Is this a coincidence? The role of examples in fostering a need for proof.

Autor/inn/en	Buchbinder, Orly; Zaslavsky, Orit
Titel	Is this a coincidence? The role of examples in fostering a need for proof.
Quelle	In: ZDM : mathematics education, 43 (2011) 2, S. 269-281 PDF als Volltext Link als defekt meldenVerfügbarkeit
Sprache	englisch
Dokumenttyp	online; gedruckt; Zeitschriftenaufsatz
ISSN	1863-9690; 1863-9704
DOI	10.1007/s11858-011-0324-7
Schlagwörter	Bildungsforschung; Pädagogische Forschung; Beweisen
Abstract	It is widely known that students often treat examples that satisfy a certain universal statement as sufficient for showing that the statement is true without recognizing the conventional need for a general proof. Our study focuses on special cases in which examples satisfy certain universal statements, either true or false in a special type of mathematical task, which we term "Is this a coincidence?". In each task of this type, a geometrical example was chosen carefully in a way that appears to illustrate a more general and potentially surprising phenomenon, which can be seen as a conjecture. In this paper, we articulate some design principles underlying the choice of examples for this type of task, and examine how such tasks may trigger a need for proof. Our findings point to two different kinds of ways of dealing with the task. One is characterized by a doubtful disposition regarding the generality of the observed phenomenon. The other kind of response was overconfidence in the conjecture even when it was false. In both cases, a need for "proof" was evoked; however, this need did not necessarily lead to a valid proof. We used this type of task with two different groups: capable high school students and experienced secondary mathematics teachers. The findings were similar in both groups.
Erfasst von	FIZ Karlsruhe - Leibniz-Institut für Informationsinfrastruktur
Update	2012/2