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140122  eng 
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a 9780306472039

100 
1 

a Tall, David
e [editor]

245 
0 
0 
a Advanced Mathematical Thinking
h Elektronische Ressource
c edited by David Tall

250 


a 1st ed. 1991

260 


a Dordrecht
b Springer Netherlands
c 1991, 1991

300 


a XVIII, 292 p
b online resource

505 
0 

a 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

653 


a Mathematics—Study and teaching

653 


a Mathematics, general

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a Mathematics Education

653 


a Mathematics

710 
2 

a SpringerLink (Online service)

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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0 

a Mathematics Education Library

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u https://doi.org/10.1007/0306472031?nosfx=y
x Verlag
3 Volltext

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0 

a 370

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a 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
