In-service teachers' conceptions of parallelogram definitions
Résumé
The present research examines middle school mathematics teachers’ conceptions of geometric definitions, and specifically whether they possess geometric conceptions at the van Hiele fourth level. Sixty two teachers participated in the research. We used an open-ended questionnaire for data collection. The questionnaire included three questions concerned with the equivalence between definitions, sufficient and necessary conditions, and deductive geometric reasoning related to definitions. We used deductive and inductive content analysis to analyse the data. We found that generally, the participating teachers did not possess the geometric conceptions at the van Hiele fourth level and had difficulties in understanding what the imperative and optional features of mathematical definitions are. In addition, the participants’ conceptions of definitions have specific features that explain why they have not attained the van Hiele fourth level.
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