You have to let the concrete set before you build with it

4th May 2018 at 00:00
Manipulatives are great for teaching maths concept, but it’s not enough to just provide boxes of kit on classroom tables – pupils have to be able to bear the load

There are more than half a million teachers in England, which likely means that we’re approaching a similar number of classrooms. To try to disseminate knowledge and ideas across that scale of enterprise is a challenge, to say the least. Even if we rely on schools and in-house CPD to convey good messages, we are looking at tens of thousands of establishments.

Inevitably, that means that some messages get lost in translation. Like a giant game of Chinese whispers, you can’t guarantee that everyone hears the same news.

A classic example of this, which has been troubling me of late, is the use of manipulatives – objects designed to help learners grasp a concept – in maths. Now, there is no doubt in my mind that the increasing availability of manipulatives in primary classrooms – and presumably those of our secondary colleagues – is a good thing. However, like with so many things, it is not as simple as it first seems.

With an increasing focus on “concrete” approaches to maths using objects, we have seen more schools investing in apparatus and making them available in the classroom. The problem is: it’s not what you do, it’s the way that you do it. Having Dienes blocks and bead strings is of no use to anybody if they don’t know what to do with them.

For a start, it’s not always obvious how the resources can help. I could provide the average primary school teacher with a bundle of algebra tiles and ask them to complete an equation such as (x2 + 4x + 3) ÷ (x + 1). If you’ve never seen or used algebra tiles before, then they probably won’t be much help. It’s only after structured teaching – probably starting with some much simpler contexts – that we are able to make use of them.

The same is true of many things. I think place-value counters can be an excellent way of showing how and why the short-division method works, but I wouldn’t recommend that any teacher make that the first thing they try to show with the counters. First, children need to become confident in using them just to represent simple numbers.

Even if children are familiar with the resource – like most children are with Dienes blocks – it’s not as simple as making them available for use. Often for solving a new type of problem, the added cognitive load of trying to work out how to represent the problem using concrete resources can just further complicate rather than simplify the process.

For that reason, it’s not enough to just provide boxes of kit on tables in lessons. Each tool needs to become familiar to its users if they are to be of any use. Only when children are familiar with concrete apparatus such as Dienes is it any good moving them on to place-value counters. And when doing so, it’s worth taking a step back with the complexity of the maths, while the children get used to thinking about how the new apparatus works.

The same is true of other representations, such as the bar method. When I was first introduced to the principle, I wanted to incorporate it into my teaching straight away. The trouble was, on top of the other mathematical thinking I was asking of my children, the new model just provided another level of challenge to get their heads around.

Manipulatives are great. I love to see them in use in classrooms. Great teaching can be supported by the concrete models that they allow us to build. But first, we need to remember that what seems instinctive to us is another new thing to learn for the children in our classes. A mountain of resources in the centre of the table is just another problem to solve.

Michael Tidd is headteacher at Medmerry Primary School in West Sussex

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