Mathematics and Mathematics Education: Cultural and Social Dimensions
Total Page:16
File Type:pdf, Size:1020Kb
Skrifter från SMDF, Nr.7 Editors: Christer Bergsten, Eva Jablonka, Tine Wedege Mathematics and Mathematics Education: Cultural and Social Dimensions Proceedings of MADIF 7 The Seventh Mathematics Education Research Seminar Stockholm, January 26-27, 2010 SMDF Svensk Förening för MatematikDidaktisk Forskning Swedish Society for Research in Mathematics Education Skrifter från Svensk Förening för MatematikDidaktisk Forskning, Nr 7 ISBN 91-973934-6-0 ISSN 1651-3274 Given to the authors 2010 SMDF Svensk Förening för Matematikdidaktisk Forskning c/o Bergsten, Matematiska institutionen Linköpings universitet SE 58183 Linköping Swedish Society for Research in Mathematics Education For information see web page www.matematikdidaktik.org Printed in Sweden by LiU-Tryck 2010 Preface This volume contains the proceedings of MADIF 7, the Seventh Swedish Mathe- matics Education Research Seminar, held in Stockholm, January 26-27, 2010. The seminars, organised by the Swedish Society for Research in Mathematics Education (SMDF), aim at enhancing the opportunities for discussion of research and exchange of perspectives, amongst junior researchers and between junior and senior researchers in the field. The first seminar took place in January 1999 at Lärarhögskolan in Stockholm and included the constitution of the SMDF. The second meeting was held in Göteborg in January 2000, the third in Norrköping in January 2002, the fourth in Malmö in January 2004, the fifth in Malmö in January 2006 and the sixth in Stockholm in January 2008. Printed proceedings of the seminars are available for all but the very first meeting. The members of the 2010 programme committee were Christer Bergsten (Linköping University), Eva Jablonka (Luleå University of Technology), Katarina Kjellström (Stockholm University), Thomas Lingefjärd (University of Gothenburg), and Tine Wedege (Malmö University). The local organiser was Katarina Kjellström. The programme of MADIF 7 included two invited plenary lectures (Paul Dowling and Tine Wedege), one plenary panel (Jo Boaler, Paul Dowling, Stephen Lerman, with Christer Bergsten as moderator), 20 paper presentations, and 18 short presentations. As the research seminars have sustained the idea of offering formats for presentation that enhance feedback and exchange, the paper presentations are organised as discussion sessions based on points raised by an invited reactor. The organising committee would like to express their thanks to the following colleagues for their commitment to the task of being reactors: Katalin Földesi, Gunnar Gjone, Simon Goodchild, Ola Helenius, Johan Häggström, Barbara Jaworski, Maria Johansson, Troels Lange, Steve Lerman, Tamsin Meaney, Peter Nyström, Elisabeth Persson, Per-Eskil Persson, Kerstin Pettersson, Mikaela Rohdin, Frode Rönning, Erika Stadler, Allan Tarp, Paola Valero. In this volume the two plenary addresses, 19 papers, and 17 short presenta- tions are included. All contributions were peer-reviewed by two or three resear- chers before presentation, and by members of the programme committee before publication. The editors are grateful to the following colleagues for providing reviews: Paul Andrews, Iiris Attorps, Jonas Bergman Ärlebäck, Ewa Bergqvist, Tomas Bergqvist, Christer Bergsten, Maria Bjerneby Häll, Lisa Björklund Boistrup, Ole Björkqvist, Morten Blomhøj, Jesper Boesen, Johann Engelbrecht, Peter Frejd, Sharada Gade, Peter Galbraight, Gunnar Gjone, Simon Goodchild, Brian Greer, i Ola Helenius, Kirsti Hemmi, Johan Häggström, Eva Jablonka, Barbara Jaworski, Gulden Karakok, Håkan Lennerstad, Lena Lindenskov, Thomas Lingefjärd, Sverker Lundin, Joanne Lobato, Per Nilsson, Eva Norén, Guri Nortvedt, Alexandre José Santos Pais, Torulf Palm, Hanna Palmér, Kerstin Pettersson, Lisser Rye Ejersbo, Fritjof Sahlström, Harry Silfverberg, Håkan Sollervall, Erika Stadler, Allan Tarp, Paola Valero, Jorryt van Bommel, Olov Viirman, Tine Wedege, Anna Wernberg, Carl Winsløw, Leigh Wood, Magnus Österholm. The organising committee and the editors would like express their gratitude to the organisers of Matematikbiennalen 2010 for financially supporting the seminar. Finally we would like to thank all participants of MADIF 7 for sustaining their engagement in an intense scholarly activity during the seminar with its tight time table, and for contributing to an open, positive and friendly atmosphere. Christer Bergsten, Eva Jablonka, Tine Wedege ii Contents Preface i Contents iii Plenary addresses Abandoning mathematics and hard labour in schools: 1 A new sociology of knowledge and curriculum reform Paul Dowling Ethnomathematics and mathematical literacy: People knowing mathematics in society 31 Tine Wedege Papers A theoretical model of the connection between the process of reading and the process of solving mathematical tasks 47 Ewa Bergqvist and Magnus Österholm A remark on didactic transposition theory 58 Christer Bergsten, Eva Jablonka and Anna Klisinska Classroom assessment in mathematics - A review of articles in two journals 69 Lisa Björklund Boistrup Revisiting perspectives on mathematical models and modelling 80 Peter Frejd On Swedish upper secondary students’ descriptions of the notions of mathematical models and modelling 91 Peter Frejd and Jonas Bergman Ärlebäck Narratives of students learning mathematics: Plurality of strategies and a strategy for practice? 