### Archive

Posts Tagged ‘average’

## Catchy MnemonicsĀ

I find most memory aids a little silly. Why learn a rhyme about horses when you can just learn the trig ratios? Why learn a rhyme about the duke of York when you can just remember the order the colours come in?

However, I find that music is a good way of remembering things. For some reason music is good for us to remember words. I can, for instance, remember the words to a great deal of 90s pop songs even though I didn’t like them and never chose to listen to them because I heard them out places and on TV so often that they got lodged in my brain forever.

This is something I have seen work well in learning maths facts. Year on year I hear pupils sing “mean is average, mean is average…” etc in lessons to remember the averages. And I also hear a great many variations on the circle song.

Last year when I was teaching kinematics one of the students said “Sir,play the SUVAT song.” I’d not heard of the SUVAT song and he found it on you tube and we listened to it. It’s simple and it’s catchy and it really helped him and his class remember those equations. So on Tuesday I played it to one of my mechanics classes. By the end of the leson I’d heard three people sing it and it has been stuck in my head all week.

What do you think about mnemonics? Do they have a place? Have you any songs or rhymes that you use to remember things or that you encourage students to use? And do they help?

Categories: #MTBoS, A Level, Maths

## What does it mean?

Today my year 11s were busy revising ahead of tomorrow’s mock exam and one of them started singing the averages song. You know the one:

“Mean is average, mean is average, mode is most, mode is most, median’s the middle, median’s the middle, range high low, range high low.”

This got me thinking about the words we use. I’ve always disliked this song as a mnemonic as it encourages people to think of the mean as the “average” when actually the mode and the median are also averages too. The median in particular is a very useful one and we need pupils to understand the distinction. I have been very impressed in recent staff meetings to hear the principal, an English teacher by trade, use the term “national median” rather than “national average”!

As I was thinking about this, though, I had the sudden realisation that I should also be feeling the same way about the term “mean”! Granted, at GCSE level we only talk about one mean, the arithmetic mean, but that doesn’t mean the geometric mean doesn’t exist. (Nor the root mean square nor harmonic mean for that matter! Other means are available)

This is a hypocrisy in the way we treat certain words. I’m not the only maths teacher who dislikes the way mean and average have become synonymous. But no one has ever mentioned that the word arithmetic is missing from the term every time we use it.

I worry that we may be setting students who go on to further study statistics up for confusion in the future by simply referring to the arithmetic mean as the mean.

Have you ever used the term arithmetic mean, or even geometric mean, with your students? Have you shared my worry? Or do you think I’m being overly pedantic and it doesn’t matter? I’d love to hear your opinion.

Categories: #MTBoS, Maths, Teaching