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Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education Volume 2

Editors Helen L. Chick Jill L. Vincent

University of Melbourne Australia 3010

The Proceedings are also available on CD-ROM and on-line at http://onlinedb.terc.edu

Copyright © 2005 left to the authors All rightsreserved ISSN 0771-100X

Cover Design and Logo: Helen Chick Printing: Design and Print Centre, University of Melbourne

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TABLE OF CONTENTS
VOLUME 2 Research Reports Adler, Jill & Davis, Zain & Kazima, Mercy & Parker, Diane & Webb, Lyn Working with learners’ mathematics: Exploring a key element of mathematical knowledge for teaching Afantiti-Lamprianou, Thekla & Williams,Julian S. & Lamprianou, Iasonas A comparison between teachers’ and pupils’ tendency to use a representativeness heuristic Ainley, Janet G. & Bills, Liz & Wilson, Kirsty Purposeful task design and the emergence of transparency Alatorre, Silvia & Figueras, Olimpia A developmental model for proportional reasoning in ratio comparison tasks Alcock, Lara & Weber, Keith Referential and syntacticapproaches to proof: Case studies from a transition course Alexandrou-Leonidou, Vassiliki & Philippou, George N. Teachers’ beliefs about students’ development of the prealgebraic concept of equation Amato, Solange Amorim Developing students’ understanding of the concept of fractions as numbers Amit, Miriam & Fried, Michael N. Multiple representations in 8th grade algebra lessons: Are learners reallygetting it? Anderson, Judy & Bobis, Janette Reform-oriented teaching practices: A survey of primary school teachers 2-1

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Arzarello, Ferdinando & Ferrara, Francesca & Robutti, Ornella & Paola, Domingo The genesis of signs by gestures. The case of Gustavo Asghari, Amir H. & Tall, David Students’ experience ofequivalence relations, a phenomenographic approach Aspinwall, Leslie & Shaw, Kenneth L. & Unal, Hasan How series problems integrating geometric and arithmetic schemes influenced prospective secondary teachers pedagogical understanding Baber, Sikunder Ali & Dahl, Bettina Dealing with learning in practice: Tools for managing the complexity of teaching and learning Baldino, Roberto R. & Cabral, Tania C. B.Situations of psychological cognitive no-growth Ball, Lynda & Stacey, Kaye Good CAS written records: Insight from teachers Banerjee, Rakhi & Subramaniam, K. Developing procedure and structure sense of arithmetic expressions Bardini, Caroline & Radford, Luis & Sabena, Cristina Struggling with variables, parameters, and indeterminate objects or how to go insane in mathematics Barnes, Mary Exploringhow power is enacted in small groups Barwell, Richard A framework for the comparison of PME research into multilingual mathematics education in different sociolinguistic settings Berger, Margot Vygotsky’s theory of concept formation and mathematics education

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Beswick, Kim Preserviceteachers’ understandings of relational and instrumental understanding Borba, Marcelo C. The transformation of mathematics in on-line courses Brodie, Karin Using cognitive and situated perspectives to understand teacher interactions with learner errors Brown, Jill P. Identification of affordances of a technology-rich teaching and learning environment (TRTLE) Bulmer, Michael & Rolka, Katrin The“A4-project”: Statistical world views expressed through pictures Callingham, Rosemary A whole-school approach to developing mental computation strategies Cao, Zhongjun & Forgasz, Helen & Bishop, Alan A comparison of perceived parental influence on mathematics learning among students in China and Australia Chan, Kah Yein & Mousley, Judith Using word problems in Malaysian mathematics education: Looking...