Suggests that secondary school students seem to have reasonably good procedural knowledge in areas of mathematics as rational numbers, probability, measurement, and data organization and interpretation. It appears, however, that students are lacking the conceptual knowledge enabling them to successfully do the assessment items on applications,…

Described is how using LOGO tools for manipulating embodiments of geometric objects helps students construct more abstract and coherent concepts. Discussions are included on developing verbal definitions versus constructing concepts, tasks for integrating turns and angles, group discussions, and maze tasks. (KR)

Proposed is a way for teachers to distinguish between rich, challenging material that encourages mathematical thinking and material that is unsuitable. Included are multistep problems that encourage a broader understanding of mathematics. (KR)

Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)

This study describes the learning of researchers who engage in mathematics teacher education as an integral part of their practice. As teacher educators working with teachers on the subject of proportional reasoning, the authors reflected on teachers solutions to a standard problem and analyzed answers that would conventionally be considered…

This paper summarizes a report designed to provide the National Science Board Commission with information about recent advances in cognitive/behavioral science relevant to mathematics, science, and technology education, as well as prospective contributions from these fields if adequate levels of support are available. Following a summary…

A 3-year study was conducted to determine the logical reasoning processes necessary to construct line graphs. Responses obtained from middle and high school science and mathematics students were classified into one of nine categories. These categories ranged from "no attempt to make a graph" to "complete graph with a statement of a…

This study was designed to test the hypothesis that use of a probability unit in ninth-grade general mathematics classes would yield student improvement in computational skill, arithmetic reasoning, and attitude toward mathematics. A 47-page unit on probability (developed for this study) covered basic terminology, probability of events, favorable,…

Examines operations of generalization, identification, discrimination, and synthesis in mathematical concept development from early childhood to late adolescence according to Vygotsky's theory of development. (MDH)

Describes the relationship between language concepts and the basic patterns of mathematical expressions. Suggests ways to improve the reading comprehension, writing ability, and reasoning skills of school and college students by integrating language topics into the mathematics curriculum. Discusses the use of language concepts in algebraic…

The authors describe one high school teacher's attempt to change her mathematics teaching in ways that are consistent with the National Council of Teachers of Mathematics'"Standards" documents. One of the coauthors is the teacher who teaches in a professional development school; the other, a researcher, conducted regular observations in…

Discussed are inconsistencies and cognitive conflict with respect to current mathematical knowledge of students and how that knowledge might be modified is discussed. The inconsistencies that students generate for themselves and those produced by the teacher are described. (KR)

Uses small axiom systems to teach logic and reasoning to first year mathematics students. Incorporates a collaborative technique to train students to write formal arguments in a nonintimidating atmosphere by applying logic informally to small axiomatic systems. Provides examples of student-designed systems. (MDH)

Discusses a variation on tiling that offers opportunities for the construction of the fundamental mathematical concept of constructing abstract units called "unitizing." Tiling integrates geometric and numerical settings to develop spatial sense and present mathematics as constructing patterns. (MDH)

Describes a study of ninth-grade students that evaluated the ability of the Word Problem Solving Tutor, a cognitive tutoring system, to improve the abstract-reasoning component of word-problem solving. Compares combinations of traditional instruction, computer-assisted instruction, and the tutoring program and discusses implications for math…