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ED489597.Pdf The 28th International Conference Of the International Group for the Psychology of Mathematics Education Volume 4 14–18 July 2004 Bergen, Norway The 28th International Conference of the International Group for the Psychology of Mathematics Education, Volume 4, Bergen, Norway 14–18 July 2004 Table of Content Research Reports – Full-Text p01-08 Situated or Abstract: The Effect of Combining Context and Structure on Constructing an Additive (Part-Part-Whole) Schema (Irit Peled; Ruth Meron) p09-16 Using Graphical Profiles to Study the Learning and Teaching of Mathematics (Dvora Peretz) p17-24 The Role of Number in Proportional Reasoning: A Prospective Teacher’s Understanding (Axelle C. Person; Sarah B. Berenson; Paula J. Greenspon) p25-32 Learning to Use CAS: Voices from a Classroom (Robyn Pierce; Kaye Stacey) p33-40 Technical School Students´ Conceptions of Tangent Lines (Márcia Maria Fusaro Pinto; Valéria Guimarães Moreira) p41-48 Elementary School Students’ Mental Representations of Fractions (Demetra Pitta-Pantazi; Eddie M. Gray; Constantinos Christou) p49-56 A Structural Model for Problem Posing (Pittalis, M.; Christou, C.; Mousoulides, N.; Pitta-Pantazi, D.) p57-64 Some Undergraduates' Experiences of Learning Mathematics (Hilary Povey; Corinne Angier) p65-72 Normalising Geometrical Constructions: A Context for the Generation of Meanings for Ratio and Proportion (Psycharis, Georgos; Kynigos, Chronis) p73-80 The Sensual and the Conceptual: Artefact-Mediated Kinesthetic Actions and Semiotic Activity (Luis Radford; Serge Demers; José Guzmán; Michele Cerulli) P81-88 A Sociocultural Account of Students’ Collective Mathematical Understanding of Polynomial Inequalities in Instrumented Activity (Ferdinand Rivera; Joanne Rossi Becker) p89-96 Infinity as a Multi-Faceted Concept in History and in the Mathematics Classroom (Ornella Robutti; Ferdinando Arzarello; Maria G. Bartolini Bussi) p97-104 Successful Undergraduate Mathematicans: A Study of Students in Two Universities (Melissa Rodd; Margaret Brown) ii The 28th International Conference of the International Group for the Psychology of Mathematics Education, Volume 4, Bergen, Norway 14–18 July 2004 Research Reports - Full-Text p105-112 Bilingual Lessons and Mathematical World Views – A German Perspective (Katrin Rolka) p113-120 The Use of Models in Teaching Proof by Mathematical Induction (Gila Ron; Tommy Dreyfus) p121-128 Reflecting on Prospective Elementary Teachers’ Mathematics Content Knowledge: The Case of Laura (Tim Rowland; Peter Huckstep; Anne Thwaites) p129-136 The Competent Use of the Analytic Method in the Solution of Algebraic Word Problems. A Didactical Model Based on a Numerical Approach with Junior High Students (Guillermo Rubio; Rafael Del Valle) p137-144 Language and Concept Development in Geometry (Frode Rønning) p145-152 The Role of Gestures in Conceptualisation: An Exploratory Study on the Integral Function (Cristina Sabena) p153-160 Psychological Aspects of Genetic Approach to Teaching Mathematics (Ildar S. Safuanov) p161-168 Routines in Non-Routine Problem Solving Processes (Wolfgang Schloeglmann) p169-176 Teacher Guidance of Knowledge Construction (Baruch Schwarz; Tommy Dreyfus; Nurit Hadas; Rina Hershkowitz) p177-184 Types of Student Reasoning on Sampling Tasks (J. Michael Shaughnessy; Matt Ciancetta; Dan Canada) p185-192 Didactic Model – Bridging a Concept with Phenomena (Beba Shternberg; Michal Yerushalmy) p193-200 Elaborating the Teacher’s Role – Towards a Professional Language (Dianne Siemon; Jo Virgona; Maria Lasso; Vanessa Parsons; Juli Cathcart) P201-208 Making the Connection: Procedural and Conceptual Students’ Use of Linking Words in Solving Problems (Adrian Simpson; Nora Zakaria) p209-216 Children’s Conceptual Understanding of Counting (Slovin, Hannah; Dougherty, Barbara J.) p217-224 Adding Fractions Using ‘Half’ as an Anchor for Reasoning (Alina Galvão Spinillo; Maria Soraia Silva Cruz) iii The 28th International Conference of the International Group for the Psychology of Mathematics Education, Volume 4, Bergen, Norway 14–18 July 2004 Research Reports - Full-Text p225-232 Persistence of Decimal Misconceptions and Readiness to Move to Expertise (Vicki Steinle; Kaye Stacey) p233-240 Molly and Equations in A2: A Case Study of Apprehending Structure (Nada Stehlíková; Adrian Simpson) p241-248 Image - Metaphor - Diagram: Visualisation in Learning Mathematics (Rudolf Sträßer; Gert Kadunz) p249-256 Images of Fractions As Processes and Images of Fractions In Processes (Marek Sulista; Jan Herman; Lucia Ilucova; Veronika Kremsova; Jiri Pribyl; Janka Ruppeldtova; Adrian Simpson; Nada Stehlikova; Michaela Ulrychova) p257-264 Describing Elements of Mathematics Lessons that Accommodate Diversity in Student Background (Peter Sullivan; Judy