This case study examined the metacognitive processes of a preservice teacher when solving a nonroutine geometry problem in a dynamic geometry environment. The main purpose of the study was to uncover and investigate patterns of metacognitive processes and to understand what circumstances, situations, and interactions in a dynamic geometry environment promoted metacognitive behaviors. An adaptation of Schoenfeld’s (1981) model of episodes and executive decisions in mathematics problem solving, and the theory of instrumentation (Rabardel, 2001) was used to identify patterns of metacognitive processes in a dynamic geometry environment. During different phases of problem solving the participant engaged in different metacognitive behaviors whereas the dynamic geometry software supported strategies that are available and/or not available on paper and pen. The effectiveness of solution paths was dependent on the presence of managerial decisions, and well-orchestrated usage of different resources, both knowledge and technology. However, the results of the study call to question to which extent engagement in metacognitive behaviors is necessarily desirable or productive.
Analysis of students’ problem-solving ability in solving geometry problem
