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ERIC Number: ED500940
Record Type: Non-Journal
Publication Date: 2003-Jul
Pages: 8
Abstractor: Author
Reference Count: 10
ISBN: N/A
ISSN: N/A
Mathematical Proof as Formal Procept in Advanced Mathematical Thinking
Chin, Erh-Tsung
International Group for the Psychology of Mathematics Education, Paper presented at the 27th International Group for the Psychology of Mathematics Education Conference Held Jointly with the 25th PME-NA Conference (Honolulu, HI, Jul 13-18, 2003), v2 p213-220
In this paper the notion of "procept" (in the sense of Gray & Tall, 1994) is extended to advanced mathematics by considering mathematical proof as "formal procept". The statement of a theorem as a symbol may theoretically evoke the proof deduction as a process that may contain sequential procedures and require the synthesis of distinct cognitive units or the general notion of the theorem as an object like a manipulable entity to be used as inputs to other theorems. Therefore, a theorem could act as a pivot between a process (method of proof) and the concept (general notion of the theorem). I hypothesise that mature theorem-based understanding (in the sense of Chin & Tall, 2000) should possess the ability to consider a theorem as a "formal procept", and it takes time to develop this ability. Some empirical evidence reveals that only a minority of the first year mathematics students at Warwick could recognise a relevant theorem as a "concept" (having a brief notion of a theorem) and did not have the theorem with the notion of its proof as a "formal procept". A year later some more successful students showed a concept of the theorem as a "formal procept" and their capability of manipulating the theorem flexibly. [For complete proceedings, see ED500859.]
International Group for the Psychology of Mathematics Education. 35 Aandwind Street, Kirstenhof, Cape Town, 7945, South Africa. Tel: +27-21-715-3559; Fax: +27-88-021-715-3559; e-mail: info@igpme.org; Web site: http://igpme.org
Publication Type: Opinion Papers; Speeches/Meeting Papers
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Taiwan