Commentary on Theories of Mathematics Education

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Contents xvii <strong>Commentary</strong> on The Fundamental Cycle of Concept Construction Underlying Various Theoretical Frameworks .............193 Bettina Dahl Introduction . .............................193 Fundamental Cycles of Concept Construction Underlying Various Theoretical Frameworks . ...................193 AnotherFrameworkofCognitiveProcesses.............196 MergingtheFrameworks.......................197 WhereAreWeasaField? ......................199 HowDoWeMoveForward?.....................200 DiscontinuityandLackofProgress ..............201 IsComplementaritytheSolution? ...............201 Are We Shooting with a Shotgun Then? . . . .........202 Scientific Growth Through Falsifications . . .........203 Unified Theory and Truth ...................204 Conclusions . .............................205 References . .............................206 Part VII Symbols and Mediation in Mathematics Education Preface to Part VII ...............................211 Stephen J. Hegedus Symbols and Mediation in Mathematics Education .............213 Luis Moreno-Armella and Bharath Sriraman Introduction . .............................213 Arithmetic: Ancient Counting Technologies .............218 Mathematics from a Dynamic Viewpoint: The Future of Mathematics Education . ...................221 Computational and Cognitive Technologies . .........222 DomainsofAbstractions.......................224 Induction and Deduction: The Computer as a Mediating Tool ....227 Algorithms, Representations and Mathematical Thinking . . . 228 Representational Fluidity in Dynamic Geometry .......230 References . .............................231 <strong>Commentary</strong> on Symbols and Mediation in Mathematics Education ...233 Gerald A. Goldin References . .............................237
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 32: Contents xix Future-Oriented Perspe
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
Page 56: 4 J. Kilpatrick One of the points o
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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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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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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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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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