Advances in Mathematics Education

Transcription

1 Advances in Mathematics Education Series editors Gabriele Kaiser, University of Hamburg, Hamburg, Germany Bharath Sriraman, The University of Montana, Missoula, MT, USA International editorial board Ubiratan D Ambrosio (São Paulo, Brazil) Jinfa Cai (Newark, NJ, USA) Helen Forgasz (Melbourne, Victoria, Australia) Jeremy Kilpatrick (Athens, GA, USA) Christine Knipping (Bremen, Germany) Oh Nam Kwon (Seoul, Korea)

2 More information about this series at

3 Uwe Gellert Joaquim Giménez Rodríguez Corinne Hahn Sonia Kafoussi Editors Educational Paths to Mathematics A C.I.E.A.E.M. Sourcebook

4 Editors Uwe Gellert Fachbereich Erziehungswissenschaft und Psychologie Freie Universität Berlin Berlin, Germany Corinne Hahn Management de l Information et des Opérations ESCP Europe Paris, France Joaquim Giménez Rodríguez Facultat de Formació del Professorat Departament de Didàctica de les Ciències Experimentals i la Matemàtica Universitat de Barcelona Barcelona, Spain Sonia Kafoussi Department of Sciences of Pre-School Education and of Educational Design University of the Aegean Rhodes, Greece ISSN ISSN (electronic) Advances in Mathematics Education ISBN ISBN (ebook) DOI / Library of Congress Control Number: Springer Cham Heidelberg New York Dordrecht London Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)

5 Acknowledgements The volume collects work which originates from presentations and discussions at the 63rd and the 64th conference of CIEAEM in the summers of 2011 in Barcelona and 2012 in Rhodes. These two conferences were organised around the themes of facilitating access and participation and of mathematics education and democracy. In both years the focus was on educational practices of mathematics inside and outside the classroom. The conferences witnessed many presentations breaking new grounds and opening up new vistas for mathematics education practice. The presentations initiated collective discussions and, in turn, these discussions deepened our insight and understanding of the many ways in which children, youth and adults may find their paths to mathematics. We want to thank all participants of the 63rd and the 64th conference of CIEAEM for their perhaps invisible but nevertheless important contribution of ideas, from which the volume benefits. As CIEAEM meetings are truly international conferences, non-native speakers of English author many chapters of this volume. Particular thanks go to Maja Schermeyer (Germany), who was very effective in improving the English of many chapters and to Catherine Whybrow (UK), who provided extensive native-english- speaker support. Birgit Abel (Germany) was highly efficient in formatting the papers. Finally, all papers have been reviewed at least twice. We thank all those who, by reviewing chapter drafts, have significantly contributed to this volume: Gilles Aldon (France), Luciana Bazzini (Italy), Nina Bohlmann (Germany), Petros Chaviaris (Greece), Julie Cwikla (USA), Javier Díez-Palomar (Spain), Uwe Gellert (Germany), Joaquim Giménez Rodríguez (Spain), Sonia Kafoussi (Greece), Nielce Meneguelo Lobo da Costa (Brasil), Luís Menezes (Portugal), Zoi Nikiforidou (UK), Hélia Oliveira (Portugal), Maria Elisabette Brisola Brito Prado (Brasil), Cristina Sabena (Italy) and Hauke Straehler-Pohl (Germany). v

6

7 Contents Educational Paths to Mathematics: Which Paths Forward to What Mathematics?... 1 Uwe Gellert and Corinne Hahn Part I Cultural Tensions in the Field of Mathematics Education Re-interpreting Students Interest in Mathematics: Youth Culture and Subjectivity Paola Valero Connecting Place and Community to Mathematics Instruction in Rural Schools Robert Klein Establishing Mathematics Classroom Culture: Concealing and Revealing the Rules of the Game Christine Knipping, David Reid, and Hauke Straehler-Pohl Part II Working with Adults Learning Mathematics In and Out of School: A Workplace Education Perspective Gail E. FitzSimons Mathematical Modelling and Bank Loan Systems: An Experience with Adults Returning to School Vera Helena Giusti de Souza, Rosana Nogueira de Lima, Tânia Maria Mendonça Campos, and Leonardo Gerardini Working with Adults: A Commentary Javier Díez-Palomar vii

