id: 06312016
dt: j
an: 2014d.00511
au: O’Reilly, Declan
ti: No sign of the numbers!
so: Math. Sch. (Leicester) 43, No. 1, 2-3 (2014).
py: 2014
pu: Mathematical Association (MA), Leicester
la: EN
cc: F40
ut: integers; alternative notation; arithmetic operations; negative numbers
ci:
li:
ab: From the text: {\it D. Küchemann} [“Positive and negative numbers", in:
K. Hart (ed.), Children’s understanding of mathematics: 11‒16.
London: John Murray. 82‒87 (1981)] has written about the difficulties
of creating models for integers that are consistent across the four
arithmetic operations. He advocates adopting a model“in which the
integers are regarded as discrete entities or objects, constructed in a
way that the positive integers cancel out the negative integers." My
aim in this paper has been to put forward such a model. In doing so, I
have adopted a shorthand notation, replacing $^+1$ by “$+$’ and
$^-1$ by ‘$-$’. Of course, in doing so, I can be accused of abusing
standard notation. I acknowledge this. However, I would point out that
almost all textbooks do something similar; instead, of writing $^-3$,
they write $-3$ and so on. In other words, they leave out the signs
whereas I leave out the numbers!
rv: