AN EXPERT NOVICE STUDY OF METACOGNITIVE BEHAVIOR IN FOUR TYPES OF MATHEMATICS PROBLEMS*

Abstract

ABSTRACT The purpose of this study was to examine the differences between the metacognitive behaviors exhibited by experts and novices. Of particular interest was the degree to which subjects managed or controlled their behavior and the extent to which solutions, particularly by experts, were schema driven. Nine novices (college freshman) and six experts (first and second year graduate students in mathematics) were asked to think aloud while solving four mathematics problems: (1) a routine problem; (2) a problem with more than one obvious path; (3) a nonroutine problem that involved the use of the skills used in the routine problem; and (4) a problem with insufficient or contradictory information. The verbal protocols provide evidence that: experts in this study possessed and used schemas to solve problems but schema use did not fully or adequately characterize expertise; of the two aspects of metacognition - beliefs about cognition and control of cognition - beliefs played a more important role than control; and assessment of work is not in and of itself useful; assessments must be acted on.