8 viii Contents Part III Working with Pre-schoolers Number in Cultures as a Playful Outdoor Activity: Making Space for Critical Mathematics Education in the Early Years Anna Chronaki, Georgia Moutzouri, and Kostas Magos Fairness Through Mathematical Problem Solving in Preschool Education Zoi Nikiforidou and Jenny Pange How Do Fair Sharing Tasks Facilitate Young Children s Access to Fractional Concepts? Julie Cwikla and Jennifer Vonk Working with Pre-schoolers: A Dual Commentary Michaela Kaslová and Sixto Romero Part IV Taking Spaces and Modalities into Account Digital Mathematical Performances: Creating a Liminal Space for Participation Susan Gerofsky Participation in Mathematics Problem-Solving Through Gestures and Narration Luciana Bazzini and Cristina Sabena Considering the Classroom Space: Towards a Multimodal Analysis of the Pedagogical Discourse Eleni Gana, Charoula Stathopoulou, and Petros Chaviaris Commentary: Semiotic Game, Semiotic Resources, Liminal Space A Revolutionary Moment in Mathematics Education! Peter Appelbaum Part V Criticising Public Discourse Numbers on the Front Page: Mathematics in the News Dimitris Chassapis and Eleni Giannakopoulou On the Role of Inconceivable Magnitude Estimation Problems to Improve Critical Thinking Lluís Albarracín and Núria Gorgorió Criticizing Public Discourse and Mathematics Education: A Commentary Charoula Stathopoulou

9 Contents ix Part VI Organising Dialogue and Enquiry Facilitating Deliberate Dialogue in Mathematics Classroom Ana Serradó, Yuly Vanegas, and Joaquim Giménez Rodríguez Inquiry-Based Mathematics Teaching: The Case of Célia Luís Menezes, Hélia Oliveira, and Ana Paula Canavarro Using Drama Techniques for Facilitating Democratic Access to Mathematical Ideas for All Learners Panayota Kotarinou and Charoula Stathopoulou Organising Dialogue and Enquiry: A Commentary Lambrecht Spijkerboer and Leonor Santos Part VII Providing Information Technology Educational Laptop Computers Integrated into Mathematics Classrooms Maria Elisabette Brisola Brito Prado and Nielce Meneguelo Lobo da Costa Technology and Education: Frameworks to Think Mathematics Education in the Twenty-First Century Gilles Aldon Technology in the Teaching and Learning of Mathematics in the Twenty-First Century: What Aspects Must Be Considered? A Commentary Fernando Hitt Part VIII Transcending Boundaries Family Math: Doing Mathematics to Increase the Democratic Participation in the Learning Process Javier Díez-Palomar Service-Learning as Teacher Education Peter Appelbaum The Learning and Teaching of Mathematics as an Emergent Property Through Interacting Systems and Interchanging Roles: A Commentary Fragkiskos Kalavasis and Corneille Kazadi Appendices Index Author Index

10

11 Contributors Lluís Albarracín Facultat de Ciències de l Educació, Universitat Autònoma de Barcelona, Barcelona, Spain Gilles Aldon Ecole Normale Supérieure de Lyon, Lyon, France Peter Appelbaum Department of Curriculum, Cultures and Child/Youth Studies, School of Education, Arcadia University, Philadelphia, PA, USA Luciana Bazzini Dipartimento di Filosofia e Scienze dell Educazione, Università di Torino, Torino, Italy Tânia Maria Mendonça Campos Post-Graduate Program in Mathematics Education, Anhanguera University, São Paulo, Brazil Ana Paula Canavarro Universidade de Évora, Évora, Portugal Dimitris Chassapis School of Educational Sciences, University of Athens, Athens, Greece Petros Chaviaris University of the Aegean, Mytilene, Greece Anna Chronaki Department of Early Childhood Education, University of Thessaly, Volos, Greece Julie Cwikla Director of Creativity & Innovation in STEM, Office of the Vice President for Research, University of Southern Mississippi, Ocean Springs, MS, USA Javier Díez-Palomar Department of Mathematics and Science Education, University of Barcelona, Barcelona, Spain Gail E. FitzSimons Melbourne Graduate School of Education, University of Melbourne, Parkville, VIC, Australia xi

