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ERIC Number: EJ921149
Record Type: Journal
Publication Date: 2011
Pages: 6
Abstractor: As Provided
Reference Count: 0
ISSN: ISSN-0228-0671
Crystalline Concepts in Long-Term Mathematical Invention and Discovery
Tall, David
For the Learning of Mathematics, v31 n1 p3-8 2011
This paper introduces the notion of "crystalline concept" as a focal idea in long-term mathematical thinking, bringing together the geometric development of Van Hiele, process-object encapsulation, and formal axiomatic systems. Each of these is a strand in the framework of "three worlds of mathematics" with its own special characteristics, but all three have an underlying structure that has deductive relationships constrained by the context. In mathematics we may make choices and construct ideas for ourselves, but once a mathematical context is established, it has a crystalline structure of relationships that we discover as a consequence of the structure.
FLM Publishing Association. 382 Education South, University of Alberta, Edmonton, Alberta T6G 2G5, Canada; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A