Describes disposition designed to provide students with some of the substance of proof as an element of the practical rationality invested in engaging students in proving. Discusses how video episodes enhance chances of eliciting the practical rationality of mathematics teaching and how these records and artifacts function in the context of a…

Discusses public indifference and student ignorance toward mathematics in the U.S. Presents a basic core of mathematics knowledge that everyone should know. (KHR)

Discusses the meaning of the phrase "mathematics is everywhere." Introduces the book "Reconstructing School Mathematics: Problems with Problems and the Real World", written by Stephen Brown, which emphasizes mathematical modeling and the connection between mathematics and students' lives. (KHR)

Investigates young people's expression of mathematical ideas with a computer, the nature of mathematical practices, and the problem of mathematical meaning from cognitive and socio-cultural perspectives. Describes a mathematical activity system designed for learning and the role of digital technologies in helping to understand and reshape the…

Categorizes the purposes of proof in mathematics and the mathematics classroom as proofs that convince or explain knowledge about mathematical truth, proofs that justify the use of terminology, and proofs that illustrate technique. Includes suggestions for pedagogy. (KHR)

Focuses on the activity system of school-teaching mathematics and the impact of mathematical modeling. Describes the Applications of and Modeling in School Mathematics Project (AMSMAP) which investigates teachers' mathematical modeling and its relationship to a hypothesized school mathematical modeling activity system. Discusses the notion of an…

Investigates what the role of arguments from physics within mathematical proof is, and how this role should be reflected in the classroom. Presents examples showing the fruitfulness of center of gravity arguments in terms of geometrical configuration and the laws of the lever. Discusses educational advantages of the use of arguments from physics…

Reviews issues related to the field of ethnomathematics. Discusses ethnomathematics from the south of Brazil with the signs of inequality and injustice that prevail there. Analyzes methodological aspects of research on the "ethnomathematics approach". (Author/MM)

Describes and reflects on a research journey from a theoretical perspective which sought to understand what it means in practice to "become critical". Based on a South African curriculum that reflects upon aspects of conflict and dialogue in mathematics pedagogy. (MM)

Discusses the question "why teach mathematics to all students"? Clarifies, elaborates, and abdicates a previous article on the same subject. (Contains 18 references.) (ASK)

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)