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Young children reasoning about symmetry in a dynamic geometry environment

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Abstract

In this paper, we investigate children’s learning of reflectional symmetry in a dynamic geometry environment. Through a classroom-based intervention involving two 1-h lessons, we analyse the changes in the children’s thinking about reflectional symmetry: first, they developed dynamic and embodied ways of thinking about symmetry after working with a pre-constructed sketch called the “symmetry machine”. Secondly, they moved from distinguishing symmetrical and asymmetrical figures statically to generalising about properties of symmetry. This was evident in the way children expressed symmetric movement through words, gestures and diagrams during the computer-based lessons as well as in the follow-up paper-and-pencil tasks. We highlight the specific roles of the teacher and of the digital technology in supporting the process of semiotic mediation through which the children learned symmetry.

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Notes

  1. The historical-epistemological root of this kind of transformation can be found in Ponselle’s principle of continuity which states that “if we suppose a given figure to change its position by having its points undergo a continuous motion without violating the conditions initially assumed to hold between them, the […] properties which hold for the first position of the figure still hold in a generalised form for all the derived figures” (cited in Greaves 2002, p. 45). In particular, continuously dragging an object will maintain the mathematical relations that were used to construct the object.

  2. The design of this microworld was inspired by a sketch created by Michael Battista.

  3. T = Teacher; S1 = Student 1, S2 = Student 2, etc.… Ss = All students.

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  1. Faculty of Education, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Oi-Lam Ng & Nathalie Sinclair

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  1. Oi-Lam Ng
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  2. Nathalie Sinclair
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Correspondence to Oi-Lam Ng.

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Ng, OL., Sinclair, N. Young children reasoning about symmetry in a dynamic geometry environment. ZDM Mathematics Education 47, 421–434 (2015). https://doi.org/10.1007/s11858-014-0660-5

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