Generating Contexts for Learning under Diverse Math Cultures in the Classroom : Between Inquiry Math and Juku Math

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This study presented a theoretical framework of contexts for learning, focusing on math lessons in the classroom. It took the collective activity system proposed by Y. Engestrom - a system composed of object, subject, tools, community, division of labor, rules and outcomes - as its analysis of unit. His theory of learning based upon cultural historical activity theory is interesting and unique in that it discusses learning not only in a given context but also in a context reconstructed by learners themselves.By doing four case studies including fieldwork in a math class at secondary level, this study expanded Engestrom's theory of learning in the following five respects. 1) Levels of activity system : seeing a classroom as a learning context in vertical and horizontal diversity of contexts. 2) Learning as individual action as well as collective activity : analysis of the characteristics and process of learning done by different members in the classroom. 3) Difference between activity and activity system and their relationship considered as reflexivity : regarding the relationship between lesson and classroom culture as an example of that between activity and activity system. 4) Process of activity : conceptualizing not only (a) discontinuous change of activity system, but also (b) continuous change of activity system and (c) process of activity. The discussion of (b) and (c) has been neglected in Engestrom's theory. Different processes of activity were analyzed as different patterns of sequence of actions. 5) Continuous change of activity system and dilemma managing : analysis of the strategies of teacher's dilemma managing in continuous change of activity system in the classroom.A comprehensive theory of contexts for learning was proposed based upon Engestrom's activity theory, which was thus expanded by the theories of situated learning, mathematical problem solving and classroom culture, and the interaction analysis.