 Jason Martin Differences between experts' and students' conceptual images of the mathematical structure of Taylor series convergence . . . . . . . . . . . . . . 267--283 Mohammed Abdul Hussain and John Monaghan and John Threlfall Teacher-student development in mathematics classrooms: Interrelated zones of free movement and promoted actions . . . . . . . . . . . . . . . . 285--302 Uwe Gellert and Joaquim Barbé and Lorena Espinoza Towards a local integration of theories: codes and praxeologies in the case of computer-based instruction . . . . . . . 303--321 Xenia Vamvakoussi and Wim Van Dooren and Lieven Verschaffel Brief Report. Educated adults are still affected by intuitions about the effect of arithmetical operations: evidence from a reaction-time study . . . . . . . 323--330 Anna Sfard Almost 20 years after: Developments in research on language and mathematics. Review of J. N. Moschkovich (Ed.) (2010) \booktitleLanguage and mathematics education: Multiple perspectives and directions for research . . . . . . . . 331--339
Marie Joubert Using digital technologies in mathematics teaching: developing an understanding of the landscape using three ``grand challenge'' themes . . . . 341--359 Allen Leung and Arthur Man Sang Lee Students' geometrical perception on a task-based dynamic geometry platform . . 361--377 Rabih Raif El Mouhayar and Murad Eid Jurdak Teachers' ability to identify and explain students' actions in near and far figural pattern generalization tasks 379--396 Michael Friedrich Otte and Tânia M. M. Campos and Alexandre S. Abido Plato, Pascal, and the dynamics of personal knowledge . . . . . . . . . . . 397--415 John M. Francisco Learning in collaborative settings: students building on each other's ideas to promote their mathematical understanding . . . . . . . . . . . . . 417--438 Beste Güçler Examining the discourse on the limit concept in a beginning-level calculus classroom . . . . . . . . . . . . . . . 439--453 Jungeun Park and Beste Güçler and Raven McCrory Teaching prospective teachers about fractions: historical and pedagogical perspectives . . . . . . . . . . . . . . 455--479 Tamsin Meaney and Deb Evans What is the responsibility of mathematics education to the Indigenous students that it serves? . . . . . . . . 481--496 Andreas Ryve and Per Nilsson and Kerstin Pettersson Analyzing effective communication in mathematics group work: The role of visual mediators and technical terms . . 497--514 Roza Leikin and Dorith Grossman Teachers modify geometry problems: from proof to investigation . . . . . . . . . 515--531
Florence Mihaela Singer and Nerida Ellerton and Jinfa Cai Problem-posing research in mathematics education: new questions and directions 1--7 Florence Mihaela Singer and Cristian Voica A problem-solving conceptual framework and its implications in designing problem-posing tasks . . . . . . . . . . 9--26 Jo Clay Olson and Libby Knott When a problem is more than a teacher's question . . . . . . . . . . . . . . . . 27--36 Cinzia Bonotto Artifacts as sources for problem-posing activities . . . . . . . . . . . . . . . 37--55 Jinfa Cai and John C. Moyer and Ning Wang and Stephen Hwang and Bikai Nie and Tammy Garber Mathematical problem posing as a measure of curricular effect on students' learning . . . . . . . . . . . . . . . . 57--69 Boris Koichu and Igor Kontorovich Dissecting success stories on mathematical problem posing: a case of the Billiard Task . . . . . . . . . . . 71--86 Nerida F. Ellerton Engaging pre-service middle-school teacher-education students in mathematical problem posing: development of an active learning framework . . . . 87--101 Shuk-kwan S. Leung Teachers implementing mathematical problem posing in the classroom: challenges and strategies . . . . . . . 103--116 Xianwei Y. Van Harpen and Norma C. Presmeg An investigation of relationships between students' mathematical problem-posing abilities and their mathematical content knowledge . . . . . 117--132 Marie Tichá and Alena Ho\vspesová Developing teachers' subject didactic competence through problem posing . . . 133--143 João Pedro da Ponte and Ana Henriques Problem posing based on investigation activities by university students . . . 145--156 Edward A. Silver Problem-posing research in mathematics education: looking back, looking around, and looking ahead . . . . . . . . . . . 157--162
Clare Lee and Sue Johnston-Wilder Learning mathematics --- letting the pupils have their say . . . . . . . . . 163--180 Esther Levenson Exploring one student's explanations at different ages: the case of Sharon . . . 181--203 Marilena Chrysostomou and Demetra Pitta-Pantazi and Chara Tsingi and Eleni Cleanthous and Constantinos Christou Examining number sense and algebraic reasoning through cognitive styles . . . 205--223 Kevin C. Moore Making sense by measuring arcs: a teaching experiment in angle measure . . 225--245 Randall E. Groth and Jennifer A. Bergner Mapping the structure of knowledge for teaching nominal categorical data analysis . . . . . . . . . . . . . . . . 247--265 Carl Winslòw and Yves Matheron and Alain Mercier Study and research courses as an epistemological model for didactics . . 267--284 Chia-Ling Chen and Patricio Herbst The interplay among gestures, discourse, and diagrams in students' geometrical reasoning . . . . . . . . . . . . . . . 285--307 Dina Tirosh and Pessia Tsamir and Esther Levenson and Michal Tabach and Ruthi Barkai Exploring young children's self-efficacy beliefs related to mathematical and nonmathematical tasks performed in kindergarten: abused and neglected children and their peers . . . . . . . . 309--322
J. Sandefur and J. Mason and G. J. Stylianides and A. Watson Generating and using examples in the proving process . . . . . . . . . . . . 323--340 Einat Heyd-Metzuyanim The co-construction of learning difficulties in mathematics --- teacher--student interactions and their role in the development of a disabled mathematical identity . . . . . . . . . 341--368 Emily C. Bouck and Gauri S. Joshi and Linley Johnson Examining calculator use among students with and without disabilities educated with different mathematical curricula 369--385 Christian Rüede How secondary level teachers and students impose personal structure on fractional expressions and equations --- an expert-novice study . . . . . . . . . 387--408 Pessia Tsamir and Regina Ovodenko University students' grasp of inflection points . . . . . . . . . . . . . . . . . 409--427 Lynn C. Hart and Susan Oesterle and Susan L. Swars The juxtaposition of instructor and student perspectives on mathematics courses for elementary teachers . . . . 429--451 Elizabeth de Freitas and Nathalie Sinclair New materialist ontologies in mathematics education: the body in/of mathematics . . . . . . . . . . . . . . 453--470 Mary Anne Heng and Akhila Sudarshan ``Bigger number means you plus!'' --- Teachers learning to use clinical interviews to understand students' mathematical thinking . . . . . . . . . 471--485 Kristin King Hess Book Review: \booktitleExpertise in mathematics instruction: an international perspective. Yeping Li and Gabriele Kaiser (Eds.) (2011) . . . . . 487--492
Laura Black and Julian Williams Contradiction and conflict between `leading identities': becoming an engineer versus becoming a `good Muslim' woman . . . . . . . . . . . . . . . . . 1--14 Alexandre Pais An ideology critique of the use-value of mathematics . . . . . . . . . . . . . . 15--34 Sarmin Hossain and Heather Mendick and Jill Adler Troubling ``understanding mathematics in-depth'': Its role in the identity work of student-teachers in England . . 35--48 Ji-Won Son How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles . . . . 49--70 Mirela Rigo-Lemini Epistemic schemes and epistemic states. A study of mathematics convincement in elementary school classes . . . . . . . 71--91 Marta T. Magiera and Leigh A. van den Kieboom and John C. Moyer An exploratory study of pre-service middle school teachers' knowledge of algebraic thinking . . . . . . . . . . . 93--113 Armando Solares and Carolyn Kieran Articulating syntactic and numeric perspectives on equivalence: the case of rational expressions . . . . . . . . . . 115--148 Annick Fagnant and Joëlle Vlassis Schematic representations in arithmetical problem solving: Analysis of their impact on grade 4 students . . 149--168 Vadim Kaimanovich Book Review: A Book about Russian Mathematics Education . . . . . . . . . 169--175
Götz Krummheuer Research on mathematics learning at the ``Center of Individual Development and Adaptive Education'' (IDeA) --- an introduction . . . . . . . . . . . . . . 177--181 Götz Krummheuer and Marianne Leuzinger-Bohleber and Marion Müller-Kirchof and Melanie Münz and Rose Vogel Explaining the mathematical creativity of a young boy: an interdisciplinary venture between mathematics education and psychoanalysis . . . . . . . . . . . 183--199 Jan Lonnemann and Janosch Linkersdörfer and Marcus Hasselhorn and Sven Lindberg Gender differences in both tails of the distribution of numerical competencies in preschool children . . . . . . . . . 201--208 Rose Vogel Mathematical situations of play and exploration . . . . . . . . . . . . . . 209--225 Birgit Brandt Everyday pedagogical practices in mathematical play situations in German ``Kindergarten'' . . . . . . . . . . . . 227--248 Götz Krummheuer The relationship between diagrammatic argumentation and narrative argumentation in the context of the development of mathematical thinking in the early years . . . . . . . . . . . . 249--265 Bert van Oers Challenges in the innovation of mathematics education for young children 267--272 Michal Tabach Commentary: The whole is greater than the sum of its parts . . . . . . . . . . 273--277
Norma Presmeg Editorial . . . . . . . . . . . . . . . 279--280 Marja van den Heuvel-Panhuizen and Angeliki Kolovou and Alexander Robitzsch Primary school students' strategies in early algebra problem solving supported by an online game . . . . . . . . . . . 281--307 Jérôme Proulx Mental mathematics, emergence of strategies, and the enactivist theory of cognition . . . . . . . . . . . . . . . 309--328 Shelly Sheats Harkness and James Stallworth Photovoice: understanding high school females' conceptions of mathematics and learning mathematics . . . . . . . . . . 329--347 Erin Elizabeth Turner and Higinio Dominguez and Susan Empson and Luz Angelica Maldonado Latino/a bilinguals and their teachers developing a shared communicative space 349--370 Mara G. Landers Towards a theory of mathematics homework as a social practice . . . . . . . . . . 371--391 Simon Goodchild and Anne Berit Fuglestad and Barbara Jaworski Critical alignment in inquiry-based practice in developing mathematics teaching . . . . . . . . . . . . . . . . 393--412 Peter Frejd Modes of modelling assessment --- a literature review . . . . . . . . . . . 413--438 Allen Leung and Anna Baccaglini-Frank and Maria Alessandra Mariotti Discernment of invariants in dynamic geometry environments . . . . . . . . . 439--460 Mirko Maracci and Claire Cazes and Fabrice Vandebrouck and Maria Alessandra Mariotti Synergies between theoretical approaches to mathematics education with technology: A case study through a cross-analysis methodology . . . . . . . 461--485 J. Sandefur and J. Mason and G. J. Stylianides and A. Watson Erratum to: Generating and using examples in the proving process . . . . 487--487
