This resource provides an overview of the connections between executive functioning (EF) and mathematics.
What is executive functioning?
Executive functioning (EF) is the name of a group of skills that helps us accomplish tasks in our world. The tasks can range from cleaning out the garage, to taking a written driver license test, to cooking with a new recipe. Core EF skills are of three types (although there is some debate as to their organization and names): we usually think of them as inhibition, working memory, and cognitive flexibility. For example, in the case of the cleaning-out-the-garage, we use inhibition to stay on task and not sit down to read a book found inexplicably in the box of old Halloween costumes; working memory to remember where we decided books should go (in a library donation box); and cognitive flexibility to figure out that although magazines are similar to books (we read them), perhaps they are best put in the recycling bin.
Above and beyond cleaning the garage, more generally inhibition entails ignoring distracting sounds or thoughts, concentrating on relevant aspects of a task or problem, resisting automatic responses (instead of blurting out the answer, we patiently raise our hands), and filtering out irrelevant information during problem solving.
Working memory involves holding, using, updating, and manipulating information in our mind. In using working memory, we temporarily store information, update it with new information as we work on the problem, and then manipulate that information in order to further the problem-solving process.
Cognitive flexibility allows us to shift our attention, try new strategies, and adapt our thoughts and behaviors in response to a change in the task. Frequently it also involves changing perspective, whether that is spatial (I wonder what that would look like from the other side?) or individual (I wonder how she feels about this?).
These specific skills are frequently related or overlapping. For instance, we tend to think of the ability to sort by color and then by shape as an example of cognitive flexibility. However, it also involves inhibition (inhibiting the previous sorting rule so that we can switch to a new one) and working memory (remembering the new rule). Together, these skills contribute to our ability in higher-order executive functioning skills such as reasoning, problem-solving, and planning and organizing.
Just like adults, children use EF skills to accomplish goals or complete tasks in their world. These EF skills develop rapidly in early childhood, and, as is the case in many other areas of development, are affected by experience.
Why is executive functioning important?
Research suggests that EF skills can positively affect motivation, persistence, and attitudes about learning. It helps children function in school settings and are correlated with later math and reading achievement. Children’s experiences can help them build EF skills, so it is important for teachers to provide the kinds of experiences that will support EF development.
What are the connections between mathematical development and executive functioning?
EF skills are needed in almost all mathematical activities. The simple act of counting a group of pennies requires considerable EF skills. The counter needs to simultaneously keep track of where she is in the number word sequence and which pennies have been already counted. This requires both working memory (Which number did I just say?) and inhibition (I already counted that penny, so I need to move on to the next penny.) More complex mathematical tasks, such as figuring out how many more peers are needed on an impromptu playground soccer team, demand even more EF skills (try it in your mind!). So, it isn’t surprising that children’s executive functioning skills are positively correlated with their mathematical skills.
Do better EF skills create better math problem-solvers? Or does doing math build EF skills? Is Andrew able to add efficiently because he has a powerful working memory, or does practice with addition help to strengthen Andrew’s working memory? Or could both factors be operative? Perhaps Andrew gets a good head start on addition because of his strong working memory and then strengthens working memory as he practices addition. Researchers aren’t quite sure about the directionality of causation between EF and math skills. What we do know is that EF skills and math development are both important in life and school. We can get a two-for-one benefit by providing children with interesting math problems that require increasing amounts of EF. Ensuring that we offer children challenging activities (problems that are just a little more difficult than what they already can do) in both math and EF will provide them with the opportunity to develop in both of these important domains.
Clements, D. H., Sarama, J., & Germeroth, C. (2016). Learning executive function and early mathematics: Directions of causal relations. Early Childhood Research Quarterly, 36, 79-90.
Diamond, A. (2013). Executive functions. Annual review of psychology, 64, 135-168.