Executive Functions: Supporting Foundational Skills for Early Math Learning
Executive function skills are closely linked to early math development in young children. What is EF, and how can parents, teachers, and caregivers support the development of these important skills?
Children begin kindergarten with varying levels of school readiness — a term often used to describe how prepared children are to succeed in school. More specifically, children who enter kindergarten with foundational math, reading, and vocabulary skills are more likely to succeed in school than those who do not. 
Many parents help to prepare their children for formal schooling by engaging in number and literacy activities. However, they may not know that they can also help to prepare their children for school by supporting the development of executive function skills.
Here we define what capacities the term executive function captures, describe why it is important for academic achievement, and offer suggestions for parents to help support the development of these important skills prior to kindergarten entry.
What is Executive Functioning?
The term executive function (EF) captures a set of cognitive skills that help children to appropriately manage their behavior and cognitive resources in order to successfully achieve a goal.  The core executive function skills include:
- inhibitory control (the ability to suppress inappropriate behavior and avoid distractions),
- working memory (the ability to hold and manipulate multiple pieces of information in mind at once),
- cognitive flexibility (the ability to shift flexibly from one situation, activity, or aspect of a problem to another), and
- planning and organization (the ability to keep a goal in mind while plotting and taking the steps necessary to achieve it).
Overall, executive functions allow young children to pay attention, remember and follow instructions and think flexibly. From this definition, it is clear that such skills should be important for success in a classroom environment and, in fact, a large body of research has emerged linking early executive functioning skills to academic achievement.
Why Do Executive Function Skills Help Us with Math?
EF skills are important for many academic skills such as reading and math. [3,4] However, EF skills seem to be especially important for early math learning (and early math learning seems to strengthen EF skills), perhaps because learning math involves mastering steps towards achieving a goal, namely the solution of a problem or puzzle. [3,4,5]
More specifically, studies have shown that young children who begin kindergarten with better executive function skills have an advantage in terms of math performance that persists into the elementary school years . This relation is not hard to understand when you think about all that goes into, for example, figuring out how many apples have been put in a basket based on those that are left on the table.
- First, you need to remember the problem that is to be solved (a subtraction problem in this case) and begin to think about how to solve it (planning and organization).
- Then, you need to remember how many apples were on the table before any were put in the basket while counting the apples that are still on the table and subtracting this number from the total (multi-step task requiring working memory).
- Then, you need to figure out a strategy for enacting each of these steps successfully (use your fingers) and be able to switch to another approach (marks on a paper) if it doesn’t get you to the right answer (cognitive flexibility).
- And, finally, you can’t get distracted by wanting to eat one of the apples (inhibitory control)!
The importance of this relation between math and EF becomes even greater in light of evidence that not only do early math skills play a role in later math achievement, but in reading achievement as well.  In fact, some have speculated that it is math’s special role in fostering EF skills that may account for this powerful link between math and other dimensions of school success. Consider the role of EF, for example, in retelling a story and in reading comprehension.
Although many early childhood programs are working actively to support the development of executive functioning skills in preschool, [6,7] parents can also play an influential role in promoting the development of these important cognitive skills at home.
How Parents Can Support EF at Home
It is well known that parent-child interactions play an influential role in the healthy development of children, including the development of EF. One way that parents can easily support EF development is by promoting these skills during everyday activities such as play. Below are some tips for how parents can support the development of strong EF skills in their children during common play activities such as Duplos®, puzzles, storybooks, and card games.
1. Planning and Organization
Before starting the activity, encourage your child to organize her materials, or set out a sequence of steps, in order to reach the end goal.
- Before playing with Duplos®, ask your child which pieces he would like to use when building the structure.
- Before starting a new puzzle, ask your child how she should organize the pieces in order to arrive at the end goal (finishing the puzzle). Perhaps she will want to separate out the border pieces first or maybe organize the pieces by color.
2. Cognitive Flexibility
While playing, encourage your child to make comparisons, shift perspectives, and approach the activity in different ways.
- While reading a storybook, promote perspective shifting by asking your child questions that allow him to take the point of view of multiple characters.
- While playing with Duplos®, ask your child to group the pieces first by color, then by shape.
- While playing, ask your child questions that invoke thinking about opposites. For example, “I say big, you say . . .”
3. Inhibitory Control
Encourage turn-taking while playing with your child. Turn-taking promotes inhibitory control, as she has to inhibit her desire to act (or respond) while waiting her turn.
- While playing with Duplos®, tell your child that you will alternate who gets to add the next piece to the structure.
- Play games in which your child is only supposed to respond when he receives a specific cue. For example, in the game Simon Says, he must follow the command (e.g., touch your nose) when he hears the words Simon says, but must inhibit his desire to respond when the command is not accompanied by the cue.
4. Working Memory
Ask your child questions or play games that require her to hold multiple pieces of information in mind in order to arrive at the correct answer.
- While playing with Duplos®, ask your child how tall the structure would be if he were to add three pieces to a two-piece structure.
- Playing card games such as the memory matching game can help to promote working memory skills. When playing this game, your child has to remember which face-down cards contain which objects in order to find a matching pair. After a few rounds, your child is holding multiple pieces of information in mind (i.e. which face-down cards contain which objects) in order to meet the objective of the game (finding as many matching pairs as possible).
By incorporating EF support into everyday play, you are helping your child develop essential cognitive skills that are important for later academic success!
Jane Hutchison is a doctoral student at Georgetown University, and a member of DREME’s Making More of Mathematics and Parent and Early Caregiver Engagement projects. Deborah Phillips is Vice Dean for Faculty at Georgetown College, a professor of developmental psychology in the Department of Psychology, and affiliated faculty at the McCourt School of Public Policy.
Development and Research in Early Math Education convenes scholars from twelve universities to advance the field of early mathematics learning and improve young children’s opportunities to learn math. For more information on the research and resources of DREME, please visit our website: https://dreme.stanford.edu
 Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., … & Sexton, H. (2007). School readiness and later achievement. Developmental psychology, 43(6), 1428.
 Center on the Developing Child (2017). Key concepts: Executive function and self-regulation. Retrieved from https://developingchild.harvard.edu/science/key-concepts/executive-function/
 Best, J. R., Miller, P. H., & Naglieri, J. A. (2011). Relations between executive function and academic achievement from ages 5 to 17 in a large, representative national sample. Learning and individual differences, 21(4), 327–336.
 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.
 McClelland, M. M., Cameron, C. E., Duncan, R., Bowles, R. P., Acock, A. C., Miao, A., & Pratt, M. E. (2014). Predictors of early growth in academic achievement: The head-toes-knees-shoulders task. Frontiers in psychology, 5.
 Bierman, K. L., Nix, R. L., Greenberg, M. T., Blair, C. & Domitrovich, C. E. (2008). Executive functions and school readiness intervention: Impact, moderation, and mediation in the Head Start REDI program. Development and Psychopathology, 20, 821–843.
 Raver, C.C., Jones, S.M., Li-Grining, C.P., Zhai, F., Bub, K., & Pressler, E. (2011). CSRP’s impact on low-income preschoolers’ pre-academic skills: Self-regulation as a mediating mechanism. Child Development, 82, 362–378.