
06498233
j
2015f.00219
Cable, John
Mathematics is always invisible, Professor Dowling.
Math. Educ. Res. J. 27, No. 3, 359384 (2015).
2015
Springer Netherlands, Dordrecht; Mathematics Education Research Group of Australasia (MERGA), Wahroonga, New South Wales, Australia
EN
C60
C50
D20
social bias
dichotomy
unwieldy complement
realistic mathematics
linguistics
concepts
formalism
language games
ME 2014a.00342
doi:10.1007/s1339401501413
Summary: This article provides a critical evaluation of a technique of analysis, the {\it Social Activity Method}, recently offered by {\it P. Dowling} [Math. Educ. Res. J. 25, No. 3, 317340 (2013; ME 2014a.00342)] as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling [loc. cit.] calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.