102 Sharada Gade Achievement as a matter of choice? 113 Eva Jablonka, Maria Johansson and Mikaela Rohdin Investigating what students do transfer: Implementation of the Actor-Oriented Transfer framework 124 Gulden Karakok iii Children’s perspectives on mathematics homework 135 Troels Lange and Tamsin Meaney Mathematical maps - Students working with geography as a global metaphor for mathematics 146 Håkan Lennerstad Mathematical competencies: A research framework 157 Johan Lithner, Ewa Bergqvist, Tomas Bergqvist, Jesper Boesen, Torulf Palm and Björn Palmberg The missing piece. An interpretation of mathematics education using some ideas from Žižek 168 Sverker Lundin An immigrant student’s identity formation in a Swedish bilingual mathematics classroom 179 Eva Norén Broadening the role of theory in mathematics education research 189 Alexandre José Santos Pais, Diana Stentoft and Paola Valero Konflikt mellan vision och möjlighet hos blivande lärare i matematik 200 Hanna Palmér University students’ contextualisations of threshold concepts in calculus 211 Kerstin Pettersson Augmented reality as support for designing a learning activity concerning the mathematical concept of scale 222 Håkan Sollervall, Per Nilsson and Daniel Spikol The transition from secondary school to university: Learning and understanding mathematics from a student perspective 231 Erika Stadler Relationships between epistemological beliefs and properties of discourse: Some empirical explorations 241 Magnus Österholm Short presentations A study of Problem Centered Approach in mathematics 251 Yukiko Asami Johansson iv Improving undergraduate mathematics teaching: Learning study – the definite integral concept 253 Iiris Attorps, Kjell Björk and Mirko Radic Klassrumsbedömning och betygsättning i gymnasiematematiken 255 Semir Becevic Val av arbetsmetoder och diskursiva strategier i syfte att främja klassrumskommunikationen om matematik. 257 Marie Bergholm Make the mathematics visible in children’s free activities in preschool - Challenges for the teaching profession 259 Kerstin Bäckman Stimulering av matematiska förmågor i en matematisk aktivitet 261 Henrik Carlsson CAS-calculators in the classroom 263 Patrik Erixon Communication of solutions of mathematical problems using Computer Algebra Systems 265 Gunnar Gjone School mathematics: An initiation into what? 267 Maria Johansson Developing a tool for analysing upper secondary school textbook tasks about proportion and proportionality 269 Anna Lundberg Scaffolding students solving multistep arithmetic word problems 271 Guri A. Nortvedt What is valued in effective mathematics lessons: Preliminary findings from a Swedish lower secondary school 273 Aihui Peng and Mikaela Nyroos A PhD-project in multiculturalism: Ethnomathematics, language or educational systems 275 Jöran Pettersson The emergence of disparity in mathematics performance: Early results from the Swedish part of a project 277 Mikaela Rohdin Discourse protection against Manyology 279 Allan Tarp v The KOM project and Adding It Up through the lens of a learning situation 281 Jorryt van Bommel, Yvonne Liljekvist, Cecilia Ottersten Nylund Undergraduate mathematics teaching through a commognitive lens - The case of functions 283 Olov Viirman E-mail addresses of the contributors 285 vi Abandoning Mathematics and Hard Labour in Schools A New Sociology of Knowledge and Curriculum Reform Paul Dowling Institute of Education, University of London, UK This paper introduces and develops aspects of social activity method (SAM) in transaction with mathematics education. The outcome of this transaction is the identification of three key issues: disciplinarity, the tendency of practices— especially school mathematics—to mark themselves out from rather than constituting themselves in functional relationship to other practices; the new massification of schooling, the widespread distribution of erstwhile elite perfor- mances; and conceptualisation, the insistence on the acquisition of mythologised (in this case, mathematical) objects that is a consequence of the ‘forensic science’ of assessment practices that are themselves facilitated by ‘teaching’ as the particular mode of pedagogic practice that is prevalent