Applying mathematics with real world connections: metacognitive characteristics of secondary students

This paper reports an intensive study of problem-solving activity of female students at the senior secondary level. The study focussed both on the mathematical processing and the underlying cognitive and metacognitive activities that led to that processing. Response maps were used to analyse and categorize the written responses from individual students while videotaped problem solving sessions and structured and free response interviews probed the students' metacognitive knowledge, strategies, decision making, beliefs and affects. Metacognitive activities were involved in all phases of the solution process with key points in students' solutions identifiable in terms of the cognitive-metacognitive framework of Garofalo and Lester (1985). On average more time was spent on orientation and execution activities with little time being spent on organisation and verification activities, however, the successful groups spent less time on orientation than the other groups. All successful groups displayed a high number of key points where metacognitive decisions could influence cognitive action. Success was accompanied by a tendency to engage in a high number of organisational activities, regulation of execution activities and evaluation activities particularly evaluation of execution but fewer opportunities where metacognitive decisions could influence cognitive actions during orientation.