Merrilyn Goos Editorial . . . . . . . . . . . . . . . 1--2 Jeff Evans and Anna Tsatsaroni and Barbara Czarnecka Mathematical images in advertising: constructing difference and shaping identity, in global consumer culture . . 3--27 Andreas Moutsios-Rentzos and Panagiotis Spyrou and Alexandra Peteinara The objectification of the right-angled triangle in the teaching of the Pythagorean Theorem: an empirical investigation . . . . . . . . . . . . . 29--51 Oduor Olande Graphical artefacts: Taxonomy of students' response to test items . . . . 53--74 Murad Eid Jurdak and Rabih Raif El Mouhayar Trends in the development of student level of reasoning in pattern generalization tasks across grade level 75--92 Yvonne Lai and Keith Weber Factors mathematicians profess to consider when presenting pedagogical proofs . . . . . . . . . . . . . . . . . 93--108 Temple A. Walkowiak and Robert Q. Berry and J. Patrick Meyer and Sara E. Rimm-Kaufman and Erin R. Ottmar Introducing an observational measure of standards-based mathematics teaching practices: Evidence of validity and score reliability . . . . . . . . . . . 109--128 Sonja Lutovac and Raimo Kaasila Pre-service teachers' future-oriented mathematical identity work . . . . . . . 129--142 Higinio Dominguez and Carlos A. López Leiva and Lena Licón Khisty Relational engagement: Proportional reasoning with bilingual Latino/a students . . . . . . . . . . . . . . . . 143--160
Juan Pablo Mejia-Ramos and Keith Weber Why and how mathematicians read proofs: further evidence from a survey study . . 161--173 Hauke Straehler-Pohl and Saínza Fernández and Uwe Gellert and Lourdes Figueiras School mathematics registers in a context of low academic expectations . . 175--199 Andrew Brantlinger Critical mathematics discourse in a high school classroom: examining patterns of student engagement and resistance . . . 201--220 Karin Brodie Learning about learner errors in professional learning communities . . . 221--239 Dae S. Hong and Kyong Mi Choi A comparison of Korean and American secondary school textbooks: the case of quadratic equations . . . . . . . . . . 241--263 Jinfa Cai and Meixia Ding and Tao Wang How do exemplary Chinese and U.S. mathematics teachers view instructional coherence? . . . . . . . . . . . . . . . 265--280 Ove Gunnar Drageset Redirecting, progressing, and focusing actions --- a framework for describing how teachers use students' comments to work with mathematics . . . . . . . . . 281--304 Victoria Sánchez and Mercedes García Sociomathematical and mathematical norms related to definition in pre-service primary teachers' discourse . . . . . . 305--320
Chronis Kynigos and Jean-Baptiste Lagrange Cross-analysis as a tool to forge connections amongst theoretical frames in using digital technologies in mathematical learning . . . . . . . . . 321--327 Mich\`ele Artigue and Maria Alessandra Mariotti Networking theoretical frames: the ReMath enterprise . . . . . . . . . . . 329--355 Candia Morgan and Chronis Kynigos Digital artefacts as representations: forging connections between a constructionist and a social semiotic perspective . . . . . . . . . . . . . . 357--379 Jean-Baptiste Lagrange and Chronis Kynigos Digital technologies to teach and learn mathematics: Context and re-contextualization . . . . . . . . . . 381--403 Luis Radford On the role of representations and artefacts in knowing and learning . . . 405--422 Lulu Healy and Ana Isabel Sacristán Towards an understanding of the shaping of research outcomes by contextual issues: reflections on the contributions of the ReMath project . . . . . . . . . 423--435
Efi Paparistodemou and Despina Potari and Demetra Pitta-Pantazi Prospective teachers' attention on geometrical tasks . . . . . . . . . . . 1--18 Andrea McCloskey The promise of ritual: a lens for understanding persistent practices in mathematics classrooms . . . . . . . . . 19--38 Jessica Pierson Bishop and Lisa L. Lamb and Randolph A. Philipp and Ian Whitacre and Bonnie P. Schappelle Using order to reason about negative numbers: the case of Violet . . . . . . 39--59 Katie Makar Young children's explorations of average through informal inferential reasoning 61--78 Lluís Albarracín and Núria Gorgorió Devising a plan to solve Fermi problems involving large numbers . . . . . . . . 79--96 David Tall and Mikhail Katz A cognitive analysis of Cauchy's conceptions of function, continuity, limit and infinitesimal, with implications for teaching the calculus 97--124 Mara V. Martinez and Bettina Pedemonte Relationship between inductive arithmetic argumentation and deductive algebraic proof . . . . . . . . . . . . 125--149
A. Bakker Characterising and developing vocational mathematical knowledge . . . . . . . . . 151--156 Lionel LaCroix Learning to see pipes mathematically: preapprentices' mathematical activity in pipe trades training . . . . . . . . . . 157--176 Wolff-Michael Roth Rules of bending, bending the rules: the geometry of electrical conduit bending in college and workplace . . . . . . . . 177--192 David Swanson and Julian Williams Making abstract mathematics concrete in and out of school . . . . . . . . . . . 193--209 Arthur Bakker and Djonie Groenveld and Monica Wijers and Sanne F. Akkerman and Koeno P. E. Gravemeijer Proportional reasoning in the laboratory: an intervention study in vocational education . . . . . . . . . . 211--221 Arthur Bakker and Sanne F. Akkerman A boundary-crossing approach to support students' integration of statistical and work-related knowledge . . . . . . . . . 223--237 Corinne Hahn Linking academic knowledge and professional experience in using statistics: a design experiment for business school students . . . . . . . . 239--251 Diana Coben and Keith Weeks Meeting the mathematical demands of the safety-critical workplace: medication dosage calculation problem-solving for nursing . . . . . . . . . . . . . . . . 253--270 Geoff Wake Making sense of and with mathematics: the interface between academic mathematics and mathematics in practice 271--290 Gail E. FitzSimons Commentary on vocational mathematics education: where mathematics education confronts the realities of people's work 291--305
Anonymous The Twenty-third ICMI Study: primary mathematics study on whole numbers . . . 307--309 Stacy A. Brown On skepticism and its role in the development of proof in the classroom 311--335 Chrissavgi Triantafillou and Despina Potari Revisiting the place value concept in the workplace context: the issue of transfer development . . . . . . . . . . 337--358 Wolff-Michael Roth and Shelby Temple On understanding variability in data: a study of graph interpretation in an advanced experimental biology laboratory 359--376 Emily P. Bonner Investigating practices of highly successful mathematics teachers of traditionally underserved students . . . 377--399 AnnaMarie Conner and Laura M. Singletary and Ryan C. Smith and Patty Anne Wagner and Richard T. Francisco Teacher support for collective argumentation: A framework for examining how teachers support students' engagement in mathematical activities 401--429
Fulvia Furinghetti and Marta Menghini The role of concrete materials in Emma Castelnuovo's view of mathematics teaching . . . . . . . . . . . . . . . . 1--6 Paul Andrews and Andreas Ryve and Kirsti Hemmi and Judy Sayers PISA, TIMSS and Finnish mathematics teaching: an enigma in search of an explanation . . . . . . . . . . . . . . 7--26 Chunlian Jiang and Stephen Hwang and Jinfa Cai Chinese and Singaporean sixth-grade students' strategies for solving problems about speed . . . . . . . . . . 27--50 Núria Planas One speaker, two languages: Learning opportunities in the mathematics classroom . . . . . . . . . . . . . . . 51--66 Eric Weber and Patrick W. Thompson Students' images of two-variable functions and their graphs . . . . . . . 67--85 Tracy Logan and Tom Lowrie and Carmel M. Diezmann Co-thought gestures: Supporting students to successfully navigate map tasks . . . 87--102 Meixia Ding and Xiaobao Li Transition from concrete to abstract representations: the distributive property in a Chinese textbook series 103--121
Candia Morgan Social theory in mathematics education: Guest editorial . . . . . . . . . . . . 123--128 Candia Morgan Understanding practices in mathematics education: structure and text . . . . . 129--143 Clive Kanes and Candia Morgan and Anna Tsatsaroni The PISA mathematics regime: knowledge structures and practices of the self . . 145--165 Anna Tsatsaroni and Jeff Evans Adult numeracy and the totally pedagogised society: PIAAC and other international surveys in the context of global educational policy on lifelong learning . . . . . . . . . . . . . . . . 167--186 Stephen Lerman Mapping the effects of policy on mathematics teacher education . . . . . 187--201 Diane Parker and Jill Adler Sociological tools in the study of knowledge and practice in mathematics teacher education . . . . . . . . . . . 203--219 Robyn Jorgensen and Peter Gates and Vanessa Roper Structural exclusion through school mathematics: using Bourdieu to understand mathematics as a social practice . . . . . . . . . . . . . . . . 221--239 Alexandre Pais and Paola Valero Whither social theory? . . . . . . . . . 241--248 Anonymous Nominations sought for the first ICMI Emma Castelnuovo Award . . . . . . . . . 249--249
Yip-Cheung Chan and Ngai-Ying Wong Worldviews, religions, and beliefs about teaching and learning: perception of mathematics teachers with different religious backgrounds . . . . . . . . . 251--277 Andrea McDonough and Peter Sullivan Seeking insights into young children's beliefs about mathematics and learning 279--296 Ivy Kidron and Tommy Dreyfus Proof image . . . . . . . . . . . . . . 297--321 Timothy Patrick Fukawa-Connelly and Charlene Newton Analyzing the teaching of advanced mathematics courses via the enacted example space . . . . . . . . . . . . . 323--349 Anne Watson and Els De Geest Department-initiated change . . . . . . 351--368 Helen Forgasz and Gilah Leder and Hazel Tan Public views on the gendering of mathematics and related careers: international comparisons . . . . . . . 369--388 Teresa Rojano and Eugenio Filloy and Luis Puig Intertextuality and sense production in the learning of algebraic methods . . . 389--407 Bruria Shayshon and Hagar Gal and Bertha Tesler and Eun-Sung Ko Teaching mathematically talented students: a cross-cultural study about their teachers' views . . . . . . . . . 409--438 Nicolas Grenier-Boley Some issues about the introduction of first concepts in linear algebra during tutorial sessions at the beginning of university . . . . . . . . . . . . . . . 439--461
