Rethinking preschool maths

At snack time, a preschool educator asks 4-year-old Lola, “How many children have chosen an apple for their snack today?” Lola needs to count the children with apples, then find the correct number magnet to stick on the board. Then the educator asks her to do the same for bananas.

This may seem like a simple task, but it requires many skills beyond simply knowing how to count. First, Lola needs to remember the rule “only apples”, and avoid counting everybody. She must pay attention while she counts, avoiding distractions in the room. The next challenge is to switch tasks from counting to finding the magnet. When she has found it, she needs to understand that the numeral means the same thing as the spoken number, and remember that number. After sticking the magnet on the board, she has to switch back to counting while focusing on a new goal, counting “only bananas”. This task no longer seems so simple. It requires a set of thinking skills known as executive functions.

What are executive functions? 

Executive functions are the skills we use to control and direct our behaviour. One is working memory, which enables us to remember information like instructions for a short period of time, and process that information to respond appropriately. The second is inhibition, which helps us to ignore distractions or irrelevant information so that we can stay focused on a task. Finally, cognitive flexibility allows us to shift ways of thinking and move from one task to another. We often use all of these skills together when planning and working towards goals. 

“Executive functions are the skills we use to control and direct our behaviour.”

Executive functions improve as children get older, and children in any preschool will differ in the degree to which they have mastered these skills. Children who have poor executive functions may struggle to control their behaviour. They might be easily distracted, have difficulty remembering instructions, and have trouble switching between different tasks or different rules. If Lola has poor executive functions, for example, she might find it difficult to count only the children who have chosen an apple and to remember the number to put on the board, even if she knows her numbers well. Having strong executive function skills, on the other hand, has been linked to several maths benefits for children that last throughout childhood and even into adulthood.

Executive functions are key for many areas of early learning, particularly in maths. For success in maths, even very young children need to be able to follow instructions, learn and apply rules, pay attention, and keep track of what they are doing. They need to adapt to new rules and information. While counting on fingers might be good strategy when adding 3 to 4, for example, this method needs to be inhibited if a child is to learn a new strategy for adding up larger numbers. 

How can educators support executive function development in preschool maths? 

The more children practise using their executive function skills in maths, the easier it will be for them to tackle new maths problems. However, practising a task that targets executive functions alone doesn’t seem to improve maths skills. This may be because executive function practice needs to be embedded in maths tasks rather than targeted in isolation.

“Young children learn best when they are playing and having fun.”

Young children learn best when they are playing and having fun. We believe that carefully judged executive function challenge while learning maths helps children to learn deeply. Our recipe for optimal preschool maths learning involves fun, engaging activities that use executive functions to work towards maths goals. Here are some suggestions:

Try hiding numbers around the classroom and giving each child a specific number to find. Children need to remember their number and avoidthe temptation to pick up someone else’s. This activity also requires number recognition and matching number words to their symbols. This game can be made even more challenging by using different shaped number cards and giving children instructions like “Find the triangle with the number 2” or “Find the square with the number 6”.

Ask children to put toy animals in size order. Then change the rule and ask them to sort the toys into piles according to colour. Can they work out which pile contains the most animals? In this activity, children have to switch goals and remember the most recent instruction, think flexibly about various characteristics of animals, focus on the task at hand, and keep track of the number of animals in each group. Through this activity, children also gain a better understanding of order, using ordinal numbers like first, second, and third, and learn to make comparisons using words like bigger and smallest. Comparing amounts can help children to develop their counting skills – they must understand that only one animal should be counted at a time and that the final number represents the total quantity, all the while keeping track of which pile is the biggest.

“We believe that carefully judged executive function challenge while learning maths helps children to learn deeply.”

Our hope for the future

Many educators we meet through our research in UK preschools are unfamiliar with the concept of executive functions and how to support their development. Given the importance of executive functions for mathematical development, we hope that incorporating executive function challenge into preschool maths activities will become more common. In the school year 2021-22, 32% of children in England failed to reach the expected standard in maths by the end of Key Stage 1, when at six to seven years of age, which highlights the need for new approaches to early maths. We believe that helping children develop executive functions skills in maths activities early on will prepare them for the more complex maths they will face in primary school.