In this paper, a focus is made on defining processes at stake in an unfamiliar situation coming from discrete mathematics which brings surprising mathematical results. The epistemological framework of Lakatos is questioned and used for the design and the analysis of the situation. The cognitive background of Vergnaud's approach enriches the study…

In the study, a part of longitudinal research focused on the emergence of mathematical knowledge structures in a learner's mind is presented. It concentrates on the analysis of introspective data gained from the author's study of a non-standard arithmetic structure in terms of the model of abstraction in context (Hershkowitz, Schwarz and Dreyfus).…

From a rhetorical perspective, Mendel's work and its reception elicit two important questions: (a) why were Mendel's arguments so compelling to 20th century biologists? And (b) why where they so roundly ignored by his contemporaries? The focus of this article is to examine the latter question while commenting on the former by employing several…

This document contains 53 plenary and contributed papers presented at the eighth Psychology of Mathematics Education (PME) meeting. Two plenary addresses focused on mathematics research in Australia and Japan, and problem solving and symbolism. Contributed papers were classified under 13 headings including: teaching and learning theory; cognition;…

This document contains plenary and contributed papers presented at the seventh PME meeting, held near Jerusalem, Israel in July 1983. Three plenary papers focused on implicit models in solving problems, discussions with teachers and children, and heuristics. Contributed papers were classified under seven headings: learning theories…

Stevens postulated that we can use the responses of a participant in a ratio scaling experiment directly to construct a psychophysical function representing the participant's sensations. Although Stevens' methods of constructing measurement scales are widely used in the behavioral sciences, the problem of which scale type is appropriate to…

Three addresses by internationally renowned mathematics researchers and a fourth paper on the role of research are presented. Each of the addresses focuses on the learning process, but from different points of view. Heinrich Bauersfeld provides an analysis of the miscommunication inherent in many teacher-student interactions. Four deficient areas…

Even after a number of innovative programs and proposals have met selective criteria, the Educational Research Commission will have a difficult task in assigning priorities and spreading resources. This paper offers many suggestions for handling the problems in research and evaluation related to innovative mathematics projects, especially K-3. For…

The establishment of Research and Instructional (R and I) Units is discussed in terms of their utility and applicability for research needs. These units are said to provide a propitious setting for rigorous educational research. Two experiments in R and I units are described--one dealing with ways to implement feedback to students on their school…