The role of methods courses to help prospective elementary teachers learn to teach mathematics was investigated. The influence of past experience on preservice teachers, their lack of subject knowledge, and the lack of time set aside for a methods course are discussed. (KR)

Comments on six theses about mathematics education are presented. How theories on teaching and learning mathematics are derived or developed, how philosophies are related, and their role in mathematics education are among the points discussed. (MNS)

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)

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

Discussed is the research method of "didactic engineering" and the potential theoretical problems of putting research findings into practical use as teaching methods in mathematics classrooms. Cited is the possible incompatibility between the theoretical principles of experimental methods and teachers' conceptions. (MDH)

After describing his research interests and classroom perspectives, the author discusses the "social construction" frame in which he suggests that teaching and learning in the mathematics classroom be viewed. Along with the three constructs of activities, communication, and negotiation, social construction offers promise for research…

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (MNS)

Suggests that student errors in mathematics be used as motivational devices and starting points for mathematical explorations, involving problem solving and problem posing activities. It is further suggested that errors can foster a deeper and more complete understanding of mathematical content and nature of mathematics itself. (PK)

Begins with the assumption that by practicing something one often learns something else. A discussion is presented on the historical and social development of knowledge, the cognitive development of students, the role of teachers, and the meaning of learning situations. (PK)

Discusses student-teachers' awareness of research and its potential role in their work as teachers, both as methodology for themselves as practicing researchers-in-action and as material developed by others. Some of the influences that led to the rise of the "teachers as researchers" program are included. (KR)

Described is the use of peer teaching, to help students to learn the difference between surface and meaningful learning and to provide feedback to the teacher. The advantages of peer teaching to teachers and students are listed. (KR)