Sources of Certainty and Uncertainty in

Mathematical Problem Solving

Kaye Stacey and Cecilia de Beato

Institute of Education, University of Melbourne, Australia

This study investigates the certainty and uncertainty that students feel as they work on a mathematical problem. It is hypothesised that the over-confidence in decisions that characterises reasoning in many fields of human endeavour is also exhibited in mathematical work and that it may partly explain why students generally are reluctant to check their work. Students who feel certain that their work is correct would see little reason to check it. In the problem used in this study, uncertainty arose in making a generalisation, but also from carrying out straightforward calculations . Students with wrong methods that gave easy arithmetic were, in the end, almost as certain that their answers were correct as students with the correct method. These observations may help to explain why students with "obviously" wrong answers do not check, why students more often check arithmetic than reasoning and the tendency for groups to choose a simple wrong solutions even when a correct solution been proposed.