Education Endowment Foundation:EEF blog: Manipulatives and representations – Helping children to ​‘see’ the maths

EEF blog: Manipulatives and representations – Helping children to ​‘see’ the maths

How representations in maths can build number sense
Author
Cat Eadle
Cat Eadle

Cat Eadle is a Specialist Dyscalculia Teacher and Co-Founder of the Dyscalculia Network. In this blog, she explains how mathematical representations, like dot patterns, can help build number sense in our young children.

Blog •2 minutes •
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“They help me to ‘see’ the number,” stated Archie.

Developing children’s number sense – their understanding of quantity and number – is a key building block in early maths development.

As a teacher, I often play games with my pupils, using dot cards, dice and dominoes to help develop their understanding.

Recommendation 3 of the EEF’s ​‘Improving Mathematics in the Early Years and Key Stage 1’ guidance report highlights manipulatives and representations as powerful tools for supporting young children to engage with ideas across many areas of mathematics.

Using manipulatives and representations purposefully can support children to develop visual images. These are beneficial to all children but are paramount for learners with dyscalculia and struggling learners, helping them to see’ the maths.

To harness their power, practitioners must help children to understand the clear links between the manipulatives or representations and the mathematical ideas they represent, and why they are using them.

Dot patterns, like dice and dominoes, are visual representations of numbers one to ten. Each number has its own specific pattern of dots which represent that number. The patterns one to six match that of dot patterns on dice or dominoes. The patterns for numbers seven to ten can be doubles or near doubles of one to six, or they can be a five + model. See the below representations.

D Ot 1
Dot Patterns using doubles/ near doubles – (Emerson and Babtie - 2014)
D Ot 2
Dot patterns using 5 + model – (Steve Chinn)

Both types of dot patterns are useful to learners. But beginning with one and ensuring the learner has a clear image in their head before gradually introducing different arrangements of the same number helps to increase children’s pattern recognition skills and use of the visual part-whole strategies.

Introducing dot patterns is a helpful way to work on subitising, counting and ordering numbers. It can also be utilised for component parts and/​or number bonds and to develop place value understanding.

Dot patterns can be displayed using various manipulatives which makes them an inclusive, easily accessible and a relatively cheap’ resource. Manipulatives could include everyday objects such as pinecones, buttons, and small toys as well as resources like counters and cubes.

Using a build it’ background (a copy of the pattern to build on top of) makes them an ideal independent tuff tray activity.

Children can benefit from practical, first-hand experiences of moving and interacting with manipulatives to see’ and develop mathematical ideas.

For more information about dyscalculia, please visit Dyscalculia Network – Unlocking Numbers

There are six videos on the Dyscalculia Network’s YouTube channel which include sharing teaching tips, game ideas for both recognising the dot patterns to 6/10, and on introducing work on doubles/​near doubles to 10.