With our conceptualization of Harre and van Langenhove's (1999) positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current mathematics education literature and…

Programed units of instruction designed with four different sequences of characterizations and exemplifications of disjunctive concepts were given to preservice elementary school teachers. Students were tested on three levels of concept attainment, with differences between strategies resulting, as one moves through the levels of cognitive…

The research objectives were to identify the middle level mathematics teachers' conceptions of mathematics teaching and learning and ascertain changes in their conceptions and instructional behavior at the end of a three-year professional development (PD) project. These changes were studied through the qualitative analysis of their reflective…

The role of negative instances in the acquisition of the mathematical concepts of distributivity and homomorphism was examined. Two treatment levels for distributivity (positive instances and positive and negative instances) and the same treatment levels for homomorphism were crossed to form a 2 x 2 factorial design with 23 subjects per cell.…

Describes a number of ways in which the adoption of the metric system in the United States will increase the effectiveness of mathematics teaching. It provides a concrete model for many concepts commonly taught in grades K-12, and thus provides a means by which confusion can be alleviated. (JR)

Three strategies were used to teach 39 community college students about partition of a set.'' Mean achievement of the Exemplification group on the exemplification test was significantly greater than the average of the means of the Characterization-followed-by-exemplification group and the Characterization-preceded-and-followed-by-exemplification…

Many students can calculate the arithmetic mean but do not understand the concept. The article presents four activities designed to help elementary and middle school students develop this concept. The activities presented assume previous exposure to the computational algorithm for the arithmetic mean. (Author/EK)

The roles of both positive and negative instances in concept formation are discussed. Based on research results, the article stresses ideas that the classroom teacher could try in order to aid concept learning. Several specific examples, based on the concept of commutivity, are given. (LS)

A didactic principle of operative concept formation is described and explained. It is argued that this principle meets current demands for practical geometric activities with concrete forms and for the exploration of the primordial relation between geometry and reality. (MK)

The effects of negative instances on the acquisition of the mathematical concepts of commutativity and associativity were examined. Also investigated were possible transfer effects that might result from the use of negative instances. For 64 ninth-grade subjects, results favored the treatments containing mixed instances and supported the transfer…

Analyzes multiplication word problems to identify the origin of children's difficulty. Emphasis is given to problems involving the concept of combination. (JN)

This article recounts the struggles of an educator as she tries to understand the nature of mathematics. (MK)

The effect on student attainment of the number of moves in a concept teaching venture is examined. Results suggest the number of moves in short ventures had little effect on attainment of mathematical concepts. However, performance increased as the number of moves in longer ventures increased. (Author/MK)

This yearbook presents theories of learning, discusses the research on which they are based, and suggests ways to apply these theories to concrete learning situations. After an introduction to the more prominent theories in chapter 1, the remaining chapters present more specific areas and questions. The next three chapters deal with motivation,…

Problems in mathematics instruction caused by students' poor reading ability are discussed. Teaching strategies based on learning theory are outlined. (MK)