In mathematics education research, proofs are often conceptualized as sequences of mathematical assertions. We argue that this ignores proofs that contain instructions to perform mathematical actions, often in the form of imperatives, which are common both in mathematical practice and in undergraduate mathematics textbooks. We consider in detail a…

Mathematics education researchers frequently use task-based interviews to gain insight into mathematicians' practice. However, there are a number of factors that should prevent mathematics educators from extrapolating how individual mathematicians respond to researcher-generated tasks in laboratory conditions, to how mathematicians practice their…

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…