Manipulatives in secondary – they work!

I’ve found the concrete-pictorial-abstract sequence is one of the best ways of teaching conceptual knowledge. In this post, I want to concentrate on one concrete tool: the numicon set.

I bought a numicon set early on in the year, on the back of Bruno Reddy’s recommendation, with the idea I would use it with small groups of my weakest pupils. In fact, its utility has far exceeded that.

Pupils at all levels have found numicon helpful. Showing a few examples under the visualiser has been a million times more effective than dodgy board drawings and whizzy PowerPoints.

First, some caveats. In order for manipulatives to be effective, a few ducks need to be in a row.

Time

If you’re planning on teaching HCF (or worse, HCF and LCM) in one lesson, give up now. Teaching like this takes more time. I spent a week on divisibility, factors and HCF (and it was more than a month after doing multiples and LCM). A luxury afforded by a mastery curriculum.

Behaviour

Numicon is not a game; it’s not a break from normal teaching; it is not done for engagement or because you want a “fun lesson”. Behaviour needs to be on point. Pupils need to be listening as carefully to your explanation with numicons as they do to an explanation on the whiteboard. Pupils need to follow your instructions as precisely and quickly with a numicon in their hands as they do with a pen in their hands.

Teacher-led and modelled

You can’t just hand some manipulatives to kids and hope they’ll figure it out. Modelling examples, being consistent and precise with vocabulary, is essential if they are to embed the conceptual knowledge into their schema.

Practice

Manipulatives are not a replacement for practice. Children need extensive drilling of routine problems. Fluency is impossible without it. Practice, practice, practice. We need to do five times more than we think.

Retention

If nothing in long term memory has changed, nothing has been learned. Most review problems in maths tend to practise procedures. I’ve come to think it’s equally important to review conceptual knowledge and underlying facts. It would be foolish to teach conceptual knowledge and then let it drop off altogether. Interleave and quiz the conceptual knowledge gained from numicon just as you would with procedural questions.

Consistency

Whenever I venture onto pinterest, I find a huge variety of manipulatives being shared as ideas for teaching maths: straws, blocks, teddies, lego, even cheerios. Better to stick consistently to a few of the same (Diennes and Numicon, say) rather than switching it up all the time. Let the kids get used to the manipulative. We want children to concentrate on the deep structure of the problem, not surface feature of the cheerio.

The range of applications is remarkable. I’m sure I’ve missed out many, and I’d love to hear about other ways I could make use of them.

Addition

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Subtraction

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Fact families

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Introducing solving equations

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Multiplication

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Lowest common multiple

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Division

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Remainders with division

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Highest common factor

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The mean

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Some upcoming uses I have planned are:

The median and mode (I didn’t teach this along with the mean because I believe in separation of minimal differences)

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Representing fractions

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Converting between mixed and improper fractions

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Ratio and fractions

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Found yourself nodding along to this? You’d probably be a great fit at Michaela. We’re doubling in size next year, and therefore recruiting in lots of subjects! Take a look at our ads or pop me an email at bisaksen@mcsbrent.co.uk

One thought on “Manipulatives in secondary – they work!

  1. Joshua

    For consistency, I’ve found an interesting difference between classroom and “home:” in the classroom, using a familiar manipulative allows you to focus attention on the mathematical concepts while a new manipulative is first taken to be a toy and it is hard to focus students’ attention. That is a clear time cost that needs to be budgeted.

    On the other hand, as a parent with my own children, using anything that is at hand has almost always worked very well. Since we do math at home, on errands around the city, while traveling, etc, that means a wide variety of manipulatives and contexts.

    I guess the underlying lesson is the same: use what is available, be creative about how it can apply to your topic, and don’t worry about wasting money and time acquiring something you don’t already have.

    However, I’m still going to buy a new set of zometools next time I’m in the US . . .

    Reply

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