
06640087
a
2016f.00776
Cable, John
Howmanyness and rank order  towards the deconstruction of `natural number'.
Pope, Sue (ed.), Proceedings of the British Society for Research into Learning Mathematics (BSRLM). Proceedings of the British congress of mathematics education, BCME8, University of Nottingham, UK, April 1417, 2014. London: British Society for Research into Learning Mathematics (BSRLM). 3340 (2014).
2014
London: British Society for Research into Learning Mathematics (BSRLM)
EN
E20
F30
D20
E40
mathematics and philosophy
foundations of mathematics
natural numbers
number concepts
cardinality
cardinal numbers
ordinal numbers
quantity and quotity
counting
numerals
addition
ME 2015b.00177
http://www.bsrlm.org.uk/BCME8/BCME805.pdf
Summary: This paper concerns a philosophical, but highly practical, issue arising at the interface between mathematics and education, and I claim that mathematics education offers insights where mathematical philosophy has ground to a halt. More specifically it concerns the two related but distinct concepts of howmanyness (alias quotity) and rank order, whose separate identities are traditionally obscured by the language of `number'. (Sometimes they are called `cardinal number' and `ordinal number'. More often they are wrapped up together as `natural number'.) The teacher of young children has the advantage over the philosopher that she works with people before they have acquired all the prejudices of their native language, and we shall build on the analysis of counting by {\it R. Gelman} and {\it C. R. Gallistel} [The child's understanding of number. Cambridge, MA: Harvard University Press (1986; ME 2015b.00177)], concluding that `natural number' as normally conceived is something of an illusion, for only quotity has the properties expected of `number', while rank order is a mere quality.