DOCUMENT RESUME ED 427 972 SE 062 274 AUTHOR Olivier, Alwyn, Ed.; Newstead, Karen, Ed. TITLE Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (22nd, Stellenbosch, South Africa, July 12-17, 1998.) Volume 4. INSTITUTION International Group for the Psychology of Mathematics Education. ISSN ISSN-0771-100X PUB DATE 1998-00-00 NOTE 366p.; For volumes 1-3, see SE 062 271-273; for the 1998 conference, see ED 416 082-085. PUB TYPE Collected Works - Proceedings (021) EDRS PRICE MF01/PC15 Plus Postage. DESCRIPTORS Algebra; *Beliefs; Cultural Influences; Data Processing; Educational Change; Educational Research; Educational Technology; Elementary Secondary Education; Foreign Countries; Fractions; Functions (Mathematics); Geometry; Knowledge Base for Teaching; Learning Theories; *Mathematics Education; Number Concepts; *Problem Solving; Proof (Mathematics); *Social Influences; Spatial Ability; Statistics; *Student Attitudes; Teacher Education; Thinking Skills ABSTRACT The fourth volume of this proceedings contains 29 full research reports continuing on from Volume 3, 84 short oral communications (abstracts only) and 34 poster presentations (abstracts only) .The full papers include: (1) "Beliefs, Teacher Education and the History of Mathematics" (George N. Philippou and Constantinos Christou); (2) "Working Class Students and the Culture of Mathematics Classrooms in the UK" (Hilary Povey and Mark Boylan); (3) "The Co-ordination of Meanings for Randomness" (Dave Pratt and Richard Noss); (4) "Learning Obstacles in Differential Equations" (Chris L. Rasmussen); (5) "Images and Definitions for the Concept of Increasing/Decreasing Function" (Shakre Rasslan and Shlomo Vinner); (6) "Why Is Proof by Contradiction Difficult?" (David A. Reid and Joann Dobbin); (7) "Self-Efficacy Beliefs as Mediators in Math Learning: A Structural Model" (Martin Risnes); (8) "Teachers' Pedagogical Content Knowledge of Geometry" (Lynn Rossouw and Eddie Smith); (9) "Conviction, Explanation and Generic Examples" (Tim Rowland);(10) "Children's Multiplicative Problem-Solving Strategies in Real-World Situations" (Silke Ruwisch);(11) "National Tests: Educating Teachers about Their Children's Mathematical Thinking" (J.T. Ryan, J.S. Williams, and B.A. Doig);(12) "Patterns of Mathematical Misunderstanding Exhibited by Calculus Students in a Problem Solving Course" (Manuel Santos-Trigo);(13) "The Evolution of Mathematical Practices: How One First-Grade Classroom learned to measure." (Michelle Stephan and Paul Cobb); (14) "Conceptualizing Mathematics Teaching: The Role of Autonomy in Stimulating Teacher Reflection" (Peter Sullivan and Judith Mousley); (15) "Learning through Reflection with Mature, Low Attaining Students" (Malcolm Swan);(16) "Using Research into Children's Understanding of the Symmetry of Dice in Order to Develop a Model of How They Perceive the Concept of a Random ZGenerator" (John M. Truran); (17) "Students' Solutions of Inequalities" (Pessia Tsamir, Nava Almog, and Dina Tirosh); (18)"Do Equilateral Polygons Have Equal Angles?" (Pessia Tsamir, Dina Tirosh, and Ruth Stavy); (19) +++++ ED427972 Has Multi-page SFR---Level=1 +++++ "Meaningfully Assembling Mathematical Pieces: An Account of a Teacher in Transition" (Ron Tzur, Martin A. Simon, Karen Heinz, and Margaret Kinzel); (20) "Research Methods of the 'North' Revisited from the 'South'" (Paola Valero and Renuka Vithal); (21) "An Experiment in Developing Proof through Pattern" (Sue Waring, Anthony Orton, and Tom Roper); (22) "What Makes a Mathematical Performance Noteworthy in Informal Teacher Assessment?" (Anne Watson);(23) "Participating in Learning Mathematics through Shared Local Practices" (Peter Winbourne and Anne Watson);(24) "Intuitive Counting Strategies of 5-6 year old Children within a Transformational Arithmetic Framework" (David Womack and Julian Williams);(25) "Differences in Teaching for Conceptual Understanding of Mathematics" (Terry Wood); (26) "Children's Beginning Knowledge of Numerals and Its Relationship to Their Knowledge of Number Words: An Exploratory, Observational Study" (Bob Wright); (27)"A Study of Argumentation in a Second-Grade Mathematics Classroom" (Erna Yackel);(28) "Teacher Perceptions, Learned Helplessness and Mathematics Achievement" (Shirley M. Yates);(29) "Students' Understandings of the Role of Counter-Examples" (Orit Zaslavsky and Gila Ron). 