DOCUMENT RESUME ED 427 970 SE 062 272 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 2. INSTITUTION International Group for the Psychology of Mathematics Education. ISSN ISSN-0771-100X PUB DATE 1998-00-00 NOTE 360p.; For volumes 1-4, see SE 062 271-274; 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 second volume of this proceedings contains the first portion of the research reports. Papers include: (1) "Learning Algebraic Strategies Using a Computerized Balance Model" (James Aczel); (2) "Children's Perception of Multiplicative Structure in Diagrams" (Bjornar Alseth); (3) "A Discussion of Different Approaches to Arithmetic Teaching" (Julia Anghileri); (4) "A Model for Analyzing the Transition to Formal Proofs in Geometry" (Ferdinando Arzarello, Chiara Micheletti, Federica Olivero, Ornella Robutti, and Domingo Paola);(5) "Dragging in Cabri and Modalities of Transition from Conjectures to Proofs in Geometry" (Ferdinando Arzarello, Chiara Micheletti, Federica Olivero, Ornella Robutti, Domingo Paola, and Gemma Gallino); (6) "The Co-Construction of Mathematical Knowledge: The Effect of an Intervention Program on Primary Pupils' Attainment" (Mike Askew, Tamara Bibby, and Margaret Brown); (7) "Dialectical Proof: Should We Teach It to Physics Students?" (Roberto Ribeiro Baldino); (8) "Lacan and the School's Credit System" (Roberto Ribeiro Baldino and Tania Cristina Baptista Cabral); (9) "Which Is the Shape of an Ellipse? A Cognitive Analysis of an Historical Debate" (Maria G. Bartolini Bussi and Maria Alessandra Mariotti); (10) "Children's Understanding of the Decimal Numbers through the Use of the Ruler" (Milena Basso, Cinzia Bonotto, and Paolo Sozio);(11) "Construction of Multiplicative Abstract Schema for Decimal-Number Numeration" (Annette R. Baturo and Tom J. Cooper);(12) "Classroom-Based Research to Evaluate a Model Staff Development Project in Mathematics" (Joanne Rossi Becker and Barbara J. Pence); (13) "Some Misconceptions Underlying First-Year Students' Understanding of 'Average Rate' and of 'Average Value'" (Jan Bezuidenhout, Piet Human, and Alwyn Olivier);(14) "Operable Definitions in Advanced Mathematics: The Case of the Least Upper Bound" (Liz Bills and David Tall); (15) "Beyond 'Street' Mathematics: The Challenge of Situated Cognition" (Jo Boaler); (16) "The 'Voices and Echoes Game' and the Interiorization of Crucial Aspects of Theoretical Knowledge in a Vygotskian Perspective: Ongoing +++++ ED427970 Has Multi-page SFR---Level=1 +++++ Research" (Paolo Boero, Bettina Pedemonte, Elisabetta Robotti, and Giampaolo Chiappini); (17) "Children's Construction of Initial Fraction Concepts" (George Booker);(18) "Graphing Calculators and Reorganization of Thinking: The Transition from Functions to Derivative" (Marcelo C. Borba and Monica E. Villarreal);(19) "Pre-Algebra: A Cognitive Perspective" (G.M. Boulton-Lewis, T. Cooper, B. Atweh, H. Pillay, and L. Wilss);(20)"The Right Baggage?" (Mary Briggs);(21) "Learner-Centered Teaching and Possibilities for Learning in South African Mathematics Classrooms" (Karin Brodie); (22) "Researching Transition in Mathematical Learning" (Tony Brown, Frank Eade, and Dave Wilson);(23) "Metaphor as Tool in Facilitating Preservice Teacher Development in Mathematical Problem Solving" (Olive Chapman); (24) "Restructuring Conceptual and Procedural Knowledge for Problem Representation" (Mohan Chinnappan); (25) "The Structure of Students' Beliefs towards the Teaching of Mathematics: Proposing and Testing a Structural Model" (Constantinos Christou and George N. Philippou); (26) "Abstract Schema versus Computational Proficiency in Percent Problem Solving" (Tom J. Cooper, Annette R. Baturo, and Shelley Dole);(27) "Implicit Cognitive Work in Putting Word Problems into Equation Form" (Anibal Cortes);(28) "Three Sides Equal Means It Is Not Isosceles" (Penelope Currie and John Pegg); (29) "Making Sense of Sine and Cosine Functions through Alternative Approaches: Computer and 'Experimental World' Contexts" (Nielce Lobo Da Costa and Sandra Magina);(30) "Teacher and Students' Flexible Thinking in Mathematics: Some Relations" (Maria Manuela M.S. David and Maria da Penha Lopes);(31) "The Influence of Metacognitive and Visual