Behaviour management and maths manipulatives

Teachers are inundated with the latest tips and advice, frustratingly, often by those who have never stepped foot in a classroom! Maths manipulatives (also known as resources) are recommended but we’ve all been there, handed out the resources and the next thing you know, three children have made a gun out of cubes, two children are trying to pocket the shiny counters and several are fighting over who gets the most multilink… so they can build the tallest tower!

What are manipulatives?

It can sound complicated but manipulatives are simply physical and visual aids that can be used to support the teaching and learning of mathematical concepts. Through play, exploration and modelling, most children find that manipulatives help them get to grips with the very abstract notions of numbers.

Commonly used manipulatives include:

• Multilink cubes
• Numicon
• Counters
• Cuisenaire rods
• Bead strings
• Balance scales
• Dice
• Dominoes
• Clock faces
• Digit cards
• Hundred squares

You don’t need to have the above. If budgets are limited then why not try some of these DIY manipulative ideas? By creating your own, you will have enough manipulatives that all children have access to them.

Why are they important?

Over the past two decades, research has indicated the positive impact of using manipulatives in the classroom. A 2013 report published in the Journal of Educational Psychology identified “statistically significant results” when teachers used manipulatives compared with when they only used abstract maths symbols.

The NCETM agrees that physical manipulatives should play a central role in maths teaching. “Manipulatives are not just for young pupils, and also not just for those who can’t understand something. They can always be of help to build or deepen understanding of a mathematical concept,” the organisation said in a post entitled 'Developing your use of manipulatives in maths teaching'.

Once children are confident using manipulatives or ‘concrete’ resources, they can then move onto pictorial representations or the ‘seeing’ stage. Here, visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they just handled and the abstract pictures, diagrams or models that represent the objects from the maths problem.

Introducing manipulatives — let them play!

Whether you have a bumper pack of manipulatives, a shared bank of resources or your very own DIY versions, it is important to teach the children how to use them independently. If manipulatives aren’t accessible to children, they become a novelty and of course, they will then be excited and want to play with them (even more!) It is essential therefore to give children an opportunity to play with and explore the manipulatives before trying to teach with them.

Introduce the manipulatives one at a time — if you don’t have enough for each child then set up a table with the manipulatives of your choice, so turns can be taken to explore them. This works well with younger years where ‘choosing tables’ are set up and there is a teacher-led ‘maths table.’

Through play and exploration, children can have a chance to work out what they think the resource would be useful for — ask questions such as:

• How could you use this?
• How could this help you when adding/subtracting?
• Why do you think they are different sizes — what could that represent?

Once the children have explored the resource and know its name, introduce a simple maths problem and ask them to use the manipulatives to help solve it. You can then model how to solve the problem using the manipulatives and guide the children step by step. This will need to be practised and reinforced regularly in younger years to build independence. Once you have done this with one resource, you can move on to another resource type, for example numicon, and repeat the same process.

Manipulative manners

Once you have introduced your resources, speak as a class and explain that they should come up with a set of rules for how they are treated and used. Giving children ownership over the manipulatives as well as the respect to make their own rules will make them feel accountable and lessen the likelihood of negative behaviours when using manipulatives. Write the rules up as a class and display them so they can be referred to.

Storing manipulatives

NRICH recommends children having access to manipulatives “Give open access to all the resources and allow the children free reign in choosing what to use to model any problem they may be tackling. I would make sure that children of all ages had this access from 3 to 11 years old and beyond.” While this is exactly what teachers would like to replicate in their classrooms, not all classes learn in the same way and this isn’t always achievable due to space, budgets and children’s prior experiences of manipulatives.

Once you have introduced a manipulative, decide as a class where you should store it. You know what works best for your class, so consider different options such as communal drawers, a maths table, individual student packs or a collection of manipulatives for each table. Set clear rules around using and treating manipulatives to ensure they are not broken or lost. Additionally, you could create a monitor for each resource so the children can take ownership and make sure they stay tidy and accounted for.

Individual resources

Class resources

Maths areas and tables

Creating a classroom culture that uses manipulatives will aid children’s fluency and help develop their ability to solve problems, reason mathematically and share! If manipulatives are introduced in a considered and gradual way, with clear boundaries from an early age, children should see them as part of everyday learning and they will not be a novelty. They will be seen as tools instead of toys — and hopefully no more multilink towers or guns!