id: 06640087
dt: a
an: 2016f.00776
au: Cable, John
ti: How-many-ness and rank order ‒ towards the deconstruction of ‘natural
number’.
so: Pope, Sue (ed.), Proceedings of the British Society for Research into
Learning Mathematics (BSRLM). Proceedings of the British congress of
mathematics education, BCME-8, University of Nottingham, UK, April
14‒17, 2014. London: British Society for Research into Learning
Mathematics (BSRLM). 33-40 (2014).
py: 2014
pu: London: British Society for Research into Learning Mathematics (BSRLM)
la: EN
cc: E20 F30 D20 E40
ut: mathematics and philosophy; foundations of mathematics; natural numbers;
number concepts; cardinality; cardinal numbers; ordinal numbers;
quantity and quotity; counting; numerals; addition
ci: ME 2015b.00177
li: http://www.bsrlm.org.uk/BCME8/BCME8-05.pdf
ab: 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 how-many-ness (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.
rv: