What do prospective mathematics teachers mean by “definitions can be proved”?

Merve Dilberoğlu (1) , Çiğdem Haser (2) , Erdinç Çakiroğlu (1)

1 METU - Middle East Technical University [Ankara]
2 University of Turku

The research reported here is part of an ongoing study in which prospective middle school mathematics teachers’ conceptions of definition are investigated through their responses to semi-structured interview questions about defining quadrilaterals. Here we present findings from their responses to a subset of the interview questions, with the purpose of understanding what they mean by the expression “definitions can be proved”- an expression commonly referenced, and considered as erroneous in the research literature. Analysis of the responses, through using thematic coding and Toulmin’s (1958) scheme, revealed that participants attributed two different meanings to the phrase: (1) proving the claim that a written definition accurately designates an intended concept and (2) proving the concept being defined (erroneous). Based on our findings, we point to a reconsideration of the phenomenon by the research community.

Mots clés: Meta-mathematical knowledge; conception of proof; conception of definition; prospective middle school mathematics teachers

Domaines: Mathématiques [math]; Education

Merve Dilberoğlu, Çiğdem Haser, Erdinç Çakiroğlu. What do prospective mathematics teachers mean by “definitions can be proved”?. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Feb 2019, Utrecht, Netherlands. ⟨hal-02398094⟩