Some errors in the learning of algebra suggest that students might have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing to analyze the students' capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process, depending on the characteristics of the algebraic…

As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

Investigates processes involved in visual estimation and processes of judgment in visual estimation situations involving proportional reasoning. Exposure to a unit in the Agam project, designed to enhance visual estimation capabilities, resulted in changes in the nine-year-old subjects' strategies, reflecting processes by which children overcome…

Provides new evidence for mathematical problem-solving abilities of preschool children. These problem-solving behaviors occurred in a study of sharing of discrete items by dealing, in which we examined the abilities of three categories of counters to solve a discrete redistribution problem. Identifies problem-solving strategies used in the context…

Describes a preservice program to prepare teachers for a curriculum based on the realistic approach. The program appeared successful in changing student teachers' views of mathematics education towards this more inquiry-oriented approach and in promoting effective teacher behavior in classrooms. Only a small number of teachers recognized the…

Learning environment that facilitated the acquisition and expression of procedural skills in LOGO was set up for children in the 10- to 12-year range. Ten participants were placed in a series of situations that required them to manipulate programing procedures in LOGO. Analysis of children's behavior revealed their competence in manipulating…

Examples from related case studies illustrate possible consequences of a social constructivist approach to learning and teaching mathematics. Discusses student tasks that promote flexibility in mathematizing subject matter; constructive versus Euclidean geometry approaches; working with real-life mathematics problems; and product versus process…

Identified and classified solution strategies of (n=49) 10th-grade students who were presented with linear programming problems in a predominantly visual setting in the form of a computerized game. Visual strategies were developed more frequently than either algebraic or mixed strategies. Appendix includes questionnaires. (Contains 11 references.)…