## Monday, 13 April 2015

### Making mode and median meaningful

So today I started the averages topic with my Year 8 set 4 of 5, and so faced that age old conundrum known by all Maths teachers - how to engage pupils in something they have seen before but only half remembered?

I decided to test a hypothesis of mine, that these pupils will have an instrumental understanding (to borrow the language from Skemp) of finding mode and median, but no understanding of what the values mean or how to use them to form judgements. So the focus of my lesson today was not finding mode or median, it was what these averages actually tell us and making judgements about which average measure we are going to use.

We looked at the idea of average age (in years) to justify mode, and then average height of a group of 10 pupils to justify median. From there we looked at trying to convince a boss to give us a pay rise (or alternatively, being the boss and being able to explain why you are not giving a rise), and similar situations (convincing parents to increase an allowance, or to purchase an extra pet), as well as the classic situation of having to choose stock for a shoe shop based on average shoe size. In these situations the averages become what they are always supposed to be, a means to an end rather than and end in themselves. Pupils were much more engaged in the processes because they could see the point in them, and it would appear that the processes themselves have become more embedded through being applied. I think from now on I will stop teaching "how to find mode, median and mean" and only teach applying averages, and trust that the calculations will take care of themselves.