| Advanced Mathematical Thinking 1991 Edition Contributor(s): Tall, David (Editor) |
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ISBN: 0792314565 ISBN-13: 9780792314561 Publisher: Springer OUR PRICE: $237.49 Product Type: Hardcover - Other Formats Published: November 1991 Annotation: This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Its three main parts focus on the nature of advanced mathematical thinking, the theory of its cognitive development, and reviews of cognitive research. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. The reviews of recent research concentrate on cognitive development and conceptual difficulties with the notions of functions, limits, infinity, analysis, proof, and the use of the computer. They provide a wide overview and an introduction to current thinking which is highly appropriate for the college professor in mathematics or the general mathematics educator. |
| Additional Information |
| BISAC Categories: - Mathematics | Study & Teaching - Education | Teaching Methods & Materials - Mathematics - Reference |
| Dewey: 510.71 |
| LCCN: 91031945 |
| Series: Mathematics Education Library |
| Physical Information: 0.75" H x 6.14" W x 9.21" (1.36 lbs) 292 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Advanced Mathematical Thinking has played a central role in the development of human civilization for over two millennia. Yet in all that time the serious study of the nature of advanced mathematical thinking - what it is, how it functions in the minds of expert mathematicians, how it can be encouraged and improved in the developing minds of students - has been limited to the reflections of a few significant individuals scattered throughout the history of mathematics. In the twentieth century the theory of mathematical education during the compulsory years of schooling to age 16 has developed its own body of empirical research, theory and practice. But the extensions of such theories to more advanced levels have only occurred in the last few years. In 1976 The International Group for the Psychology of Mathematics (known as PME) was formed and has met annually at different venues round the world to share research ideas. In 1985 a Working Group of PME was formed to focus on Advanced Mathematical Thinking with a major aim of producing this volume. The text begins with an introductory chapter on the psychology of advanced mathema- cal thinking, with the remaining chapters grouped under three headings: - the nature of advanced mathematical thinking, - cognitive theory, and - reviews of the progress of cognitive research into different areas of advanced mathematics. |