Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Some pedagogical aspects of proof

Some pedagogical aspects of proof Interchange, Vol. 21, No. 1 (Spring, 1990), 6-13 Gila Hanna The Ontario Institute for Studies in Education In discussing the role of proof in mathematics education it seems helpful to distinguish among different perceptions of proof. It is particularly useful, I believe, to consider the following three aspects, around whichi will organize my comments. 1. Formal proof: proof as a theoretical concept in formal logic (or metalogic), which may be thought of as the ideal which actual mathematical practice only approximates. 2. Acceptable proof: proof as a normative concept that defines what is acceptable to qualified mathematicians. 3. The teaching of proof: proof as an activity in mathematics education which serves to elucidate ideas worth conveying to the student. Formal Proof A formal proof of a given sentence is a finite sequence of sentences such that the first sentence is an axiom, each of the following sentences is either an axiom or has been de- rived from preceding sentences by applying rules of inference, and the last sentence is the one to be proved. Such a proof is, in principle, mechanizable, and eliminates the psychological aspects of proof. The formal approach to proof was developed, in fact, to eliminate http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Interchange Springer Journals

Some pedagogical aspects of proof

Interchange , Volume 21 (1) – May 16, 2005

Loading next page...
 
/lp/springer-journals/some-pedagogical-aspects-of-proof-1Me1yKpTI5

References (12)

Publisher
Springer Journals
Copyright
Copyright
Subject
Education; Educational Policy and Politics; Educational Philosophy
ISSN
0826-4805
eISSN
1573-1790
DOI
10.1007/BF01809605
Publisher site
See Article on Publisher Site

Abstract

Interchange, Vol. 21, No. 1 (Spring, 1990), 6-13 Gila Hanna The Ontario Institute for Studies in Education In discussing the role of proof in mathematics education it seems helpful to distinguish among different perceptions of proof. It is particularly useful, I believe, to consider the following three aspects, around whichi will organize my comments. 1. Formal proof: proof as a theoretical concept in formal logic (or metalogic), which may be thought of as the ideal which actual mathematical practice only approximates. 2. Acceptable proof: proof as a normative concept that defines what is acceptable to qualified mathematicians. 3. The teaching of proof: proof as an activity in mathematics education which serves to elucidate ideas worth conveying to the student. Formal Proof A formal proof of a given sentence is a finite sequence of sentences such that the first sentence is an axiom, each of the following sentences is either an axiom or has been de- rived from preceding sentences by applying rules of inference, and the last sentence is the one to be proved. Such a proof is, in principle, mechanizable, and eliminates the psychological aspects of proof. The formal approach to proof was developed, in fact, to eliminate

Journal

InterchangeSpringer Journals

Published: May 16, 2005

There are no references for this article.