The organization of instruction is described in terms of four basic aspects of teaching mathematics: (1) recognizing sufficient conditions for concepts, (2) recognizing characteristics of concepts, (3) selecting examples, and (4) determining when a concept can be applied. (SD)

Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system. (PVD)

Presents activities to help students develop the notion of geometric congruence and similarity in a hands-on environment. (ASK)

Discusses the interconnection among the various modes of the TI-92 calculator (geometry, data graphing, function graphing, and algebra) and how the power of visualization is extended to provide multiple approaches to complex problem situations. Provides a graphing problem with illustrations and results. (AIM)

Presents the results of a case study which looked at the mathematics classroom of one teacher trying to teach mathematics with meaning to pupils or lower ability at the secondary level. Contrasts methods of teaching linear equations to a variety of ability levels and uses the Pirie-Kieren model to account for the successful growth in understanding…

Data were collected from 540 fifth-grade students on problem solving, justification, and explanation of fractions. Fewer than 10% performed adequately on the explanation task. Students who received a seven-day instructional program on fractions in measurement contexts performed better than students receiving traditional part-whole instruction.…

Describes an interdisciplinary unit on the environment and space travel in which students plan a fictional departure from Earth which is on the brink of destruction from environmental waste and neglect. Students travel through concepts in environmental education, math, art, English, and astronomy before reaching their destination with a clearer…

Studied the use of multimedia cases to support teacher education in learning to mathematize and didactize and to learn how to use multimedia cases with their student teachers. Findings from the study of one course result in a six-step framework for working with multimedia cases. (SLD)

Studied the effectiveness of a teacher training approach in which preservice mathematics teachers conduct and analyze one-to-one mathematics assessment interviews with primary-aged children. Findings from interviews with five teachers and a focus group of six indicate teachers are more aware of the strategies children use including their variety…

Presents an approach to explaining a relation, a - b = -(b - a), that is difficult for algebra students to understand. The approach came about as a result of discussions with students in which they provided many novel explanations. (DDR)

Presents to second graders the concept of an n-gon, characterized by a commutative diagram which is composed of four ways of judging a given figure. Observes that some children gave persuading arguments containing a critical idea and the concept formation corresponding to a structure-preserved transformation in the diagram. (AIM)

Suggests that involving Russian experts in solving concrete educational problems and providing curriculum development in the United States could be very useful. A primary goal would be to change the attitudes and beliefs of teachers and to extend teachers' views on teaching mathematics. (AIM)

Describes a professional development project to increase teachers' understanding of proportional reasoning, the thinking patterns associated with proportional reasoning, and the applications of proportional reasoning across the middle-grades curriculum. (YDS)

Discusses the importance of identifying and describing the pattern by students in algebra class. Provides some examples showing the usefulness of the method seeing the pattern from mathematical materials. (YP)

Presented is a method where a quadratic equation is solved and from its roots the eigenvalues and corresponding eigenvectors are determined immediately. Included are the proposition, the procedure, and comments. (KR)