Research School Network: Seeing, feeling, understanding Allison Carvalho discusses the use of concrete and visual resources in mathematics by older learners in key stages 2 and 3

I admire the creativity of Early Years educators. I really do. 

Every day, they work with a broad range of manipulatives and images to introduce concepts and procedures. There’s so much exploration and play that I wonder when consistent use of manipulatives and images for all stops and how this affects learners who struggle with the acquisition of foundational facts that underpin so many other areas of Maths. 

Let’s look at recommendation 2 (pages 10 – 13) of the EEF’s Guidance Report Improving Mathematics in Key Stages 2 and 3. It encourages the use of multiple manipulatives and representations because they ​‘can be powerful tools for supporting pupils to engage with mathematical ideas … The aim is to use [them] to reveal mathematical structures and enable pupils to understand and use mathematics independently’.

The report provides examples of how visuals and manipulatives can develop thinking about, for instance, fractions, multiples and algebra. It also explains that manipulatives should allow pupils to understand maths by ​‘illuminating the underlying general relationships, not just ​‘getting them to the right answer’ to a specific problem’.

The beauty of a manipulative is that it is not a number. Manipulatives can represent numbers, whatever numbers we wish. A manipulative is a representation and, as such, can be a leap of imagination for all learners once they have mastered how to use it. 

For example, cuisenaire rods have no marks, so students only understand their value by knowing that the yellow rod is five (or 50, 500, 0.5 etc.). That rod must be compared to the others to understand how its ​‘fiveness’ exists in relation to them.

Beyond maths specialists, perhaps beauty and imagination are not usually words that students hear in association with mathematics. Could changing this help to alleviate subject-related anxiety?

Professor Steve Chinn, a leading expert in the field of maths difficulties, is inspiring me to think about manipulatives differently, as do fellow experts Judy Hornigold and Professor Mahesh Sharma. The EEF’s guidance report is an anchor to which I can return when reflecting, ​‘How can I help children to understand x, y, or z?’

I began this blog by wondering. Now, at the end, I wonder:

1) How do we observe progress in problem-solving that has been achieved with the use of manipulatives?
2) Do we, and, consequently, learners, believe that only the lowest attainers ​‘need’ manipulatives throughout KS2 and KS3? Why?
3) Are older children embarrassed about using manipulatives? If so, why and what are the sources of this feeling?

Allison Carvalho is a Specialist Teacher and Dyslexia Assessor at Kaizen Primary School in Plaistow, East London.

Further reading

Improving Mathematics in Key Stages 2 and 3

Professor Steve Chinn is author of The Trouble with Maths (2020), Routledge
http://www.stevechinn.co.uk/bo…

Professor Mahesh Sharma established Mathematics for All, which provides resources for learners and educators: https://mathematicsforall.org/}

Judy Hornigold is an independent education consultant, specialising in dyslexia and dyscalculia:
https://mathsnoproblem.com/per…

Other blogs by Allison: 

Does cognitive science imply ​‘quick fixes’?
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