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Tuesday, 23 April 2013

Reader, I married him: Going with the flow on ratios

I overheard some year 11s today talking about one of their earlier lessons and getting quite agitated about it. “It’s just structure, structure, structure in those lessons” said one of them. “I think she plans for every second” said another.

At first I wanted to laugh. I have no idea who they were talking about (and have no desire to know either), but whoever it was sounded like an excellent teacher and I thought the students just didn’t know what was good for them. “Every second planned” they’d said. Crikey. It sounds like the work of a very organised person. Hats off to them.

But then I wondered; why were the girls so agitated about it? They are highly motivated students, the sort that have been turning up for after school revision every week since they were in year 9. They’re not afraid of working hard.

The answer seemed to come in the final comments I heard:

“She never lets us just go with the flow” said a different student. “Yeah,” said the first, “she should just let us get on with it”.

This little conversation links in to an issue that I come back to time and again in my teaching practice. How much independence should we allow/encourage? How much is too much? Do students do better in lessons where “every second is planned” or in lessons when teachers “let us get on with it” a bit more.  An interesting seam, but I think I’ll save mining that one for another day.

Following another thread, it made me think about the lesson I’d just taught. It was year 9 and we were doing ratios. I knew that I’d put together quite a boring lesson. Originally I’d wanted to do something really creative involving the ratio of the string lengths of musical notes, but I hadn’t sorted things out in time and I was stuck with a boring stack of textbook questions. So I started the lesson feeling a bit uninspired, and explained how to simplify ratios into the form 1:n.

The girls were not impressed. What was the point? You can’t get 0.64 of a person. Why not just simplify them in the normal way?

So I said the first thing that came into my head and it went a bit like this:

Well, when I was at university there was a bit of an issue about the ratio of boys compared to girls. My university was split into colleges and some colleges had very different ratios. One college might have had a ratio of 11:10, but another might have been more like 7:3.

They looked interested, so I ploughed on….

So in some colleges, the number of boys and girls was fairly equal, in others there were lots more boys compared to the girls. If you were choosing a college, you might want to know the ratio of boys compared to girls and pick somewhere based on that. It might be difficult to compare the ratios, because you can't tell straight away if 3:7 is better than 16: 21, but if you had them in the ratio 1:n you would always be comparing like with like. Ideally the ratio would be 1:1 or pretty close (I was rambling at this point) although to be honest….. my college wasn’t that equal (really should have stopped to think at this stage)…but I suppose it did have its advantages I mean I’m marrying one of them so it worked out quite well for me

Cue raucous laughter and bright red face from me.

This definitely wasn’t a case of every second planned, but it certainly livened things up. It took a while for them to calm down and stop pointing out how red I’d gone, but they were clearly interested in the idea. So I ditched the textbook and made up some ratios on the board saying that they were the male/female ratios of different colleges. The students had to simplify them into the form 1: n, then explain which one they would like to go to.

Nearly all of them said the one with the ratio closest to 1:1, so we then ranked the answers in order from most fair to least fair ratio and had a useful discussion about ordering and comparing decimal numbers (is 1:1.6 equally as unfair as 1:0.6? Some of them thought it was at first).

I wish I’d thought of this idea before the lesson. I’ve since been online and looked at the male/female ratios on different courses at Oxford and the results are sadly unsurprising, but they are interesting and hugely relevant to a group of bright young things at an all girls school. The male/female ratio in history is 1:1.02 and in English it’s 1:1.7, but in maths it’s 1:0.44, in engineering it’s 1:0.3 and in physics its 1:0.2.

So definitely an idea worth using again, and despite the momentary embarrassment – I think it shows that it doesn't hurt to “go with the flow" occaisionally.


  1. Ha, nice save with a relevant context.

    I've been stuck on introducing this with lemonade over the last 2 years (i.e. which is the strongest lemonade?) and student-to-teacher ratios in different Countries (i.e. which Country would you most like to learn in?). Think I'll give this a go next time.

    I would have thought that the girls and boys would've wanted a ratio which was stacked more heavily on the opposite gender at Uni? :)

    1. I thought they would go for that too! But after they'd finished laughing and actually done the task, they went all coy and decided that they would prefer 1:1