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UBC Theses and Dissertations

Collective clutter and co-emerging complexity : enactivism and mathematical paths of understanding Thom, Jennifer Susan


This thesis reports on a qualitative study in which three fifth grade children were presented with six nonroutine mathematical problems involving six different 3-D pyramids, constructed out of multi-link cubes1. The children were videotaped while they worked without any adult help as a cooperative group to solve the pyramid problems. During these sessions, the students produced various 3-D cube models, 2-D drawings, and written records of arithmetic calculations as their solutions to the six problems. Through the lens of enactivism, this study describes and interprets the coevolutionary processes of the group's path of mathematical understandings as it unfolded during the six videotaped sessions. The results revealed building, drawing, and numbering as modes of representation of this group's problem solving work. An analysis of these three modes of representation explored the co-emergence of the children's individual and collective understandings, as well as the interrelationships which existed between their spatial structuring and their use of numerical operations in solving the pyramid problems.

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