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Sixty Years (or so) of Language Data in Mathematics Education

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Language and Communication in Mathematics Education

Part of the book series: ICME-13 Monographs ((ICME13Mo))

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Abstract

This chapter, based both on pre-ICME-13 conference documents as well as on the author’s actual panel presentation made at TSG 31, covers a range of themes concerned with the issues of ‘language data’ in mathematics education. It also addresses several instances from its history, including word problems, classroom language and transcription, in addition to the mathematics register, its syntax, semantics and pragmatics.

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Notes

  1. 1.

    For a previous ICME, held in Québec in 1992, I prepared a talk (which I was unable to give) entitled ‘Another psychology of mathematics education’ (see Pimm, 1994).

  2. 2.

    The same is true, interestingly, of papers on mathematics education and technology (see Sinclair, 2017). However, while there are general technology and education journals (as there are for linguistics and education), there are not any specialist language and mathematics education journals comparable with Digital Experiences in Mathematics Education or STEMmy journals such as The Canadian Journal of Science, Mathematics and Technology Education.

  3. 3.

    This article title contains a very nice play on the wording of Michael Polanyi’s (1966/2009) startling claim-as-fact, in his book The Tacit Dimension, that, ‘we can know more than we can tell’ (p. 4; italics in original). Curiously, the header throughout Nisbett and Wilson’s article is the subtitle, ‘verbal reports on mental processes’, which contains more characters than the actual main title.

  4. 4.

    Including the possibility of it being situated behind an ear of the teacher, thereby mirroring the teacher’s eye-line. Without intending this to be an instance of product placement, see Looxcie.

  5. 5.

    Ah, deixis—‘this very book’ refers to (points at) the book I presume you, dear reader, are currently reading, not the book Jefferson’s chapter is in.

  6. 6.

    This connects more widely to issues of metaphor (as potentially central to mathematics and not just poetry)—see Zwicky (2003, 2010) and Pimm (1987, 2010). After all, it was Goethe who proclaimed, “Mathematics is pure poetry”.

  7. 7.

    What particularly comes to mind for me from this aphorism are such terms with negative definitions, like irrational or non-recurring or discontinuous.

  8. 8.

    See Pimm (2004).

  9. 9.

    In the early part of the twentieth century, there was considerable interest in the notion of ‘arrested motion’ in sculpture, endeavouring to capture the dynamic in the static. In a Paris Review interview, writer William Faulkner asserted:

    The aim of every artist is to arrest motion, which is life, by artificial means and hold it fixed so that 100 years later when a stranger looks at it, it moves again since it is life. […] This is the artist’s way of scribbling […] oblivion through which he must someday pass. (1956, pp. 49–50)

    This contrasts interestingly with historian of science Catherine Chevalley’s comments about her father Claude, a core Bourbaki mathematician:

    For him [Claude Chevalley], mathematical rigour consisted of producing a new object which could then become immutable. If you look at the way my father worked, it seems that it was this which counted more than anything, this production of an object which, subsequently, became inert, in short dead. It could no longer be altered or transformed. This was, however, without a single negative connotation. Yet it should probably be said that my father was probably the only member of Bourbaki who saw mathematics as a means of putting objects to death for aesthetic reasons. (in Chouchan, 1995, pp. 37–38; my translation)

    There is also a significant sense in which language—not least mathematical language (especially the written)—provides a means for arresting motion:

    a point is an instance,

    arrested motion – the geometric,

    its unsigned art.

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Acknowledgements

I am grateful to David Wagner and Judit N. Moschkovich for comments on earlier drafts, as well as Nathalie Sinclair, my ideal reader.

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Authors and Affiliations

  1. Simon Fraser University, Burnaby, Canada

    David Pimm

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  1. David Pimm
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Correspondence to David Pimm .

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Editors and Affiliations

  1. Education Department, University of California, Santa Cruz, Santa Cruz, California, USA

    Judit N. Moschkovich

  2. Faculty of Education, University of New Brunswick, Fredericton, New Brunswick, Canada

    David Wagner

  3. Centre for Education Innovation and Action, Tata Institute of Social Sciences, Bombay, India

    Arindam Bose

  4. Faculty of Education, State University of Campinas, Campinas, São Paulo, Brazil

    Jackeline Rodrigues Mendes

  5. Institut für Erziehungswissenschaft, Technische Universität Dresden, Dresden, Germany

    Marcus Schütte

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Pimm, D. (2018). Sixty Years (or so) of Language Data in Mathematics Education. In: Moschkovich, J., Wagner, D., Bose, A., Rodrigues Mendes, J., Schütte, M. (eds) Language and Communication in Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-75055-2_2

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