Discusses examples of the detailed explanations that students offered in response to a written, open-ended geometry task, especially the ways in which students communicated their knowledge. Illustrates how different students may select different methods of communication such as using text, diagrams, or mathematical symbols to display their…

Illustrates the varied mathematical reasoning involved when a geometric construction problem is solved with three different manipulative tools. (Author/NB)

Investigates problems called "cranium crackers" and focuses on number sense, logical reasoning, data analysis, geometry, measurement, and algebraic thinking. (Author/NB)

Describes the idea of teaching as active learning and defines direction in mathematics teaching as action and perception. Presents an example of a mathematics classroom activity in which students are centered. (KHR)

The exploration, discovery, and generation of attractive two-dimensional designs as an approach to informal geometry and spatial learning is discussed. Six activities with brief instructions are presented. (CW)

Illustrates how heuristics can provide a psychological narrative of Hippocrates' and Archytas' thinking on the duplication of the cube. Four general heuristic techniques were used. (YP)

Proposes that the writing of proofs in geometry class can be a vehicle for attaining the goals of problem solving, reasoning, and communication in the mathematics classroom. Presents a student-teacher dialogue illustrating this process. (11 references) (MKR)

Investigates the problem of finding all triangles that have natural-number sides for which the area is numerically equal to the perimeter. (ASK)

This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and…

The authors have attempted to implement "less is more" in a variety of educational contexts. The schools they have been part of include a pilot school in Boston, New Mission High School(New Mission), a charter school in Fitchburg, North Central Charter Essential School (NCCES), and a charter school in Devens, Francis W. Parker Charter…

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 4-6, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, whole numbers, number theory, fractions, decimals, geometry, ratio, proportion, percent, probability, sets, and…

A series of problems involving number theory, the law of cosines, and geometric interpretations of solutions to equations is discussed. (SD)

The nature of measurement, the standard measurement concepts are discussed in terms of children's preconceptions and activities for building measurement concepts through primary school instruction. A broad range of activities including counting, computation, calibration, and relating measure to size is presented. The metric system is briefly…

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

This study was undertaken to explore the problem solving processes of secondary-school students. Geometry students were given an experimenter-constructed test of convergent and divergent thinking and classified as high on both, high convergent, high divergent, or low on both. Of these 105 students, 49 were selected for individual observation as…