A problem involving the search for an equivalence class of triangles is viewed to provide several exciting and satisfying moments of insight. After solving the original problem, there is a brief discussion of a slight variation and several notes regarding related theorems and ideas. References for additional exploration are provided. (MP)

The article discusses the classic problem: "Given an equilateral triangle and a point P inside the triangle, what is the sum of the distances from P to the three sides?" The problem is used to illustrate the generative nature of problem-posing using the heuristic "What happens if...?" (PK)

This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

Presents a cooperative-learning lesson in which high school students visit stations equipped with different tools to establish the midpoint of a Pixy Stix, a brand of candy-filled straw. Provides solutions for two potential stations, suggestions to extend the activity, and two activity worksheets. (MDH)

"Principles and Standards for School Mathematics" (NCTM 2000) proposes that mathematics instruction provide opportunities for students to engage in mathematical inquiry and in meaning-making through discourse. Mathematics teachers are encouraged to build on student discoveries in designing subsequent instruction. In this article, the author…

Presents a unit to review geometric concepts and problem solving by having students work cooperatively to discover geometric shapes constructed from two congruent right triangles obtained from cutting a rectangle along its diagonal. Students report their findings both orally and in writing. (MDH)

Presents a question designed to launch a discovery journey through conjecture, research, serendipitous encounters, proof, answers, and new questions. Reports some discoveries and suggests ways in which to incorporate this strategy into classrooms. Presents a geometry project that incorporates this problem-solving approach to mathematics. (JRH)

This study is one of several conducted by the authors in their investigation of the use of "higher order rules" in the solution of problems. The focus of the current experiment was determination of the compatibility of identified rules with the knowledge of average teenagers, and of the extent to which instruction in higher order rules…

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)

An activity-based unit on congruence and similarity is described. The themes underlying the unit are the usefulness of analogy in determining mathematical principles, and the notion that the number of conditions imposed on figures affects the number of factors which must be specified to insure congruence or similarity. (SD)

A computer language that can be used by people of all ages, Logo allows children the freedom to direct their own learning. Integrating Logo into the curriculum provides students the opportunity to program a computer, to engage in logical, sequential thinking and planning, to solve problems, and to manipulate text, language, graphics, and music…

The use of a ruler with two parallel Straight edges as a tool in geometric constructions is presented, based on ideas that are fairly standard in high school geometry courses. The constructions are seen as potential challenges that provide opportunities for inventiveness by students. (MP)

Geometric construction problems are recommended as sources of stimulating exercises for mathematics classes. (MP)

A discussion of the reasons for the new design of international standard typing paper (AY) with dimensions of 210 mm by 297 mm leads to a discussion of the ratio of the sides and geometric concepts involving similar rectangles. (MP)