Abstract
This paper starts from some observations about Presmeg’s paper ‘Mathematics education research embracing arts and sciences’ also published in this issue. The main topics discussed here are disciplinary boundaries, method and, briefly, certainty and trust. Specific interdisciplinary examples of work come from the history of mathematics (Diophantus’s Arithmetica), from linguistics (hedging, in relation to Toulmin’s argumentation scheme and Peirce’s notion of abduction) and from contemporary poetry and poetics.
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Notes
To make a start,
out of particulars
and make them general, rolling
up the sum, by defective means—
Sniffing the trees,
just another dog
among a lot of dogs.
(Williams 1946/1985, p. 259)
In his attempt to trace the origins and shifting meanings of this word, Tahta (2001) offered the following source notes:
Thus: mathematicize: (a) to consider or treat in a mathematical manner, (b) to reason mathematically; to make mathematical calculations. 1849: Froude, Nemesis 161—“The dry mathematicizing reason” 1885: Mrs H. Ward, Amiel's Journal (18 December 1859, l 131)—“his strength lies in mathematicizing morals”.
And: mathematize: 1719: Freethinker, no 117, p. 7… 1833: Newman, Letters (1891, l 365)… 1894: University Extension Journal 1 Oct 11/2 “The author has carefully avoided the error of needlessly mathematizing what can be better described in words”.
I am aware that it is a commonplace pedant’s remark to distinguish ‘method’ from ‘methodology’, where the latter word refers to a discipline like any other ‘-ology’, in this case the study of method. And a ‘methodologist’ (including Garfinkel’s self-delineation as an ‘ethnomethodologist’) is someone who practices that discipline. But while there were significant conceptual shifts when ‘geometry’ became ‘a geometry’ thereby allowing ‘geometries’ (likewise with algebra), permitting ‘methodology’ to stand for ‘method’ and then to morph into ‘methodologies’ worries away at me. And Presmeg’s phrase “a methodology of mixed methods” seemed both opaque and convoluted in the extreme.
When John (14:6) reports Jesus saying, “I am the way, the truth and the life”, ‘way’ is οδος in his original Greek. And οδος, like via in Latin and unlike dao in Chinese, is attached to a human being.
The metaphor of ‘gold standard’ research is so strange, in that the US going off the gold standard in 1934 is what is widely considered to have been a major contributor to the ending of the great Depression (though present circumstances transpiring as I write might surpass that, of course).
I took gentle exception to the marginalizing effect of Presmeg’s “even linguistics”.
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Pimm, D. Method, certainty and trust across disciplinary boundaries. ZDM Mathematics Education 41, 155–159 (2009). https://doi.org/10.1007/s11858-008-0164-2
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DOI: https://doi.org/10.1007/s11858-008-0164-2