Executive Functioning and Mathematics

Andrew Davis, CEI Intern, and Christine Mason

Principals and teachers report that it is particularly hard to raise math performance. Whether the attempted solution at your school has been to drill more on basic facts, or more experience with problem solving, digital programs, or integrating math as part of STEM, you may continue to be distressed. Does the following sound familiar?  A student submits a math test to his teacher. The first steps in the long division problems are all correct, but he forgets steps and gets the wrong answer in the end. The student also rushed through other problems, performing the wrong operations, and heading straight to the automatic answers that had been shared in class. These problems are not uncommon. At other times, students can perform the math operations that they did in class, but make simple mistakes with math calculations. However, math is not just difficult for these students; math education in the United States is infamously unimpressive.  (Schleicher & Davidson, 2012).

Math Performance in the US Falls Behind Many Other Countries

In 2015, the United States ranked 40th in the world on the Program for International Student Assessment (PISA) (OCED, 2016). This is 23 points lower than the average among all countries.  It continues to be frustrating to see that although wealth is greater in the U.S., many countries with fewer resources outperform US students when it comes to math. Slovakia, for example, performs about the same as the United States, but spends around $62,000 less.  Korea, one of countries demonstrating the highest student achievement in math on PISA, spends well below the average spending by other countries per student.

While math skills are essential, many people in the U.S. don’t have adequate math skills and abilities. An estimated one-fifth of adults in the U.S. have numeracy skills below what is needed for everyday situations (Department for Education and Skills, 2003), and less than 50% of our children perform above the proficient level in math (U.S. Department of Education, 2016).

Math: Complex, Multi-dimensional Operations

What else can be done to boost math scores? Perhaps something can be gained by turning to neuroscience and considering how to improve a student’s attention, focus, and memory skills. Executive Functioning (EF) refers to a family of cognitive processes that help individuals plan, organize, focus, problem solve, and complete tasks.  ‘Executive functions (EFs) make possible mentally playing with ideas; taking the time to think before acting; meeting novel, unanticipated challenges; resisting temptations; and staying focused,’ (Diamond, 2013, p.155).  These EF skills involve switching, working memory, and inhibition. They support our ability to shift our focus from one task or stimulus to another (shifting); apply what we remember about the most relevant information (working memory); and stop distracting or automatic thoughts in order to continue to focus on a specific task (inhibition) (see Davis, 2017).  These three components of EF support our math capabilities. With math, students must constantly process input, holding information in one’s working memory, and then applying previously learned information in a specific sequence.

EF skills are critical throughout mathematical equations, from the start to the end. Math can be thought of as a second language, where the ‘words are mostly used to translate visuospatial and quantitative concepts into a set of symbols that can be more easily manipulated’ (McCloskey, 2013). Math may involve linguistic (using words), numerative (using symbols and numbers), and visuospatial (pictures, diagrams, etc.) dimensions as the students work through problems. As student’s problem solve they consider the relationships between numbers or calculation syntax in specific situations.  These are all skills that challenge one’s EF. (See Figure 1). 

Figure 1. An Integrative Model Specifying Processes, Abilities, Lexicons, Skills, Memory, and EF for Mental Math Problem-Solving Taken from: McCloskey, G. (2013). Executive Functions and Mathematics: A Neuropsychological Perspective

Figure 1 primarily demonstrates how working memory is used in math:

  • Before the problem even starts, one must know what the lexicons or words mean and have the knowledge of how to do the procedures.
  • Next, one must evaluate how the problem is given: in a diagram, in words, or in standard math symbols.
  • One then must create a procedure of how to attack the problem and perform the various mathematical steps of said procedure.

This may seem simple, but performing those steps requires knowledge of the mathematical concepts that you are trying to perform, using the proper procedure with accuracy, and being able to do all of this within a limited amount of time.  Furthermore, as shown on the diagram, all these different steps require EF skills to go between them and require EF again if there is a need to go back, review what one has done, or proceed in a different sequence. EF requires effort, and therefore a long and difficult math problem may drain someone’s effort to the point where the student goes back to an automatic processing of the problem, where they try to apply a short-cut that may not be adequate or appropriate for a specific problem.

As displayed in the previous diagram,  working memory is one of the more important aspects of EF for math (David, 2012). This is also supported by a meta-analysis  (Friso-van den Bos et. al, 2013) that revealed that verbal executive working memory had a strong relationship with math; however, visuospatial executive short-term storage, and verbal short-term storage also were found to be associated with math capabilities.

How Teachers can Enhance Executive Functioning to Improve Math Skills

Blair and Raver (2014) examined the impact of an educational approach known as Tools of the Mind (Bodrova & Leong, 2006) for children in kindergarten classrooms.  This approach focuses on EF as a primary mechanism through which children progress academically and socially.  Their study involved 29 schools which were either assigned to the treatment or control group, with around six children per classroom participating. Teachers provided individualized support based on how well a child is doing on EF specific skills.  Children were asked to meet with their teachers to set goals and reflect on their learning, and peer interactions are used to help support reflective behavior and social competence.  Results showed that there were significant positive effects on a measure of working memory (the backward digit span task) in math.  A positive effect on reading and vocabulary was also noted.  Blair, with other researchers (2015) also found similar results, suggesting that math performance in particular may be specifically associated with EF skills.

References

Blair, C., & Raver, C. (2014). Closing the achievement gap through modification of neurocognitive and neuroendocrine function: Results from a cluster randomized controlled trial of an innovative approach to the education of children in kindergarten. PLoS ONE, 9(11). doi:10.1371/journal.pone.0112393

Blair, C., Ursache, A., Greenberg, M., & Vernon-Feagans, L. (2015). Multiple aspects of self-regulation uniquely predict mathematics but not letter’“word knowledge in the early elementary grades. Developmental Psychology,51(4), 459-472. doi:10.1037/a0038813

Bodrova, E., & Leong, D. J. (2006). Tools of the mind: The Vygotskian approach to early childhood education (2nd ed.). Upper Saddle River: Pearson.

Bos, I. F., Ven, S. H., Kroesbergen, E. H., & Luit, J. E. (2013). Working memory and mathematics in primary school children: A meta-analysis. Educational Research Review,10, 29-44. doi:10.1016/j.edurev.2013.05.003

David , C. V. (2012). Working memory deficits in Math learning difficulties: a meta-analysis. International Journal of Developmental Disabilities, 58:2, 67-84. doi: 10.1179/2047387711Y.0000000007

Department for Education and Skills (2003). The Skills for Life survey: A national needs and impact survey of literacy, numeracy and ICT skills. London: HMSO.

Diamond, A. (2013). Executive functions. Annual Review of Psychology,64(1), 135-168. doi:10.1146/annurev-psych-113011-143750

McCloskey, G. (2013). Executive Functions and Mathematics: A Neuropsychological Perspective

OECD (2016), PISA 2015 Results (Volume I): Excellence and Equity in Education, PISA, OECD Publishing, Paris, https://doi.org/10.1787/9789264266490-en.

Schleicher, A., & Davidson, M. (2012). Programme for International Student Assessment 2012 (PISA) Results from Pisa 2012: United States(pp. 1-10, Country Specific Overview). Paris, France: Organization for Economic Cooperation and Development.

U.S. Department of Education, National Center for Education Statistics (2016). The Condition of Education 2016 (NCES 2016’“144). Washington, DC: U.S. Department of Education, National Center for Education Statistics.

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