Mathematics is always invisible, Professor Dowling. (English)

Math. Educ. Res. J. 27, No. 3, 359-384 (2015).

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, 317‒340 (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.