## Sunday, 20 August 2017

### How important is it to teach maths for understanding?

Over the summer I have been reflecting on the 9-1 GCSE papers that were sat back in June. In particular I was remembering hearing about and talking to people back in 2013 and 2014 when we were getting the first details of the 'new' GCSE and one of the key aims being to try and make sure pupils are understanding maths rather than just being taught certain procedures in order to solve certain questions. One of the questions that struck me as evidence of this appeared in the AQA Non-calculator papers:
Those people who have taught GCSE Maths for a while will be familiar with the more typical question about averages from grouped tables from the previous specification, which looks a little more like this:
Both of these questions are worth 4 marks but the way those 4 marks are earned is very different. In the second question from the older spec, the marks are given for:
(1) identifying the midpoints of each class as the average time taken for each person in the group,
(2) multiplying the midpoint of each class by the frequency of each class to work out an estimate for the total time taken for each class of people,
(3) adding these estimates to give an estimate of the overall time taken for all 40 people, then
(4) dividing the estimate of the total time taken by 40 to give an estimate of the mean time taken.

The point here is that many teachers, and I include myself in this during my early career days, would approach the teaching of this concept without any of the explanation I have given above, simplifying the whole thing to a straightforward procedure:
(1) Write down the midpoints of each class
(2) Multiply the midpoint by the frequency