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Mean-Invariant Polynomial Intersections: A Case Study in Generalisation

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Notes

  1. For example, taken from the internet: two people tackling the same specific problem, probably course work from the IB: https://nrich.maths.org/discus/messages/67613/68454.html and http://nrich.maths.org/discus/messages/67613/69786.html.

  2. http://mcs.open.ac.uk/jhm3/Applets%20&%20Animations/Applets%20&%20Animations.html and look for Lagrange & Cubics.

References

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  • Gattegno, C. (1970). What we owe children: The subordination of teaching to learning. London: Routledge & Kegan Paul.

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  • Horwitz, A. (undated). Using mathematica to prove and animate a property of cubic polynomials. http://archives.math.utk.edu/ICTCM/VOL08/C035/paper.pdf. Accessed Nov 2008.

  • Lascoux, A. (2003). Symmetric functions and combinatorial operators on polynomials. CBMS regional conference series in mathematics, vol. 99. Washington: American Mathematical Society.

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  • Macdonald, I. (1975/1999). Symmetric Functions and Hall Polynomials. Oxford Mathematical Monographs. Oxford: Oxford University Press.

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Authors and Affiliations

  1. Open University, Milton Keynes, UK

    John Mason

  2. University of Oxford, Oxford, UK

    John Mason

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  1. John Mason
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Correspondence to John Mason.

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This column will publish short (from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain-teasers involving the use of computers or computational theory. Snapshots are subject to peer review.

In this snapshot, John Mason alternates between a traditional mathematical treatment of a geometry problem about the tangent to a cubic polynomial and an exploration of it with dynamic geometry software. With each alternation, we get a more generalized view of the problem, losing the tangents and the cubics along the way.

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Mason, J. Mean-Invariant Polynomial Intersections: A Case Study in Generalisation. Tech Know Learn 16, 183–192 (2011). https://doi.org/10.1007/s10758-011-9185-y

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  • DOI: https://doi.org/10.1007/s10758-011-9185-y

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