Friday, 26 September 2014

Even more...

As I said, the UK government wants "harder sums". It wants rigour. Picture phalanxes of Roman centurions - very comfortable with their Roman numbers - marching rigorously up very straight roads, their shields held close together. Nothing gets past them.

My strategy for conquest is different. I've made a list of some of its components. Like Caesar's Gaul, so far it's got three parts:

First part:

I. Pick subjects that give power.

II. Find the subjects where kids can be creative,

III. Go into history and biography

Second part:

IV. Enthusiasm

V. Discussion

VI. Presentation

Third part:

VII. Climb up and down the ladder of abstraction 

- § - § - § - § - § - § - § - § - 

But now I'm going to add another part:

VIII. Estimation

I asked my friend Charlie who works as an engineer what maths he thought really needed to be taught at school. Estimation, he said, you need that all the time. And luckily it's become more accessible and more engaging than ever with Andrew Stadel's . I've used this with my Y4 class last year, and we're going to start again next week. What's so great about it, is that the kids are interested in the estimation and they like the challenge. They especially like it when there's a video "reveal" at the end.

I have this idea that if we like it, we'll start creating estimation challenges in the Year 4 classrooms, maybe begin an estimation blog, perhaps begin to find estimations to do at home too, photo or video.After that we get other classes to have a go.  Nothing too ambitious. First we take Manhattan, then we take Berlin.

My trial challenge was not a complete success, but it's helped me to get the measure of what's involved:

Anyway, here's Mr Stadel talking about what he does:

IX. The real world

To be honest, this is something I know I don't do enough of. Using real things, real places, things you might find at home. We've just been looking at reading scales, and for the first time we've got the classes to look for dials and scales at home this week. The range is amazing: weighing scales, a barometer, pressure gauges on pumps, a metronome, the rpm and the speedometer in car, a clock... and some things from an aeroplane: how level you are and speed. There is just so much to talk about.
In fact I can't stick to the real world. We did a bit of not-so-real world with our creation of meters to measure things not normally measured. The idea was to create a bit more attachment to our dial by investing more in it than usual.
It gave us a good chance to talk about what kind of units you might invent, as well as looking what the un-numbered marks represented. It also meant we could spend a bit more time on dials and still be doing fresh things.

X. Modelling!

This as Turtle Gunn Toms says in a comment on Graham Fletcher's excellent post on modelling, means taking a situation and mathematising it.

It's another thing I really don't do enough of. Probably none of us do enough of it! The ideal is a situation where you have a question, you put numbers to it, out comes some kind of answer.

It's a lot harder to find good examples for the primary / elementary classroom. I'd like to have a collection of this kind of mathematical modelling question.

Here's one I'm thinking of trying soon: I was talking to the kids: "Here I am, standing in the middle of the room..." and it occurred to me, "Where  exactly is the centre of the room? How would you work that out?" I said my thoughts out loud of course.

Not a very natural question perhaps, but I'd be interested to see how the class go about answering that. Some estimation first of all of course...


  1. Sounds like a solid plan, Simon. Keep us posted.

  2. Hello Simon,
    I've so enjoyed reading your thoughts and those of your students. I'm going to post the crazy meter beside my desk so my colleagues can be forewarned of my current status. Not sure if you are familiar with Joe Shwartz' take on Andrew's estimation 180- beautiful implementation at the elementary level. If not, here you go-
    I've learned a great deal from Joe's blog. I'm looking forward to digging into your gold mine as well! Thanks for taking the time to document your teaching. Lovely.

  3. Thanks Turtle.
    I just discovered Joe's blog a short while ago, and love it. But I hadn't seen that post, so thanks. I need to go back and read those early posts! I like the idea of using a number line to show the too-low and too-high estimates.

  4. To complement estimation, I suggest doing a lot of measurement, too.

    I am probably preaching to the choir here, but want to add a couple anecdotes about estimation and related number sense in the real world. Two years ago, I interviewed a young analyst for a job at my investment firm. She grew up in China and was nearly on their math olympiad team. When I asked her to estimate the height of the ceiling in our office, she had absolutely no idea, from half a meter to 100 meters. In other words, a great facility with mathematical manipulations and tricks, but no concrete understanding of numbers or measures.

    The other issue comes has come up in many forms with many very skilled people: they build a complex model to precisely calculate some answer (a market price, a risk quantity) and get an answer that is completely unreasonable (wrong by orders of magnitude). Inevitably, there is some small bug lurking in their code, but the real problem is that they didn't have alternative simplifications, heuristics, estimates, or overall number sense to relate to what the final answer should be (approximately).

  5. Thanks Joshua. I always like hearing about how this matters in life outside school.

    Yes, measurement. When I do estimation with my young kids, they often need some context with measurements even before they can make an estimation. So, we've just been using Andrew Stadel's Day 112: "What percent and degrees of the pie have been eaten?"
    and they need some teaching about what percent and degrees are. They mostly know that 100% is all of it. So, small step, 50% is half, slightly bigger step, 25% is a quarter (fourth). Then they can estimate. Same with degrees, except here 90° is the known, so we can start from there.

    With heights, we get out the metre rod, just for a quick reminder about what a metre actually is. So, even with estimation, there's teaching about measurement - there has to be. And naturally we do lots of measurement in other situations too.

    Your second issue is really important, isn't it, How best to encourage the kind of reality testing that's needed is a really interesting question for us teachers. I think part of it is in making it pleasurable, and once again Andrew's approach seems to really do this. Exactly why it's fun I can't say. On the other hand, in the context of measuring, insisting on an estimate first often seems to be frustrating to students: they want to get on with the measuring, they want to get the "right" answer by measuring and the estimate seems to get devalued.