The author suggests that spreadsheet computer programs can be an effective tool in the mathematics classroom. In addition to being used to solve many real-world problems, spreadsheets can be used to promote understanding of concepts and principles from geometry, algebra, and trigonometry. (PK)

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

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)

The authors argue that mathematics curricula and teachers should set as objectives the development of logical processes, concepts, and language. The teaching materials described in this article have been used to help second, fourth, and seventh graders become skillful in the use of logic. (PK)

This set of activity sheets requires students to organize and display data with a box-and-whiskers graph. Students use the plot as a summary display to detect patterns and to highlight the important features of the data for purposes of comparison. (PK)

Because most schools do not have courses in formal logic, teachers must teach this topic as it comes up naturally through class discussions in algebra, geometry, or general mathematics. This article shows how teachers can capitalize on students' ways of thinking to lead them to a greater understanding of logical relationships. (PK)

A fairly traditional precalculus problem is modified to address some common concerns with the teaching of problem solving. Areas of problem solving which are illustrated include: posing the problem; modeling the problem; transforming the data; and examining the solution. (PK)

Why calculators should be used for testing, as well as for instruction, is discussed. The focus of the curriculum would shift from computation to deeper development of concepts and to mathematical modeling. A broader curriculum would result. (MNS)

Illustrated are how explorative assignments can help to expose and identify learning problems. Some assignments that address these problems and some techniques and benefits of using writing assignments are provided. (MNS)

Discussed are trends in performance across the last three National Assessment of Educational Progress (NAEP) mathematics assessments for students in grades 7 and 11, and reports on indicators of instructional activity. The results suggest that achievement in mathematics has taken a modest upturn in the 1980s. (MNS)

A beginning solution and generalization are given to a problem on area and perimeter presented in a previous article. Various figures are used to illustrate how posing problems and identifying increasingly general methods promotes problem-solving maturity. (MNS)

Topics from graph theory are introduced at an informal level and thereby made accessible to the majority of secondary school students. Three worksheets are included. (MNS)

An approach to teaching factors and terms is offered that builds directly on students' knowledge of arithmetic. Errors arising from factor and term confusions are noted, followed by the pedagogical strategy of exploration, invention, and discovery. (MNS)

Argues that before topics are added to or deleted from the traditional mathematics curriculum, it should be determined how technology can be used to teach that content. (PK)

Reports on the seventh grade and eleventh grade results of the fourth mathematics assessment of the National Assessment of Educational Progress. Addresses students' performance on variables and relations, geometry, fundamental methods of mathematics, and attitudes. (PK)