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Mathematics Education and Society – MES 1-197 Coordinators: Gates, Peter & Zevenbergen, Robyn Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education Prague, Czech Republic July 16-21, 2006 Volume 1 Plenaries, Research Forums, Discussion Groups, Working Session, Short Oral Communications, Posters Editors: Jarmila Novotná Hana Moraová, Magdalena Krátká, Naďa Stehlíková Charles University in Prague Faculty of Education Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education Volume 1 Editors Jarmila Novotná Hana Moraová Magdalena Krátká Naďa Stehlíková Charles University in Prague Faculty of Education Czech Republic The Proceedings are also available on CD-ROM Copyright © 2006 left to the authors All rights reserved ISSN 0771-100X Logo: Ivan Špirk Cover Design: Jarmila Novotná & Ivan Špirk Printing: Atelier Guimaec, s.r.o 1 - ii PME30 — 2006 TABLE OF CONTENTS VOLUME 1 Table of Contents 1-iii Introduction 1-xlvii Welcome 1-xxxiii The International Group for the Psychology of Mathematics 1-lvii Education Proceedings of previous PME conferences 1-lix The review process of PME30 1-lxi List of PME30 reviewers 1-lxii Index of presentations by research domains 1-lxvi List of authors 1-lxix Plenary Lectures Brousseau, Guy 1-3 Mathematics, didactical engineering and observation Presmeg, Norma 1-19 A semiotic view of the role of imagery and Inscriptions in mathematics teaching and learning Štech, Stanislav 1-35 School mathematics as a developmental activity Tsamir, Pessia & Tirosh, Dina 1-49 PME 1 to 30 – Summing up and looking ahead: A personal perspective on infinite sets PME30 — 2006 1- iii Plenary Panel Lins, Romulo (Panel coordinator) 1-67 A centre and a mathematics Gooya, Zahra 1-73 The necessity of collaborations between mathematicians and mathematics educators: Way to have “Mathematics is the center” Groves, Susie 1-77 Generic versus subject specific pedagogy – Should mathematics be in the centre? Krainer, Konrad 1-84 How can schools put mathematics in their centre? Improvement = content + community + context Rojano, Teresa 1-90 Mathematics in the centre: The case of specific didactics Research Forums RF01 Teachers researching with university academics 1-95 Coordinators: Novotná, Jarmila & Zack, Vicki & Rosen, Gershon & Lebethe, Agatha & Brown, Laurinda & Breen, Chris Brown, Laurinda & Coles, Alf 1-96 Seeing more and differently – telling stories: Collaborative research on mathematics teaching and learning Hošpesová, Alena & Macháčková, Jana & Tichá, Marie 1-99 Joint reflection as a way to cooperation between researchers and teachers Lebethe, Agatha & Eddy, Neil & Bennie, Kendal 1-103 Opening the space of possibilities: Tales from three teachers Novotná, Jarmila & Pelantová, Alena 1-106 Diverse roles, shared responsibility Poirier, Louise 1-109 Research with teachers: the model of collaborative research: Study of joint development mechanisms for an approach to the teaching of mathematics to Inuit children in Kindergarten and Primary grades 1 and 2 1 - iv PME30 — 2006 Rosen, Gershon 1-112 Developing a voice Zack, Vicki & Reid, David 1-116 Learning about mathematics and about mathematics learning through and in collaboration RF02 Exemplification: The use of examples in teaching and learning 1-125 mathematics Coordinators: Bills, Liz & Mason, John & Watson, Anne & Zaslavsky, Orit Additional Contributors: Goldenberg, Paul & Rowland, Tim & Zazkis, Rina Bills, Liz & Dreyfus, Tommy & Mason, John & Tsamir, Pessia & 1-126 Watson, Anne & Zaslavsky, Orit Exemplification in mathematics education RF03 The conceptual change approach in the learning and teaching 1-155 of mathematics: An introduction Coordinator: Vosniadou, Stella Tirosh, Dina & Tsamir, Pessia 1-159 Conceptual change in mathematics learning: The case of infinite sets Vamvakoussi, Xenia & Vosniadou, Stella 1-161 Aspects of students’ understanding of rational numbers Merenluoto, Kaarina & Lehtinen, Erno 1-163 Conceptual change in the number concept: Dealing with continuity and limit Van Dooren, Wim & De Bock, Dirk & Verschaffel, Lieven 1-165 The linear imperative: Searching for the roots and the impact of the over-use of proportionality Biza, Irene & Zachariades, Theodossios 1-168 Conceptual change in advanced mathematical thinking: The case of tangent line PME30 — 2006 1 - v Christou, Konstantinos P. & Vosniadou, Stella 1-170 Students’ interpretation of the use of literal symbols in algebra – A conceptual change approach Resnick, Lauren B. 1-173 The dilemma of mathematical intuition in learning Greer, Brian 1-175 Designing for conceptual change Discussion Groups DG01 Abstraction in mathematics learning 1-187 Coordinators: Mitchelmore, Michael & Ozmantar, Mehmet Fatih & White, Paul DG02 Indigenous communities and mathematics education: Research 1-188 issues