Theories Of Mathematics Education - Toc

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Series Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gabriele Kaiser and Bharath Sriraman

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Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

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Introduction A Synthesized and Forward-Oriented Case for Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . Bharath Sriraman, Lyn English

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Contributing Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Part I

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Preface to Part I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jeremy Kilpatrick

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Surveying Theories and Philosophies of Mathematics Education . . . . . Bharath Sriraman and Lyn English

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Part II

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Preface to Part II Ernest’s Reflections on Theories of Learning . . . . . . Bharath Sriraman and Nick Haverhals

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Reflections on Theories of Learning . . . . . . . . . . . . . . . . . . . . . Paul Ernest

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Commentary 1 on Reflections on Theories of Learning by Paul Ernest . . Simon Goodchild

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Commentary 2 on Reflections on Theories of Learning . . . . . . . . . . . Paul Ernest

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Part III

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Preface to Part III Theoretical, Conceptual, and Philosophical Foundations for Mathematics Education Research: Timeless Necessities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lyn D. English

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On the Theoretical, Conceptual, and Philosophical Foundations for Research in Mathematics Education . . . . . . . . . . . . . . . . Frank K. Lester

61 62 63 64

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Commentary on Mathematics Education Research, Its Nature, and Its Purpose: A Discussion of Lester’s Paper . . . . . . . . . . . . . . . . 105 Guershon Harel

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Part IV

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Theories of Mathematics Education: Is Plurality a Problem? . . . . . . . 119 Stephen Lerman Commentary to Knowledge Formation in Mathematics Education: Social Turn, Rival Discourses or Anything Goes? . . . . . . . . . . . 133 Eva Jablonka and Christer Bergsten

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Preface to Part IV Theories as Lenses: A Preface on Steve Lerman’s Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Norma Presmeg

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79 80 81 82 83 84 85 86 87 88 89 90 91 92

Part V

Preface to Part V The Increasing Importance of Mathematics Education as a Design Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Lyn D. English Re-conceptualizing Mathematics Education as a Design Science . . . . . 146 Richard Lesh and Bharath Sriraman Commentary 1 An Analysis of Lesh & Sriraman’s Paper: Mathematics Education as a Design Science . . . . . . . . . . . . . . . . . . . . . . 189 Miriam Amit

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Commentary 2 A review of Lesh & Sriraman’s Mathematics Education as a Design Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Claus Michelsen

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Commentary 3 An Analysis of the Normative and Descriptive Claims Supporting Mathematics Education as Design Science . . . . . . . . 203 David N. Boote

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Part VI

Preface to Part VI The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks by John Pegg and David Tall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Stephen J. Hegedus The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks . . . . . . . . . . . . . . . . . . . . . . . . . 217 John Pegg and David Tall

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Commentary Various Theoretical Frameworks in Concept Construction and How to Move Forward in Constructing Theory . . . . . . . . . . 231 Bettina Dahl

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118 119 120 121 122 123

Part VII

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Preface to Part VII Symbols and Mediation in Mathematics Education by Luis Moreno-Armella & Bharath Sriraman . . . . . . . . . . . . 243 Stephen J. Hegedus Symbols and Mediation in Mathematics Education . . . . . . . . . . . . . 245 Luis Moreno-Armella and Bharath Sriraman

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Commentary on Symbols and Mediation in Mathematics Education by Moreno-Armella and Sriraman . . . . . . . . . . . . . . . . . . . . . 261 Gerald A. Goldin

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Part VIII

131 132 133 134 135 136 137 138

Problem Solving Heuristics, Affect, and Discrete Mathematics: A Representational Discussion . . . . . . . . . . . . . . . . . . . . . . 269 Gerald A. Goldin Commentary Teaching Mathematics Through Problem Solving: A Future Direction of Problem Solving Research . . . . . . . . . . . 275 Jinfa Cai

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Part IX

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Preface to Part IX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 Jinfa Cai

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Problem Solving for the 21st Century . . . . . . . . . . . . . . . . . . . . 289 Lyn English and Bharath Sriraman Commentary 1 to Problem Solving for the 21st Century . . . . . . . . . . 331 Peter Grootenboer

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Commentary 2 Back to the Future or Forward to the Past: Problem Solving for the 21st Century . . . . . . . . . . . . . . . . . . . . . . . 341 Alan Zollman

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Part X

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Preface to Part X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 Layne Kalbfleisch

