Uses a graphing calculator to demonstrate that dividing by a fraction is the same as multiplying by the reciprocal. Students graph a division problem and an equivalent problem, multiplying by the reciprocal. They find that the graphs are the same. (SKS)

Describes three activities in discrete mathematics that involve coloring geometric objects: counting colored regions of overlapping simple closed curves, counting colored triangulations of polygons, and determining the number of colors required to paint the plane so that no two points one inch apart are the same color. (MKR)

Reviews research on importance of strong professional communities for supporting reform. National Center for Research in Mathematical Sciences Education (NCRMSE) found significant correlation between teachers' professional community and reformed mathematics instruction. Urban Mathematics Collaboratives (UMC), Quantitative Understanding: Amplifying…

Analyzes a discussion among students as they try to find the perimeter and area of an irregular shape on a geoboard. Considers implications for teaching and suggests reflecting on discourse, students' attributes, and mathematical tasks. (DF)

Discusses several dynamic geometry constructions with rectangles. Advocates use of software like Geometer's Sketchpad and Cabri Geometry for fostering fresh insight into traditional geometric theorems. Illustrates problem-solving methods not possible with pencil and paper. (MTE)

Compares observed to expected counts of white, African American, and Hispanic major-league baseball players (n=650) in 1989. Uses chi-square values to determine that racial differences are highly significant for pitcher, catcher, shortstop, and outfielder. Includes appendix with 1993 player counts and seven suggested student activities. (SEW)

Introduces concepts of modern algebraic group theory in the form of a game. Peg boards and rubber bands represent nonnumerical group elements and are manipulated under the operation of reorienting a regular polygon. Symmetry groups are used to explore set properties, as well as commutative and noncommutative operations. (CMS)

Explains standard drawing layouts and rules for creating orthographic and isometric views of a three-dimensional object. Normal and inclined surfaces are also discussed. Concludes with recommended classroom activities. Includes reproducible student worksheets. (FDR)

Discusses the importance of calculators in the teaching and learning of mathematics. Argues that affordable graphing calculators let all mathematics students use computer visualization on a regular basis for both in-class and out-of-class activities. (ASK)

Explores a workable definition of mathematical structure and a rationale for teaching mathematical structure in the secondary school. Continues with mathematical structure appropriate for secondary mathematics teachers and suggestions for teaching mathematical structure in the secondary school. Contains 11 references. (ASK)

Discusses methods of using small dry-erase boards with each student so that students can do work in class and readily change answers. Notes that the boards are large enough so students can easily see other students' work for feedback purposes. (MVL)

Presents an extension of the hog game that satisfies the mathematical process activities of observing patterns; forming, testing and proving hypotheses; and applying and extending proved results. Discusses use of technology in the investigation of problems and in the process of devising and validating general rules. (ASK)

Presents an interesting problem intended to introduce students to an application of algebra and to help them make the transition from arithmetic to algebra. Uses different problem representations including making successive approximations, interpreting graphs, and solving equations. Discusses pedagogical issues involved. Contains 11 references.…

Contains 10 miscellaneous mathematics questions and their answers that teachers can use in their lessons. Topics include estimation, prime numbers, line equations, and investment strategies. (ASK)

Describes an activity whose objectives are to encode and decode messages using linear functions and their inverses; to use modular arithmetic, including use of the reciprocal for simple equation solving; to analyze patterns and make and test conjectures; to communicate procedures and algorithms; and to use problem-solving strategies. (ASK)