Appropriating geometric series as a cultural tool: a study of student collaborative learning |
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Authors: | Martin Carlsen |
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Institution: | (1) University of Agder, Kristiansand, Norway |
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Abstract: | The aim of this article is to illustrate how students, through collaborative small-group problem solving, appropriate the
concept of geometric series. Student appropriation of cultural tools is dependent on five sociocultural aspects: involvement
in joint activity, shared focus of attention, shared meanings for utterances, transforming actions and utterances and use
of pre-existing cultural knowledge from the classroom in small-group problem solving. As an analytical point of departure,
four mathematical theoretical components are identified when appropriating the cultural tool of geometric series: (1) estimating
of parameters, (2) establishing of the general term, (3) composing of the sum and (4) deciding on convergence. Analyses of
five excerpts focused on the students’ social processes of knowledge objectification and the corresponding semiotic means,
i.e., lecture notes, linguistic devices, gestures, head movements and gaze, to obtain shared foci and meanings. The investigation
of these processes unveils the manner in which the students established links to pre-existing mathematical knowledge in the
classroom and how they simultaneously combined the various mathematical theoretical components that go into appropriating
the cultural tool of geometric series. From the excerpts, it is evident that the students’ participation changes throughout
their involvement in the problem-solving process. The students are gaining mathematical knowing through a process of transforming
and by establishing shared meanings for the concept and its theoretical components. |
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Keywords: | |
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