The taxicab locus of Apollonius: promoting exploratory routes to the punchline using rich undergraduate tasks

MILES, Richard (2018). The taxicab locus of Apollonius: promoting exploratory routes to the punchline using rich undergraduate tasks. International Journal of Mathematical Education in Science and Technology, 1-9.

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Official URL: https://www.tandfonline.com/doi/abs/10.1080/002073...
Link to published version:: https://doi.org/10.1080/0020739x.2018.1555725
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    Abstract

    A key motivational tactic in undergraduate mathematics teaching is to launch topics with fundamental questions that originate from surprising or remarkable phenomena. Nonetheless, constructing a sequence of tasks that promotes students' own routes to resolving such questions is challenging. This note aims to address this challenge in two ways. First, to illustrate the motivational tactic, the taxicab manifestation of a locus attributed to Apollonius is introduced and a natural question arising from comparison with the analogous Euclidean locus is considered, namely, does the taxicab locus of Apollonius ever coincide with a taxicab circle? Second, a companion sequence of rich undergraduate tasks is elaborated using theoretical design principles, with the tasks culminating in this fundamental geometric question. This note therefore provides a design approach that can be replicated in undergraduate teaching contexts based around similarly motivating mathematical phenomena.

    Item Type: Article
    Additional Information: ** From Crossref via Jisc Publications Router **Journal IDs: pissn 0020-739X; eissn 1464-5211
    Uncontrolled Keywords: Applied Mathematics, Education, Mathematics (miscellaneous)
    Identification Number: https://doi.org/10.1080/0020739x.2018.1555725
    Page Range: 1-9
    SWORD Depositor: Margaret Boot
    Depositing User: Margaret Boot
    Date Deposited: 03 Jan 2019 09:41
    Last Modified: 10 Dec 2019 01:18
    URI: http://shura.shu.ac.uk/id/eprint/23680

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