Eleanor Armour-Thomas

Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics

The purpose of this exploratory study was to use a “teaching as problem solving” perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning teachers of secondary school mathematics. A metacognitive framework was developed to examine the thoughts of teachers before, during and after lesson enactments. Data were obtained through observations, lesson plans, videotapes, and audiotapes of structured interviews during the course of one semester. Data analysis suggests that the metacognition of teachers plays a well-defined role in classroom practice. These findings provide useful insights for researchers and teacher educators in their preservice and inservice mathematics programs.

Construct Validation of Metacognition

Abstract Recent investigations have established the importance of metacognition in the acquisition and application of learning skills in diverse domains of inquiry. Despite the voluminous theoretical and empirical research, there remain some unanswered questions regarding the specific components underlying the construct and whether these components are differentially employed as a function of context. Using a self-report measure developed for this study, we sought answers to these questions among a sample of 126 high school students. Factor analysis of the items revealed six components of metacognition that accounted for 62% of the explained variance. Furthermore, the analysis indicated that the components were interdependent and were used across all types of problem-solving situations. The results, although no more than a first step in the construct-validation process, contribute to a more informed understanding of the nature and function of the metacognition construct in different contexts.