Merrilyn Goos Editorial . . . . . . . . . . . . . . . 1--2 Lyndon C. Martin and Jo Towers Growing mathematical understanding through Collective Image Making, Collective Image Having, and Collective Property Noticing . . . . . . . . . . . 3--18 William Zahner The rise and run of a computational understanding of slope in a conceptually focused bilingual algebra class . . . . 19--41 Shulamit Kapon and Gila Ron and Rina Hershkowitz and Tommy Dreyfus Perceiving permutations as distinct outcomes: the accommodation of a complex knowledge system . . . . . . . . . . . . 43--64 Leonor Santos and Sílvia Semana Developing mathematics written communication through expository writing supported by assessment strategies . . . 65--87 Anika Dreher and Sebastian Kuntze Teachers' professional knowledge and noticing: The case of multiple representations in the mathematics classroom . . . . . . . . . . . . . . . 89--114 David L. Trumpower Aspects of first year statistics students' reasoning when performing intuitive analysis of variance: effects of within- and between-group variability 115--136 Andonis Zagorianakos and Anna Shvarts The role of intuition in the process of objectification of mathematical phenomena from a Husserlian perspective: a case study . . . . . . . . . . . . . . 137--157 William Byers How humans learn to think mathematically: Exploring the three worlds of mathematics, by David Tall. (2013) . . . . . . . . . . . . . . . . . 159--162
Rina Zazkis and Boris Koichu A fictional dialogue on infinitude of primes: introducing virtual duoethnography . . . . . . . . . . . . . 163--181 Ivy Kidron and David Tall The roles of visualization and symbolism in the potential and actual infinity of the limit process . . . . . . . . . . . 183--199 Fernando Hitt and Alejandro S. González-Martín Covariation between variables in a modelling process: The ACODESA (collaborative learning, scientific debate and self-reflection) method . . . 201--219 Wolff-Michael Roth and Jean-François Maheux The visible and the invisible: mathematics as revelation . . . . . . . 221--238 Jon D. Davis and Nicole L. Fonger An analytical framework for categorizing the use of CAS symbolic manipulation in textbooks . . . . . . . . . . . . . . . 239--258 Chris Rasmussen and Megan Wawro and Michelle Zandieh Examining individual and collective level mathematical progress . . . . . . 259--281 Anna Sfard Book Review: When Oksapmin number system met Western arithmetic --- Answering the question of how cognitive and cultural change induce each other. [Saxe, G. B. (2012) \booktitleCultural Development of Mathematical Ideas. Papua New Guinea studies Cambridge, UK: Cambridge University Press. 393 pages. Hardback: ISBN: 978-0-521-76166-6. Paperback: ISBN: 978-1-107-68569-7. Online ISBN: 978-1-139-04536-0. Book DOI: \tt https://doi.org/10.1017/CBO9781139045360. \pounds 64] 283--290
Dani Ben-Zvi and Arthur Bakker and Katie Makar Learning to reason from samples . . . . 291--303 Clifford Konold and Traci Higgins and Susan Jo Russell and Khalimahtul Khalil Data seen through different lenses . . . 305--325 Joan Garfield and Laura Le and Andrew Zieffler and Dani Ben-Zvi Developing students' reasoning about samples and sampling variability as a path to expert statistical thinking . . 327--342 Maxine Pfannkuch and Pip Arnold and Chris J. Wild What I see is not quite the way it really is: students' emergent reasoning about sampling variability . . . . . . . 343--360 Jennifer Noll and Stacey Hancock Proper and paradigmatic metonymy as a lens for characterizing student conceptions of distributions and sampling . . . . . . . . . . . . . . . . 361--383 Maria Meletiou-Mavrotheris and Efi Paparistodemou Developing students' reasoning about samples and sampling in the context of informal inferences . . . . . . . . . . 385--404 Janet Ainley and Robert Gould and Dave Pratt Learning to reason from samples: commentary from the perspectives of task design and the emergence of ``big data'' 405--412
Rachel Lambert Constructing and resisting disability in mathematics classrooms: a case study exploring the impact of different pedagogies . . . . . . . . . . . . . . . 1--18 Kai-Lin Yang and Hui-Yu Hsu and Fou-Lai Lin and Jian-Cheng Chen and Ying-Hao Cheng Exploring the educative power of an experienced mathematics teacher educator-researcher . . . . . . . . . . 19--39 Ariyadi Wijaya and Marja van den Heuvel-Panhuizen and Michiel Doorman Opportunity-to-learn context-based tasks provided by mathematics textbooks . . . 41--65 Liisa Tainio and Anu Laine Emotion work and affective stance in the mathematics classroom: the case of IRE sequences in Finnish classroom interaction . . . . . . . . . . . . . . 67--87 Heather L. Johnson Together yet separate: Students' associating amounts of change in quantities involved in rate of change 89--110 Moses W. Ngware and James Ciera and Peter K. Musyoka and Moses Oketch Quality of teaching mathematics and learning achievement gains: evidence from primary schools in Kenya . . . . . 111--131 José Antonio González-Calero and David Arnau and Belén Laserna-Belenguer Influence of additive and multiplicative structure and direction of comparison on the reversal error . . . . . . . . . . . 133--147
Anonymous Call for papers . . . . . . . . . . . . 149--150 Hans Jòrgen Braathe and Yvette Solomon Choosing mathematics: the narrative of the self as a site of agency . . . . . . 151--166 Eva Norén Agency and positioning in a multilingual mathematics classroom . . . . . . . . . 167--184 Beth A. Herbel-Eisenmann and David Wagner and Kate R. Johnson and Heejoo Suh and Hanna Figueras Positioning in mathematics education: revelations on an imported theory . . . 185--204 Michael Weiss and Patricio Herbst The role of theory building in the teaching of secondary geometry . . . . . 205--229 Michael Weiss and Patricio Herbst Erratum to: The role of theory building in the teaching of secondary geometry 231--231 Jungeun Park Is the derivative a function? If so, how do we teach it? . . . . . . . . . . . . 233--250 Kajsa Bråting and Johanna Pejlare On the relations between historical epistemology and students' conceptual developments in mathematics . . . . . . 251--265 Raymond Flores and Esther Koontz and Fethi A. Inan and Mara Alagic Multiple representation instruction first versus traditional algorithmic instruction first: Impact in middle school mathematics classrooms . . . . . 267--281 Tatjana Hodnik \vCade\vz and Vida Manfreda Kolar Comparison of types of generalizations and problem-solving schemas used to solve a mathematical problem . . . . . . 283--306
Dominique Passelaigue and Valérie Munier Schoolteacher trainees' difficulties about the concepts of attribute and measurement . . . . . . . . . . . . . . 307--336 Ian Jones and Matthew Inglis The problem of assessing problem solving: can comparative judgement help? 337--355 Morten Misfeldt and Mikkel Willum Johansen Research mathematicians' practices in selecting mathematical problems . . . . 357--373 Alexandre Pais Symbolising the real of mathematics education . . . . . . . . . . . . . . . 375--391 Stanis\law Schukajlow and André Krug and Katrin Rakoczy Effects of prompting multiple solutions for modelling problems on students' performance . . . . . . . . . . . . . . 393--417 Zelha Tunç-Pekkan An analysis of elementary school children's fractional knowledge depicted with circle, rectangle, and number line representations . . . . . . . . . . . . 419--441
Adrian Simpson The anatomy of a mathematical proof: Implications for analyses with Toulmin's scheme . . . . . . . . . . . . . . . . . 1--17 Ferdinando Arzarello and Ornella Robutti and Mike Thomas Growth point and gestures: looking inside mathematical meanings . . . . . . 19--37 Jo Van Hoof and Lieven Verschaffel and Wim Van Dooren Inappropriately applying natural number properties in rational number tasks: characterizing the development of the natural number bias through primary and secondary education . . . . . . . . . . 39--56 Janne Fauskanger Challenges in measuring teachers' knowledge . . . . . . . . . . . . . . . 57--73 Nicholas H. Wasserman Unpacking teachers' moves in the classroom: navigating micro- and macro-levels of mathematical complexity 75--93 Gail E. FitzSimons Book Review: \booktitleMathematics & mathematics education: searching for common ground. Fried, M. N., & Dreyfus, T. (Eds.) (2014) . . . . . . . . . . . . 95--103
Sibel Kazak and Rupert Wegerif and Taro Fujita The importance of dialogic processes to conceptual development in mathematics 105--120 Keiko Hino Comparing multiple solutions in the structured problem solving: Deconstructing Japanese lessons from learner's perspective . . . . . . . . . 121--141 Annica Andersson and Paola Valero and Tamsin Meaney ``I am [not always] a maths hater'': Shifting students' identity narratives in context . . . . . . . . . . . . . . . 143--161 Michal Tabach and Talli Nachlieli Classroom engagement towards using definitions for developing mathematical objects: the case of function . . . . . 163--187 Siew Yee Lim and Elaine Chapman Effects of using history as a tool to teach mathematics on students' attitudes, anxiety, motivation and achievement in grade 11 classrooms . . . 189--212 Gail FitzSimons Educational studies in mathematics book review: Editor's comment . . . . . . . . 213--213 Francesca Ferrara Book Review: When mathematics and mathematics education come to matter: A review of Elizabeth de Freitas and Nathalie Sinclair's \booktitleMathematics and the Body: Material Entanglements in the Classroom (2014) . . . . . . . . . . . . . . . . . 215--220 Frances K. Harper and Heejoo Suh and Julie Nurnberger-Haag and Beth Herbel-Eisenmann Book Review: A review of the book by Elizabeth de Freitas and Nathalie Sinclair (2014). \booktitleMathematics and the body: Material entanglements in the classroom . . . . . . . . . . . . . 221--230 Jungeun Park Erratum to: Is the derivative a function? If so, how do we teach it? . . 231--231
Aaron Weinberg and Tim Fukawa-Connelly and Emilie Wiesner Characterizing instructor gestures in a lecture in a proof-based mathematics class . . . . . . . . . . . . . . . . . 233--258 Uffe Thomas Jankvist and Mogens Niss A framework for designing a research-based ``maths counsellor'' teacher programme . . . . . . . . . . . 259--284 Leslie Dietiker Mathematical story: a metaphor for mathematics curriculum . . . . . . . . . 285--302 Erlina Ronda Growth points in linking representations of function: a research-based framework 303--319 Michal Ayalon and Anne Watson and Steve Lerman Functions represented as linear sequential data: relationships between presentation and student responses . . . 321--339 Marsha Ing and Noreen M. Webb and Megan L. Franke and Angela C. Turrou and Jacqueline Wong and Nami Shin and Cecilia H. Fernandez Student participation in elementary mathematics classrooms: the missing link between teacher practices and student achievement? . . . . . . . . . . . . . . 341--356 Mich\`ele Artigue Book review: \booktitleThe mathematics teacher in the digital era, Alison Clark--Wilson, Ornella Robutti and Nathalie Sinclair (Eds.) (2014) . . . . 357--362
