STUDENTS' CERTAINTY AND CHECKING BEHAVIOUR DURING MATHEMATICAL PROBLEM SOLVING

CECILIA DEL BEATO and KAYE STACEY

Institute of Education, University of Melbourne

This study investigates the certainty and uncertainty that students feel as they work on a mathematical problem and how this relates to the checking that they carry out. 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, students became uncertain when they moved from a particular case where they could count to a much larger case where a general rule was required. They also became uncertain when the arithmetic became harder - the size of this effect had not been expected. 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. Students often did not know how to use extra information to check their answers. About half of the students who were correct became less certain after being given supporting information.