In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…

Conviction is a central construct in mathematics education research on justification and proof. In this paper, we claim that it is important to distinguish between absolute conviction and relative conviction. We argue that researchers in mathematics education frequently have not done so and this has lead to researchers making unwarranted claims…

Many mathematics educators have noted that mathematicians do not only read proofs to gain conviction but also to obtain insight. The goal of this article is to discuss what this insight is from mathematicians' perspective. Based on interviews with nine research-active mathematicians, two sources of insight are discussed. The first is reading a…