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Transposition of Knowledge: Encountering Proportionality in an Algebra Task

Journal article
Authors Anna L.V. Lundberg
Cecilia Kilhamn
Published in International Journal of Science and Mathematics Education
Volume 16
Issue 3
Pages 559–579
ISSN 1571-0068
Publication year 2018
Published at The Linnaeus Centre for Research on Learning, Interaction, and Mediated Communication in Contemporary Society (LinCS)
Department of Pedagogical, Curricular and Professional Studies
Pages 559–579
Language en
Keywords Algebra Anthropological theory of the didactic (ATD) Contextualization Proportional reasoning Textbook tasks
Subject categories Mathematics, Other Mathematics, Educational Sciences, Didactics


This article reports on an analysis of the process in which knowledge to be taught was transposed into knowledge actually taught, concerning a task including proportional relationships in an algebra setting in a grade 6 classroom. We identified affordances and constraints of the task by describing the mathematical praxeology of the two different types of knowledge exposed, in the task as such and in the activity of the classroom. Through the teacher’s explicit process of reasoning, modeling, revising, solving, and repeatedly explaining the task, we found that the transposition of knowl- edge was seriously affected by the contextualization of the task. Modeling word problems about everyday situations has its limitations and can, as in this case, make the problem unsolvable unless it is accepted as a Btextbook task^ disguised as real but adjusted to the norms of school mathematics. Such constraints may obscure mathe- matical ideas afforded by the task. We conclude that learning opportunities embedded in a task do not necessarily surface when a task is treated in a classroom setting

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