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…

Mathematics education is viewed as a process imbedded in social interaction. Alternatives to seven widely recognized modeling perspectives that provide conceptual foundations for mathematics learning are discussed. (MP)

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)

Demonstrates that Vygotskian theory can support two opposing interpretations: supporting reform and undermining reform. Discussion is organized by: sociocultural perspectives, Marxist influences on historical analysis and the role of labor, semiotics and psychological tools, dialectic of thought and language, conceptual development, and learning…

Discussed is the research method of "didactic engineering" and the potential theoretical problems of putting research findings into practical use as teaching methods in mathematics classrooms. Cited is the possible incompatibility between the theoretical principles of experimental methods and teachers' conceptions. (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…

Discusses formalizing in mathematics and provides anecdotal illustrations of formalizing in a constructivist environment, using students aged 12 and 8 involved in fraction work. (Contains 19 references.) (MKR)

Discussed are categorization schema, with elaborations about attendant epistemological obstacles, concerning the twin notions of understanding and comprehension, per se, as well as the processes affecting their attainment. Included is an example of such a schema involving the concept of the limit of a numerical sequence. (JJK)

Pre-experimental interviews conducted with three children to investigate three aspects of the nature of counting are detailed. Sixteen findings related to the counting of perceptual items are summarized. (MP)

Reports a study designed to identify 9 and 11 year olds' ways of drawing nets of solids and to provide opportunities for them to reflect on their models in whole class discussions. Results indicated that children's views of solids' nets progressed from more global and holistic to more quantitative and analytic. (MDH)

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 the portion of a larger study of A-level British students understandings of calculus that deals with ambiguities inherent in the phrases "tends to,""approaches,""converges," and "limit." Responses to two questionnaires indicate that the four phrases generate everyday connotations that are at odds…

Presents the reactions of a mathematics educator and a mathematician to a seven-year-old student's response for finding square numbers. Reflects on the mathematician's focus on the mathematics of the problem and the mathematics educator's focus on the student's systematic way of working, and discusses the common focus of student creativity. (MDH)