Merrilyn Goos Editorial . . . . . . . . . . . . . . . 1--2 Anonymous The Hans Freudenthal Medal for 2015 goes to Jill Adler, University of the Witwatersrand, Johannesburg, South Africa . . . . . . . . . . . . . . . . . 3--4 Anonymous The Felix Klein Medal for 2015 goes to Alan J. Bishop, Emeritus Professor of Education, Monash University, Australia 5--6 Tu\ugrul Kar An error correction about problem posing on a linear graph . . . . . . . . . . . 7--8 Jinfa Cai and Stephen Hwang and John C. Moyer Mathematical problem posing as a measure of curricular effect on students' learning: a response . . . . . . . . . . 9--10 Peter Frejd and Christer Bergsten Mathematical modelling as a professional task . . . . . . . . . . . . . . . . . . 11--35 David A. Yopp and Rob Ely When does an argument use a generic example? . . . . . . . . . . . . . . . . 37--53 Yvette Solomon and Darinka Radovic and Laura Black ``I can actually be very feminine here'': contradiction and hybridity in becoming a female mathematician . . . . 55--71 David Kollosche Criticising with Foucault: towards a guiding framework for socio-political studies in mathematics education . . . . 73--86 Gustavo Martínez-Sierra and María del Socorro García-González Undergraduate mathematics students' emotional experiences in Linear Algebra courses . . . . . . . . . . . . . . . . 87--106 Vicenç Font Moll and María Trigueros and Edelmira Badillo and Norma Rubio Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA . . . . . . . . . . . . . . 107--122 Csaba Csíkos Strategies and performance in elementary students' three-digit mental addition 123--139 Yeping Li and Jianxing Xu Book Review: \booktitleStudent voice in mathematics classrooms around the world. Berinderjeet Kaur, Glenda Anthony, Minoru Ohtani, and David Clarke (Eds.) (2013) . . . . . . . . . . . . . . . . . 141--148
Ivy Kidron Epistemology and networking theories . . 149--163 Thorsten Scheiner New light on old horizon: Constructing mathematical concepts, underlying abstraction processes, and sense making strategies . . . . . . . . . . . . . . . 165--183 Elizabeth de Freitas Material encounters and media events: what kind of mathematics can a body do? 185--202 Aaron Weinberg and Emilie Wiesner and Tim Fukawa-Connelly Mathematics lectures as narratives: insights from network graph methodology 203--226 Kate le Roux and Jill Adler A critical discourse analysis of practical problems in a foundation mathematics course at a South African university . . . . . . . . . . . . . . . 227--246 Elise Lockwood and Bryan R. Gibson Combinatorial tasks and outcome listing: Examining productive listing among undergraduate students . . . . . . . . . 247--270 Colin Foster Confidence and competence with mathematical procedures . . . . . . . . 271--288 Ian Jones Book Review: \booktitleAlgebra teaching around the world. Frederick K. S. Leung, Kyungmee Park, Derek Holton, & David Clarke (Eds.) (2014) . . . . . . . . . . 289--294
Anonymous Call for papers . . . . . . . . . . . . 295--297 Michal Tabach and Talli Nachlieli Communicational perspectives on learning and teaching mathematics: prologue . . . 299--306 Oi-Lam Ng The interplay between language, gestures, dragging and diagrams in bilingual learners' mathematical communications . . . . . . . . . . . . . 307--326 Marcy B. Wood Rituals and right answers: barriers and supports to autonomous activity . . . . 327--348 Einat Heyd-Metzuyanim and Mellony Graven Between people-pleasing and mathematizing: South African learners' struggle for numeracy . . . . . . . . . 349--373 Beste Güçler Making implicit metalevel rules of the discourse on function explicit topics of reflection in the classroom to foster student learning . . . . . . . . . . . . 375--393 Jungeun Park Communicational approach to study textbook discourse on the derivative . . 395--421 Norma Presmeg Commognition as a lens for research . . 423--430
Francesca Ferrara and Nathalie Sinclair An early algebra approach to pattern generalisation: Actualising the virtual through words, gestures and toilet paper 1--19 Linda Venenciano and Ronald Heck Proposing and testing a model to explain traits of algebra preparedness . . . . . 21--35 Paul Ernest The unit of analysis in mathematics education: bridging the political-technical divide? . . . . . . 37--58 Julian Williams Alienation in mathematics education: critique and development of neo-Vygotskian perspectives . . . . . . 59--73 Tony Brown Rationality and belief in learning mathematics . . . . . . . . . . . . . . 75--90 Robert Gunnarsson and Wang Wei Sönnerhed and Bernt Hernell Does it help to use mathematically superfluous brackets when teaching the rules for the order of operations? . . . 91--105 Robert Gunnarsson and Wang Wei Sönnerhed and Bernt Hernell Erratum to: Does it help to use mathematically superfluous brackets when teaching the rules for the order of operations? . . . . . . . . . . . . . . 107--107 Ivonne Sandoval and Edgar Possani An analysis of different representations for vectors and planes in $ \mathbb {R}^3 $ . . . . . . . . . . . . . . . . 109--127 Elena Castro-Rodríguez and Demetra Pitta-Pantazi and Luis Rico and Pedro Gómez Prospective teachers' understanding of the multiplicative part-whole relationship of fraction . . . . . . . . 129--146
Kotaro Komatsu A framework for proofs and refutations in school mathematics: Increasing content by deductive guessing . . . . . 147--162 Stephanie A. Casey and Courtney Nagle Students' use of slope conceptualizations when reasoning about the line of best fit . . . . . . . . . . 163--177 Suzanne D. Magargee and Judith E. Beauford Do explicit number names accelerate pre-kindergarteners' numeracy and place value acquisition? . . . . . . . . . . . 179--192 Annette Hilton and Geoff Hilton and Shelley Dole and Merrilyn Goos Promoting middle school students' proportional reasoning skills through an ongoing professional development programme for teachers . . . . . . . . . 193--219 Kevin C. Moore and Kevin R. LaForest and Hee Jung Kim Putting the unit in pre-service secondary teachers' unit circle . . . . 221--241 Kevin C. Moore and Kevin R. LaForest and Hee Jung Kim Erratum to: Putting the unit in pre-service secondary teachers' unit circle . . . . . . . . . . . . . . . . . 243--243 Frederick Peck and Michael Matassa Reinventing fractions and division as they are used in algebra: the power of preformal productions . . . . . . . . . 245--278 Snezana Lawrence Book Review: The power of a great introduction. Karp, Alexander, Schubring, Gert (Eds.) (2014). \booktitleHandbook on the history of mathematics education . . . . . . . . . 279--285
Tony Brown and Yvette Solomon and Julian Williams Theory in and for mathematics education: in pursuit of a critical agenda . . . . 287--297 Anna Llewellyn Problematising the pursuit of progress in mathematics education . . . . . . . . 299--314 Kathleen T. Nolan Schooling novice mathematics teachers on structures and strategies: a Bourdieuian perspective on the role of ``others'' in classroom practices . . . . . . . . . . 315--329 Richard Barwell Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic . . . . . . . . . 331--345 Alexandre Pais At the intersection between the subject and the political: a contribution to an ongoing discussion . . . . . . . . . . . 347--359 Elena Nardi Where form and substance meet: using the narrative approach of re-storying to generate research findings and community rapprochement in (university) mathematics education . . . . . . . . . 361--377 Paul Ernest The problem of certainty in mathematics 379--393 Mark Boylan Ethical dimensions of mathematics education . . . . . . . . . . . . . . . 395--409 Ole Skovsmose An intentionality interpretation of meaning in mathematics education . . . . 411--424
Martin Carlsen and Ingvald Erfjord and Per Sigurd Hundeland and John Monaghan Kindergarten teachers' orchestration of mathematical activities afforded by technology: agency and mediation . . . . 1--17 Lisa Darragh Identity research in mathematics education . . . . . . . . . . . . . . . 19--33 Carmen Samper and Patricia Perry and Leonor Camargo and Adalira Sáenz-Ludlow and Óscar Molina A dilemma that underlies an existence proof in geometry . . . . . . . . . . . 35--50 João Pedro da Ponte and Marisa Quaresma Teachers' professional practice conducting mathematical discussions . . 51--66 Alan F. Chow and James P. Van Haneghan Transfer of solutions to conditional probability problems: effects of example problem format, solution format, and problem context . . . . . . . . . . . . 67--85 Wolff-Michael Roth Growing-making mathematics: a dynamic perspective on people, materials, and movement in classrooms . . . . . . . . . 87--103 Ji-Won Son Moving beyond a traditional algorithm in whole number subtraction: Preservice teachers' responses to a student's invented strategy . . . . . . . . . . . 105--129
Ulrich Kortenkamp and John Monaghan and Luc Trouche Jonathan M. Borwein (1951--2016): exploring, experiencing and experimenting in mathematics --- an inspiring journey in mathematics . . . . 131--136 Martin A. Simon and Melike Kara and Nicora Placa and Hakan Sandir Categorizing and promoting reversibility of mathematical concepts . . . . . . . . 137--153 Dov Zazkis and Keith Weber and Juan Pablo Mejía-Ramos Bridging the gap between graphical arguments and verbal-symbolic proofs in a real analysis context . . . . . . . . 155--173 Chronoula Voutsina Oral counting sequences: a theoretical discussion and analysis through the lens of representational redescription . . . 175--193 Sylvia Coutat and Colette Laborde and Philippe R. Richard L'apprentissage instrumenté de propriétés en géométrie: propédeutique \`a l'acquisition d'une compétence de démonstration. (French) [The instrumented learning of properties in geometry: propedeutic to the acquisition of a competence in demonstration] . . . . . . 195--221 Igor' Kontorovich and Rina Zazkis Turn vs. shape: teachers cope with incompatible perspectives on angle . . . 223--243 Amy J. Hackenberg and Mi Yeon Lee Students' distributive reasoning with fractions and unknowns . . . . . . . . . 245--263 Arthur Bakker Book Review: Networking theories as an example of boundary crossing. Angelika Bikner-Ahsbahs and Susanne Prediger (Eds.) (2014). \booktitleNetworking of theories as a research practice in mathematics education . . . . . . . . . 265--273
