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!






We Did It!

Right, it seems like we have found out what to do with the screenshot from yesterday!  Thank you Mr Google!

So, even though it’s a day later than planned, here is a screenshot of one of our activity pages. This is an introduction to measure. Higher up our ladder there are activities that lead on from this introduction.  Further up we split the measures into the individual topics of; length, mass (weight), capacity and volume and time.  As you can see, at this Orange Level, the activities are very much play based.

measure orange

The learning comes with good questioning by the leader of the activity and allowing your child to think about his/her responses.  We believe if children enjoy maths activities then they will enjoy maths. When devising our activities we have tried, at all times, to make the activity enjoyable.


Maths Activities to Support Home Educators

Anne and I wanted to show you a screen shot of an one of a set of activities we have devised to support Home Educators in their endeavours to lead their children in maths.

Unfortunately when we put the screenshot up as an image on this post, the whole page couldn’t be seen.

If you follow the link below to our website, you will see, on the public pages, links to screenshots from the site, this will give you more of an idea about the support we are able to give you, as you lead your child (ages 5 to 11) with maths.


Should I just give my child the answer if he/she has no idea?

When working alongside children Pam and I rarely give the answer. We ask questions that help the child we are working with to come to a conclusion for him/herself. This takes time and needs to be done in a supportive environment, in order for the child to feel he/she has the time to really think.

One of the joys of Home Educating is that you have the time, plenty of time, which really means you can support your child’s maths learning.

Obviously there will be times when your child can see no way forward with a new concept or answering a problem.  That’s when questioning comes into its own.

How questions can support mathematical thinking.

If your child works things out for him/herself, even with your support, it will boost his/her self confidence. Once he/she starts to believe in his/her abilities in maths, then next time your child will be more confident to ‘have a go’.

The kind of questions you ask are important.  There has been much research on questioning.

Full paper about styles of questioning the article above was taken from

Sometimes though it is important just to give the answer and move on.  You will know with your child when it is the right time to do this. If your child has no idea how to move forward, even with your questioning support, then it is better just to give the solution.  That will mean you can move forward together.


What do I do if my child keeps getting things wrong?

Well! Anne has a favourite saying when it comes to learning and maths. ‘Mistakes are our friends.’ This always makes children laugh, as they are used to maths being all about getting it right!

Anne and I believe that making mistakes is an important part of learning maths.  It may seem odd but in making mistakes it means that your child is ‘having a go’. Without the confidence to have a go, very little learning takes place.

With you beside him/her, your child is in a great position to give it a go. You can foster an environment where thinking for him/herself and having a go are valued.

Learning from our mistakes means that together you can unpick where your child went wrong and work out an alternative way to tackle the problem or question.

It’s very tempting just to give your child the right answer and sometimes that might be the right thing to do. On the whole though, more learning takes place if your child, along with your support, works it out for him/herself.

So the answer to the question above is: celebrate the effort your child has put in to finding a solution; unpick the reasons for the wrong answers together and use your findings to ‘have another go’.

Interesting! Even a maths teacher can hate maths.

When I was looking around for other maths blogs, I came across this one:

Ben Orlin’s Blog about Maths

Reading this will help those of us who are educating children, either at home or at school.

Ben explains how he became a maths hater.

It is interesting for us to understand that lack of ability or application in maths can be caused by something as simple as being ‘turned off’ maths.

There’s a little bit of Ben in all of us and it is much easier to give up and give in rather than keep trying.

I hope it will make you, like it did me, see things differently and mean that you will be able to offer your child, as you sit next to him/her, the support he/she needs to overcome any anxiety he/she might be feeling and begin to conquer the fear of maths before it takes hold.


First blog post

Anne and I have lots of experience in and knowledge about maths.  We have spent many years supporting children with maths and encouraging them to develop a CAN do attitude to maths.

Now we are retired, we are keen to support parents, especially Home Educators, so they can do the same with their children.

Learning to set up a blog has been challenging but we have managed it, so here goes!