When a child who is struggling is taken back far enough so their level of understanding is reached, they can often move forward from there very quickly. You know you’ve reached their level of understanding when you see a child have an ‘aha’ moment. Usually this is a much earlier stage than anyone realises, but it is their true level of understanding in that particular area, and they will regain confidence by working at this level for a while.
How to find a child’s true level of understanding in Maths
Give it a story
If a maths problem involves just numbers, or numbers and symbols, create an accompanying story to make the problem easier for the child to imagine.
For example, 110 – □ = 49 could be interpreted as:
We had 110 balloons outside at a party. Some of them blew away and now there are only 49 left. How many blew away?
If the maths is already some type of word problem, begin by reducing the size of the numbers.
Reduce the size of the numbers
Children find it very difficult to picture large numbers in their heads, and we often see them pushed too far too soon into this sort of abstraction. Reducing the size of the numbers is a recommended initial step back for children who are not understanding. This helps them to visualise the maths problem or situation in their heads and often this is enough to help them reach their point of understanding. So if there were 3-digit numbers in the problem, change them to 2-digit numbers below 20 or even 10.
For example, if a child still doesn’t understand what to do with 110 – □ = 49 when you’ve made up an accompanying story, change the numbers to 20 – □ = 2, or even 5 – □ = 1.
Draw a diagram to represent the situation
If the child still doesn’t understand after you’ve attached a story and reduced the numbers, draw a diagram using symbols such as circles to represent the situation.
Draw pictures of the actual objects in the story
Pictures of the actual objects in the story are even easier to understand than diagrams.
With the balloon diagram above, you could just add a string to each circle to turn it into a picture of a balloon.
Use counters, straws, blocks or pasta shells
If pictures of balloons aren’t working, then use hands-on materials to represent the story.
As you begin to tell the story, put out 5 actual objects. Explain that “Some blew away, but we don’t know how many. But we do know that 1 was left.” Separate 1 from the 5 five objects so that they can see that 4 blew away.
Using the objects, go over the problem again, this time talking about the two parts and the whole amount:
Point to the 5 objects and explain that these are the balloons that they took outside, and then say ‘This the whole amount of balloons in the story’.
Point to 1 object and explain that this is the balloon that was left, and also say ‘This is one part of the balloons’.
Point to 4 objects and explain that these are the balloons that blew away, and also say ‘This is the other part of the balloons. This is what we needed to find out.’
Use the actual objects
If representational objects aren’t working, use actual balloons.
Act it out
The earliest stage of all is to get the child to act out the story.
They can use balloons and take them outside, pretend some blew away and show the one that was left.
Or, if you happen to have 5 kids around, you can get them to pretend to be balloons and act out the story as you narrate it.