These exercises explore both square and nonsquare rhombi constructed on dot-paper grids. The materials are designed to provide reinforcement of geometric concepts, construction of figures from their symmetric properties, and discovery of figures related to each other by transformations. Student access to geoboards is encouraged as helpful. (MP)

Four stages of problem solving are believed to occur in programing. Spirolaterals are discussed as specific examples of programing activity that have mathematical and programing interest. The BASIC programing language is used on the Apple II computer to provide examples of possible solutions to the problems posed. (MP)

The following ideas are included: (1) solving a quadratic equation geometrically by completing the square, which helped a class of secondary physics students understand the formulas; and (2) a way of teaching factoring of quadratic trinomials that is based on the behavior of odd and even numerals under addition and multiplication. (MP)

Examples and nonexamples of geometric concepts are discussed. Four guidelines for selecting and using geometric examples and nonexamples are presented. (MK)

A variety of geoboard activities for use with primary children is suggested. (MK)

Adults' geometric analogy solution was investigated as a function of systematic variations in the information structure of items. Latency data from verification of true and false items were recorded. A model incorporating assumptions about the form of item representation, working memory factors, and processing components and strategies was…

A program designed in BASIC for the Apple II computer that uses high resolution graphics to display geometric transformations is described. The four distance-preserving transformations included are translations, rotations, reflections, and glide-reflections. Shape-preserving dilations are also covered. (MP)

A method of teaching multiplication facts to remedial students using fingers and an alternate geometric proof developed by students are suggested. (MK)

This is a review of the current research in mathematics involving breadth of ideas. Research includes topics in number theory, classification of all finite simple groups, the representation of group aids in their application to the study of symmetry. (Author/SA)

The author argues against some topics included in the standard high school mathematics curriculum, including traditional algebraic word problems, trinomial factoring, complicated fractional expressions, and some geometric theorems and proofs. (MP)

The process that Hippasus of Metapontum (ca. 470 B.C.) may have used to discover irrational numbers is reconstructed. (MP)

The Poincare group, the group of transformations of the plane which preserve the Minkowski distance between points, is derived as compositions of suitably defined reflections in straight lines. It is shown that any such transformations must be one of four types. (Author/JN)

The effect of testing format on achievement was investigated. Statistical analysis indicated no significant differences between any of the four formats used. (MK)

As a part of the investigation into children's understanding of mathematics undertaken by the Concepts in Secondary Mathematics and Science (CSMS) project, students in English secondary schools were given a class test on transformation geometry. This is a discussion of the results of the third-year sample, who were about 14 years old. (Author/MK)

A method is presented for determining cube roots on a calculator with square root facility that has a rapid rate of convergence. (MP)