The emergence of a proof image is often an important stage in a learner's construction of a proof. In this paper, we introduce, characterize, and exemplify the notion of proof image. We also investigate how proof images emerge. Our approach starts from the learner's efforts to construct a justification without (or before) attempting any…

This paper focuses on the first session of a professional development course revolving around the topic of mathematical statements and their appropriate proving methods. It analyzes the interactive development of the teachers' knowledge by focusing on the relation between the mathematical statements, the instructor, and the teachers. Different…

Proof by mathematical induction is known to be conceptually difficult for high school students. This paper presents results from interviews with six experienced high school teachers, concerning the use of models in teaching mathematical induction. Along with creative and adequate use of models, we found explanations, models and examples that…