Only young children need to use objects when learning new maths. True or False?

I wouldn’t like to tell you how many times we have heard this during our work with children learning maths.  We have heard this from head teachers; other teachers; parents and often from the children themselves.

Often when children came in to work with Pam and I they were amazed to see a pile of maths equipment in the middle of the table. We found the older the children the more encouragement they needed to use it.

While instinctively we always knew that working with objects made learning easier, it was after studying to be Numbers Count teachers that we now have the theory to back up our practice.

This theory was written by Jerome Seymour Bruner, is a psychologist who has made significant contributions to human cognitive psychology and cognitive learning theory in educational psychology.

In his research on the development of children, Bruner suggests that, when presented with a new concept in mathematics, children learn best when the concept is introduced as follows:

Enactive Phase

Regardless of his/her age your child needs to actively use objects to explore any new concept .

For Example:

Addition – Have 2 groups of cars, biscuits or lego bricks, add one group to the other then count by moving the objects.

Fractions – Have a pizza; a cake or cut out shapes to cut up.

Fractions of a Number – To find a third of 12, give your child the correct number of objects (these can be anything as long as they can be physically moved.)

Use post-its to show the fraction, for example 3 post-its for thirds.

Now share (divide) the objects between the post-its.

That will give 3 objects on each post-it so one quarter of 12 is 3. From here you can push 3 post-its together to find three quarters.


In order to fully understand any new concept, your child will need lots of enactive practise before they are ready to move on.

This stage is both necessary and important for complete understanding.

Iconic Phase

Once your child is confidently using the objects and successfully answering the problems, he/she can move onto this phase.

Here, pictures, drawings or marks on the paper represent the objects.

For example, use drawn cars instead of real ones or dots instead of biscuits, etc.

These images can still be counted/crossed out/marked to assist with the calculation.


Symbolic Phase

Once your child is confidently using the drawn objects or marks to represent objects and successfully answering the problems, he/she can move onto this phase. Here, calculations are given exclusively with symbols and words.

For example, 5 – 3 or 1/4 of 12

In order for real understanding to occur, it is important that you support your child through these stages.

In our experience, children who have not been through these phases, when learning a new concept, struggle to understand, to a sufficient depth, to be able to build on the concept in the future.

So, as far as we are concerned the answer to the title question is FALSE! FALSE! FALSE!






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Anne and Pam are friends and colleagues with an obsession for improving maths attainment through raising self-esteem.

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