Independence in Maths learning


Last night I received a email from a pupil in my class asking very nicely if she could have some extra maths homework. I was delighted and tweeted about it, of course!

But then this morning Oliver Quinlan replied that it would have been even better if she had contacted me to say “Here is some great learning I have done” rather than asking me to set her some work.

This really made me stop and think. This child is very bright, highly motivated and keen to learn. In her own time she researches all the topics we study in class, emails me facts and interesting websites she has found, writes novels and has shared them with me on Google Docs so that I can see she not only writes, but spends a lot of time editing her own work. Yet maths is the only subject she has asked me to “set work” for.

Similarly, in self-directed learning, the children have been able to locate resources and activities for everything but maths. None of the Y5 teachers routinely use textbooks or worksheets, yet when the children are seeking to practice their maths skills this is invariably what they have been asking for.

Is there something about maths that makes it hard to see a logical “next step” to study? In recent months I have had lots of parents ask me to set “catch up” extra work for pupils. I have been happy to do this, based on analysis of their areas of strength and weakness using data from in class work and tests. However, this always seems to have to take the form of extra questions and worksheets. In the past I have set homework that was just “Learn the 8 times table”, for example, and this was very unpopular – the parents were very keen to have “a sheet” to do.

We have been doing “Class Maths” every single week all year. In these sessions, as I have blogged earlier, we set challenging and rich problems from the NRich website, which require deep thinking, application of mathematical knowledge and skills, and great resilience. I had thought that this was serving to provide context and meaning to the skills based lessons, but perhaps this is not the case – or is just not enough?

I had actually noticed a bit of a problem developing in class maths recently. When working on solving a set problem, the children are fine – very motivated, keen to solve the problem and share their reasoning. However, last week I set them a task which was an open-ended investigation – which, crucially, had not yet been solved. It involved the children looking at spinners and working out which number properties (eg odd numbers, multiples of 3) would be most likely to come up on different spinners. At first it was fine, as they soon discovered that the best property to choose was “multiple of 1” followed by “odd”, “even”, or “multiple of 2”, and that if you picked something very random like “multiples of 1.4” your numbers would very rarely come up. This led to a good discussion about probability and their realisation that if you picked “multiples of 3” and span the spinners 100 times, your numbers would probably come up about 33 times.

However – after this, their task was to design different spinners and investigate what difference this would make. At this point, they floundered. There wasn’t a clear problem for them to solve, and they soon lost interest. I had thought some would be interested in trying out spinners with decimal numbers or only odd numbers, for example, but it really didn’t spark them off. I’ve noticed this before when setting problems with no real, clear solution. It’s a shame because interest in just asking “what if” is a massive part of maths, and life!

So I guess I have to work on developing this interest in pursuing different lines of enquiry! I did briefly the other week I think when the children were talking about speeds and I pondered whether Usain Bolt running as fast as he does in the 100m would set off a speed camera in a 20mph zone, so a group of children took this off and tried to work out whether he would, but then this is still a question with a solution – you really want them to be wondering about different speed limits, different creatures that might set off different cameras etc. Or, ideally, not needing me to set the question in the first place – that they would have thought of it themselves then tried to work out how to do it!

Ah it’s a puzzler. So what do I need to do to get children to see that they can find their own ways into developing their maths skills, can set themselves challenging tasks and find ways to solve them – without necessarily asking me to give them THE DREADED “SHEET”??!!


6 responses »

  1. It certainly is a puzzle! I suspect it comes from the fact that we have taught maths very much as a ‘there is always an answer to find’ approach. It is black / white, right /wrong. The PR for maths has not been about it being creative sadly. We would struggle to ‘mark’ it! I wonder what the VCOP equivalent is?!

  2. I think what this comes down to is modeling and experience. You are obviously passionate about writing and literacy, and this will come across hundreds of times a day in the small interactions you have with children. You will see and suggest opportunities that could be opened up for independent learning in this area because that is where your interests lie, and as a result the children in your class will begin to pick up on these opportunities and notice their own.

    Someone with a similarly strong interest in Maths is likely to do the same, they will link the everyday to it’s mathematical context, drip feeding this idea that Maths can be used to solve everyday problems, and persue interesting lines of enquiry. They will make the learning possibilities visible in their approach, and as a result the children will start to spot these possibilities themselves.

    The hard part is not nurturing this approach in children, it is nurturing it in yourself, making yourself expose the possibilities for learning in a habitual way in an area that may not be your main passion. I wonder if this is possible, or even desirable? Should we accept that teachers have their own passions and will only truly inspire in these particular areas? Or, should we try to be ‘all things to all people’ even in our passions?

    • Now at first when i read this I thought, “But I do love maths!” But it’s very true, I don’t “see” possibilities in maths all the time the same way I see them in literacy. I love solving a good puzzle or tricky maths exam question, but someone has to set those for me, I don’t naturally think them up myself, whereas I can see an interesting picture or sentence and an idea for a story just pops up. Very interesting…

  3. Use the behavior you describe having observed in them (asking you to set a clear, definite goal for them), to change said behavior. You say you want them to ask their own questions, create their own problems, and find a new direction of study on their own, right? Well, teach them to, they way you know they respond well to. Meaning, give them worksheets where the answers they have to fill in ARE questions, not numbers. First, show them how to produce questions in sequence. Just become yourself a question factory in front of them, out loud, and write your unstoppable stream of questions on the board, in a somewhat organized way. Second, you start asking meta-questions, questions about the questions. Which of these questions are easy? Which are hard? Which seem important? Have you ever thought about any of these questions before? Which questions seem related to each other? In what way? What questions make sense? Which ones seem utterly incomprehensible? Are any of these questions somehow applicable to real life? How many interesting questions do they find on the board? If they had to chose 3 questions to go find the answer for, which one would they choose first? Can they come up with a question longer than the longest on the board? Third, help them discover some simple way to classify question types, a way that works for them. The idea is to move their focus from “I imitate the teacher at manipulating numbers,” to “I imitate the teacher at manipulating questions.” Even if you succeed only in showing them how to mechanically churn out a couple of standard question types, this will already be an invaluable habit in their learning process, as opposed to never creating math questions on their own. Last but not least, after a brief lesson on a specific topic, you give them worksheets where they have to write down questions, not numerical answers. Move them up from the realm of “questions are questions about numbers, and numbers are the objects,” to the higher level of “questions are legitimate objects in and of themselves, and we can directly work with questions as our toys.” However, you have to lead the way, by example, in a consistent, systematic manner, for them to really acquire this new thinking habit / perspective. You have to show them how it’s done first.

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