Two articles are provided that respond to the paper, "Is the Proof in the Practice" by Tony Barnard (Sep. 1989). Authors emphasize interesting, creative, and discovery-oriented mathematics instruction instead of memorizing. (YP)

Discusses geometric construction problems. Presents four ways to construct a regular octagon using different conditions. Provides drawings showing the constructions. (YP)

Discussed is a high school mathematics curriculum for students pursuing majors in collegiate business programs. Proposed are different emphases in the curriculum by different career fields such as audit manager, marketing manager, and production manager. (YP)

Presents a method for using matrix algebra and computers to encode and decode secret messages. Provides examples of coding procedures, a short review of matrix multiplication, and a BASIC program for use with secret messages containing up to 1000 numbers. (RT)

Examines secondary school students' ability to interpret representations of three-dimensional objects including prototypes of component, perspective drawings, orthogonal views, descriptions by coordinates, verbal descriptions, and verbal quasi-descriptions. Students were given four identical wooden cubes and asked to construct the objects. Reports…

Investigates the understanding of particular mathematical words or terms of secondary school students in Belfast. Presents sample items and results of two tests. Discusses some implications for the teaching of mathematics. (YP)

Described are the methodology of MUT (Mathematical Understanding of Taiwan Students) program and CSMS (Concepts in Secondary Mathematics and Science) program. This study compared languages, learning motivations, and teaching methods in Taiwan and England using the two programs. Some implications for mathematics education are discussed. (YP)

A police officer presented a question about a formula on speeding. This application was a good real-world example of radicals to present in an algebra class. How it was used is presented. (MNS)

Mathematical proofs often leave students unconvinced or without understanding of what has been proved, because they provide no visual-geometric representation. Presented are geometric models for the finite geometric series when r is a whole number, and the infinite geometric series when r is the reciprocal of a whole number. (MNS)

Describes the use of step-functions in modelling instruction. Classifies modelling into three categories: direct, analogical, and creative application. Provides and discusses modelling postal rates and other problems as examples. (YP)

Presented are mathematical games in six categories of mathematical objectives: learn the language of mathematics; use mathematical notation; know facts; develop skills; understand concepts; and devise strategies. Numbers of players, rules, and diagrams are provided for each problem. (YP)

A structured system of visual features is seen to parallel the propositional hierarchy of operations usually associated with the parsing of algebraic expressions. Women more than men were found to depend on these visual cues. Possible causes and consequences are discussed. Subjects were secondary and college students. (Author/DC)

Secondary geometry students were tested for van Hiele level of thinking, geometry knowledge and achievement, and proof-writing achievement. Proof-writing achievement correlated significantly with van Hiele level entering geometry knowledge and geometry achievement. The predictive validity of the van Hiele model was supported. (Author/DC)

Discusses the benefits and possible side effects of learning mathematics through routine exercises. Suggests some teaching strategies including different exercises, different symbols, making examples, and counterexamples. (YP)

This article discusses the impact of symbolic-manipulation systems on secondary school mathematics curriculum. Characteristics and possible roles for the symbolic systems are explored. Four references are listed. (YP)