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)

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 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)