The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…

This article reports on the activity of two pairs of sixth grade students who participated in an 8-month teaching experiment that investigated the students' construction of fraction composition schemes. A fraction composition scheme consists of the operations and concepts used to determine, for example, the size of 1/3 of 1/5 of a whole in…

The aim of this study is to describe and analyze students' levels of understanding of exponents within the context of procedural and conceptual learning via the conceptual change and prototypes' theory. The study was conducted with 202 secondary school students with the use of a questionnaire and semi-structured interviews. The results suggest…

Presents a summary report of a discussion subgroup of the Algebra Working Group at the Seventh International Conference on Mathematics Education held in Quebec City, Canada in August 1992. Argues that pre-algebra should be viewed as a continuation of arithmetic that asks different questions about numbers. (12 references) (Author/MKR)

Why students have difficulty with a proof (such as Cantor's) is discussed, with the focus on proof by contradiction. Methods may fail due to the difficulty of the concept and lack of understanding of how students are thinking. (MNS)

A theoretical discussion of categorization, unit structures and structured units, and fractions as operators was introduced. The thinking of grade-three students (n=3) with regard to the meaning of fractions was investigated in two teaching episodes using the computer environments of SuperPaint and CopyCat. (Contains 14 references.) (MKR)

Using case studies that are functionalist in orientation and computational in technique, the role of control knowledge in developing constructive thinking is illustrated. Further, the integration of related knowledge structures, emanating from diverse sensory modes and pertaining to both place value in addition and angle relationships in geometry,…