The Invisible Demands of Mathematics

We just practiced ratios yesterday in class. How have they already forgotten it today? I watched this student solve the first two steps of an algebra equation correctly. Then halfway through, they forgot what they were solving for, rewrote the equation incorrectly, and arrived at the wrong answer. Why is it that the first thing students seem to forget after the summer break is their multiplication facts? 

Sound familiar? You are not alone. 

As teachers, we instinctively assume there is a gap in understanding the math and that we need to reteach. Sometimes that is true; however, recent research suggests that something else is at play.

Most of us associate math with teaching numbers, procedures, concepts, formulas, and problem-solving strategies. Yet many students who understand all of the above struggle to successfully do the math. Emerging research has found that this gap between knowing the math and actually doing it lies in the often-overlooked brain process of executive functioning. Executive function is a set of cognitive processes and skills that allow an individual to focus, plan, organize, remember, and execute tasks. In a school setting, this translates to the core executive function skills of working memory, impulse control, and cognitive flexibility. These are the sets of skills that help students succeed in class. 

Let’s, for a moment, visualize a middle school math class where the teacher has presented a word problem. The student has to read and decode the word problem, pay attention to the numbers, recognize and ignore unnecessary details, understand what is asked, decide on the operation, plan a strategy, do the calculation, and check for accuracy, all while holding the numbers in their working memory. Sounds like juggling three balls and running an obstacle course at the same time, right? Math is not just about numbers; it is a cognitive obstacle course. 

In a recent longitudinal research study involving more than 104,000 students, it was found that executive functioning predicts later mathematics achievement. What’s more, the study also revealed that working memory emerged as the strongest predictor (Tette et al., 2026) of long-term mathematical achievement. This finding aligned with an earlier study that made the same claim, but for neurodiverse students. The new research extended it to all students. 

Brain imaging also tells a similar story. Evidence of a direct correlation between math and executive function came from two major 2023 research reviews (Tablante et al., 2023; Yang, X., et al., 2023) that examined brain imaging studies of children with math difficulties. Unusual activity in brain regions responsible for executive functions was observed in children with math difficulties. This suggested that it is not just number-processing difficulties at play, but also difficulties with core executive functions.

It is undeniable that executive functions are essential for learning mathematics, but teaching them in isolation is like teaching a game and its tactics separately. Teaching executive functions as a standalone program does improve performance on the trained skill; however,  it is unlikely to improve math learning due to the lack of transferability. Students don't first develop executive functions and then use them later in math. They develop them as they engage in meaningful mathematical thinking. The support needs to be embedded within math learning itself. 

So how can we address the underlying issue? How do we prepare students for this cognitive obstacle course? How do we embed executive function (EF) support in the lesson? We start by asking two essential questions and using the Math-EF Tool in the planning stage:

1. What does the brain have to hold, filter, switch, or sequence separately from the math itself? 

This will automatically rewire your brain to pause and connect each step to the EF skill required, which can then lead to exploring scaffolds needed to support the EF skill. 

2. If I strip away the EF demand, would the student still struggle? 

This tells you whether to reteach math content or scaffold EF.

The Math-EF Tool

Once the EF skill required is identified, use the downloadable Math-EF Tool to select a matching classroom strategy and/or scaffolding. 

Let’s look at an example from a sixth-grade word problem: A school is organizing a field trip. One bus seats 48 students. There are 173 students going. How many buses are needed? 

The problem looks fairly simple. However, now let's analyze it through the Math-EF Tool lens.

What are the executive function demands in this lesson?

1. Attention - to read all the information carefully.

2. Working Memory - to hold the numbers 173 and 48 while understanding the problem and deciding the operation.

3. Planning - to decide whether to divide or multiply, and what to do with the remainder in case of division.

4. Organization - to ensure the correct line-up of the numbers while doing long division.

5. Impulse Control - to resist writing the remainder 29 as the final answer.

6. Cognitive Flexibility - interpret the remainder 29 in context.

7. Self-Monitoring - to check whether the answer is reasonable.

Math EFTool HERE

Important consideration that dovetails with this model:

• Solve the problem yourself to better understand moments when you have had to re-read, hold information, resist impulsive decision-making, etc. It is also equally critical to separate the math content from task demands. A student might understand the concept of fractions conceptually, but might struggle with the operations involved because of the amount of information to hold, or because the directionality of division can be confusing when dividing fractions. 

• Keep the thinking and steps visible. Talking through your thought process as you work out a problem externalizes working memory, which then supports the student's problem-solving ability. 

• As teachers, in the name of teaching tips and tricks, we are often guilty of emphasizing keywords over structure. For example, more indicates addition or less indicates subtraction. While it may be true in some cases, it is not in other contexts. Moreover, simply looking for keywords takes away young minds' cognitive flexibility and critical-thinking abilities, which, in turn, feed impulsivity.

The Math-EF framework is not an intervention or remediation; it is a tier 1 strategy that benefits every student. The goal is not to lower the bar for some students; it is to remove the hidden barriers and noise for everyone.

So the next time a student stumbles, pause before concluding that they did not understand the math. Instead, ask what executive functions are we asking their brain to use along with the math?

References

Gaia Scerif, Blakey, E., Gattas, S., Hawes, Z., Howard, S. J., Merkley, R., O’Connor, R., & Simms, V. (2023). Making the executive ‘function’ for the foundations of mathematics: The need for explicit theories of change for early interventions. Educational Psychology Review, 35(4). https://doi.org/10.1007/s10648-023-09824-3

Horowitz-Kraus, T., Cirino, P. T., Cutting, L. E., Hughes-Berheim, S. S., Wilkey, E. D., Barnes, M. A., Rosch, K. S., & Church, J. A. (2026). The interplay between executive function and learning disabilities: Developmental cognitive neuroscience perspectives on reading, math, and ADHD. Developmental Cognitive Neuroscience, 79(June 2026, 101722), 101722. https://doi.org/10.1016/j.dcn.2026.101722

Tette, P. P. M., Justi, C. N. G., & Dos Reis Justi, F. R. (2026). The relationship between executive functions and mathematics: A systematic review with meta-analysis of longitudinal studies. Psicologia, Reflexao E Critica : Revista Semestral Do Departamento de Psicologia Da UFRGS, 39(1), 3. https://doi.org/10.1186/s41155-025-00362-1

Tablante, J., Krossa, L., Azimi, T., & Chen, L. (2023). "Dysfunctions associated with the intraparietal sulcus and a distributed network in individuals with math learning difficulties: an ALE meta-analysis." Human Brain Mapping, 44, 2726–2740. https://doi.org/10.1002/hbm.26243