**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.]

Descriptors: Mathematical Logic, Validity, Mathematics Instruction, College Mathematics, College Students, Mathematical Concepts, Foreign Countries, Symbols (Mathematics)

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