Compares and contrasts the approaches to mathematics in Montessori schools and traditional schools. Suggests that in a traditional curriculum, math is studied as a separate subject and isolated discipline, in an abstract format, with the entire group of children moving together through the prescribed curriculum. In contrast, the Montessori school…

Described is a game that is used to introduce the concept of multiplying integers. Serving as a physical model for the concept, "Froggie Frolic" races frogs along a number line by moves that indicate direction, magnitude, and number of jumps, thus modeling integer multiplication. A teacher's guide and worksheets are provided. (MDH)

Describes the development of the "Standards Beliefs Instrument," an instrument to measure teachers' beliefs about the NCTM "Curriculum and Evaluation Standards." Discusses implications for using the instrument for self reflection, assessment of teachers' perspectives toward the vision of the "Standards," and…

Reports misconceptions identified in students with respect to the topic of parallel lines and the teaching strategies found to be useful in challenging those misconceptions. (11 references) (MDH)

Presents a survey of 78 pre- and in-service elementary teachers in a midwestern region to examine the relationship between mathematics anxiety, perceptual preference, and previous mathematics instructional experiences with workbooks and manipulatives. Results indicate that the variables significant in predicting mathematics anxiety were…

Describes the Mathematics Correspondence School that was organized in late 1960s and still directed by the author, to serve about 1,000 Russian secondary students in small cities and remote villages. Discusses this project's extension to other disciplines, and the introduction of English versions of the school's textbooks via this regular journal…

Describes an evaluation of two video modules developed at the University of Plymouth (United Kingdom) to interest and motivate students in learning mathematics. Videos to teach the concepts of motion and of momentum and collisions are described; students' and teachers' attitudes are discussed; and evaluations of revised versions are reported.…

Discusses possible approaches to solving the problem of how many different triangles can be formed on an n x n geoboard and the different geometric concepts utilized to formulate a solution. Approaches include counting strategies, writing a computer program, and using difference equations. (MDH)

Discusses dilemmas teachers may face when shifting their concept of teaching or tutoring from explaining or telling to a constructivist perspective of facilitating the development of students' knowledge structures. Examines teachers' decisions during a 20-minute segment of dialogue between a student and teacher while studying linear functions. (14…

Describes an activity to construct polyhedra resembling molecular structures. Each face forms regular polygons made up of balls. Step-by-step directions are provided to perform the constructions. (MDH)

Presents two worksheets that ask students to count and classify the triangles that can be formed with a given total number of toothpicks or a given number of toothpicks for one side of the triangle. A third worksheet asks students to identify patterns observed during the investigations. Provides reproducible worksheets. (MDH)

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)

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)

Presents real life vignettes of a fifth grade teacher teaching mathematics. The teacher intended her students to find mathematics engaging, work cooperatively, and solve problems that relate to real life experiences. Noted a questionable focus and outcome for the teaching activities. (BB)

This case study illustrates an important change in one fifth grade teacher's views about mathematics teaching that occurred over the course of a year as a result of California's movement to reform mathematics teaching. However, the change did not appear to be reflected in the teacher's classroom practices. (BB)