King Woon Yau and Ida Ah Chee Mok Insights from students' private work in their notebooks: how do students learn from the teacher's examples? . . . . . . 275--292 Anna-Lena Ekdahl and Hamsa Venkat and Ulla Runesson Coding teaching for simultaneity and connections . . . . . . . . . . . . . . 293--313 José Antonio Fernández-Plaza and Adrian Simpson Three concepts or one? Students' understanding of basic limit concepts 315--332 Karina J. Wilkie Students' use of variables and multiple representations in generalizing functional relationships prior to secondary school . . . . . . . . . . . . 333--361 Ji-Eun Lee and Kyoung-Tae Kim Pre-service teachers' conceptions of effective teacher talk: their critical reflections on a sample teacher-student dialogue . . . . . . . . . . . . . . . . 363--381 N. Metaxas and D. Potari and T. Zachariades Analysis of a teacher's pedagogical arguments using Toulmin's model and argumentation schemes . . . . . . . . . 383--397 Arthur Bakker and Djonie Groenveld and Monica Wijers and Sanne F. Akkerman and Koeno P. E. Gravemeijer Erratum to: Proportional reasoning in the laboratory: an intervention study in vocational education . . . . . . . . . . 399--399
Merrilyn Goos Editorial . . . . . . . . . . . . . . . 1--3 Lara Alcock and Adrian Simpson Interactions between defining, explaining and classifying: the case of increasing and decreasing sequences . . 5--19 Francesca Ferrara and Giulia Ferrari Agency and assemblage in pattern generalisation: a materialist approach to learning . . . . . . . . . . . . . . 21--36 Takeshi Miyakawa Comparative analysis on the nature of proof to be taught in geometry: the cases of French and Japanese lower secondary schools . . . . . . . . . . . 37--54 Ketty M. Sarouphim and Madona Chartouny Mathematics education in Lebanon: gender differences in attitudes and achievement 55--68 Yi Mao and Tyreke White and Philip M. Sadler and Gerhard Sonnert The association of precollege use of calculators with student performance in college calculus . . . . . . . . . . . . 69--83 José Domingo Villarroel and Olga Sanz Ortega A study regarding the spontaneous use of geometric shapes in young children's drawings . . . . . . . . . . . . . . . . 85--95 Fernando Hitt and Mireille Saboya and Carlos Cortés Zavala Rupture or continuity: The arithmetico--algebraic thinking as an alternative in a modelling process in a paper and pencil and technology environment . . . . . . . . . . . . . . 97--116
Martin A. Simon Explicating mathematical concept and mathematical conception as theoretical constructs for mathematics education research . . . . . . . . . . . . . . . . 117--137 Claudia Corriveau Secondary-to-tertiary comparison through the lens of ways of doing mathematics in relation to functions: a study in collaboration with teachers . . . . . . 139--160 Gabriele Kaiser and Sigrid Blömeke and Johannes König and Andreas Busse and Martina Döhrmann and Jessica Hoth Professional competencies of (prospective) mathematics teachers --- cognitive versus situated approaches . . 161--182 Gabriele Kaiser and Sigrid Blömeke and Johannes König and Andreas Busse and Martina Döhrmann and Jessica Hoth Erratum to: Professional competencies of (prospective) mathematics teachers --- cognitive versus situated approaches . . 183--184 Matthias Glade and Susanne Prediger Students' individual schematization pathways --- empirical reconstructions for the case of part-of-part determination for fractions . . . . . . 185--203 Christopher J. Sangwin and Ian Jones Asymmetry in student achievement on multiple-choice and constructed-response items in reversible mathematics processes . . . . . . . . . . . . . . . 205--222 Mikio Miyazaki and Taro Fujita and Keith Jones Students' understanding of the structure of deductive proof . . . . . . . . . . . 223--239
Paul Christian Dawkins and John Paul Cook Guiding reinvention of conventional tools of mathematical logic: students' reasoning about mathematical disjunctions . . . . . . . . . . . . . . 241--256 Birgit Pepin and Binyan Xu and Luc Trouche and Chongyang Wang Developing a deeper understanding of mathematics teaching expertise: an examination of three Chinese mathematics teachers' resource systems as windows into their work and expertise . . . . . 257--274 Maura Iori Objects, signs, and representations in the semio-cognitive analysis of the processes involved in teaching and learning mathematics: A Duvalian perspective . . . . . . . . . . . . . . 275--291 David Mogari Using culturally relevant teaching in a co-educational mathematics class of a patriarchal community . . . . . . . . . 293--307 Gulay Bozkurt and Kenneth Ruthven Classroom-based professional expertise: a mathematics teacher's practice with technology . . . . . . . . . . . . . . . 309--328 Santiago Cueto and Juan León and M. Alejandra Sorto and Alejandra Miranda Teachers' pedagogical content knowledge and mathematics achievement of students in Peru . . . . . . . . . . . . . . . . 329--345
Claudia Corriveau and Nadine Bednarz The secondary--tertiary transition viewed as a change in mathematical cultures: an exploration concerning symbolism and its use . . . . . . . . . 1--19 Michelle Zandieh and Jessica Ellis and Chris Rasmussen A characterization of a unified notion of mathematical function: the case of high school function and linear transformation . . . . . . . . . . . . . 21--38 Marianna Bosch and Josep Gascón and María Trigueros Dialogue between theories interpreted as research praxeologies: the case of APOS and the ATD . . . . . . . . . . . . . . 39--52 Johanna Rellensmann and Stanislaw Schukajlow and Claudia Leopold Make a drawing. Effects of strategic knowledge, drawing accuracy, and type of drawing on students' mathematical modelling performance . . . . . . . . . 53--78 Andrea Knapp and Racheal Landers and Senfeng Liang and Vetrece Jefferson We all as a family are graduating tonight: a case for mathematical knowledge for parental involvement . . . 79--95 Wolff-Michael Roth Astonishment: a post-constructivist investigation into mathematics as passion . . . . . . . . . . . . . . . . 97--111 Brian Greer Review of ``All positive action starts with criticism: Hans Freudenthal and the didactics of mathematics'' (2015). Translated from ``Elke positieve actie begint met critiek: Hans Freudenthal en de didactiek van de wiskunde'' by Sacha la Bastide-van Gemert (Springer, 2006). English translation by Marianne Vincken and William Third, co-ordinated by Arthur Bakker . . . . . . . . . . . . . 113--122
Paul Christian Dawkins and Keith Weber Values and norms of proof for mathematicians and students . . . . . . 123--142 Catherine D. Bruce and Brent Davis and Nathalie Sinclair and Lynn McGarvey and David Hallowell and Michelle Drefs and Krista Francis and Zachary Hawes and Joan Moss and Joanne Mulligan and Yukari Okamoto and Walter Whiteley and Geoff Woolcott Understanding gaps in research networks: using ``spatial reasoning'' as a window into the importance of networked educational research . . . . . . . . . . 143--161 Eivind Kaspersen and Birgit Pepin and Svein Arne Sikko Measuring STEM students' mathematical identities . . . . . . . . . . . . . . . 163--179 Maria Blanton and Bárbara M. Brizuela and Angela Murphy Gardiner and Katie Sawrey and Ashley Newman-Owens A progression in first-grade children's thinking about variable and variable notation in functional relationships . . 181--202 Konstantinos Stouraitis and Despina Potari and Jeppe Skott Contradictions, dialectical oppositions and shifts in teaching mathematics . . . 203--217 Tamsin Meaney and Toril Eskeland Rangnes Book Review: \booktitleHow research fields change --- the documentation of a process. Anjum Halai and Philip Clarkson (Eds.) (2016) Teaching and learning mathematics in multilingual classrooms 219--227
Hyman Bass Designing opportunities to learn mathematics theory-building practices 229--244 Alik Palatnik and Boris Koichu Sense making in the context of algebraic activities . . . . . . . . . . . . . . . 245--262 Anthony Fernandes and Leslie H. Kahn and Marta Civil A closer look at bilingual students' use of multimodality in the context of an area comparison problem from a large-scale assessment . . . . . . . . . 263--282 Colin Foster and Matthew Inglis Teachers' appraisals of adjectives relating to mathematics tasks . . . . . 283--301 Ann Downton and Peter Sullivan Posing complex problems requiring multiplicative thinking prompts students to use sophisticated strategies and build mathematical connections . . . . . 303--328 Gail E. FitzSimons and Lisa Björklund Boistrup In the workplace mathematics does not announce itself: towards overcoming the hiatus between mathematics education and work . . . . . . . . . . . . . . . . . . 329--349 Claudia Corriveau and Nadine Bednarz Erratum to: The secondary--tertiary transition viewed as a change in mathematical cultures: an exploration concerning symbolism and its use . . . . 351--351 Margaret Walshaw Book Review: \booktitleLeveraging the potential of research on classroom discourse for enhancing mathematics teaching and learning, Jill Adler and Anna Sfard (Eds.) (2017) Research for Educational Change: Transforming Researchers ' Insights Into Improvement in Mathematics Teaching and Learning . . 353--357
Doris Jeannotte and Carolyn Kieran A conceptual model of mathematical reasoning for school mathematics . . . . 1--16 Alexander Schüler-Meyer Students' development of structure sense for the distributive law . . . . . . . . 17--32 Travis Weiland Problematizing statistical literacy: An intersection of critical and statistical literacies . . . . . . . . . . . . . . . 33--47 Zvia Markovits and Helen Forgasz ``Mathematics is like a lion'': Elementary students' beliefs about mathematics . . . . . . . . . . . . . . 49--64 Janine Remillard and Ok-Kyeong Kim Knowledge of curriculum embedded mathematics: exploring a critical domain of teaching . . . . . . . . . . . . . . 65--81 Pessia Tsamir and Dina Tirosh and Esther S. Levenson and Ruthi Barkai and Michal Tabach Repeating patterns in kindergarten: findings from children's enactments of two activities . . . . . . . . . . . . . 83--99 Jinxia Xie and Joanna O. Masingila Examining Interactions between Problem Posing and Problem Solving with Prospective Primary Teachers: A Case of Using Fractions . . . . . . . . . . . . 101--118
Gabriel J. Stylianides and Andreas J. Stylianides Research-based interventions in the area of proof: the past, the present, and the future . . . . . . . . . . . . . . . . . 119--127 Kotaro Komatsu Fostering empirical examination after proof construction in secondary school geometry . . . . . . . . . . . . . . . . 129--144 Jorge Fiallo and Angel Gutiérrez Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course . . . . . . . . . . 145--167 Joana Mata-Pereira and João-Pedro da Ponte Enhancing students' mathematical reasoning in the classroom: teacher actions facilitating generalization and justification . . . . . . . . . . . . . 169--186 Mika Gabel and Tommy Dreyfus Affecting the flow of a proof by creating presence --- a case study in Number Theory . . . . . . . . . . . . . 187--205 Elda Guala and Paolo Boero Cultural analysis of mathematical content in teacher education: the case of Elementary Arithmetic Theorems . . . 207--227 Lianghuo Fan and Chunxia Qi and Xiaomei Liu and Yi Wang and Mengwei Lin Does a transformation approach improve students' ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms . . . . . . 229--248 Somali Roy and Matthew Inglis and Lara Alcock Multimedia resources designed to support learning from written proofs: an eye-movement study . . . . . . . . . . . 249--266 Elena Nardi and Eric Knuth Changing classroom culture, curricula, and instruction for proof and proving: how amenable to scaling up, practicable for curricular integration, and capable of producing long-lasting effects are current interventions? . . . . . . . . . 267--274
