We consider here a number of ideas for the classroom or lecture theatre associated with the mensuration of solids. In particular, the volumes of various tetrahedra are obtained in an indirect manner (by way of prisms and square-based pyramids). This activity develops problem-solving skills, spatial visualization and a from-first-principles…

Anne Roche and Doug Clarke discuss the importance of developing students' persistence in relation to problem solving during the use of challenging tasks. They provide a useful list of strategies that teachers can use to encourage persistence amongst their students.

This practice guide presents five recommendations intended to help educators improve students' understanding of, and problem-solving success with, fractions. Recommendations progress from proposals for how to build rudimentary understanding of fractions in young children; to ideas for helping older children understand the meaning of fractions and…

This article presents a hands-on experiment that covers many areas of high school mathematics. Included are the notions of patterns, proof, triangular numbers and various aspects of problem solving. The problem involves the arrangements of a school of fish using split peas or buttons to represent the fish. (Contains 4 figures.)

This article, which describes integrating virtual manipulatives with the teaching of probability at the elementary level, puts a "virtual spin" on the teaching of probability to provide more opportunities for students to experience successful learning. The traditional use of concrete manipulatives is enhanced with virtual coins and spinners from…

Fourteen steps are suggested: perceive problem, decode written symbols, formulate general meaning, translate the general message into the mathematical message, determine question(s), gather data, analyze relationships, decide on processes, estimate answers, encode data into mathematical sentences, perform operations, answer questions, and check…

Students use tables of anthropometric data, their own measurements, underlying principles of physics, and math to solve a problem. The problem is to determine the height of a wall mirror, and where to mount it, so that 90% of the clientele can view their entire length without stretching or bending. (Author)

This document presents ideas and activities for teaching algebra. The section on "Week by Week Essentials" provides seven resources in a weekly format. It includes writing ideas that provide an algebra prompt and requires students to organize their thoughts and present them in a coherent fashion, and connections to the real world that…

An exhibit at the San Francisco Exploratorium is used to discuss problem solving and illustrate optimization. The solution is discussed in detail. (MNS)

The problem "Given three planar points, find a point such that the sum of the distances from that point to the three points is a minimum" is discussed from several points of view. A solution that uses only calculus and geometry is examined in detail. (MNS)

Examines the problem-solving processes of social studies and mathematics and discusses their commonalities. Considers how those processes might be taught so that students will see that there is indeed a relationship between those two seemingly discrete disciplines. (RS)

Finding a fractional number equal to an infinite decimal is solved by two usual methods. Then a third method is discussed that allows students to avoid having to confront the idea of an attained infinity of symbols. (MNS)

The article offers suggestions for helping gifted elementary students learn to use independent thinking skills to challenge their own thinking as well as to solve mathematical problems. (DB)

Presents an overview of how a number of cognitive factors are involved in solving quantitative problems by secondary-school students categorized as skilled and less-skilled. Gives illustrations for the solving of basic and complex composite problems in chemistry. Suggests directions for enhancing instruction in problem solving based in this…

Demonstrated is how the concept of equivalence classes modulo n can provide a basis for solving a wide range of problems. Five problems are presented and described to illustrate the power and usefulness of modular arithmetic in problem solving. (MNS)