The ontological problem is "what exists?" The answer regarding the part of consciousness which is related to left hemisphere is that only individual discrete objects exist; objects are regarded one at a time. The answer regarding the part of consciousness which is related to right hemisphere is only comprehensive entities exist; each…

This in-depth examination of a line explores several ways that the infinite nature and finite representation of a line can be perceived. These attempts to understand the nature of the line give insights into the nature of understanding itself. (MDH)

Discussed is the importance of establishing the link between students' understanding of mathematics in real world settings and the symbolism used to represent that mathematics. Examples provide evidence that students and sometimes teachers fail to establish that link. References are given for resources providing strategies and contexts to assist…

Discussed are supercalculator capabilities and possible teaching implications. Included are six examples that use a supercalculator for topics that include volume, graphing, algebra, polynomials, matrices, and elementary calculus. A short review of the research on supercomputers in education and the impact they could have on the curriculum is…

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)

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)