Advanced Mathematical Thinking

• Corporate Author: SpringerLink (Online service)
• Other Authors: Tall, David (Editor)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands, 1991.
• Series: Mathematics Education Library ; 11
• Subjects: Education.; Mathematics.; Mathematics > Study and teaching.; Mathematics Education.; Mathematics, general.

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 encoura...

Table of Contents:

• The Psychology of Advanced Mathematical Thinking
• The Nature of Advanced Mathematical Thingking
• Advanced Mathematical Thinking Processes
• Mathematical Creativity
• Mathematical Proof
• Cognitive Theory of Advanced Mathematical Thinking
• The Role of Definitions in the Teaching and Learning of Mathematics
• The Role of Conceptual Entities and Their Symbols in Building Advanced Mathematical Concepts
• Reflective Abstraction in Advanced Mathematical Thinking
• Research into the Teaching and Learning of Advanced Mathematical Thinking
• Research in Teaching and Learning Mathematics at an Advanced Level
• Functions and Associated Learning Difficulties
• Limits
• Analysis
• The Role of Studients’ Intuitions of Infinity in Teaching the Cantorian Theory
• Research on Mathematical Proof
• Advanced Mathematical Thinking and the Computer
• Epilogue
• Reflections.