Mousley; Robyn Zevenbergen) p265-272 Orchestrating Mathematical Proof Through the Use of Digital Tools (Rosamund Sutherland; Federica Olivero; Marnie Weeden)) p273-280 School-Based Community of Teachers and Outcomes for Students (Paola Sztajn; Martha Alexsaht-Snider; Dorothy Y. White; Amy Hackenberg) p281-288 Thinking Through Three Worlds of Mathematics (David Tall) p289-296 The Effect of Students’ Roles on the Establishment of Shared Meanings During Problem Solving (Konstantinos Tatsis; Eugenia Koleza) p297-304 Integrating CAS Calculators Into Mathematics Learning: Partnership Issues (Michael O. J. Thomas; Ye Yoon Hong) p305-312 The Development of Structure in the Number System (Noel Thomas) p313-320 Orientations to Numeracy: Teachers’ Confidence and Disposition to Use Mathematics Across the Curriculum (Steve Thornton; John Hogan) p321-328 Efficiency and Adaptiveness of Multiple School-Taught Strategies in the Domain of Simple Addition (Joke Torbeyns; Lieven Verschaffel; Pol Ghesquière)) p329-336 Supporting Teachers on Developing Teaching Norms Based on Children’s Learning Mathematics (Wen-Huan Tsai) p337-344 Prospective Teachers’ Images and Definitions: The Case of Inflection Points (Pessia Tsamir; Regina Ovodenko p345-352 Fostering Mathematical Meaning Via Scientific Inquiry: A Case Study (Ron Tzur; Rita A. Hagevik; Mary E. Watson) iv The 28th International Conference of the International Group for the Psychology of Mathematics Education, Volume 4, Bergen, Norway 14–18 July 2004 Research Reports - Full-Text p353-360 Students Building Isomorphisms (Elizabeth B. Uptegrove; Carolyn A. Maher) p361-368 How Do High School Students Interpret Parameters in Algebra? (Sonia Ursini; María Trigueros) p369-376 Causes Underlying Pre-Service Teachers’ Negative Beliefs and Anxieties About Mathematics (Liisa Uusimaki; Rod Nason) p377-384 Fractions in Adult’s Elementary School: The Case of Lucina (Marta Elena Valdemoros- Alvarez) p385-392 Students’ Overreliance on Proportionality: Evidence from Primary School Pupils Solving Arithmetic Word Problems (Wim Van Dooren; Dirk De Bock; An Hessels; Dirk Janssens; Lieven Verschaffel) p393-400 From Functions to Equations: Introduction of Algebraic Thinking to 13 Year-Old Students (Petros Verikios; Vasiliki Farmaki; Nikos Klaoudatos) P401-408 Critical Awareness of Voice in Mathematics Classroom Discourse: Learning the Steps in the ‘Dance of Agency’ (David Wagner) p409-416 Metaphors and Cultural Models Afford Communication Repairs of Breakdowns Between Mathematical Discourses (G.D. Wake; J.S. Williams) p417-424 Generalising Arithmetic: Supporting the Process in the Early Years (Elizabeth Warren) p425-432 A Framework for Describing the Processes that Undergraduates Use to Construct Proofs (Weber, Keith) p433-440 The Nature of Spontaneity in High Quality Mathematics Learning Experiences (Gaye Williams) p441-448 Spreadsheet Generalising and Paper and Pencil Generalising (Wilson, Kirsty; Ainley, Janet; Bills, Liz) p449-456 A Comparison of a Visual-Spatial Approach and a Verbal Approach to Teaching Mathematics (Woolner, Pamela) p457-464 Differentiation of Students’ Reasoning on Linear and Quadratic Geometric Number Patterns (Kai-Lin Yang; Fou-Lai Lin) p465-472 Map Construction as a Context for Studying the Notion of Variable Scale (Nikoleta Yiannoutsou; Chronis Kynigos) v The 28th International Conference of the International Group for the Psychology of Mathematics Education, Volume 4, Bergen, Norway 14–18 July 2004 Research Reports - Full-Text p473-480 Understanding How the Concept of Fractions Develops: A Vygotskian Perspective (Kaori Yoshida) p481-488 Secondary Mathematics Teachers’ Knowledge Concerning the Concept of Limit and Continuity (Zachariades, T.; Mastorides, E.) p489-496 Characteristics of Mathematical Problem Solving Tutoring in an Informal Setting (Orit Zaslavsky; Iris Zodik) p497-504 Making Sense of Irrational Numbers: Focusing on Representation (Rina Zazkis; Natasa Sirotic) p505-512 Numeracy Practices of Young Workers (Robyn Zevenbergen; Kelly Zevenbergen) vi SITUATED OR ABSTRACT: THE EFFECT OF COMBINING CONTEXT AND STRUCTURE ON CONSTRUCTING AN ADDITIVE (PART-PART-WHOLE) SCHEMA Ruth Meron and Irit Peled University of Haifa, Israel This study investigated the development of an additive schema from the perspective of the schema's flexibility in coping with new context and unfamiliar semantic structure. It followed 27 first graders who learned addition and subtraction using an experimental curriculum. The instruction involved a didactical model combining the context of two stories with a structured part-part-whole schema. In addition to collecting data from the whole class, eight children were individually interviewed. The development of their additive structure was examined by comparing the
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