What is essential in mathematics education? In my opinion the mathematics curriculum must provide the average student with the tools to effectively address significant problems in that student’s life. This article concerns an approach to teaching mathematics that facilitates the student seeing the connection between the process of solving non-routine mathematics problems and solving significant problems in the student’s life. The approach is embedded in a curriculum of non-routine problems field-tested from 1984 to 1995 in a secondary school setting and later applied in an undergraduate mathematics course in problem-solving. In this article I will define a non-routine problem; discuss a few examples of non-routine problems including some that facilitate the student seeing the connection between the process of solving non-routine mathematics problems and solving significant problems in the student’s life; and suggest guidelines for implementing a curriculum of non-routine problems.
