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)…

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 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)