The role of mental discipline theory in the history of mathematics education is considered. The author argues that we now remember mental discipline theory only as a caricature of what it was; moreover, it persists among both teachers and researchers. (MNS)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)

Principles on which the teaching of mathematics is based are discussed. Sections concern the skill principle, the curriculum principle, and learning strategy, with many classroom illustrations. (MNS)

The constructivist perspective, which holds that children's learning of subject matter is an interaction between what they are taught and what they bring to a learning situation, could be used to improve mathematics teacher education. (PK)

Begins with the assumption that by practicing something one often learns something else. A discussion is presented on the historical and social development of knowledge, the cognitive development of students, the role of teachers, and the meaning of learning situations. (PK)