Explains why mathematics lectures have a special role in stimulating the imagination and why attending lectures has a significant role in inducting students into their university's mathematical community. (KHR)

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)

Describes a college geometry course centered around challenging, open-ended problems that invite students to draw upon their experiences and share their understandings. Includes discussion of sample problems; writing assignments; classroom dialog; student comments and insights about geometry, mathematics, and themselves and mathematics; and…

Several ways to present two theorems (concerning a square matrix and a property of prime numbers) are demonstrated. One way for each theorem is more stimulating, better setting the stage for the proofs. Several methods of presenting proofs are illustrated, with the outcomes considered from the learner's viewpoint. (MNS)

Reflects on four years of teaching a course called Principle of Major Teachers for pre-service elementary school teachers. Identifies and describes the discord between their formal mathematical knowledge and their informal language used in the context of elementary number theory. Presents encouraging results from a code-switching experiment.…

Examples from arithmetic, algebra, and calculus show that analogy and metaphor are as central to the expression of mathematical meaning as they are to expression of meaning in natural language. (MP)

An experimental study designed to study a teaching system to help students develop and understand the meaning of mathematics is described. Debates, a key aspect of this method, were viewed favorably by a majority of the students. (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)

The need for improving the dialog between teacher and student is promoted as an important step towards improving the mathematics curriculum. (MP)

Discusses students' writing in mathematics, focusing on (1) creating stories; (2) writing mathematical essays; (3) expressing feelings and beliefs about mathematics through diaries and anecdotes; and (4) the use of dialogs. The strategies considered have been used at the high school and remedial college levels. (JN)

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)

Describes a mathematics course for prospective elementary teachers that has teaching and learning mathematics via problem solving at its core. Presents a problem-solving activity involving number theory and reactions by the students and teacher to the activity. (MDH)

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)