School of Mathematical Sciences: Educational Mathematics
University of Northern Colorado
Type of Resources
Place of Publication
University of Northern Colorado
Metacognition has long been identified as an essential component of the problem-solving process. While the language of metacognition has been conveyed in teaching, research, and policy, much of the research on metacognition does not describe the explicit role metacognition plays during students’ real-time problem-solving process. Moreover, metacognitive interventions are typically disconnected from the natural mathematical activity and discourse within a classroom community. Research concerning metacognition and metacognitive interventions has historically adopted an acquisition metaphor for learning. This qualitative study takes a participationist lens to consider metacognition as a problem-solving habit of mind, a normative way of thinking to which students become attuned by participating in authentic problem-solving situations. This study explored one such situation, in which “portfolio” problem-solving sessions and write-ups were used to mediate metacognitive thinking in a first-year mathematics content course for pre-service elementary teachers. Six qualitative data sources were collected and analyzed: (1) recorded classroom sessions, (2) three individual interviews with 15 of the 24 students, (3) two interviews with the instructor of record, (4) students’ written artifacts, (5) recorded planning sessions with the instructor, and (6) journal reflections written by the instructor and myself, the researcher, after each class session. Two levels of analysis were employed to characterize sociocultural complexity surrounding students’ problem-solving activity. Results of micro-level analysis revealed a shift from product- to process-focused metacognitive norms. Through participation in authentic problem-solving situations, namely the portfolio problems, students problem-solving activity transformed in a way that afforded them opportunities to readily engage in process-focused metacognitive actions. Macro-level analysis utilized activity theory to operationalize the participation structure of the classroom and document the development of metacognitive norms, highlighting social mediators of activity and contradictions as catalysts for change. Results of macro-level analysis illustrated a correspondence between the shift in normative metacognitive actions identified in micro-level analysis, broader transformations of students’ problem-solving activity, and the teacher’s shifting goals and actions in response to students’ problem solving. This work extends previous research on metacognitive interventions, demonstrating that “embeddedness” of metacognitive activity during problem solving is beyond just the content, but also embedded in the collective classroom culture. Moreover, activity theory captured students’ agency in negotiating their problem-solving activity, suggesting its continued use by researchers wishing to adopt an anti-deficit framing. This research has additional implications for teaching content courses for pre-service teachers. Students’ metacognitive activity was very much situated in the sociocultural context of the classroom, especially their dual identities as current mathematics students and future teachers. For the pre-service teachers to value mathematical problem-solving habits of mind, legitimate participation meant as students, not just as future teachers, of mathematics. Finally, this study provides broader insight into how instructors can support undergraduate students’ process-focused metacognitive activity during problem solving through a combination of Inquiry-Based Learning (IBL) techniques and explicit reflection on real-time problem-solving processes.
Dean's Citation for Excellence