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)

Develops in detail implications for teaching of the arbitrary and necessary curriculum divide. Discusses practical ways forward for teachers who plan lessons and work in the classroom with sensitivity to this divide. Concentrates on teaching and learning arbitrary aspects of the curriculum. Arbitrary is in realm of memory and students have the job…

Investigates the question, Can the mathematics students are taught be cast in such a form that it can be apprehended with the abilities they have and if so, how? Focuses on the language of student abilities, the nature of abilities, and individual differences. (MM)

Discusses issues related to orality, aurality, and literacy in the teaching and understanding of mathematics. Also discusses ritual and tradition in mathematics instruction. (MM)

Discusses the mathematics of Theo van Doesburg's painting, Arithmetic Composition 1. Investigates ratios and symmetries as well as relationships among geometrical forms in the painting. (MM)

Disscusses the history of Theo van Doesburg's painting Arithmetic Composition 1. Relates the work to that of Mondrian and Malevich. (MM)

The third of three articles considers the necessary, which lies in the realm of awareness. Discusses the nature of awareness and its relationship to mathematics learning. (MM)

Addresses the question of what mathematicians can do for mathematics education. Discusses mathematization as the mental processes which produce mathematics. (MM)

Presents a conversation between Lesley Lee and David Pimm about David Wheeler. Discusses the concept of complementarist epistemology. (MM)

Contrasts classroom discourse in one particular class with existing work which suggests that inquiry mathematics is something introduced by teachers and often met by resistance by children. Highlights the difficulties of categorizing children according to 'mathematical ability'. (MM)

Introduces a metaphor for conceptually-oriented mathematics teachers and discusses possible implications for mathematics teacher preparation and professional development. (MM)

Describes work with elementary school students which combines a documentary approach to humanizing mathematics education together with two other artifactual approaches: students' own construction of objects and documents imitating those studied and using ancient calculating devices in modern reconstruction. (MM)

Describes the process of the generation of an International Commission on Mathematics Instruction (ICMI) report. Analyzes a particular volume, 'History in Mathematics Education', in detail. (MM)

Discusses reflections on a videotaped geometry lesson from a Japanese classroom. Contrasts the lesson with the work of a group of teachers on a B.Ed. program who were given the same problem-solving task as the Japanese pupils. (MM)

Presents a study aimed at exploring (a) developmental pedagogy perspectives in early childhood conceptions of shape in space, and (b) evaluating the teacher's work in terms of what is of benefit to children from being involved in this approach to learning. (MM)