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An early algebra approach to pattern generalisation: actualising the virtual through words, gestures and toilet paper. (English)
Educ. Stud. Math. 92, No. 1, 1-19 (2016).
Summary: This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based relationships that relate variables. We propose a new approach to pattern generalisation that seeks to help children (grades 2 and 3) work both recursively and functionally, and to see how these two modes are connected through the notion of variable. We argue that a crucial change must occur in order for young learners to develop a flexible algebraic discourse. We draw on {\it A. Sfard}’s [Thinking as communicating. Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press (2008; ME 2011d.00346)] communication approach and on {\it G. Châtelet}’s [Figuring space. Philosophy, mathematics and physics. Dordrecht: Kluwer Academic Publishers (2000)] notion of the {\it virtual} in order to pursue this argument. We also root our analyses within a new materialist perspective that seeks to describe phenomena in terms of {\it material entanglement}, which include, in our classroom research context, not just the children and the teacher, but also words, gestures, physical objects and arrangements, as well as numbers, operations and variables.
Classification: H22 U62 D42 C52
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