Commentary on Theories of Mathematics Education

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Contents xix Future-Oriented Perspectives on the Teaching and Learning ofProblemSolving...................270 Mathematical Modelling . ...................271 Modelling as an Advance on Existing Classroom Problem Solving.........................273 An Example of an Interdisciplinary Mathematical Modelling Problem.........................274 Cycles of Development Displayed by One Group of Children 276 Students’ Learning in Working The First Fleet Problem . . . 278 Mathematical Modelling with Young Learners: A Focus on StatisticalReasoning......................279 Concluding Points ..........................282 Appendix: First Fleet Data Table .............284 References . .............................286 <strong>Commentary</strong> 1 on Problem Solving for the 21 st Century ..........291 Peter Grootenboer Introduction . .............................291 Complexity..............................291 Mathematical Modelling .......................292 FutureDirections...........................294 Concluding Comments ........................295 References . .............................295 <strong>Commentary</strong> 2 on Problem Solving for the 21 st Century ..........297 Alan Zollman ForwardtothePast? .........................300 References . .............................301 Part X Embodied Minds and Dancing Brains: New Opportunities for Research in Mathematics Education Preface to Part X ................................305 Layne Kalbfleisch References . .............................306 Embodied Minds and Dancing Brains: New Opportunities for Research in Mathematics Education ........................309 Stephen R. Campbell Introduction . .............................309 First:WhyBother?..........................311 Second: Some Preliminary Rationale ................312 Third: Cognitive and Educational Neuroscience . . .........314 Fourth: Embodied Cognition . . ...................316 Fifth: Toward Defining Mathematics Educational Neuroscience . . 319
Page 2: Advances in Mathematics Education E
Page 6: Prof. Bharath Sriraman Dept of Math
Page 10: vi Series Preface a regular topic s
Page 14: Introduction A Synthesized and Forw
Page 18: Introduction xi Campbell, J. (Ed.)
Page 22: xiv Contents Reflections on Theorie
Page 26: xvi Contents Lack of Cumulativeness
Page 30: xviii Contents Part VIII Problem So
Page 36: Contents xxi The Basis of Truth-Fin
Page 40: Contents xxiii Networking of Theori
Page 44: Contents xxv Part XVIII Knowing Mor
Page 48: xxviii Contributors Gerald A. Goldi
Page 52: xxx Contributors Hillary VanSpronse
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Surveying Theories and Philosophies
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Preface to Part II Ernest’s Refle
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Preface to Part II Ernest’s Refle
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Reflections on Theories of Learning
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50 S. Goodchild and then identifies
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52 S. Goodchild two issues for each
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54 P. Ernest However, as this discu
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56 P. Ernest roots in the humanisti
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58 P. Ernest Table 2 Mathematics kn
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60 P. Ernest say, our responsibilit
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Preface to Part III Theoretical, Co
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On the Theoretical, Conceptual, and
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88 G. Harel that the ultimate purpo
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90 G. Harel enquiry system, one mus
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92 G. Harel (a) scholars in a broad
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94 G. Harel Harel, G. (2008). What
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98 N. Presmeg interview—a dramati
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100 S. Lerman A Language of Researc
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102 S. Lerman cognition. Adler and
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104 S. Lerman social linguistics, c
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106 S. Lerman tailed year by year t
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108 S. Lerman can be applied, but p
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Commentary on Theo
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122 L.D. English researchers draw o
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124 R. Lesh and B. Sriraman Arguabl
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126 R. Lesh and B. Sriraman new use
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128 R. Lesh and B. Sriraman many sc
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130 R. Lesh and B. Sriraman (philos
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132 R. Lesh and B. Sriraman less gr
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134 R. Lesh and B. Sriraman Fig. 1
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138 R. Lesh and B. Sriraman spite o
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140 R. Lesh and B. Sriraman assumpt
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142 R. Lesh and B. Sriraman solving
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146 R. Lesh and B. Sriraman Coray,
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148 M. Amit One reason why mathemat
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Commentary 2 on Re
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Commentary 2 on Re
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160 D.N. Boote generative metaphors
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162 D.N. Boote of knowledge, the hi
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164 D.N. Boote This suggests anothe
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166 D.N. Boote closest to describin
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168 D.N. Boote Sandoval, W. A., & B
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172 S.J. Hegedus learning environme
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174 J. Pegg and D. Tall growth of k
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176 J. Pegg and D. Tall Local Cycle
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178 J. Pegg and D. Tall imaging of
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180 J. Pegg and D. Tall This cycle
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182 J. Pegg and D. Tall Table 3 Loc
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184 J. Pegg and D. Tall The questio
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186 J. Pegg and D. Tall sessment in
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188 J. Pegg and D. Tall Local cycle
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190 J. Pegg and D. Tall The second
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192 J. Pegg and D. Tall Pegg, J. (1
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194 B. Dahl time and the existence
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196 B. Dahl Pegg and Tall have show
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198 B. Dahl Table 3 Overview of the
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200 B. Dahl 2005, 2006b; Hansen 200
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202 B. Dahl Can we reconcile this d
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204 B. Dahl Unified Theory and Trut
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206 B. Dahl mathematics education?
