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Tensions in the Design of Mathematical Technological Environments: Tools and Tasks for the Teaching of Linear Functions

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Digital Technologies in Designing Mathematics Education Tasks

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 8))

Abstract

The design of tasks for the exploration of mathematical concepts involving technology can take several starting points. In many cases the ‘tool’ is predefined as an existing mathematics application with an embedded set of design principles that shape the mathematical tasks that are possible. In other cases, the tool and tasks are designed through a more dynamic process whereby designers and educators engage in a discourse that influences the resulting tasks. The chapter will begin with a brief description of a longitudinal study, and its theoretical framework that resulted in a rubric to inform the design of tasks that privilege the exploration of mathematical variants and invariants (Clark-Wilson and Timotheus in ICMI study 22 task design in mathematics education, UK: Oxford, 2013; Clark-Wilson in How does a multi-representational mathematical ICT tool mediate teachers’ mathematical and pedagogical knowledge concerning variance and invariance? 2010). This rubric is then used as a construct for the post-priori analysis of two tasks that introduced the concept of linear functions and that use different technologies. Conclusions will be drawn that highlight subtle tensions that relate to the mathematical knowledge at stake and to the design principles of the underlying technology and task.

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Notes

  1. 1.

    This was replaced by a new National Curriculum in 2013 (Department of Education 2013).

  2. 2.

    The students in most English state schools are organised into setted mathematics classes, according to their prior attainment.

  3. 3.

    From graphing calculators and software packages such as Mouseplotter (BBC Micro), Coypu (Acorn/PC), Omnigraph (PC) and Autograph (PC/Mac/iPad).

  4. 4.

    The pupils are not given guidance on how to do this in the pupil workbook. Also, during their initial professional development teachers are discouraged from demonstrating the different ways to edit the software to pupils before pupils have had an opportunity to explore the editing functionality for themselves.

  5. 5.

    The teacher did begin the lesson by reminding the students that, in order to generate each graph, the computer used a ‘function machine’—an idea and representation that was familiar to the students.

  6. 6.

    More information can be found at: http://www.nuffieldfoundation.org/developing-teachers-mathematical-knowledge-using-digital-technology.

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Acknowledgments

This chapter draws on research from two studies. The TI-Nspire evaluation study was funded by Texas Instruments and has been subsequently reported in Clark-Wilson (2008). Cornerstone Maths was generously funded by the Li Ka Shing Foundation as a multi-year collaborative project between London Knowledge Lab, UCL Institute of Education and SRI International, USA, and directed by Celia Hoyles, Richard Noss, Jeremy Roschelle and Phil Vahey.

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  1. UCL Knowledge Lab, University College London, London, UK

    Alison Clark-Wilson

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  1. Alison Clark-Wilson
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Correspondence to Alison Clark-Wilson .

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Editors and Affiliations

  1. Department of Education Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong SAR, China

    Allen Leung

  2. Department of Mathematics “G. Castelnuovo”, “Sapienza” University of Rome, Rome, Italy

    Anna Baccaglini-Frank

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Clark-Wilson, A. (2017). Tensions in the Design of Mathematical Technological Environments: Tools and Tasks for the Teaching of Linear Functions. In: Leung, A., Baccaglini-Frank, A. (eds) Digital Technologies in Designing Mathematics Education Tasks. Mathematics Education in the Digital Era, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-43423-0_16

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  • DOI: https://doi.org/10.1007/978-3-319-43423-0_16

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