Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2009-12-23
  • Publisher: Psychology Pres

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The development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores a vast range of psychological questions related to mathematical cognition, and provides fascinating insights for researchers and students of cognition and instructors of mathematics.

Table of Contents

The Authorp. vii
Prefacep. ix
What Is Mathematics?p. 1
Countingp. 17
Numbersp. 41
Deduction and Abstractionp. 79
Proofsp. 97
Informal Reasoning in Mathematicsp. 137
Representation in Mathematicsp. 161
Infinityp. 191
Infinitesimalsp. 217
Predilections, Presumptions, and Personalitiesp. 249
Esthetics and the Joys of Mathematicsp. 277
The Usefulness of Mathematicsp. 319
Foundations and the "Stuff" of Mathematicsp. 343
Preschool Development of Numerical and Mathematical Skillsp. 373
Mathematics in Schoolp. 391
Mathematical Problem Solvingp. 423
Final Thoughtsp. 461
Referencesp. 471
Appendix: Notable (Deceased) Mathematicians, Logicians, Philosophers, and Scientists Mentioned in the Textp. 555
Author Indexp. 563
Subject Indexp. 57
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