12 xii Contributors Eleni Gana Department of Special Education, University of Thessaly, Volos, Greece Uwe Gellert Fachbereich Erziehungswissenschaft und Psychologie, Freie Universität Berlin, Berlin, Germany Leonardo Gerardini Colégio Dante Alighieri, São Paulo, Brazil Susan Gerofsky Department of Curriculum and Pedagogy, University of British Columbia, Vancouver, BC, Canada Eleni Giannakopoulou Educational Studies Unit, Hellenic Open University, Athens, Greece Joaquim Giménez Rodríguez Facultat de Formació del Professorat, Departament de Didàctica de les Ciències Experimentals i la Matemàtica, Universitat de Barcelona, Barcelona, Spain Vera Helena Giusti de Souza Post-Graduate Program in Mathematics Education, Anhanguera University, São Paulo, Brazil Núria Gorgorió Facultat de Ciències de l Educació, Universitat Autònoma de Barcelona, Barcelona, Spain Corinne Hahn Management de l Information et des Opérations, ESCP Europe, Paris, France Fernando Hitt Département de Mathématiques, Université du Québec à Montréal, Montréal, QC, Canada Fragkiskos Kalavasis Faculty of Humanities, Department of Sciences for Preschool Education and Educational Design, University of the Aegean, Rhodes, Greece Michaela Kaslová Faculty of Education, Charles University, Prague, Czech Republic Corneille Kazadi Université du Québec à Trois-Rivières, Trois-Rivières, Canada Robert Klein Ohio University, Athens, OH, USA Christine Knipping Universität Bremen, Bremen, Germany Panayota Kotarinou Department of Special Education, University of Thessaly, Volos, Greece Nielce Meneguelo Lobo da Costa Post-graduation Program of Mathematics Education, Anhanguera University of São Paulo, UNIAN, São Paulo, Brazil Kostas Magos Department of Early Childhood Education, University of Thessaly, Volos, Greece Luís Menezes Escola Superior de Educação de Viseu, Viseu, Portugal

13 Contributors xiii Georgia Moutzouri Department of Early Childhood Education, University of Thessaly, Volos, Greece Zoi Nikiforidou Department of Early Childhood, Liverpool Hope University, Liverpool, UK Rosana Nogueira de Lima Post-Graduate Program in Mathematics Education, Anhanguera University, São Paulo, Brazil Hélia Oliveira Instituto de Educação da, Universidade de Lisboa, Lisbon, Portugal Jenny Pange Department of Preschool Education, University of Ioannina, Ioannina, Greece Maria Elisabette Brisola Brito Prado Post-graduation Program of Mathematics Education, Anhanguera University of São Paulo, UNIAN, São Paulo, Brazil Applied Information Technology Center of Education, State University of Campinas, UNICAMP, Campinas, Brazil David Reid Universität Bremen, Bremen, Germany Sixto Romero Escuela Técnica Superior de Ingeniería, Universidad de Huelva, Huelva, Spain Cristina Sabena Dipartimento di Filosofia e Scienze dell Educazione, Università di Torino, Torino, Italy Leonor Santos Instituto de Educação, Universidade de Lisboa, Lisbon, Portugal Ana Serradó Department of Science, Mathematics and Technology, La Salle- Buen Consejo, Cádiz, Spain Lambrecht Spijkerboer APS-International, Utrecht, The Netherlands Charoula Stathopoulou Department of Special Education, University of Thessaly, Volos, Greece Hauke Straehler-Pohl Freie Universität Berlin, Berlin, Germany Paola Valero Aalborg University, Aalborg, Denmark Yuly Vanegas Departament de Didàctica de la Matemàtica i de les Ciències Experimentals, Universitat Autònoma de Barcelona, Barcelona, Spain Jennifer Vonk Associate Professor, Department of Psychology, Oakland University, Rochester, MI, USA