Semantic and Syntactic Proof Productions

Autor/inn/en	Weber, Keith; Alcock, Lara
Titel	Semantic and Syntactic Proof Productions
Quelle	In: Educational Studies in Mathematics, 56 (2004) 2-3, S.209-234 (26 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1023/B:EDUC.0000040410.57253.a1
Schlagwörter	Mathematical Logic; Validity; Mathematical Concepts; Case Studies; Semantics; Syntax; Inferences; Symbols (Mathematics); Mathematics Education; Theories + Suchen Sie Ihr Suchwort? Mathematical logics; Mathematische Logik; Gültigkeit; Case study; Fallstudie; Case Study; Semantik; Inference; Inferenz; Mathematische Bildung; Theory; Theorie
Abstract	In this paper, we distinguish between two ways that an individual can construct a formal proof. We define a syntactic proof production to occur when the prover draws inferences by manipulating symbolic formulae in a logically permissible way. We define a semantic proof production to occur when the prover uses instantiations of mathematical concepts to guide the formal inferences that he or she draws. We present two independent exploratory case studies from group theory and real analysis that illustrate both types of proofs. We conclude by discussing what types of concept understanding are required for each type of proof production and by illustrating the weaknesses of syntactic proof productions. (Author).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10