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Abstraction Through Game Play

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Abstract

This paper examines the computer game play of an 11-year-old boy. In the course of building a virtual house he developed and used, without assistance, an artefact and an accompanying strategy to ensure that his house was symmetric. We argue that the creation and use of this artefact-strategy is a mathematical abstraction. The discussion contributes to knowledge on mathematical abstraction: of non-traditional knowledge; without teacher mediation; through game play. The paper also considers learning without instruction/instructional design and questions received distinctions between scientific and everyday knowledge.

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Notes

  1. We suspect that abstraction differs over disciplines, hence reference to mathematical abstraction, but we shall, henceforth, leave the ‘mathematical’ as implicit and refer to abstraction.

  2. ‘Strategy’ in this paper may be thought of as a procedure for rigourously attaining a goal or as an heuristic, as in ‘strategy games’ (see http://nrich.maths.org/2546).

  3. We do not go into details of similarities here because extended arguments for similarities between Davydov’s approach and many of these approaches have been made in co-authored papers with the second author: Dreyfus and Monaghan (2009); Monaghan and Ozmantar (2006b); Ozmantar and Monaghan (2007).

  4. See also Pratt and Noss (2002).

  5. ‘Goals’ is used in two distinct ways in mathematics education literature: the goal of activity, e.g. Leont’ev (1978), and emergent goals, ‘must do’ things that come into being during activity and often pass away, e.g. Saxe (1991). Reference to goals in this paper are to emergent goals.

  6. Costas said 1,500 pounds instead of 1,400 in this estimation, however we regard it as his attempt to approximate the calculation.

  7. Costas thought that he had put the two cubes in the middle of the plot but he had not. He lost track counting and misjudged. However, he based his building upon the “false” idea of those two cubes set in the middle of the plot.

  8. In a lecture on Costas’ work a participant said “but I use strategies like Costas’ when I do do-it-yourself around the home, it is pretty trivial”. To this we repeat, from Sect. 2, “new mathematics will depend on the person(s)—what is new to one person may be familiar to another”.

  9. Educational Researcher, 32(1), 2003.

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Acknowledgments

An early version of this paper appeared in PME, Avraamidou and Monaghan (2009). We would like to thank three reviewers who made very useful comments on the original submission. We dedicate this paper to the memory of Phil Scott (1953–2011), a lovely man who did so much to develop scholarship on Vygotsky’s distinction between everyday and scientific concepts and who provided personal comment on a draft of this paper.

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  1. School of Education, University of Leeds, Leeds, UK

    Antri Avraamidou, John Monaghan & Aisha Walker

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  1. Antri Avraamidou
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Correspondence to John Monaghan.

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Avraamidou, A., Monaghan, J. & Walker, A. Abstraction Through Game Play. Tech Know Learn 17, 1–21 (2012). https://doi.org/10.1007/s10758-012-9189-2

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