This paper explores how the science of interpretation (hermeneutics) may offer an approach to describing the nature of how one develops understanding during mathematical activity. The discussion centers on personal interpretation and its interactive relationship between mathematics and mathematical activity without focusing upon the distinction…

Discusses ways to improve the understanding of problems involving combination and complementation. Analyzes three children's initial mental representations, procedures, and reflections when presented with four different situations. Concludes with the impacts of the logico-mathematical relation of inclusion in these processes. Contains 31…

The results of six studies of children's use of logic and logical connectives are compared and discussed in conjunction with Piaget's theories. (SD)

Arguing that the teaching of stochastic processes should reflect the experience and reality of the student, the author urges concentration on fundamental ideas. The development of intuition should be encouraged, and to this end continuity in teaching and a spiralled curriculum are important. (SD)

The mathematical solution to a Piagetian experiment involving topological concepts reported in a recent book is labeled as a sham. The correct solution is given and discussed. (MP)

Two major periods of development in proportional reasoning are identified by analysis of a 23-item experiment given to subjects between 6 and 16 years of age. (MP)

The author shows some causes of failure in the creation of mathematical concepts. One is the stiffening of concept cores, which prevents identification of atypical exemplars and solution of atypical problems and causes a bifurcation between the natural system of everyday concepts and the formal system of school concepts. (Author/MDH)

The thought processes of 507 elementary, secondary, and university students engaged in problem-solving situations are examined in this study. Results indicated that pupils who got correct answers often showed incorrect reasoning justifications. No significant sex differences were indicated. (MP)

Presented is a theory of how competence with written mathematical symbols develops, tracing a succession of cognitive processes that cumulate to yield competence. Arguments supporting the theory are drawn from the history, philosophy, and psychology of mathematics. (MNS)

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

Sketches a theory for designing teaching based on mathematical activity, situations, tasks, and interventions, exposing and resolving cognitive conflicts, changes of structure and context, feedback, reflection and review. Reviews the main psychological principles underlying this theory, then considers some examples of teaching designs in light of…

Investigated the upper limits of (n=22) seventh-grade students' informal processes in solving first degree equations in one unknown prior to instruction. Results indicated the existence of a cognitive gap between arithmetic and algebra characterized as the students' inability to operate spontaneously with or on the unknown. (37 references)…

An attempt is made to elaborate on the connections and differences between the objective and subjective elements of mathematical knowledge using case study analysis relative to how an epistemological perspective about probability and randomness impacts upon a short classroom teaching episode. (19 references) (Author/JJK)

Discusses changes in student attitudes, beliefs, behavior, and the nature and quality of mathematics activity in the classroom resulting from a constructivist-oriented inservice program for teachers (K-12). Although instruction focused more on conceptual understanding, student scores on standardized tests were maintained. Appendix includes…