Maths manipulatives and hands on concrete resources have always been acceptable in the Early Years, Foundation Stage and Key Stage 1 classroom as a method of teaching primary Maths concepts, but shouldn’t we be making more use of them to help pupils at Key Stage 2, especially when following a mastery approach?
If you’re new to Maths manipulative or are just starting on a Singapore or Asian Maths journey, you’ll want to read our blog: Your Quick Guide to Becoming a Maths Mastery Expert.
If you know you just want to grab a copy of one of our most popular resources ever, here’s the link to the list of the 15 best hands on manipulative examples and how to use them: Download the Ultimate Guide to Maths Manipulatives.
Counting cubes, making ‘cookies’ out of play dough, using plastic coins to pay for these ‘cookies’ are key ways to teach concepts to younger pupils and help teach maths yet by deeming them babyish and ‘too childish’ for Key Stage 2 pupils we are make learning for them more difficult to ‘see’ and we decrease the chances of children realising the concepts for themselves (essentially, we could be denying children the most powerful type of learning!)
Using manipulatives to help teach KS2 Maths
At first, children need hands on and visual hooks to understand new concepts in Maths. This is true whether they are simply learning to count or exploring patterns in algebra. With Mathematics itself being abstract, concrete Maths manipulatives provide the learner a ‘window’ in, to make sense of the problem at hand by touching them, playing with them, exploring the patterns and relationships which make a huge difference between understanding for depth or just for procedure. Research has shown that teaching with physical manipulatives has significant positive impact on learning in Maths (Carbonneau, K.J., Marley, S.C. & Selig, J.P. 2013), a summary of their main findings can be accessed here.
Certainly, the Asian-style model of Mathematics teaching strongly advocates using manipulatives in the classroom, with the‘concrete, pictorial, abstract’ approach they’ve popularised. But before you think, “Great – let’s just get out some practical resources each lesson and all pupils will succeed!”, there is more! You see, it’s also about how pupils use the equipment and relate what they are doing practically to the problem you’ve asked them to solve!
The Ultimate Guide to Maths Manipulatives
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Hands on resources are a tool
It is fundamental that children understand that what they have in their hands is a tool to help them make sense of the underpinning ideas of Maths, and not as a implement to depend on to work out the Maths each time. If the latter happens, then children become dependent on the equipment and the manipulative then becomes a ‘crutch’ to rely on.
What not to do with manipulatives in a classroom
My own experiences draws me back to a lesson I observed where the teacher, with the utmost of good intentions, set about teaching her Y3 class all about subtraction with decomposition, with the use of Dienes blocks.
Fantastic you may think! So did I. Until I realised that she had gone about it in a fashion where she was demonstrating and modelling how to decompose the numbers by just telling them what to do as opposed to letting the class find out for themselves. It then became apparent that many children in the class were simply mimicking the procedure of decomposition they had seen their teacher do, without any real understanding of what was going on. They followed the ‘steps’ and although came to the correct solution with the blocks, could not then relate this back to the algorithm that was subsequently taught later on. Just because practical equipment is being used, if not used correctly, it will actually have a detrimental effect.
Mastery involves variation
As you know, the key to mastery is the ability to use and apply while making sense of Mathematics across topics, one step towards achieving this is through variation – variation of the problem posed, but also variation on the manipulatives used. By this I mean, there is not just one practical resource used for a particular type of question. For instance, when teaching number and place value, you could use Numicon, bead strings, Dienes blocks, place value counters…the list goes on!
This is one respect in which the Concrete Pictorial Abstract or CPA Approach meshes extremely well with manipulative use. Read our blog explaining CPA to get some examples of how you might introduce varied manipulatives into the classroom.
Let the pupils choose the resources for greater depth
If we are encouraging children to become independent learners, they should then also have the choice of which manipulative they think would best suit the task and then be able to reflect on and explain what they did. To encourage more depth of understanding, could the student use different manipulatives to prove the same answer?
Free guide to the best manipulatives even when you’re on a budget
So, once you know you need them, how do you choose the best resource for your primary classroom? Well, ordinarily it’s a case of trial and error, and nabbing a few ideas from your teacher friends. But no longer. We’ve done the legwork for you so here is our Ultimate Guide to hands on resources that really make a difference in Maths lessons. And best of all we’ve included lots of ideas to get them on the cheap.
Is your favourite resource in our guide? If not, let us know and we’ll consider it for the next version. As usual, we’d love to know your thoughts. Please email firstname.lastname@example.org