This paper describes aspects of 13 year-olds activity in mathematics as emerged during the implementation of proportional geometric tasks in the classroom. Pupils were working in pairs using a piece of software specially designed for multiple representation (symbolic and graphical) of the variation in parametric procedures with dynamic…

This paper is based on the preparatory study of a doctoral study in which we learned to consider defining in the realm of organizing. In particular, having engaged students in a situation based on "equivalence relations" (from an expert point of view), we report two different ways of organizing the given situation. One of them results in a "new"…

This is a step-by-step guidebook that is designed to help students on the quantitative section of the SAT. This guidebook produces an understanding of key mathematical concepts as the various topics are covered by the text, and, unlike other SAT guides, lists skills and capabilities, that if mastered will result in well-prepared students. More…

This study investigates student understanding of the part-whole concept in mathematics at an independent two-year post-secondary institution in New Mexico. The mathematics portion of the Tests of Adult Basic Education (TABE) Summary Form was used as the evaluative instrument. Evidence for a lack of part-whole concept understanding as a hidden…

Based on an individual interest theory as a sensitising theory, empirical data are used to gain social interest concepts, as there are situated collective interest and interest-dense situation. These concepts serve as a basis for a social extension of a psychological interest theory. Its construction combines social interactions, the dynamic of…

In this study, we explore six students' conceptions of Z[subscript n] in an effort to understand students' conceptions of quotient groups in general. We discovered that there were three different ways our students thought about Z[subscript n], namely as infinite sets, element-set combinations, and representative elements. We explore how…

In trying to help students pass the Texas Academic Skills Program (TASP) Examination, changes have been found to occur in the student before efforts at teaching mathematics are effective. A literature review was conducted to seek a philosophical basis to support theories of helping learners. Various learning theories was searched and found that…

A probability problem concerned with drawing balls of a given color from an urn is discussed. Two methods of solution result from two different views of the problem. (JP)

The development of set theory concepts in the early grades is stressed. Examples of set concepts and language essential to other topics in mathematics are discussed. (JP)