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Record Nr. |
UNINA9910790052703321 |
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Autore |
Nickerson Raymond S. |
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Titolo |
Mathematical reasoning : patterns, problems, conjectures, and proofs / / Raymond S. Nickerson |
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Pubbl/distr/stampa |
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New York : , : Psychology Press, , 2010 |
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ISBN |
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1-136-94538-5 |
1-283-10585-3 |
9786613105851 |
1-136-94539-3 |
0-203-84802-0 |
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Descrizione fisica |
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1 online resource (597 p.) |
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Classificazione |
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Disciplina |
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Soggetti |
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Mathematical analysis |
Reasoning |
Logic, Symbolic and mathematical |
Problem solving |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and indexes. |
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Nota di contenuto |
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Cover; Mathematical Reasoning: Patterns, problems, conjectures, and proofs; Copyright; Contents; The Author; Preface; 1. What Is Mathematics?; 2. Counting; 3. Numbers; 4. Deduction and Abstraction; 5. Proofs; 6. Informal Reasoning in Mathematics; 7. Representation in Mathematics; 8. Infinity; 9. Infinitesimals; 10. Predilections, Presumptions, and Personalities; 11. Esthetics and the Joys of Mathematics; 12. The Usefulness of Mathematics; 13. Foundations and the "Stuff" of Mathematics; 14. Preschool Development of Numerical and Mathematical Skills; 15. Mathematics in School |
16. Mathematical Problem Solving17. Final Thoughts; References; Appendix: Notable (Deceased) Mathematicians, Logicians, Philosophers, and Scientists Mentioned in the Text; Author Index; Subject Index |
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Sommario/riassunto |
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"This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the 'truths' |
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of mathematics are discoveries or inventions and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as "beautiful"? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction." "This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book's insights illuminating."--BOOK JACKET. |
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