Yasmine Abtahi and Mellony Graven and Stephen Lerman Conceptualising the more knowledgeable other within a multi-directional ZPD . . 275--287 M. J. A. Bunck and E. Terlien and M. van Groenestijn and S. W. M. Toll and J. E. H. Van Luit Observing and analyzing children's mathematical development, based on action theory . . . . . . . . . . . . . 289--304 Stéphane Clivaz Teaching multidigit multiplication: combining multiple frameworks to analyse a class episode . . . . . . . . . . . . 305--325 Mi Yeon Lee Pre-service teachers' flexibility with referent units in solving a fraction division problem . . . . . . . . . . . . 327--348 David Guillemette History of mathematics in secondary school teachers' training: towards a nonviolent mathematics education . . . . 349--365 Luis Radford and Wolff-Michael Roth Alienation in mathematics education: a problem considered from neo-Vygotskian approaches . . . . . . . . . . . . . . . 367--380 Keith Jones and Chronoula Voutsina Book Review: \booktitleApproaches to qualitative research in mathematics education: Examples of methodology and methods, edited by Angelika Bikner--Ahsbahs, Christine Knipping, & Norma Presmeg. (2015) . . . . . . . . . 381--390 Gail FitzSimons Book review Editor's comment . . . . . . 391--391
Merrilyn Goos Editorial . . . . . . . . . . . . . . . 1--3 Igor' Kontorovich Why Johnny struggles when familiar concepts are taken to a new mathematical domain: towards a polysemous approach 5--20 Einat Heyd-Metzuyanim and Charles Munter and James Greeno Conflicting frames: a case of misalignment between professional development efforts and a teacher's practice in a high school mathematics classroom . . . . . . . . . . . . . . . 21--37 Miwa Aoki Takeuchi Power and identity in immigrant parents' involvement in early years mathematics learning . . . . . . . . . . . . . . . . 39--53 Nicole L. Louie Culture and ideology in mathematics teacher noticing . . . . . . . . . . . . 55--69 Hamsa Venkat and Mike Askew Mediating primary mathematics: theory, concepts, and a framework for studying practice . . . . . . . . . . . . . . . . 71--92 Teo Paoletti and Irma E. Stevens and Natalie L. F. Hobson and Kevin C. Moore and Kevin R. LaForest Inverse function: Pre-service teachers' techniques and meanings . . . . . . . . 93--109 Keith Weber Book review: Baruch B. Schwarz and Michael J. Baker (Eds) (Foreword by L. B. Resnick with F. Schantz) (2017) \booktitleDialogue, Argumentation and Education: History, Theory and Practice 111--118 Keith Weber Correction to: Book review: Baruch B. Schwarz and Michael J. Baker (Foreword by L. B. Resnick with F. Schantz) (2017) \booktitleDialogue, Argumentation and Education: History, Theory and Practice 119--119
Colin Foster Developing mathematical fluency: comparing exercises and rich tasks . . . 121--141 Rina Zazkis and Annette Rouleau Order of operations: On convention and met-before acronyms . . . . . . . . . . 143--162 Aisling Leavy and Mairead Hourigan The role of perceptual similarity, context, and situation when selecting attributes: considerations made by 5--6-year-olds in data modeling environments . . . . . . . . . . . . . . 163--183 Christine Chambris The influence of theoretical mathematical foundations on teaching and learning: a case study of whole numbers in elementary school . . . . . . . . . . 185--207 Bharath Sriraman Book review: \booktitleAnthropomorphizing mathematics education. Review of Hauke Staehler--Pohl, Nina Bohlmann, and Alexandre Pais (Eds). (2017). \booktitleThe disorder of mathematics education: challenging the sociopolitical dimensions of research. 329 pp. . . . . . . . . . . . . . . . . 209--213
Steven R. Jones Prototype images in mathematics education: the case of the graphical representation of the definite integral 215--234 Karina J. Wilkie and Peter Sullivan Exploring intrinsic and extrinsic motivational aspects of middle school students' aspirations for their mathematics learning . . . . . . . . . . 235--254 Anne Watson and Michal Ayalon and Stephen Lerman Comparison of students' understanding of functions in classes following English and Israeli national curricula . . . . . 255--272 Michal Tabach and Baruch B. Schwarz Professional development of mathematics teachers toward the facilitation of small-group collaboration . . . . . . . 273--298 Heather Lynn Johnson and Evan McClintock A link between students' discernment of variation in unidirectional change and their use of quantitative variational reasoning . . . . . . . . . . . . . . . 299--316
Teo Paoletti and Victoria Krupnik and Dimitrios Papadopoulos and Joseph Olsen and Tim Fukawa-Connelly and Keith Weber Teacher questioning and invitations to participate in advanced mathematics lectures . . . . . . . . . . . . . . . . 1--17 María C. Cañadas and Marta Molina and Aurora del Río Meanings given to algebraic symbolism in problem-posing . . . . . . . . . . . . . 19--37 Ernest C. D. M. van Lieshout and Iro Xenidou-Dervou Pictorial representations of simple arithmetic problems are not always helpful: a cognitive load perspective 39--55 Maria Chimoni and Demetra Pitta-Pantazi and Constantinos Christou Examining early algebraic thinking: insights from empirical data . . . . . . 57--76 Trine Foyn and Yvette Solomon and Hans Jòrgen Braathe Clever girls' stories: the girl they call a nerd . . . . . . . . . . . . . . 77--93 Maura Iori Teachers' awareness of the semio-cognitive dimension of learning mathematics . . . . . . . . . . . . . . 95--113
John C. Moyer and Victoria Robison and Jinfa Cai Attitudes of high-school students taught using traditional and reform mathematics curricula in middle school: a retrospective analysis . . . . . . . . . 115--134 Ke Wang and Xiao-qin Wang and Yeping Li and Michael S. Rugh A framework for integrating the history of mathematics into teaching in Shanghai 135--155 Katarina Gvozdic and Emmanuel Sander When intuitive conceptions overshadow pedagogical content knowledge: Teachers' conceptions of students' arithmetic word problem solving strategies . . . . . . . 157--175 Molly L. Kelton and Jasmine Y. Ma Reconfiguring mathematical settings and activity through multi-party, whole-body collaboration . . . . . . . . . . . . . 177--196 Fou-Lai Lin and Kai-Lin Yang and Hui-Yu Hsu and Jian-Cheng Chen Mathematics teacher educator-researchers' perspectives on the use of theory in facilitating teacher growth . . . . . . . . . . . . . 197--214
Núria Planas Language as resource: a key notion for understanding the complexity of mathematics learning . . . . . . . . . . 215--229 Alejandro S. González-Martín and Elena Nardi and Irene Biza From resource to document: scaffolding content and organising student learning in teachers' documentation work on the teaching of series . . . . . . . . . . . 231--252 Sonja Lutovac and Raimo Kaasila An elementary teacher's narrative identity work at two points in time two decades apart . . . . . . . . . . . . . 253--267 Marcelo C. Borba and Aparecida Santana de Souza Chiari and Helber Rangel Formiga Leite de Almeida Interactions in virtual learning environments: new roles for digital technology . . . . . . . . . . . . . . . 269--286 David Kollosche Social functions of mathematics education: a framework for socio-political studies . . . . . . . . 287--303
Isabelle Demonty and Joëlle Vlassis and Annick Fagnant Algebraic thinking, pattern activities and knowledge for teaching at the transition between primary and secondary school . . . . . . . . . . . . . . . . . 1--19 Darinka Radovic and Laura Black and Julian Williams and Christian E. Salas Towards conceptual coherence in the research on mathematics learner identity: a systematic review of the literature . . . . . . . . . . . . . . . 21--42 Carlos Soneira and José Antonio González-Calero and David Arnau An assessment of the sources of the reversal error through classic and new variables . . . . . . . . . . . . . . . 43--56 Jeffrey Craig The promises of numeracy . . . . . . . . 57--71 Neila de Toledo e Toledo and Gelsa Knijnik and Paola Valero Mathematics education in the neoliberal and corporate curriculum: the case of Brazilian agricultural high schools . . 73--87 Rabih El Mouhayar Trends of progression of student level of reasoning and generalization in numerical and figural reasoning approaches in pattern generalization . . 89--107 Nerida F. Ellerton Book Review: NCTM's \booktitleCompendium: finding a balance between historical details, contemporary practices, and future resources. Jinfa Cai (Ed.) (2017) \booktitleCompendium for research in mathematics education 109--123
Thomas de Vittori Analyzing the use of history in mathematics education: issues and challenges around Balacheff's cK$ \not c $ model . . . . . . . . . . . . . . . . 125--136 Jennifer A. Czocher How does validating activity contribute to the modeling process? . . . . . . . . 137--159 Kirstin Erath and Susanne Prediger and Uta Quasthoff and Vivien Heller Discourse competence as important part of academic language proficiency in mathematics classrooms: the case of explaining to learn and learning to explain . . . . . . . . . . . . . . . . 161--179 Jennifer Hall and Jo Towers and Lyndon C. Martin Using I poems to illuminate the complexity of students' mathematical identities . . . . . . . . . . . . . . . 181--196 Fien Depaepe and Patrick Van Roy and Joke Torbeyns and Thilo Kleickmann and Wim Van Dooren and Lieven Verschaffel Stimulating pre-service teachers' content and pedagogical content knowledge on rational numbers . . . . . 197--216 Arjen de Vetten and Judith Schoonenboom and Ronald Keijzer and Bert van Oers The development of informal statistical inference content knowledge of pre-service primary school teachers during a teacher college intervention 217--234 Alexandre Pais Book Review: The limits of pluralism. Bharath Sriraman (Ed.) (2017) \booktitleHumanizing mathematics and its philosophy: Essays celebrating the 90th birthday of Reuben Hersh . . . . . . . . 235--240
Merrilyn Goos Editorial . . . . . . . . . . . . . . . 241--242 Jinfa Cai and Roza Leikin Call for papers: \booktitleEducational Studies in Mathematics special issue . . 243--244 Yan Zhu and Gabriele Kaiser and Jinfa Cai Gender equity in mathematical achievement: the case of China . . . . . 245--260 Ofer Marmur and Rina Zazkis Space of fuzziness: avoidance of deterministic decisions in the case of the inverse function . . . . . . . . . . 261--275 Martin Carlsen Upper secondary students' mathematical reasoning on a sinusoidal function . . . 277--291 Alik Palatnik and Dor Abrahamson Rhythmic movement as a tacit enactment goal mobilizes the emergence of mathematical structures . . . . . . . . 293--309 Yìlmaz Zengin Examination of the constructed dynamic bridge between the concepts of differential and derivative with the integration of GeoGebra and the ACODESA method . . . . . . . . . . . . . . . . . 311--333 Tatjana Hodnik \vCade\vz and Vida Manfreda Kolar How fifth-grade pupils reason about fractions: a reliance on part-whole subconstructs . . . . . . . . . . . . . 335--357 Colleen M. Eddy Book review: \booktitleMathematics for all: From fantasy to reality. Murad Jurdak and Renuka Vithal (Eds.) (2018) Sociopolitical dimensions of mathematics education: from the margin to the mainstream . . . . . . . . . . . . . . . 359--362
