Problem solving and reasoning in the learning of mathematics

Abstract

In Australia we have been concerned to ensure that our citizens are numerate and able to use mathematics in their daily personal and working lives. More recently mathematics curriculum writers and educators have acknowledged the need for students to be creative thinkers and problem solvers, not only when using mathematics in our daily lives, but also to contribute to improving our society and economy and enhance the employment opportunities for young people. These two examples provide illustrations of tasks that can be used to develop students’ understanding of algebraic concepts in both primary and secondary curriculum and to engage learners in problem solving and reasoning, especially justifying and generalizing