and findings Coordinators: Baturo, Annette & Amit, Miriam & Lee, Hsiu-Fei DG03 Participation, thought and language in the context of mathematics 1-189 education (2nd year) Coordinators: da Rocha Falcão, Jorge Tarcísio & Frade, Cristina & Lins, Romulo & Meira, Luciano & Winbourne, Peter DG04 Facilitating teacher change 1-190 Coordinators: Hannula, Markku S. & Sullivan, Peter DG05 Troubling learners’ and teachers’ relationships with 1-191 mathematics: Theoretical perspectives on researching learning mathematics Coordinators: Cotton, Tony & Hardy, Tansy & Mendick, Heather & Povey, Hilary & Walshaw, Margaret & Hanley, Una DG06 Towards new perspectives and new methodologies for the use of 1-192 technology in mathematics education Coordinators: Lins, Bibi & Giraldo, Victor & Carvalho, Luiz Mariano & Edwards, Laurie DG07 The mathematics textbook – A critical artefact? 1-193 Coordinators: Pepin, Birgit & Grevholm, Barbro & Straessser, Rudolf 1 - vi PME30 — 2006 DG08 Argumentation and mathematics education: Some unifying 1-194 thoughts Coordinators: Schwarz, Baruch & Boero, Paolo DG09 Mathematics and gender: Setting research agendas 1-195 Coordinators: Steinthorsdottir, Olof Bjorg & Rossi Becker, Joanne & Forgasz, Helen DG10 Learners learning through their own activity: Multiple 1-196 perspectives Coordinators: Simon, Martin A. & Dougherty, Barbara DG11 Mathematics education and society – MES 1-197 Coordinators: Gates, Peter & Zevenbergen, Robyn Working Sessions WS01 Designing mathematical research-situations for the classroom 1-201 Coordinators: Knoll, Eva & Ouvrier-Buffet, Cécile WS02 COSIMA – An opportunity for mathematical communication 1-202 Coordinators: Cockburn, Anne D. & Peter-Koop, Andrea WS03 What is effective mathematics teaching? East meets West 1-203 Coordinators: Cai, Jinfa & Perry, Bob & Ying, Wong Ngai & Kaiser, Gabrielle & Maass, Katja WS04 Gesture, multimodality, and embodiment in mathematics 1-204 Coordinators: Edwards, Laurie & Robutti, Ornella & Bolite Frant, Janete WS05 Teaching and learning mathematics in multilingual classrooms 1-205 Coordinators: Barwell, Richard & Civil, Marta & Díez-Palomar, Javier & Moschkovich, Judit & Planas, Núria & Setati, Mamokgethi WS06 Complexity research and mathematics education 1-206 Coordinators: Davis, Brent & Simmt, Elaine & Sumara, Dennis PME30 — 2006 1 - vii WS07 Purposeful professional development for mathematics teacher 1-207 educators Coordinators: McMahon, Teresa & Sztajn, Paola & Ghousseini, Hala & Loewenberg Ball, Deborah WS08 Intuitive vs. analytical thinking: A view from cognitive psychology 1-208 Coordinators: Ejersbo, Lisser Rye & Inglis, Matthew & Leron, Uri Short Oral Communications Abar, Celina A. A. P. & de Assis, Leila Souto 1-211 The mathematics teachers’ conceptions about the possible uses of learning objects from RIVED-Brazil project Abdul-Rahman, Shafia 1-212 On the way to understanding integration Abu-Naja, Muhammad & Amit, Miriam 1-213 The impact of graphic-calculator use on Bedouin students’ learning functions Alagic, Mara 1-214 How to put it all together? Redesigning learning activities to meet the needs of elementary teacher candidates Anku, Sitsofe E. 1-215 Reading mathematics textbook as a storybook Arnau, David & Puig, Luis 1-216 Naming and referring to quantities when solving word problems in a spreadsheet environment Back, Jenni 1-217 If it divides by 4, it must divide by 8: Argument and argumentation in elementary school mathematics classrooms Barkai, Ruthi & Dreyfus, Tommy & Tirosh, Dina & Tsamir, Pessia 1-218 Universal and existential mathematical statements – Secondary school teachers’ responses Benke, Gertraud 1-219 Situations, linear functions and the ‘real world’ 1 - viii PME30 — 2006 Berenson, Sarah B. & Michael, Joan J. & Vouk, Malden 1-220 The relationship between high school mathematics and career choices among high achieving young women Blair, Kristen Pilner 1-221 Students’ understanding of ambiguity in symbols Bobis, Janette & Anderson, Judy 1-222 Reform-oriented teaching practices and the influence of school context Bogomolny, Marianna 1-223 Approaching linear (in)dependence with example-generation Bolite Frant, Janete & Font, Vicenç & Acevedo, Jorge 1-224 Metaphors in teacher’s discourse: Graphing functions Bowers, Janet & Nickerson, Susan 1-225 Designing instructional programs that facilitate increased reflection Braverman, Alex & Samovol, Peter & Applebaum, Mark 1-226 Conformism in teaching mathematics Brocardo, Joana & Serrazina, Lurdes & Rocha, Isabel 1-227 Constructing multiplication: Can pupils develop models for thinking? Brown, Susan A. 1-228 The trigonometric connection: Students’ understanding of sine and cosine Bulmer, Michael & Lea, Bronwyn & Rolka, Katrin 1-229 Student beliefs and attitudes from poetry writing
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