Theorems that admit exceptions, including a remark on Toulmin.

Autor/in	Jahnke, Hans Niels
Titel	Theorems that admit exceptions, including a remark on Toulmin.
Quelle	In: ZDM : mathematics education, 40 (2008) 3, S. 363-371 PDF als Volltext Link als defekt meldenVerfügbarkeit
Sprache	englisch
Dokumenttyp	online; gedruckt; Zeitschriftenaufsatz
ISSN	1863-9690; 1863-9704
DOI	10.1007/s11858-008-0097-9
Schlagwörter	Denken; Mathematik; Mathematikunterricht; Mathematische Sprache; Beweis; Beweisen; Fachsprache; Theorie
Abstract	It is a plausible assumption that proof-novices try to make sense of the meaning of mathematical proof out of the perspective of every day thinking. In every day thinking, however, the domain of objects to which a general statement refers is not completely and definitely determined. Thus the very notion of a "universally valid statement" is not as obvious as it might seem. The phenomenon of a statement with an indefinite domain of reference can also be found in the history of mathematics when authors spoke of "theorems that admit exceptions". Without having understood and accepted the theoretical nature of the idea of a universally valid statement the logical distinctions between, for example an implication and its converse loose their meaning for the learner. This might explain some disappointing findings of empirical research. Following a proposal by Inglis, Mejia-Ramos and Simpson it is suggested that in modelling mathematical thinking in proof situations the full scheme of Toulmin should be used including qualifications and rebuttals rather than a reduced version as is frequently done.
Erfasst von	FIZ Karlsruhe - Leibniz-Institut für Informationsinfrastruktur
Update	2010/2