## A tale of two classes

Two things happened this week that seemed entirely linked. The first occurred in a year 10 lesson, we were finding the area and perimeter of sectors and one lad said “why can’t you just give us the formula and not bother showing where it comes from?”. Later in the week one a year 11 was working on a past paper question and she asked, “why can’t it just tell you what to do, instead of making you have to work it out?”

The answer to both is simple, it is because we are teaching maths to give you an understanding of the subject, and as such an understanding of the world. I worry that in some classrooms students are just given formulae and told algorithms to solve things. This could even be effective as long as the exam papers are predictable and you can recognise what you need to do in the question. But it leads to no deeper understanding and reduces the whole subject to basic substitution and makes a farce of the whole matter.

I feel this has been entirely doable on the current GCSE, and I hope the new specifications will see papers that test a deeper knowledge and understanding of mathematical concepts. I hope that the new specifications mean more testing of the ability to select the correct maths to solve a problem, which is a real mathematical skill.

If the GCSE manages this it may lead to learners being more A level ready, and allow for more rounded mathematicians going forward. It will hopefully see more students understand the beauty of the subject, and see how much fun it can be.

Reblogged this on The Echo Chamber.

Okay, I have to say it:

It all depends what you mean by “understanding”.

Lots of bad ideas in maths come from the idea of teaching understanding rather than how to just carry out the procedure. On the other hand, there are plenty of procedures we don’t want kids to use blindly, can’t expect them to remember, or which might actually undermine future learning.

It’s always a balance and it always tends to depend on the task at hand. But I don’t think there are easy answers here. I’ll probably always use diagrams to explain sharing in a ratio and encourage students to use the diagram to recall the procedure, but equally I’ll probably always emphasise memorising how to find the nth term.

Always worth recalling the excess of teaching to understanding.

Yes, but surely you would at least explain why ypu find the nth term that way, even though you would advise memorising the procedure? I agree memorising imperative to increase fluency, but surely it helps to see why?

What’s worrying to me is that this implies that not only is it possible students are just being given formulas, but it is likely that this is how those students have made it through their mathematics courses if they are reacting to your teaching techniques in such a way.

I’ve yet to have any adult students that knew where addition comes from in the long multiplication technique (this is always a Day 1 question for my classes whether I’m teaching the remedial courses or calc 2).

Aye, that is the real worrying part.