The development of mental representations as a problem solving activity

Abstract This study examined the development of mental representations in problem solving situations. The study incorporated a constructivist perspective on learning, including the view that mental representations evolve as mathematical conceptions. Fourteen first-year college students were interviewed as they solved a set of similar algebra word problems. All interviews were videotaped and written transcripts of the solvers' verbal responses were prepared. The analysis of the solvers' solution activity focused on identifying and describing their cognitive actions in resolving genuinely problematic situations they faced while solving the tasks. The results of the analysis included a description of three increasingly abstract levels of structural knowledge. The results suggest a framework for a theory of representation that is activity-based, and consistent with a view of knowledge based on the idea of viability.

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