Problem solving is one of the main components of mathematics education. This document treats problem solving as a process to be used for learning skills across the mathematics curriculum. Definition of problem solving, the environments promoting problem solving, teaching behaviors and attitudes that enhance problem solving, the criteria for good…

The findings of this study support the positive effect of constructivist learning practices, specifically on emphasis on problem solving strategies and their effect on student mathematics achievement. The results also suggest that setting, certification, teaching experience, gender, and minority status are factors related to the use of…

Examples, exercises, and solutions involving compound growth are contributed that emphasize the areas of lending, borrowing, and investing. It is felt these areas present a wealth of opportunities for mathematical modeling, the development of algorithms, and practical applications, and can be fully explored throughout typical secondary…

The use of exercises that students can perform independently of any calculating aids and in a reasonably brief space of time is promoted, so that pupils can concentrate on the processes involved and any relationships of interest. Some examples are presented with the goal of increasing learning promoted. (MP)

To help mathematics teachers introduce and reinforce concepts and processes by using relevant problems, several such problems are presented and discussed. (MNS)

Five problems are given which are designed to challenge gifted students while giving them opportunities to use algebraic concepts. Solutions are provided. (MNS)

Problems involving multicolored cubes are discussed with examples of Instant Insanity and Rubik's Cube cited. Sections cover defining chameleonic cubes, producing such a cube, and extending understanding to multidimensional cubes. One theorem proved is that for each positive integer, every cube of that size is chameleonic. (MP)

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

Programmable calculators are useful tools in the classroom that are often overlooked. This report gives examples of problems and activities that can be brought within the scope of such calculators. (MP)

An excursion in applied mathematics is detailed in a lesson deemed well-suited for the high school student or undergraduate. The problem focuses on an experimental missile guidance system simulated in the laboratory. (MP)

Analogies between topics in algebra and in arithmetic are noted. It is suggested that algebra teachers should consider how to take advantage of student backgrounds in arithmetic by exploiting these analogies. (MP)

This report explains the mathematical origin of the Annual Percentage Rate (APR) approximation often used in elementary Business Mathematics courses. (MP)

A problem considered an interesting challenge to students with a good command of algebra and trigonometry is presented. (MP)

An approach to teaching geometry is promoted that allows students to decide for themselves what they could prove from given information. Such an approach allows pupil involvement in the personal process of discovering mathematical ideas and formulating problems. It is noted these methods will not work for all. (MP)