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Embodied Minds and Dancing Brains: New Opportunities for Research in Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . 359 Stephen R. Campbell

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Commentary New Waves of Research on Learning and Teaching: Commentary on Stephen Campbell, ‘Embodied Minds and Dancing Brains: New Opportunities for Research in Mathematical Education’ 405 Scott Makeig

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Part XI

174 175 176 177

Preface to Part XI DNR-Based Instruction in Mathematics as a Conceptual Framework By Guershon Harel . . . . . . . . . . . . . . 417 Luis Moreno-Armella

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DNR-Based Instruction in Mathematics as a Conceptual Framework . . 419 Guershon Harel

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Commentary On Proof and Certainty- Some Educational Implications . 443 Bharath Sriraman, Hillary VanSpronsen, and Nick Haverhals

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Part XII

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Appreciating Scientificity in Qualitative Research . . . . . . . . . . . . . . 455 Stephen J. Hegedus

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Part XIII

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Preface to Part XIII Studying Goals and Beliefs in the Context of Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 Gerald A. Goldin

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199 200 201 202 203 204 205

Understanding a Teacher’s Actions in the Classroom by Applying Schoenfeld’s Theory Teaching-In-Context: Reflecting on Goals and Beliefs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Günter Türner, Katrin Rolka, Bettina Rüsken, and Bharath Sriraman Commentary The Interplay Between the General and the Specific: The Case of the Teaching-In-Context Theory . . . . . . . . . . . . . . 495 Dina Tirosh and Pessia Tsamir

206 207

Part XIV

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Preface to Part XIV Feminist Pedagogy and Mathematics . . . . . . . . . 505 Gabriele Kaiser

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Feminist Pedagogy and Mathematics Judith E. Jacobs

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Commentary 1 Reflections on “Feminist Pedagogy and Mathematics” . . 515 Gilah C. Leder

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Commentary 2 Mathematics Achievement and Gender: A Case of “No Difference” from Turkey . . . . . . . . . . . . . . . . . . . . . . . . . 521 Safure Bulut, Bekir Gur, and Bharath Sriraman Commentary 3 An Attempt to Androgynse the Gender Debate in Mathematics Education: The Case of Iceland . . . . . . . . . . . . . 541 Gudbjorg Palsdottir and Bharath Sriraman

225 226

Part XV

227 228 229 230

Preface to Part XV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 Tommy Dreyfus

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Networking of Theories – an Approach for Exploiting the Diversity of Theoretical Approaches . . . . . . . . . . . . . . . . . . . . . . . . . 561 Angelika Bikner-Ahsbahs and Susanne Prediger

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Commentary to “Networking of Theories – an Approach for Exploiting the Diversity of Theoretical Approaches”: Some Comments . . . . . 581 Ferdinando Arzarello

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Part XVI

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Preface to Part XVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 Susanne Prediger and Angelika Bikner-Ahsbahs

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On Networking Strategies and Theories’ Compatibility: Learning from an Effective Combination of Theories in a Research Project . . . . . 593 Helga Jungwirth

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Modalities of a Local Integration of Theories in Mathematics Education . 623 Uwe Gellert

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Commentary Harmony and Conflict in the Networking of Theories. A Commentary to ‘On Networking Strategies and Theories’ Compatibility’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 647 Uwe Gellert Commentary Connecting Theories in Mathematics Education: From Bricoleur to Reflective Practitioner . . . . . . . . . . . . . . . . . . . 653 Tine Wedege

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Part XVII

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Preface to Part XVII The Importance of Complex Systems in K-12 Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . . 665 Richard Lesh Complexity Theories and Theories of Learning: Literature Reviews and Syntheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669 Andy Hurford

271 272 273 274 275 276

Part XVIII

Preface to Part XVIII Breathing New Life into Mathematics Education . 711 Bharath Sriraman

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Knowing More Than We Can Tell . . . . . . . . . . . . . . . . . . . . . . 713 Nathalie Sinclair

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Commentary The Tacit, the Covert and the Compulsive Need to Know . . 733 David Pimm

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Part XIX

Politicizing Mathematics Education: Has Politics Gone too Far? Or Not Far Enough? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741 Bharath Sriraman, Matt Roscoe and Lyn English Commentary Critical Mathematics for Critical Times . . . . . . . . . . . 773 Keiko Yasukawa Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781

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Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803

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