Arthur Bakker Editorial . . . . . . . . . . . . . . . 1--2 Anonymous Announcements . . . . . . . . . . . . . 3--6 Carlotta Soldano and Yael Luz and Ferdinando Arzarello and Michal Yerushalmy Technology-based inquiry in geometry: semantic games through the lens of variation . . . . . . . . . . . . . . . 7--23 Helena Roos Inclusion in mathematics education: an ideology, a way of teaching, or both? 25--41 Stanislaw Schukajlow and Kay Achmetli and Katrin Rakoczy Does constructing multiple solutions for real-world problems affect self-efficacy? . . . . . . . . . . . . . 43--60 Simon Weixler and Daniel Sommerhoff and Stefan Ufer The empirical law of large numbers and the hospital problem: systematic investigation of the impact of multiple task and person characteristics . . . . 61--82 Gloria Sánchez-Matamoros and Ceneida Fernández and Salvador Llinares Relationships among prospective secondary mathematics teachers' skills of attending, interpreting and responding to students' understanding 83--99 Ghislaine Gueudet Book Review: Curricular resources and their classroom implementation: Contributions (and limitations) of a focus on mathematical tasks. Gabriel J. Stylianides (Ed.) (2016) \booktitleCurricular resources and classroom use. The case of mathematics 101--108 Fulvia Furinghetti Book Review: The long story of the history in mathematics education. Kathleen M. Clark, Tinne Hoff Kjeldsen, Sebastian Schorcht, & Constantinos Tzanakis (Eds.) (2018). \booktitleMathematics, education and history. Towards a harmonious partnership . . . . . . . . . . . . . . 109--116
Paul Christian Dawkins and Matthew Inglis and Nicholas Wasserman The use(s) of is in mathematics . . . . 117--137 Margot Berger Different reading styles for mathematics text . . . . . . . . . . . . . . . . . . 139--159 Joris Mithalal and Nicolas Balacheff The instrumental deconstruction as a link between drawing and geometrical figure . . . . . . . . . . . . . . . . . 161--176 Luz Valoyes-Chávez On the making of a new mathematics teacher: professional development, subjectivation, and resistance to change 177--191 Jorryt van Bommel and Hanna Palmér Book Review: \booktitleBuilding the foundation: Whole numbers in the primary grades. Maria G. Bartolini Bussi and Xu Hua Sun (Eds.) (2018) The 23rd ICMI study --- new ICMI study series . . . . 193--199
Sophie Batchelor and Joke Torbeyns and Lieven Verschaffel Affect and mathematics in young children: an introduction . . . . . . . 201--209 Ann Dowker and Olivia Cheriton and Rachel Horton and Winifred Mark Relationships between attitudes and performance in young children's mathematics . . . . . . . . . . . . . . 211--230 Dominic Petronzi and Paul Staples and David Sheffield and Thomas E. Hunt and Sandra Fitton-Wilde Further development of the Children's Mathematics Anxiety Scale UK (CMAS-UK) for ages 4--7 years . . . . . . . . . . 231--249 Janne Lepola and Minna Hannula-Sormunen Spontaneous focusing on numerosity and motivational orientations as predictors of arithmetical skills from kindergarten to grade 2 . . . . . . . . . . . . . . . 251--269 Maria Chiara Passolunghi and Elisa Cargnelutti and Sandra Pellizzoni The relation between cognitive and emotional factors and arithmetic problem-solving . . . . . . . . . . . . 271--290 Pietro Di Martino Pupils' view of problems: the evolution from kindergarten to the end of primary school . . . . . . . . . . . . . . . . . 291--307 Markku S. Hannula Young learners' mathematics-related affect: A commentary on concepts, methods, and developmental trends . . . 309--316 Andreas Obersteiner Multiple pathways between affect and mathematical competence in young children--- commentary on the studies in the Special Issue . . . . . . . . . . . 317--323
Arthur Bakker A virtual special issue to celebrate 100 volumes of \booktitleEducational Studies in Mathematics: former editors' choices 1--5 Danny Beckers Why to publish on mathematics education so as to be useful? \booktitleEducational Studies in Mathematics and its founder Hans Freudenthal . . . . . . . . . . . . . . 7--17 Naneh Apkarian and Michal Tabach and Tommy Dreyfus and Chris Rasmussen The Sierpi\'nski smoothie: blending area and perimeter . . . . . . . . . . . . . 19--34 Rebecca Dibbs Forged in failure: engagement patterns for successful students repeating calculus . . . . . . . . . . . . . . . . 35--50 Jenni Ingram and Nick Andrews and Andrea Pitt When students offer explanations without the teacher explicitly asking them to 51--66 Uffe Thomas Jankvist and Morten Misfeldt and Mario Sánchez Aguilar What happens when CAS procedures are objectified? --- the case of ``solve'' and ``desolve'' . . . . . . . . . . . . 67--81 Andrew Izsák and Sybilla Beckmann Developing a coherent approach to multiplication and measurement . . . . . 83--103 Jean-Paul Fischer and Bruno Vilette and Sophie Joffredo-Lebrun and Mireille Morellato and Céline Le Normand and Calliste Scheibling-Seve and Jean-François Richard Should we continue to teach standard written algorithms for the arithmetical operations? The example of subtraction 105--121 Maike Schindler and Achim J. Lilienthal Domain-specific interpretation of eye tracking data: towards a refined use of the eye-mind hypothesis for the field of geometry . . . . . . . . . . . . . . . . 123--139
Einat Heyd-Metzuyanim and Mellony Graven Rituals and explorations in mathematical teaching and learning: introduction to the special issue . . . . . . . . . . . 141--151 Irit Lavie and Aya Steiner and Anna Sfard Routines we live by: from ritual to exploration . . . . . . . . . . . . . . 153--176 Alf Coles and Nathalie Sinclair Ritualisation in early number work . . . 177--194 Andrea McCloskey and Gwendolyn Lloyd and Courtney Lynch Theorizing mathematics instruction using ritual: tensions in teaching fractions in a fifth grade classroom . . . . . . . 195--213 Sally-Ann Robertson and Mellony Graven Exploratory mathematics talk in a second language: a sociolinguistic perspective 215--232 Olov Viirman and Elena Nardi Negotiating different disciplinary discourses: biology students' ritualized and exploratory participation in mathematical modeling activities . . . . 233--252 Talli Nachlieli and Michal Tabach Ritual-enabling opportunities-to-learn in mathematics classrooms . . . . . . . 253--271 Einat Heyd-Metzuyanim and Margaret Smith and Victoria Bill and Lauren B. Resnick From ritual to explorative participation in discourse-rich instructional practices: a case study of teacher learning through professional development . . . . . . . . . . . . . . 273--289 Jill Adler Learning about mathematics teaching and learning from studying rituals and ritualization? A commentary . . . . . . 291--299
Vilma Mesa and David Wagner Behind the door: a critical look at the process of publication in \booktitleEducational Studies in Mathematics . . . . . . . . . . . . . . 301--324 Wes Maciejewski and Jon R. Star Justifications for choices made in procedures . . . . . . . . . . . . . . . 325--340 Taro Fujita and Jonathan Doney and Rupert Wegerif Students' collaborative decision-making processes in defining and classifying quadrilaterals: a semiotic/dialogic approach . . . . . . . . . . . . . . . . 341--356 Thorsten Scheiner and Márcia M. F. Pinto Emerging perspectives in mathematical cognition: contextualizing, complementizing, and complexifying . . . 357--372 Alexandre Pais Mathematics, capitalism and biosocial research . . . . . . . . . . . . . . . . 373--386 Paola Iannone and Dominic Miller Guided notes for university mathematics and their impact on students' note-taking behaviour . . . . . . . . . 387--404 Der-Ching Yang Development of a three-tier number sense test for fifth-grade students . . . . . 405--424 Lisa Darragh and Luz Valoyes-Chávez Blurred lines: producing the mathematics student through discourses of special educational needs in the context of reform mathematics in Chile . . . . . . 425--439 Anke Grotlüschen and Klaus Buddeberg Book Review: Numeracy as social practice. Global and local perspectives. Keiko Yasukawa, Alan Rogers, Kara Jackson, & Brian V. Street (Eds.) (2018) \booktitleNumeracy: the new kid on the block? . . . . . . . . . . . . . . . . . 441--448
Arthur Bakker and Jinfa Cai and Lyn English and Gabriele Kaiser and Vilma Mesa and Wim Van Dooren Beyond small, medium, or large: points of consideration when interpreting effect sizes . . . . . . . . . . . . . . 1--8 Mogens Niss and Tomas Hòjgaard Mathematical competencies revisited . . 9--28 Eirini Geraniou and Uffe Thomas Jankvist Towards a definition of ``mathematical digital competency'' . . . . . . . . . . 29--45 Chronoula Voutsina and Lois George and Keith Jones Microgenetic analysis of young children's shifts of attention in arithmetic tasks: underlying dynamics of change in phases of seemingly stable task performance . . . . . . . . . . . . 47--74 Higinio Dominguez Theorizing reciprocal noticing with non-dominant students in mathematics . . 75--89 Maulfry Worthington and Marjolein Dobber and Bert van Oers The development of mathematical abstraction in the nursery . . . . . . . 91--110 Wolff-Michael Roth and Margaret Walshaw Affect and emotions in mathematics education: toward a holistic psychology of mathematics education . . . . . . . . 111--125 Lihua Xu and David Clarke Speaking or not speaking as a cultural practice: analysis of mathematics classroom discourse in Shanghai, Seoul, and Melbourne . . . . . . . . . . . . . 127--146 Mich\`ele Artigue Book review: \booktitleThe legacy of Felix Klein. H.-G. Weigand, W. McCallum, M. Menghini, M. Neubrand and G. Schubring (Eds.) (2019) . . . . . . . . 147--152
Jessica Brooke Ernest and Daniel L. Reinholz and Niral Shah Hidden competence: women's mathematical participation in public and private classroom spaces . . . . . . . . . . . . 153--172 Jinxin Zhu and Ming Ming Chiu Early home numeracy activities and later mathematics achievement: early numeracy, interest, and self-efficacy as mediators 173--191 Maria Blanton and Isil Isler-Baykal and Rena Stroud and Ana Stephens and Eric Knuth and Angela Murphy Gardiner Growth in children's understanding of generalizing and representing mathematical structure and relationships 193--219 Ali Barahmand ``Tending to the midpoint'': an intuitive rule in mathematical thinking 221--238 Hagar Gal When the use of cognitive conflict is ineffective --- problematic learning situations in geometry . . . . . . . . . 239--256 Nadia Azrou and Abdelkader Khelladi Why do students write poor proof texts? A case study on undergraduates' proof writing . . . . . . . . . . . . . . . . 257--274 Tânia C. B. Cabral and Roberto Ribeiro Baldino The credit system and the summative assessment splitting moment . . . . . . 275--288 Dongchen Zhao and Christian Bokhove Book Review: What is the most important source of teachers' knowledge? Lianghuo Fan (2014) \booktitleInvestigating the pedagogy of mathematics: how do teachers develop their knowledge? . . . . . . . . 289--298 Jérôme Proulx and Jean-François Maheux Effect sizes, epistemological issues, and identity of mathematics education research: a commentary on editorial 102(1) . . . . . . . . . . . . . . . . . 299--302
