Based on input from several scholars, Gascón and Nicolás (2017) attempted "to start a dialogue aimed at laying the foundations for a better understanding and a scientific cooperation between different theories in Didactics." Consistent with that goal, I examine uninterrogated assumptions that shaped their analysis. I assert that such…

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…

Explores (n=113) computer science majors' understanding of Lagrange's Theorem (the order of a subgroup divides the order of a finite group), its converse, and its applications. (SW)

Contends that the role of mistakes and corrections of mistakes in classroom practice reveals a certain philosophy of mathematics and that the way mistakes are handled promotes such an implicit philosophy. (MKR)

Raises a number of questions about knowledge generation from mathematics education and the nature of pedagogical information in the field. Considers two main activities within the realm of mathematics education: (1) pursuing investigations to improve instruction and (2) redefining the boundaries of mathematics as a subject. (DDR)

Five contributors report on their perspectives of the seventh International Congress on Mathematical Education (ICME): (1) "Thoughts of an ICME Regular" (Z. Usiskin); (2) "Encouragements and Disturbances" (D. L. Brekke); (3) "A Brief Note on Errors" (A. Lax); (4) "Then and Now" (L. Rogers); and (5)…

Provides examples and a discussion of the Inquiry Cooperation Model (ICM). The ICM is a way of describing a pattern of communicative cooperation between teacher and students. It tries to develop students' preconceptions into mathematical competence. Contains 15 references. (DDR)

Discussed are the recognition and the relevance, in terms of teacher/student awareness and subsequent effective teacher treatment techniques, of cognitive disequilibrium as experienced by the student, when such disequilibrium is provoked by mathematical contradictions and/or counterexamples, within the classroom paradigm of constructivism. (JJK)

Presents contributions by six mathematics teachers responding to the question: "How has the history of mathematics mattered to me in my mathematics teaching?" Answers touch the topics of how and why, how benefits are accrued, use of original texts, integration into core curriculum courses, and pitfalls of history. (MDH)

Presents the portion of a larger study of A-level British students understandings of calculus that deals with ambiguities inherent in the phrases "tends to,""approaches,""converges," and "limit." Responses to two questionnaires indicate that the four phrases generate everyday connotations that are at odds…

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)