A quasi-systematic strategy of devising rule sets for problem solving is applied to ruler and compass geometrical constructions. "Lower order" rules consisting of basic skills and "higher order" rules which govern the selection and combination of lower order rules are identified by an analysis of problem types; three types of…

This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

The overall results of the fourth U.S.A. Mathematical Olympiad are discussed. The names of the eight finalists are listed, as are the problems in the test. (SD)

Beginning with an analysis of the golden rectangle, the author shows how a series of problems for student investigation arise from queries concerning changes in conditions and analogous situations. (SD)

Six different methods were used by students to solve the problem of finding the area of a given trapezoid. A seventh method used by textbooks is also discussed. (MP)

This problem solving strategy is illustrated by examples from the fields of algebra, trigonometry, geometry, and calculus. (MP)

Graphical solutions are illustrated for several algebra problems including finding roots of a quadratic equation, solving mixture and motion word problems, factoring the difference of two squares, and constructing the square root of a positive number. (MN)

A problem is discussed in which students investigate the properties of the perfect triangle. (MNS)

Presents activities involving the addition of antinumbers (which uses novel numerical characters); a puzzle which combines practice in working with polynomials and solving simple equations with intriguing facts about turkets; and searching for the number of different right triangles in a given square grid (which helps develop spatial…

A possible logical flaw based on similar triangles is discussed with the Sherlock Holmes mystery, "The Muskgrave Ritual." The possible flaw has to do with the need for two trees to have equal growth rates over a 250-year period in order for the solution presented to work. (MP)

Suggests that sex differences in spatial visualization and restructurization are confounded by differences in attitudes toward mathematics and mathematical abilities as well as by task and ego-oriented factors. Subjects were 86 male and female college students. (Author/MP)

A journal called the Ladies' Diary published from 1704 to 1841, presented mathematical problems, and solutions to the problems. The purposes of the journal are compared to those of Scientific American today. (SD)

Profiles a middle school mathematics teacher and examines her use of two problems from a pilot version of a 6th grade unit developed by a mathematics curriculum project. Reports that problem-solving-oriented curricula provide opportunities for students to make mathematics connections and leads to student confusion and uncertainty. Contains 35…