This monograph was developed with the intention of addressing the concerns of high school mathematics teachers in Alberta (Canada) who want to base their programs on problem solving but have questions about effective and efficient ways to do so. Considered are the most basic philosophical questions, and a framework is provided to use in solving…

Presents six problems from an alternative approach to homework traditionally given to follow-up lectures. Stresses the advantage of longer term exercises which allow for creativity and independence on the part of the student. Problems include: "System Model,""Open-Loop Simulation,""PID Control,""Dahlin…

Discusses figurate number learning activities using patterns and manipulative models. Provides examples of square numbers, triangular numbers, pentagonal numbers, hexagonal numbers, and oblong numbers. (YP)

Provides a discussion and an example of a problem which occurs in mathematical contests or entrance examinations and deals with the question of the magnitude of exponentials. Includes additional illustrative examples. (RT)

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)

Argues that there is a sense of surprise and wonder that can result from looking back at problem solutions and there is a potential for then creating unexpected, even memorable, alternative solutions. Example problems with routine solutions and alternative approaches uncovered while "looking back" at the solution are given. (PK)

Describes a take-home exam story problem based on stoichiometry. Requires the student to determine the percentage of phosphoric acid in a large container of nitric acid if a man fell into it. Provides assumptions, clues, and an acceptable solution. (MVL)