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208 B. Dahl Marshall, I., & Zohar,
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212 S.J. Hegedus The authors then b
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214 L. Moreno-Armella and B. Sriram
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234 G.A. Goldin In connection with
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236 G.A. Goldin of particular mathe
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Problem Solving Heuristics, Affect,
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Commentary on Prob
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Commentary on Prob
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Commentary on Prob
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Commentary on Prob
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Preface to Part IX Jinfa Cai As the
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Problem Solving for the 21 st Centu
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298 A. Zollman Even though all nati
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300 A. Zollman vancing problem-solv
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Preface to Part X Layne Kalbfleisch
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Preface to Part X 307 Barth, H., La
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310 S.R. Campbell ignated as “the
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312 S.R. Campbell typically loath t
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314 S.R. Campbell Various manners i
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316 S.R. Campbell educational pract
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318 S.R. Campbell and so on, have t
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320 S.R. Campbell Fig. 1 Interdisci
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322 S.R. Campbell they can work jus
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324 S.R. Campbell however, while ce
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326 S.R. Campbell mentation (such a
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328 S.R. Campbell Campbell, S. R. (
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330 S.R. Campbell Lee, K. (2003). N
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Commentary on Embo
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Commentary on Embo
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342 L. Moreno-Armella complex consi
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344 G. Harel teaching, and learning
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346 G. Harel development spanning a
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348 G. Harel Offer two values for t
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350 G. Harel We are looking for pos
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352 G. Harel 2. We found that the a
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354 G. Harel stance on the nature o
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356 G. Harel As I engaged deeply in
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358 G. Harel Through such repeated
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360 G. Harel reasoning that reinfor
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362 G. Harel (Fragment 13). Still f
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364 G. Harel Fig. 9 Quantitative ap
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366 G. Harel References Anderson, J
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Commentary on DNR-
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Appreciating Scientificity in Quali
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Preface to Part XIII Studying Goals
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Preface to Part XIII 399 Davis, R.
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402 G. Törner et al. analysis. In
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404 G. Törner et al. also focused
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406 G. Törner et al. structure of
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408 G. Törner et al. turn in the t
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410 G. Törner et al. some open tas
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412 G. Törner et al. This belief n
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414 G. Törner et al. Bundle (C): B
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416 G. Törner et al. instance char
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418 G. Törner et al. Ball, D. L. (
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420 G. Törner et al. Törner, G. (
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422 D. Tirosh and P. Tsamir The tea
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424 D. Tirosh and P. Tsamir that sh
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426 D. Tirosh and P. Tsamir our com
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Preface to Part XIV Feminist Pedago
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Preface to Part XIV 433 more import
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436 J.E. Jacobs of the school curri
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438 J.E. Jacobs Chart 1: Women’s
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440 J.E. Jacobs through induction w
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442 J.E. Jacobs ways of knowing. Th
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444 J.E. Jacobs impeccable reasonin
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446 J.E. Jacobs Hanson, K. (1992).
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448 G.C. Leder Different Faces of F
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450 G.C. Leder sources, Kaiser and
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452 G.C. Leder have witnessed vario
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454 G.C. Leder Klein, S. S. (Ed.) (
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456 S. Bulut et al. or class, resea
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458 S. Bulut et al. Table 2 Higher
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460 S. Bulut et al. Table 4 Studies
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462 S. Bulut et al. Table 8 Number
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464 S. Bulut et al. Conclusion Alth
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466 S. Bulut et al. Ubuz, B. (1999)
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468 G. Pálsdóttir and B. Sriraman
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Preface to Part XV Tommy Dreyfus As
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Preface to Part XV 481 one’s own
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484 A. Bikner-Ahsbahs and S. Predig
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508 F. Arzarello 3. Strategies for
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510 F. Arzarello Since mathematics
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512 F. Arzarello different lenses i
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516 S. Prediger and A. Bikner-Ahsba
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On Networking Strategies and Theori
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538 U. Gellert open towards the com
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540 U. Gellert Explicitness in Math
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542 U. Gellert no attempt of checki
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544 U. Gellert race to 20 is not ma
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546 U. Gellert It is quite clear fr
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548 U. Gellert classroom practice,
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550 U. Gellert Gravemeijer, K. (199
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552 U. Gellert It is interesting th
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554 U. Gellert research phenomenon
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556 T. Wedege on action—when work
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558 T. Wedege From Bricoleur to Ref
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Preface to Part XVII The Importance
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The Importance of Complex Systems i
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Complexity Theories and Theories of
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594 B. Sriraman of the eminent arti
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596 N. Sinclair collections of sign
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598 N. Sinclair Fig. 1 The frozen g
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600 N. Sinclair gesture. While it i
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602 N. Sinclair that the values of
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604 N. Sinclair students in France.
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606 N. Sinclair was responsible for
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608 N. Sinclair and elation felt by
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610 N. Sinclair in taking Walkerdin
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612 N. Sinclair Núñez, R. (2006).
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614 D. Pimm In this chapter, I will
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616 D. Pimm fact that the ancient E
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618 D. Pimm Mathematics tries to de
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622 B. Sriraman et al. mathematics
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624 B. Sriraman et al. politics is
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626 B. Sriraman et al. • a homoge
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628 B. Sriraman et al. and promotio
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630 B. Sriraman et al. “abstract
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632 B. Sriraman et al. carried out
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634 B. Sriraman et al. can then be
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636 B. Sriraman et al. References A
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638 B. Sriraman et al. Sriraman, B.
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640 K. Yasukawa This opens up the q
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642 K. Yasukawa treatments that the
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Author Index A Abelson, R., 413, 41
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Author Index 647 Bryant, P., 268, 2
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Author Index 649 Elliott, P., 279,
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Author Index 651 Henn, H.-W., 319,
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Author Index 653 Lenoir, T., 9, 30
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Author Index 655 Pappas, S., 281, 2
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Author Index 657 Sica, A., 164, 167
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Author Index 659 Watters, J. J., 27
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662 Subject Index 234, 316, 324, 33
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664 Subject Index 200, 203, 205-206
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666 Subject Index 299, 300, 341, 38
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668 Subject Index learning environm
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