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Posts Tagged ‘vocabulary’

## What does it mean?

April 29, 2014 3 comments

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

## Vocabulary and maths are not mutually exclusive

June 21, 2013 Leave a comment

My favourite area of maths is the pure maths side. Following it down to KS3 and 4 that means I like number and algebra best (and bits of shape). Leaving data handling as my least favourite. (Although teaching some S2 this half term has kindle a desire to teach more A level stats, and I do love some probability and the associated game theories, and other areas of data, but that’s for another day.)

The reason I mention this here is by way of explaining why I have taught only a small amount of the data topics over the last year. (I don’t mean I skip over them, just that when a class is split and the other teacher asks “do you wanna do data or algebra?” I always choose algebra, which normally pleases them too.)

Next week, however, I am embarking on a module in probability with my new year 11 class (they are “new year 11”, as in we move up at spring bank, not a new class to me.) They are a high set of intelligent pupils, and as such I will be teaching topics such as tree diagrams. Today I was planning the lesson and I noticed something strange: there is no mention of the terms “mutually exclusive” or “independent events” anywhere, not on the examboard spec, the SoW nor the resources I was looking through. It struck me as strange.

I then had a look at the DoEs draft spec for 2014, the term independent IS there (hurrah!), but the term “mutually exclusive” is missing. I feel vocabulary is important in general, but subject specific vocabulary is imperative if we are to ensure the next generation of mathematicians and game theorists are to make any ground!

Another thing happened today too, one of my sixth formers referred to brackets as “Parentheses”, this is a term I am familiar with, and one the girl in question grew up with, but the rest of the class had never heard. Again, it was an example of vocabulary disappearing in Britain, and I think this is something we should be aware of. This coupled with the fact a student teacher we had needed to explain the words “tedious” and “petulant” to a top set year ten a few months ago makes me think this vocabulary gap needs to be addressed. (Mark Miller has written a series of posts on vocabulary here )

We all go out of our way to include literacy in our lessons, which is great. Words like “linear”, “quadratic”, “expression” etc are revisited again and again, even the lowest ability classed I teach can use these well, and correctly, in the context of mathematical discussions. However, I think we need to go further, we need to use vocabulary such as “mutually exclusive”, and “iteration”, and other such things that don’t specifically appear on our syllabus (“iteration” is on the new draft!). We also need to go further, we need to use a wider vocabulary in our discussions with pupils to increase their own vocabulary.

Addition: I’ve been thinking, this could be an issue specific to the type of pupils we get at our inner city school, I’d be interested to hear how wide vocabularies of teenagers are at other schools with different pupil compositions.