Algorithms vs Understanding

I was interested to see on the BBC News website that apparently maths education is a hot topic in the U.S. at the moment.

The obvious cheap shot comes to mind – that it’s rather bizarre that a method of teaching primary age kids maths is more controversial than risking said primary kids getting hold of guns in their house. But it’s interesting to read what it’s all about, nonetheless.

It sounds like a battle that’s been fought a few times over here – teaching traditional methods of addition, subtraction etc (where you put the numbers vertically above each other and subtract each column in turn) versus alternative approaches.

Inevitably there are always some parents who object on principle to their child not being taught in the same way they were. The impulse to think that change can never be an improvement seems very prevalent anyway, and then you add here the potentially threatening idea of parents not being able to understand what kids are doing… heaven forbid!  But even if you put such poor reasons aside, there is some logic to the argument. The old-style algorithms were efficient for pen-and-paper work, and once learnt, were easy to implement and made errors not too hard to detect.

So why change?  Simply because following an algorithm is very different to understanding. You tend to see this demonstrated very effectively with fractions. Many kids have learnt the rules about adding, subtracting, multiplying and dividing fractions, and can implement them effectively. However, if you give them something rather unfamiliar-looking, those rules can be prone to going out of their head. You see a related problem when kids have been taught (often at their primary school grrrrr) to solve equations using the “take it over the other side and change the sign” approach – they can do that very quickly, and get the answers right, but it’s completely unhelpful as an approach when more complex equations are encountered, and teaching that focused on the algorithm never led them to develop the genuine understanding.

I’m not saying I wouldn’t teach the algorithms. But I’d do it at the end, after developing the understanding, along the lines of “look, there’s this neat little trick that can sometimes speed things up”. The only other time I do it is when an external examination is approaching, and we’re trying for a quick fix for a kid who’s had problems grasping the principles. In other circumstances, we should be doing what promotes long-term understanding, not defaulting to the “follow these rules and you’ll get a nice line of ticks” which in the long term does nothing to develop mathematical ability, but simply renders the child a less speedy and less accurate version of an electronic calculator – producing answers without understanding.



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