ABSTRACT
Subtraction is one of those topics which, I suspect, most of us think we have mastered from a very early age. Six take away four is two: what could be easier? Oh that it were so simple!
For many years I thought I knew pretty well all there was to know about subtraction. There was a slight hiatus when I came across negative numbers but I soon picked up the idea that, ‘Two minuses make a plus’ (For those unfamiliar with this, if you are confronted by two minus signs side by side and you interpret them as a plus, then the correct answer will result. Thus, for example, 6−(−2)=8. (The reasoning behind this should become clear later on the chapter.) It was only, if I am honest, when I became involved in teacher education that I really began to examine the notion of subtraction and, being even more honest, I was appalled by my earlier ignorance. It was not that I found the various forms of subtraction particularly difficult but rather that I had been totally unaware of them. I hope none of my pupils suffered as a result for, as noted in the introduction, if children are misled-albeit unwittingly-into having very narrow, rigid conceptions of a topic, then it can hinder their later mathematical progress (see, for example, Haylock and Cockburn, 1997).