Katja Maass and Paul Cobb and Konrad Krainer and Despina Potari Different ways to implement innovative teaching approaches at scale . . . . . . 303--318 Daniel J. Heck and Courtney L. Plumley and Despina A. Stylianou and Adrienne A. Smith and Gwendolyn Moffett Scaling up innovative learning in mathematics: exploring the effect of different professional development approaches on teacher knowledge, beliefs, and instructional practice . . 319--342 Alison Clark-Wilson and Celia Hoyles A research-informed web-based professional development toolkit to support technology-enhanced mathematics teaching at scale . . . . . . . . . . . 343--359 Susanne Prediger and Claudia Fischer and Christoph Selter and Christian Schöber Combining material- and community-based implementation strategies for scaling up: the case of supporting low-achieving middle school students . . . . . . . . . 361--378 Andreas Ryve and Kirsti Hemmi Educational policy to improve mathematics instruction at scale: conceptualizing contextual factors . . . 379--394 Konrad Krainer and Stefan Zehetmeier and Barbara Hanfstingl and Franz Rauch and Tanja Tscheinig Insights into scaling up a nationwide learning and teaching initiative on various levels . . . . . . . . . . . . . 395--415 Despina Potari and Giorgos Psycharis and Charalampos Sakonidis and Theodossios Zachariades Collaborative design of a reform-oriented mathematics curriculum: contradictions and boundaries across teaching, research, and policy . . . . . 417--434 Paul Drijvers and Hanneke Kodde-Buitenhuis and Michiel Doorman Assessing mathematical thinking as part of curriculum reform in The Netherlands 435--456
Arthur Bakker Editorial . . . . . . . . . . . . . . . 1--5 Merrilyn Goos and Sila Kaya Understanding and promoting students' mathematical thinking: a review of research published in ESM . . . . . . . 7--25 Anne-Sophie Supply and Wim Van Dooren and Stephanie Lem and Patrick Onghena Assessing young children's ability to compare probabilities . . . . . . . . . 27--42 Kristen Lew and Juan Pablo Mejía Ramos Linguistic conventions of mathematical proof writing across pedagogical contexts . . . . . . . . . . . . . . . . 43--62 Kathleen Melhuish and Brittney Ellis and Michael D. Hicks Group theory students' perceptions of binary operation . . . . . . . . . . . . 63--81 Osama Swidan and Cristina Sabena and Ferdinando Arzarello Disclosure of mathematical relationships with a digital tool: a three layer-model of meaning . . . . . . . . . . . . . . . 83--101 Kathryn M. Rich Book Review: \booktitleDigital technologies in designing mathematics education tasks: Potential and pitfalls. Allen Leung and Anna Baccaglini--Frank (Eds.): (2017) . . . . . . . . . . . . . 103--108 Simon Goodchild Book Review: \booktitleThe philosophy of mathematics education today. Paul Ernest (Ed.) (2018) . . . . . . . . . . . . . . 109--119 Alik Palatnik A pedagogical potential of one mathematical inaccuracy . . . . . . . . 121--124 Adrian Simpson On the misinterpretation of effect size 125--133 Sally-Ann Robertson and Mellony Graven Correction to: Exploratory mathematics talk in a second language: a sociolinguistic perspective . . . . . . 135--135 Einat Heyd-Metzuyanim and Mellony Graven Correction to: Rituals and explorations in mathematical teaching and learning: introduction to the special issue . . . 137--137
Michal Tabach and Chris Rasmussen and Tommy Dreyfus and Naneh Apkarian Towards an argumentative grammar for networking: a case of coordinating two approaches . . . . . . . . . . . . . . . 139--155 Angelika Kullberg and Camilla Björklund and Irma Brkovic and Ulla Runesson Kempe Effects of learning addition and subtraction in preschool by making the first ten numbers and their relations visible with finger patterns . . . . . . 157--172 Elise Lockwood and John S. Caughman and Keith Weber An essay on proof, conviction, and explanation: multiple representation systems in combinatorics . . . . . . . . 173--189 Ioannis Papadopoulos and Robert Gunnarsson Exploring the way rational expressions trigger the use of ``mental'' brackets by primary school students . . . . . . . 191--207 Corinna Hankeln Mathematical modeling in Germany and France: a comparison of students' modeling processes . . . . . . . . . . . 209--229 Rachel Lambert and Paulo Tan Book review: David Kollosche, Renato de Souza, Michel Knigge, Miriam Godoy Penteado, and Ole Skovsmose (Eds.) (2019) \booktitleInclusive mathematics education: state-of-the-art research from Brazil and Germany . . . . . . . . 231--239 Xinrong Yang and Gabriele Kaiser Book Review: \booktitleProfessional development of mathematics teachers- an Asian perspective. Berinderjeet Kaur, Oh Nam Kwon, Yew Hoong Leong (Eds.) (2017) 241--249
Nadav Ehrenfeld and Ilana S. Horn Initiation-entry-focus-exit and participation: a framework for understanding teacher groupwork monitoring routines . . . . . . . . . . 251--272 María S. García González and Gustavo Martínez Sierra The history of a teacher's relief of his mathematics anxiety: the case of Diego 273--291 Calliste Scheibling-S\`eve and Elena Pasquinelli and Emmanuel Sander Assessing conceptual knowledge through solving arithmetic word problems . . . . 293--311 Paola Iannone and Christoph Czichowsky and Johannes Ruf The impact of high stakes oral performance assessment on students' approaches to learning: a case study . . 313--337 Cathrine Kazunga and Sarah Bansilal An APOS analysis of solving systems of equations using the inverse matrix method . . . . . . . . . . . . . . . . . 339--358 Melissa Andrade-Molina and Alex Montecino and Mario Sánchez Aguilar Beyond quality metrics: defying journal rankings as the philosopher's stone of mathematics education research . . . . . 359--374 Andreas Moutsios-Rentzos Book Review: Andreas J. Stylianides (2016), \booktitleProving in the elementary mathematics classroom . . . . 375--381 Marta Menghini Book Review: Digging into the memory of mathematics education. Fulvia Furinghetti, Alexander Karp (Eds.) (2018). \booktitleResearching the history of mathematics education. An international overview . . . . . . . . . 383--389
Arthur Bakker and David Wagner Pandemic: lessons for today and tomorrow? . . . . . . . . . . . . . . . 1--4 Gabrielle Oslington and Joanne Mulligan and Penny Van Bergen Third-graders' predictive reasoning strategies . . . . . . . . . . . . . . . 5--24 Andrea Maffia and Maria Alessandra Mariotti From action to symbols: giving meaning to the symbolic representation of the distributive law in primary school . . . 25--40 Anette Bagger and Helena Roos and Margareta Engvall Directions of intentionalities in special needs education in mathematics 41--63 Emily R. Fyfe and Percival G. Matthews and Eric Amsel College developmental math students' knowledge of the equal sign . . . . . . 65--85 Amy Ellis and Robert Ely and Brandon Singleton and Halil Tasova Scaling-continuous variation: supporting students' algebraic reasoning . . . . . 87--103 Yeon Kim Teacher community for high school mathematics instruction: strengths and challenges . . . . . . . . . . . . . . . 105--125 Thorsten Scheiner Dealing with opposing theoretical perspectives: knowledge in structures or knowledge in pieces? . . . . . . . . . . 127--145
Anselm R. Strohmaier and Kelsey J. MacKay and Andreas Obersteiner and Kristina M. Reiss Eye-tracking methodology in mathematics education research: A systematic literature review . . . . . . . . . . . 147--200 Osnat Molad and Esther S. Levenson and Sigal Levy Individual and group mathematical creativity among post-high school students . . . . . . . . . . . . . . . . 201--220 Sung-Jae Moon and Kyeong-Hwa Lee Deleuzian actualizations of the multiplicative concept: a study of perceptual flow and the transformation of learning assemblages . . . . . . . . 221--237 Aditya P. Adiredja and Michelle Zandieh The lived experience of linear algebra: a counter-story about women of color in mathematics . . . . . . . . . . . . . . 239--260 Ricardo Nemirovsky and Francesca Ferrara and Giulia Ferrari and Natividad Adamuz-Povedano Body motion, early algebra, and the colours of abstraction . . . . . . . . . 261--283 Anne R. Teppo Book Review: International and national reflections on The Netherlands didactics of mathematics education . . . . . . . . 285--298
David Wagner and Arthur Bakker and Tamsin Meaney and Vilma Mesa and Susanne Prediger and Wim Van Dooren What can we do against racism in mathematics education research? . . . . 299--311 Jennifer L. Ruef and Michelle M. Jacob and G. Keith Walker and Virginia R. Beavert Why indigenous languages matter for mathematics education: a case study of Ichishkíin . . . . . . . . . . . . . . . 313--332 Jennifer Langer-Osuna and Jen Munson and Emma Gargroetzi and Immanuel Williams and Rosa Chavez ``So what are we working on?'': how student authority relations shift during collaborative mathematics activity . . . 333--349 Kyunghee Moon New approaches for two-variable inequality graphs utilizing the Cartesian Connection and the APOS theory 351--367 Ulrika Ryan and Anna Chronaki A joke on precision? Revisiting ``precision'' in the school mathematics discourse . . . . . . . . . . . . . . . 369--384 Einat Heyd-Metzuyanim and Talli Nachlieli and Merav Weingarden and Rinat Baor Adapting a professional development program for cognitively demanding instruction across shifting contexts . . 385--403 Tine Degrande and Lieven Verschaffel and Wim Van Dooren To add or to multiply in open problems? Unraveling children's relational preference using a mixed-method approach 405--430 Kristín Bjarnadóttir Book Review: Approaching the core of the modern mathematics movement. Dirk De Bock and Geert Vanpaemel (Eds.) (2019) \booktitleRods, sets and arrows --- the rise and fall of modern mathematics in Belgium . . . . . . . . . . . . . . . . 431--438 Helena A. Grant Book Review: Keeping mathematics education real and fair: connecting the disconnections. Constantinos Xenofontos (Ed.) (2019) \booktitleEquity in mathematics education: addressing a changing world . . . . . . . . . . . . . 439--444
Joe Olsen and Kristen Lew and Keith Weber Metaphors for learning and doing mathematics in advanced mathematics lectures . . . . . . . . . . . . . . . . 1--17 Aslì Çakìr and Hatice Akkoç Examining socio-mathematical norms related to problem posing: a cas