Understanding what a proof is: a classroom-based approach.

Autor/inn/en	Jahnke, Hans Niels; Wambach, Ralf
Titel	Understanding what a proof is: a classroom-based approach.
Quelle	In: ZDM : mathematics education, 45 (2013) 3, S. 469-482 PDF als Volltext Link als defekt meldenVerfügbarkeit
Sprache	englisch
Dokumenttyp	online; gedruckt; Zeitschriftenaufsatz
ISSN	1863-9690; 1863-9704
DOI	10.1007/s11858-013-0502-x
Schlagwörter	Verstehen; Didaktik; Unterricht; Mathematikunterricht; Beweis; Intervention; Verständnis
Abstract	Being unaware of the assumptions underlying a deductive argument is widespread among learners and is a major stumbling block to their understanding of proof. Thus, the basic idea of the present paper is that at some points in the course of secondary education there should be classroom-based interventions addressing this difficulty and making the axiomatic organization of mathematics a theme. Students should be made aware that there are axioms in mathematics, what their role is and how mathematicians come to agree about which axioms should be accepted. An axiom which is not yet accepted is simply a hypothesis. A hypothesis is evaluated by deductively drawing consequences and by investigating whether these consequences agree with experience or should be accepted for other reasons. The teaching intervention discussed in this paper exemplifies this idea by way of the example of ancient attempts at modelling the path of the sun, the so-called "anomaly of the sun". It is investigated to what extent the teaching intervention fostered students' understanding of the conditionality of mathematical/astronomical statements, that is, of the fact that the truth of these statements is dependent on the initial hypotheses.
Erfasst von	FIZ Karlsruhe - Leibniz-Institut für Informationsinfrastruktur
Update	2014/1