Linking Application and Acquisition of

Mathematical Ideas

Through Open Problem Solving

Kaye Stacey

Institute of Education

University of Melbourne

Abstract

There have been substantial advances in teaching using open problem solving in Australia in the last decade, brought about by a desire for improving learning experiences and new curricula and assessment. The term "problem solving" encompasses both real world applications of mathematics and pure mathematical investigations. Experience of solving problems is essential, as is active reflection on that experience. Students' ability to solve problems can be improved by the acquisition of good habits of working. The successful implementation of heuristic strategies is difficult to teach, but the development of a classroom vocabulary for discussing process aspects contributes to awareness of mathematical thinking. Two contrasting problem solving programs have both assisted students to consider problems more fully, to be more prepared to explore and understand, and to be less prone to superficially manipulating the numbers in the question.