Making mathematical learning stick

There is a unique beauty in watching children grappling with a rich mathematical task. Ideas are shared and explored; theories are tested, and different opinions arise; frustration and confusion must be overcome. New, joyful discoveries are made!

We want young children to become truly immersed in purposeful, playful mathematical practice, and to feel a genuine ownership of their maths experiences. We’re aiming to prompt rich mathematical conversations – guided by a skilled practitioner.

I start by beginning to create a line using some of the sticks. Then I ask the question ‘How many sticks to make a line across the table?’ Children discuss whether it will be more than ten sticks, less than ten sticks or exactly ten sticks.

Once each child has made a prediction, they are desperate to see if they are correct. We count the sticks and recount to check. And to everyone’s surprise, it was eight sticks! One child stated that eight is less than ten. Another child clarified that eight is two less than ten.

But, we wondered, might it be possible to create a line using exactly ten sticks? Now, the conversations began in earnest and various methods were trialled. The children tried to make another line. But much to their dissatisfaction, once again there were only eight sticks in their line.

At this point, it is important for a practitioner to be aware of the different concepts and ideas that attention can be directed to.

It might be the precise use of language, like the use of the words ‘longer/shorter’ rather than ‘bigger/smaller’. Or we could explore the commutative law, for example seeing that if the same sticks are rearranged, the length of the line is unchanged.

Initially, the children simply rearranged the sticks. But after a few failed attempts and some gentle prompting, a new idea was formed. Longer sticks should be replaced by shorter sticks! A line of ten sticks was made.

Different challenges can then be introduced. What if we use a set of shorter sticks? Or we could take turns to position the sticks – the winner being the person who places down the last stick.

In developing conversations and extending thinking, practitioners may drip-feed key language or draw attention to the specific ideas given or actions performed by the children.

However, it is crucial that children retain ownership of how the task can continue to be explored. We want the search for the solution to continue when we step away.

In doing so, we lay the foundation for the children to become playful, articulate, and creative mathematicians.