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A Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education Volume 4 Editors: Alwyn Olivier and Karen Newstead University of Stellenbosch BEST COPY AVAILABLE Stellenbosch, South Africa 1998 3 Proceedings of the 22'd Conference of the International Group for the Psychology of Mathematics Education Volume 4 Published by the Program Committee of the 22nd PME Conference. Stellenbosch, South Africa Editors: Alwyn Olivier and Karen Newstead Faculty of Education The University of Stellenbosch Stellenbosch South Africa 7600 Fax: +27 21 887 2616 E-mail: [email protected] Copyright 1998 left to the individual authors ISSN 0771-100X 4 Printed by Kwik Kopy Printing Bellville, South Africa 4 - ii CONTENTS OF VOLUME 4 Research Reports (continued from Vol. 3) Philippou. George N. & Christou, Constantinos 4-1 Beliefs, teacher education and the history of mathematics Povey Hilary & Boylan, Mark 4-9 Working class students and the culture of mathematics classrooms in the UK Pratt. Dave & Noss, Richard 4-17 The co-ordination of meanings for randomness Rasmussen, Chris L. 4-25 Learning obstacles in differential equations Rasslan Shakre & Vinner, Shlomo 4-33 Images and definitions for the concept of increasing / decreasing function Reid. David A & Dobbin, Joann 4-41 Why is proof by contradiction difficult? Risnes, Martin 4-49 Self-efficacy beliefs as mediators in math learning: A structural model Rossouw. Lynn & Smith, Eddie 4-57 Teachers'pedagogical content knowledge of geometry Rowland, Tim 4-65 Conviction, explanation and generic examples Ruwisch, Silke 4-73 Children's multiplicative problem-solving strategies in real-world situations Ryan. J.T Williams, J.S. & Doig, B.A. 4-81 National tests: educating teachers about their children's mathematical thinking Santos-Trigo, Manuel 4-89 Patterns of mathematical misunderstanding exhibited by calculus students in a problem solving course Stephan Michelle & Cobb, Paul 4-97 The evolution of mathematical practices: How one first-grade classroom learned to measure Sullivan, Peter & Mousley, Judith 4-105 Conceptualising mathematics teaching: The role of autonomy in stimulating teacher reflection Swan, Malcolm 4-113 Learning through reflection with mature, low attaining students Truran, John M. 4-121 Using msearch into children's understanding of the symmetry of dice in order to develop a model of how they perceive the concept of a random generator Tsamir, Pessia; Alimg,ligya & Tirosh, Dina 4-129 Students' solutions of inequalities Tsamir. Pessia. Tirosh, Dina & Stavy, Ruth 4-137 Do equilateral polygons have equal angles? Tzur. Ron; Simon, Martin A.; Heinz, Karen & Kinzel, Margaret 4-145 Meaningfully assembling mathematical pieces: An account ofa teacher in transition 4-ui 5 Valeib, Paola & Vithal, Renuka 4-153 Research methods of the "north" revisited from the "south" Waring, Sue. Orton. Anthony & Roper, Tom 4-161 An experiment in developing proof through pattern Watson, Anne 4-169 What makes a mathematical performance noteworthy in informal teacher assessment? Winbourne Peter & Watson, Anne 4-177 Participating in learning mathematics through shared local practices Womack. David & Williams, Julian 4-185 Intuitive counting strategies of 5-6 year old children within a transfonnational arithmetic framework Wood, Terry 4-193 Differences in teaching for conceptual understanding of mathematics Wright, Bob 4-201 Children's beginning knowledge of numerals and its relationship to their knowledge of number words: An exploratory, observational study Yackel, Erna 4-209 A study of argumentation in a second-grade mathematics classroom Yates, Shirley M. 4-217 Teacher perceptions, learned helplessness and mathematics achievement Zaslavsky Orit & Ron, Gila 4-225 Students' understandings of the role of counter-examples Short Oral Communications Aharoni, Dan & Vile, Adam 4-235 Quo vadis? - The "AC-arrow" in data-structures learning compared to mathematics learning Benson, Alexis P. & Harnisch, Delwyn L. 4-236 The relation between algebra students' mathematics anxiety and their college entrance exams BergerMargot 4-237 Graphic calculators: An interpretative framework Wenner, Mary E. 4-238 Encouraging everyday cognition in the classroom Broekmann, Irene 4-239 The Ratlor