The mathematical curriculum of the next millennium should harness children's motivation without losing their mathematics. Envisages that the computer might offer just the context to help do this. Presents snapshots from two case studies. (Contains 18 references.) (ASK)

The origins of the emphasis on formal proof are discussed as well as more recent views. Factors in acceptance of a proof and the social process of acceptance by mathematicians are included. The impact of formal proof on the curriculum and implications for teaching are given. (DC)

Argues for the use of multiple approaches to instruction as a way to encourage students to be active critics instead of passive recipients. Presents six classroom scenes in historical sequence that review both the mathematical story and the art of teaching. (DDR)

A major component of student difficulty with algebra is the inability to make sense of the algebra symbol system as a language. Accordingly, remedies should be sought by considering algebra in a linguistic sense. (PK)

Provides details of a study on mathematics learning that applies Bruner's concept of format of interaction which is employed in language acquisition theory and in understanding mathematical augmentation. Describes the interactions among tutors, students, and their linear algebra text. (DDR)

Discusses using the computer to promote versatile learning of higher order concepts in algebra and calculus. Generic organizers, generic difficulties, and differences between mathematical and cognitive approaches are considered. (YP)

Reports on the findings of an examination of 32 linear algebra textbooks. The examination, to determine existing approaches to teaching the topics, was in preparation for developing a linear algebra program for high school students. (PK)