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Broadening the sense of ‘dynamic’: a microworld to support students’ mathematical generalisation

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Abstract

In this paper, we seek to broaden the sense in which the word ‘dynamic’ is applied to computational media. Focussing exclusively on the problem of design, the paper describes work in progress, which aims to build a computational system that supports students’ engagement with mathematical generalisation in a collaborative classroom environment by helping them to begin to see its power and to express it for themselves and for others. We present students’ strengths and challenges in appreciating structure and expressing generalities that inform our overall system design. We then describe the main features of the microworld that lies at the core of our system. In conclusion, we point to further steps in the design process to develop a system that is more adaptive to students’ and teachers’ actions and needs.

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Notes

  1. See http://www.migen.org/ for more details. Funded by the ESRC/EPSRC Teaching and Learning Research Programme (Technology Enhanced Learning); Award no: RES-139-25-0381.

  2. Throughout the paper we refer to grey and black tiles. The system of course provides a number of different colours.

  3. Gravemeijer (1999) discusses the notion of mathematical activity within ‘realistic mathematics education’; that is informal ways of modelling serve as a basis for developing more formal mathematical knowledge. ‘At first a model is constituted as a context-specific model… then changes character it becomes an entity of its own, and as such it can function as a model for more formal mathematical reasoning’ (ibid).

  4. For preliminary descriptions of this aspect of the work, see Cocea et al. (2008).

  5. We are grateful to Mike Thomas for naming what we were trying to do.

  6. As with other features this is not the only way we expect students to allocate colours; an alternative is to allocate colours as attributes of a pattern. We are investigating, through student sessions, the best way to afford this functionality.

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Authors and Affiliations

  1. London Knowledge Lab, Institute of Education/Birkbeck College, University of London, London, WC1N 3QS, UK

    Richard Noss, Celia Hoyles, Manolis Mavrikis, Eirini Geraniou, Sergio Gutierrez-Santos & Darren Pearce

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  1. Richard Noss
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  2. Celia Hoyles
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  3. Manolis Mavrikis
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  4. Eirini Geraniou
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  5. Sergio Gutierrez-Santos
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  6. Darren Pearce
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Correspondence to Manolis Mavrikis.

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Noss, R., Hoyles, C., Mavrikis, M. et al. Broadening the sense of ‘dynamic’: a microworld to support students’ mathematical generalisation. ZDM Mathematics Education 41, 493–503 (2009). https://doi.org/10.1007/s11858-009-0182-8

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