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The process of learning mathematics /
The Process of Learning Mathematics describes the process of learning mathematics and covers topics ranging from the nature of mathematics to the role of intuition and logic in mathematics; the thought processes involved in the teaching of mathematics; reflective intelligence and the use of symbols;...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford ; New York :
Pergamon Press,
[1972]
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| Edición: | [1st ed.]. |
| Colección: | Commonwealth and international library. Mathematical topics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; The Process of Learning Mathematics; Copyright Page; Table of Contents; Contributors; Foreword; Chapter 1. The Nature of Mathematics; Bibliography; Chapter 2. The Nature of Mathematics-Another View; Introduction; The Word Mathematics; Is Mathematics Useful?; Pure and Applied Mathematics; Is Mathematics an Empirical Science?; What is Pure Mathematics About?; What is the Connection between Mathematics and the Physical Universe?; Making Pictures; The Structure of Mathematics Thinking; The Importance of Symbols; Axiomatics; Bibliography and Reading List.
- Chapter 3. The Role of IntuitionSuggestions for Further Reading; Chapter 4. The Role of Logic; Introduction; I. Logical Procedures; II. Methods of Proof; III. Axiomatic Systems; IV. Errors; V. The Role of Logic in the Development of Mathematics; References; Chapter 5. Generalisation and Structure; 1. Introduction; 2. Generalisation; 3. The Evolution of a Subject; 4. Approximations; 5. Problems of Applied Mathematics and Technology; 6. Some Miscellaneous Topics; Conclusion; Chapter 6. Attempts to Investigate the Learning of Mathematics; Methods of Investigation; Number and a Number System.
- Selected ReferencesChapter 7. The Growth of Logical Thinking; Processes in the Development of Thinking; Periods of Development; An Illustrative Example; The Function of Language in Thinking; The Formation of Concepts; Adolescent Thinking; Conclusions; References; Chapter 8. Schematic Learning; Consequences for Teaching; Assimilation and Accommodation; Basic Mathematics Schemas; Chapter 9. Reflective Intelligence, and the Use of Symbols; Sensori-Motor and Reflective Intelligence; Reflective Activity in Mathematics; The Contribution of Symbols; Communicating and Reflecting.
- Some other Functions of SymbolsReferences; For Further Reading; Chapter 10. Motivation, Emotional and Interpersonal Factors; References; Suggestions for Further Reading; Chapter 11. Investigational Methods; Chapter 12. A Note on Discovery; Discovery; Further Reading; Chapter 13. Structural Apparatus; Suggested Reading; Chapter 14. Computer-assisted Instruction; I. Computation; II. Programming; III. Programming for C.A.I.; IV. C.A.I, in the Future; Further Reading; Chapter 15. The Uses of Programmed Material in British Schools and Colleges; Summarising our Common Background; References.
- Chapter 16. The Midlands Mathematics ExperimentReferences; Chapter 17. Scottish Mathematics Group; Chapter 18. School Mathematics Project; The Initial Stages; References; Chapter 19. Nuffield Foundation Mathematics Teaching Project; APPENDIX A: PILOT AREAS; APPENDIX B: TEAM MEMBERS; APPENDIX C: CONSULTATIVE COMMITTEE; APPENDIX D: SUMMARY OF THE CONTENTS OF THE BOOKS PUBLISHED BY JUNE 1970; APPENDIX E: SUMMARY OF THE PROVISIONAL CONTENTS OF PROJECTED GUIDES AND OTHER BOOKS UNPUBLISHED BY JUNE 1970; APPENDIX F: FILMS AND APPARATUS PRODUCED BY, OR IN CONJUNCTION WITH, THE PROJECT.