How the computer as a metaphor affects our understanding of the processes of learning and teaching is explored. After describing reflection and recursion in mathematics and their roles in thinking and learning, models of the mind and teaching effects are discussed, with self-awareness as a theme. (MNS)

Examination of the development of the standards documents of the National Council of Teachers of Mathematics (NCTM) points to constructivism as the central view of learning that underlies the reform movement in mathematics education. Constructivism is a theory of how learning occurs. It assumes that knowledge is not passively received, but rather…

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)