This dissertation explores the question of how strategic and conceptual knowledge co-develop over the course of several episodes of mathematical problem solving. The core analytic work involves an in-depth microgenetic case study of a single pre-algebra student, Liam, who over six hours of videotaped interaction with a tutor/researcher constructs a deterministic and essentially algebraic algorithm for solving algebra word problems that have an underlying linear structure. Over six hours of videotaped interaction with a tutor/researcher, Liam's later and conceptually more sophisticated strategy is seen to emerge as a gradual refinement of his initial strategy. This focal case study is used to develop a theoretical model of how strategic and conceptual knowledge co-evolve. A novel aspect of the present analysis is that both strategies and the knowledge needed to implement them in problem solving are modeled as complex knowledge systems. The analytic methodology employed in developing the theoretical model is a coordination of Knowledge Analysis (diSessa, 1993; Sherin, 2001) and Microgenetic Learning Analysis (Parnafes & diSessa, submitted; Schoenfeld, Smith, & Arcavi, 1993). The model of co-development of strategic and conceptual knowledge that is developed through the analysis is one of mutual bootstrapping: (1) Within a given strategic frame, a solver activates a particular projection of conceptual knowledge and (2) As the solver creates new conceptual schemes in the context of working within a given particular strategic frame, novel refinements to existing strategies can emerge.
|Advisor:||Schoenfeld, Alan H.|
|Commitee:||Saxe, Geoffrey B., diSessa, Andrea A.|
|School:||University of California, Berkeley|
|Department:||Science & Mathematics Education|
|School Location:||United States -- California|
|Source:||DAI-A 73/07(E), Dissertation Abstracts International|
|Keywords:||Conceptual knowledge, Epistemology, Learning, Mathematics, Problem-solving, Strategic knowledge|
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