Transposition of Knowledge: Encountering Proportionality in an Algebra Task

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...

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Bibliographic Details
Published in:International journal of science and mathematics education 2018-02, Vol.16 (3), p.559-579
Main Authors: Lundberg, Anna. L. V., Kilhamn, Cecilia
Format: Article
Language:English
Subjects:
Algebra
Algebra Anthropological theory of the didactic (ATD) Contextualization Proportional reasoning Textbook tasks
Annan matematik
Classrooms
Didactics
Didaktik
Education
Educational Sciences
Grade 6
Matematik
Mathematical analysis
Mathematical Concepts
Mathematical models
Mathematical sciences
Mathematics Education
Mathematics Instruction
Mathematics Teachers
Norms
Other Mathematics
Science Education
Utbildningsvetenskap
Word Problems (Mathematics)
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Summary: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 knowledge 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 “textbook task” disguised as real but adjusted to the norms of school mathematics. Such constraints may obscure mathematical 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.
ISSN:1571-0068
1573-1774
1573-1774
DOI:10.1007/s10763-016-9781-3