In this primer, we aim to put forward our current views regarding the points of synergy between equity, executive function, and mathematics education and cognition that are relevant to the EF+Math program. The literature shared herein is not exhaustive, but instead is a high-level overview of aspects of these fields that are relevant to the work of EF+Math, with the intention that the information shared stimulates discussion and innovation at this intersection.Many sources of evidence—including learning science research and teacher expertise—reveal that every child is equipped to excel in mathematics, and yet disparities in mathematics performance still persist.

For instance, children’s understanding of numbers (‘number sense’) predicts later math knowledge and can show measurable differences by socioeconomic status (SES) and race as early as preschool (e.g., Bailey, Siegler & Geary, 2014). Early mathematics knowledge is related to long-term educational outcomes, as well as a person’s career attainment and health outcomes (e.g., Knuth, Stephens, Blanton & Gardiner, 2016; Rittle-Johnson, Fyfe, Hofer, & Farran, 2016). Given that there are no inherent differences in abilities in students from different races/ethnicities or household income levels, observed performance differences are instead likely driven by differences in opportunities to build math abilities given to students from different races/ethnicities or household income levels, with students of color and students in poverty more often held back, offered less challenging math curricula, and held to lower expectations (among other factors) than their peers from higher income households or their white peers (e.g., Carbonara, 2005; Chunn, 1998; Oakes, 1995; Sorhagen, 2013).

Thus, a core, and yet addressable, issue in mathematics education is the need to reduce inequalities between students’ opportunities to learn and to be given opportunities to be challenged in mathematics (e.g., Byrnes & Wasik, 2009; TNTP, 2018). We will support programs that tackle these challenges head-on.Despite structural inequities that perpetuate math performance differences, every child possesses foundational assets that enable them to learn what they deem important to learn. One set of skills associated with success in mathematics is executive functioning (EF) ability.EFs are thought to include three separable, yet interacting processes, often referred to as cognitive flexibility, working memory, and inhibitory/attentional control (Miyake et al., 2000):

• Cognitive flexibility refers to shifting one’s attention between or otherwise managing multiple tasks, goals, rules, or perspectives. An example in mathematics is when a student needs to switch back and forth quickly and easily between solving multiplication and subtraction problems.

• Working memory involves holding and working with information in one’s mind. An example in mathematics is when a student is doing algebra and is holding in mind which steps they completed on one side of the equation and the answer they got so they can balance it on the other side.

• Inhibitory/Attentional control is the ability to focus on the information or tasks that are important or relevant to you and ignoring or inhibiting distractions or behaviors that are not important or relevant to you. An 1. Introduction EF+MATH program | 5 example in mathematics is ignoring irrelevant details when solving word problems and focusing on the information needed to complete the task.

While substantial individual differences in EFs exist, all three components of EF on average have been found to be related to performance on mathematics tasks, and to predict mathematics achievement longitudinally (e.g., Bull & Lee, 2014; Cragg & Gilmore, 2014; Ribner, 2019). Teachers have also observed that EFs are important for math learning based on their experience in the classroom (Gilmore & Cragg, 2014).

Indeed, one study found that teachers’ ratings of students’ EF abilities predicted gains in mathematics skills over an 8 month period (Fuhs, Farran, & Nesbitt, 2015), though it’s probable that teacher expectations of both mathematics and EF skills may be correlated and thus predictive of math performance. Mathematics requires all three components of executive function: thinking flexibly, holding and updating important information in working memory (e.g., Fuchs et al., 2008; Raghubar et al., 2010), and inhibiting misconceptions and irrelevant information or rules (e.g., Cragg et al., 2017; Gomez et al., 2015).