Justification in True/False Questions Given by Future Mathematics Teachers

Abstract:

We analyze the justifications given by a group of students of Mathematics Degree in questions about numerical sequences, of the True / False type, at the end of the disciplines Sequences and Series (6th semester) and Introduction to the Real Analysis (8th semester). Semi-structured interviews with these disciplines’ professors and related researches in Mathematics Education have guided the elaboration of questions proposed to participants and the semistructured interviews with three of them, in those two moments of the investigation. The interaction of algorithmic, intuitive and formal aspects, the notions of intuitive-numerical and logical-formal aspects and the development of Advanced Mathematical Thinking processes are the theoretical ideas that gave support to carry out analyzes of participants’ protocols and interviews. These analyses reveal misconceptions about elaborating justifications in Mathematics, and most participants, at the end of Introduction to Real Analysis discipline, have continued to present particular examples in order to justify statements they have classified as true.

Keywords:
Mathematics education; Mathematical thinking; Initial teacher training; Logic