UC Irvine

Self-regulated learning (SRL), the ability to set goals and monitor and control progress toward these goals, is an important part of a positive mathematical disposition. Within SRL, accurate metacognitive monitoring is necessary to drive control processes. Students who display this accuracy are said to be calibrated, and although calibration is a growing area of research within Educational Psychology, unanswered questions remain about the nature of calibration: how it should be measured, its role as a dynamic aspect of metacognition, and how best to improve it. This dissertation uses a rich source of data on student calibration and achievement within an online mathematics curriculum (ST Math) to approach these questions and present results on calibration as representative of a complex system of metacognition.

This dissertation presents evidence that calibration is best represented as two separate monitoring processes, one for confidence and one for uncertainty; these processes can be operationalized through the measures of Sensitivity and Specificity. In Study 1, comparisons with other commonly used measures of calibration indicate that Sensitivity and Specificity have a relative robustness to most patterns of missing data and greater strength as predictors. Other commonly used calibration measures suffer greatly from missing data inherent in real-world patterns of question answering.

Study 2 characterizes metacognitive monitoring as part of a dynamic system that varies depending on task. In this study, variance in calibration is associated with variance in performance gain within the same student across ST Math quizzes. Both Sensitivity and Specificity are predictors of this gain, but greater confidence when correct (Sensitivity) is more strongly associated with performance gains between quizzes than is greater uncertainty when incorrect (Specificity).

Study 3 evaluates the potential of ST Math as a calibration intervention. After a year's practice and feedback with ST Math, students display greater Specificity, but lower Sensitivity, indicating that ST Math made the students more uncertain. Study 3 also explores how change in calibration is related to change in achievement, finding no relation between growth in calibration and growth in achievement, either within or outside of ST Math.