Examining evidence of metacognition by preservice secondary mathematics teachers while solving tasks situated in the secondary curriculum
The study's goal was to examine the metacognitive practices and problem solving by preservice secondary mathematics teachers within secondary core content areas. The effort to analyze and describe the processes led to qualitative methods, a multiple case study. Transcripts of problem solving sessions and interviews were coded for the presence of multiple strategies, descriptive language, and use of metacognitive stages. From this coding, detailed accounts of the participants' problem solving were developed and analyzed. Findings revealed conceptual and procedural obstacles existed when participants sought to find an efficient solution to some of the problem solving tasks. Half of the participants struggled with using algebraic symbolization to represent a relationship and all had difficulty describing the variability that existed within sets of data. Both of these skills are integral components of the current secondary curriculum. The analysis also revealed findings concerning the preservice teachers' mathematical practices. A study of the stages of problem solving suggested that the participants' had limited persistence in problem solving and restricted attention to reflection on the processes used. Similarly, an analysis of their language demonstrated incomplete development of concept definition and ineffective use of terminology in a mathematical context.