Discusses a way to help children retain the desire to understand mathematical ideas and to carry out routine procedures. Describes a method using computers to teach linear equations and calculus. Eight references are listed. (YP)

Presents a lesson to compute differences of positive and negative numbers using historical events of science. Describes the skills, concepts, objectives, rationale, outline, procedure, evaluation, and extensions of the lesson. Provides a list of events in the history of science. (YP)

Describes the steps for making overhead manipulative materials on base-10 blocks, colored chips, place-value charts, number lines, and grids. Suggests the materials, procedures, and uses. (YP)

Provides two examples of the "regular falsi" method using geometry and a computer program. (YP)

Provides four activities asking students to observe and classify star patterns and to identify polygons and continuous paths while observing similarities and differences. Presents the objectives, directions, extensions, answers, references, and worksheet for each activity. (YP)

Discusses the application of probabilistic ideas, especially Monte Carlo simulation, to calculus. Describes some applications using the Monte Carlo method: Riemann sums; maximizing and minimizing a function; mean value theorems; and testing conjectures. (YP)

Examines the role of visualization within the process of geometrical concept attainment for students in grades five through eight, preservice elementary teachers, and inservice senior elementary teachers. Investigates the "bitrian" and "biquad" examples, numbers of critical attributes, elements in triangles, judgment in quadrilateral examples, and…

Mathematics is perceived as a boring subject by some secondary students. Lists and describes 10 types of mathematical surprises across the secondary mathematics curriculum that help to make mathematics more interesting. (YP)

Describes the definition and characteristics of a regular polyhedron, tessellation, and pseudopolyhedra with diagrams. Discusses the nature of simplex, hypercube, and cross-polytope in the fourth dimension and beyond. (YP)

This article shows the application of the ratio concept to the working of a 10-speed bicycle using a formula and tables. Two references are listed. (YP)

Two studies investigated the following: (1) the perceptions of college math teachers and students (n=27) of the clarity of three explanations of a standard problem solution procedure and (2) the extent to which math teachers' and students' (n=23) oral presentations showed some awareness of the general mathematics principles inherent in three math…

Presents an example of the use of historical materials in developing the concept of logarithm. A description of the unit includes the origins of the word logarithm and the objectives, organization, and implementation of the unit. The historical development establishes the connection between arithmetic and geometric progressions and logarithms.…

Describes a three-week summer institute for middle school teachers in which they explored quantitative reasoning, the notion of variable, various algebraic concepts, and proportional reasoning. Activities included journal writing, field experience, and sharing time. (MKR)

Illustrates use of rule space as a tool for cognitive analysis of students' mathematical behavior. The rule-space approach is explained and used to classify students according to two methods for solving linear algebraic equations in one unknown and diagnose their knowledge states on this topic. (Author/MDH)

Presents three patterns found in math for elementary students. Spirolaterals are patterns made by repeatedly tracing a series of three numbers in four directions on dot paper. Tessellating can be a combination of teaching about patterns, geometry, and art. The King's Problem requires recognition of a problem to find a solution. (PR)