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).…

This paper examines the change in young children's understanding of equals as equivalence over a three-year period and their ability to express this understanding in real world problems. Seventy-six children participated in the longitudinal study. The results indicate that approximately one third of the sample had an understanding of equals as…

The concept of function is central in mathematics and grows in importance as one progresses in depth and breadth of understanding mathematics. Results from national assessment progress reports indicate that the majority of students do not comprehend the concepts of function and graphing. Technology has the potential to improve the understanding of…

This document consists of the two issues of the "AMATYC Review" published during volume year 1997-1998. Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regularly…

This study explored a model for students development of the understandings and skills that are involved in being able to construct graphical representations of data and to interpret these graphs. The study examined four components of prior understanding required for graphic representation that were adapted from a learning map from the Atlas of…

Investigated students' (N=110) understanding of elementary calculus using clinical interview method. Analysis of responses to tasks concerning differentiation and rate of change led to detailed data concerning degree of understanding attained and common errors/misconceptions. Implications for mathematics instruction are discussed. (This is a…

Current practices in teaching about distributivity of multiplication over addition and subtraction are reviewed. Then a study is described in which two inventories were administered to 83 eighth-grade students; scores were low. Suggestions for teaching distributivity are presented. (MNS)

Several major factors must be considered when developing or assessing tutorial microcomputer software for mathematics instruction. Both learning considerations and curriculum considerations are discussed in some detail. (MNS)

A dialog shows how student-teacher interaction on problems can help students learn. Fifty sample problems are provided as starting points for class discussions from grade three through college. Six purposes such problems can serve are identified. A method of classroom presentation, the mathematical scavenger hunt, is discussed. (MP)

Ways to use styrofoam egg cartons and plastic eggs to enhance mathematics instruction are detailed. These materials are viewed as inexpensive, colorful, and easy to obtain. Suggestions for using them to teach concepts related to whole numbers and fractions are provided. (MP)

Activities designed for use with middle-school students to help them discover intriguing number patterns and practice their arithmetic skills with fractions are presented. It is felt that work with repeating number patterns should be both fun and instructive for middle-school and prealgebra students at all development levels. (MP)

Several studies are presented which deal with more/less from a positive perspective based on what children can do, in the hope that results might be helpful to primary school teachers and to teacher educators who work with them. It is felt teacher awareness may help instructors. (MP)

Pattern recognition is viewed as a fundamental cognitive skill that lays the groundwork for the ability to form abstractions and generalizations. Incorporating patterning into the curriculum of young children is encouraged. (MP)

Student exploration at a secondary school level of fraction relationships using special graphs is described. (MP)