Investigates magical mathematical moments in order to seek to understand what they are and how they happen, to look for examples, and to reflect on their impact on students' mathematics learning. Describes magical moments as they appear in references in the literature and characterizes those moments. Provides examples from classrooms. (Contains 27…

Reports results of a four-year experiment integrating writing into secondary mathematics classrooms. Discusses (1) the development of a pedagogical model for mathematics journal keeping; and (2) the practicalities of implementing journal writing in the curriculum. Includes sample journal entries. (12 references) (MDH)

Some questions about the relevance of the philosophy of mathematics to mathematics teaching and to early mathematics learning are discussed. Books by Lakatos, Davis and Hersh, and Kitcher are referred to extensively, with comments on a variety of instructional practices. (MNS)

Views the mathematics curriculum in terms of things that can be worked out by someone (necessary) and things about which everyone needs to be informed (arbitrary). This view clarifies the roles that teachers and students have within the complexities of teaching and learning. (Contains 11 references.) (ASK)

Genre analysis is a form of discourse analysis that can provide useful and sometimes surprising new perspectives on understanding teaching and learning. Uses two examples to illustrate the application of genre analysis in mathematics education. (Contains 23 references.) (ASK)

How the author moved from concern about research to development of prescriptive models of heuristic problem solving and the exploration of metacognition and belief systems is discussed. Student beliefs about problem solving, and their corollaries, are included. (MNS)

Some pedagogical problems in Chinese numeration are described. They involve the teaching and learning of how to speak numerals with fluency in Chinese, using Hindu-Arabic written numbers. An alternative approach which stresses regularity is proposed. (MNS)

Discusses the dichotomy right/wrong in students' images of mathematics as they start to work at becoming teachers. Shares stories as teacher educators with a filter of dichotomies that seem to be avoidable. Identifies ways to overcome those dichotomies. (Contains 18 references.) (ASK)

Discussed is the importance of establishing the link between students' understanding of mathematics in real world settings and the symbolism used to represent that mathematics. Examples provide evidence that students and sometimes teachers fail to establish that link. References are given for resources providing strategies and contexts to assist…

Some basic issues which may lay the groundwork for a historical approach to teaching mathematics by developing the concept of ethnomathematics are presented. A historical review and relationships between history and pedagogy are discussed in detail. (MNS)

Describes a study which took place in a grade 9 classroom that consisted of five groups with 3-5 pupils in a group. Pupils were required to calculate the areas of a number of shapes on a geoboard. Concludes that a teacher working with pupils in small groups brings new challenges for mathematics teachers. (Contains 11 references.) (ASK)

The roles of skills and meaning in mathematics are discussed, with concern expressed over the little time spent on developing understanding. Approaches to proportion are described, levels of meaning are proposed, and proportion as a unifying idea for geometry are among the topics discussed. (MNS)

How students are convinced that they have the correct solution to a problem, free of contradiction, is discussed. The role of counterexamples and the need for a situational analysis of problem-solving behaviors are each included. (MNS)

Some concrete examples of the use of historical materials in developing certain topics from precalculus and calculus are presented. Ideas which can be introduced with a reformulated curriculum are discussed in five areas: algorithms, combinatorics, logarithms, trigonometry, and mathematical models. (MNS)

How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)