Scaffolds on the Predominance of the Linear Model" (Dirk De Bock, Lieven Verschaffel, and Dirk Janssens); (32)"To Teach Definitions in Geometry or Teach To Define?" (Michael De Villiers); (33) "Student thinking about Models of Growth and Decay" (Helen M. Doerr); (34) "Analysis of a Long Term Construction of the Angle Concept in the Field of Experience of Sunshadows" (Nadia Douek);(35) "On Verbal Addition and Subtraction in Mozambican Bantu Languages" (Jan Draisma);(36) "Teachers' Beliefs and the 'Problem' of the Social" (Paula Ensor);(37) "From Number Patterns to Algebra: A Cognitive Reflection on a Cape Flats Experience" (Clyde B.A. Felix); (38)"Affective Dimensions and Tertiary Mathematics Students" (Helen J. Forgasz and Gilah C. Leder);(39) "Social Class Inequalities in Mathematics Achievement: A Multilevel Analysis of T1MSS South Africa Data" (George Frempong); (40) "Context Influence on Mathematical Reasoning" (Fulvia Furinghetti and Domingo Paola); (41) "What Do They Really Think? What Students Think about the Median and Bisector of an Angle in the Triangle, What They Say and What Their Teachers Know about It" (Hagar Gal); (42) "Levels of Generalization in Linear Patterns" (Juan Antonio Garcia-Cruz and Antonio Martinon); (43) "The Evolution of Pupils' Ideas of Construction and Proof Using Hand-Held Dynamic Geometry Technology" (John Gardiner and Brian Hudson); and (44) "Cognitive Unity of Theorems and Difficulty of Proof" (Rosella Garuti, Paolo Boero, and Enrica Lemut). (ASK) ******************************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. ******************************************************************************** alb Mb U S DEPARTMENT OF EDUCATION Office of Educahonal Research and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced,as 1 awed from the person or organization originating it PERMISSION TO REPRODUCE AND O Minor changes have been made to DISSEMINATETHIS MATERIAL HAS improve reproduction quality BEEN GRANTED BY Points of view or opinions stated in this document do not necessarily represent official OERI position or policy TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) 1 k 1247 July 1998 \1%11tItosch, southAl%41 BEST COPY AVAILABLE - - Proceedings of the 22nd Conference of the International Group for the PsyChology of Mathematics Education Volume 2 Editors: Alwyrraiutérand Karen Newstead University of Si&enbosch Stellenbosch, South Africa BEST COPY AVAILABLE 1998 Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education Volume 2 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 Printed by Kwik Kopy Printing Bellville, South Africa 2 - ii CONTENTS OF VOLUME 2 Research Reports Aczel, James 2-1 Learning algebraic strategies using a computerised balance model Alseth, Bjornar 2-9 Children's perception of multiplicative structure in diagrams Anghileri, Julia 2-17 A discussion of different approaches to arithmetic teaching Arzarello. Ferdinando; Micheletti, Chiara; Olivero, Federica; Robutti, Omella & Paola, Domingo 2-24 A model for analysing the transition to formal proofs in geometry Arzarello, Ferdinando; Micheletti, Chiara; Olivero. Federica; Robutti, Ornella; Paola, Domingo & Gallino, Gemma 2-32 Dragging in Cabri and modalities of transition from conjectures to proofs in geometry akeLvAElie; Bibby, Tamara & Brown, Margaret 2-40 The co-construction of mathematical knowledge: The effect of an intervention programme on primary pupils' attainment Baldino, Roberto Ribeiro 2-48 Dialectical proof: Should we teach it to physics students? Baldino, Roberto Ribeiro & Cabral. Tânia Cristina Baptista 2-56 Lacan and the school's credit system Bartolini Bussi. Maria G, & Mariotti, Maria Alessandra 2-64 Vl/hich is the shape of an ellipse? A cognitive analysis of an historical debate Basso, Milena; Bonotto, Cinzia & Sorzio. Paolo 2-72 Children's understanding of the decimal numbers through the use of the ruler Baturo. Annette R. & Cooper, Tom J. 2-80 Construction of multiplicative abstract schema for decimal-number numeration Becker. Joanne Rossi & Pence, Barbara J. 2-88 Classroom-based research to evaluate a model staff development project in mathematics Bezuidenhout. Jan; Human, Piet & Olivier, Alwyn 2-96