
06312016
j
2014d.00511
O'Reilly, Declan
No sign of the numbers!
Math. Sch. (Leicester) 43, No. 1, 23 (2014).
2014
Mathematical Association (MA), Leicester
EN
F40
integers
alternative notation
arithmetic operations
negative numbers
From the text: {\it D. K\"uchemann} [``Positive and negative numbers", in: K. Hart (ed.), Children's understanding of mathematics: 1116. London: John Murray. 8287 (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!