Some questions about the relevance of the philosophy of mathematics to mathematics teaching and to early mathematics learning are discussed. Books by Lakatos, Davis and Hersh, and Kitcher are referred to extensively, with comments on a variety of instructional practices. (MNS)

The mechanism of routine practice and problem solving that is used as a method of teaching and learning is not simply interpreted as a way in which students only mechanically imitate and memorize rules and skills. Manipulative practice is the genetic place of mathematical thinking and the foundation of concept formation. (ASK)

Describes a study which took place in a grade 9 classroom that consisted of five groups with 3-5 pupils in a group. Pupils were required to calculate the areas of a number of shapes on a geoboard. Concludes that a teacher working with pupils in small groups brings new challenges for mathematics teachers. (Contains 11 references.) (ASK)