Abstract
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.
Highlights
At the beginning of the 21st century the rapid mathematization of work in all areas relevant for work and social context influenced the mathematics that society needs
Problem solving plays a prominent role in the curriculum as it is an essential part of mathematical knowledge and performance, and it is considered to be the heart of mathematics
This paper presents findings from a case study related to a secondary mathematics preservice teacher
Summary
At the beginning of the 21st century the rapid mathematization of work in all areas relevant for work and social context influenced the mathematics that society needs. As a consequence, these created unprecedented challenges in school mathematics (Fey, Hollenbeck, & Wray, 2010). Since the 1980s mathematics educators have agreed upon the idea of developing problem solving ability. Research (e.g., Garofalo & Lester, 1985; Schoenfeld, 1985, 1987; Silver, 1994) shows that students’ low problem solving performance is due to lack of metacognitive behaviors. Metacognition is a critical component in cognitive function and cognitive development
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