Research shows that high math performance is linked with various positive life outcomes. However, we do not yet have a full understanding of which cognitive abilities allow some people to succeed in math more than others. The Brannon lab welcomed Dr. Miriam Rosenberg-Lee to talk about the role of inhibitory control in math learning and performance.

Rosenberg-Lee, an assistant professor of psychology at Rutgers University, began by speaking about the broad societal implications of numeracy. She cited a study that discussed how numeracy predicts HIV outcomes, as patients with stronger numerical skills are better able to manage a complex cocktail of medications. Similarly, numeracy predicts foreclosure rates in subprime mortgages.

Rosenberg-Lee noted that in these studies, numeracy is defined as rational number knowledge, or understanding of fractions and decimals. In fact, studies have shown that fraction skills uniquely predict college algebra scores (Matthews and Hubbard) and standardized math scores (Siegler et al). Executive functions such as visuo-spatial working memory and inhibitory control have also been shown to predict math achievement.

One possible explanation for the connection between rational number skills and math achievement involves inhibitory control and the whole-number bias. *Whole-number* *bias* refers to the difficulty that students have when learning about rational numbers because they do not follow the same rules as whole numbers. For example, multiplying rational numbers does not always increase their quantity, and a rational number with more digits is not necessarily larger than one with fewer digits. To master rational numbers, children have to use inhibitory control to overcome the conflicting rules that they have learned about whole numbers.

One example of whole number bias can be seen in a decimal comparison task. While people can easily identify that 0.80 is larger than 0.27, they take longer to identify that 0.8 is larger than 0.27 because 0.8 has fewer digits. To recognize that 0.8 is larger, they must inhibit their knowledge about whole numbers. This phenomenon is known as the *string length compatibility* *effect* or the *semantic interference effect*.

Rosenberg-Lee discussed a study where she investigated whether performance on the decimal comparison task is correlated with general math achievement and explored which executive functions contribute to decimal comparison performance. In the study, 76 undergraduates completed a decimal comparison task which prompted them to pick the larger of two decimals. In some trials, the two numbers had different numbers of digits, and the number of digits was either consistent with magnitude (e.g. 0.87 and 0.2) or inconsistent with magnitude (e.g. 0.27 and 0.8). Trials in which both decimals had the same number of digits were used as controls. Subjects were also given a Woodcock Johnson standardized math assessment, demographic surveys, and several executive function tasks including a Stroop test, a backwards spatial scan task, and a task switching exercise.

Rosenberg-Lee found that Woodcock Johnson math scores were predicted by performance on the mixed inconsistent decimal comparison task, the incongruent Stroop trials, and the backwards spatial object scan task. Age also had a significant effect on results—older subjects generally performed worse on the decimal comparison task. When age was taken into account, the only predictors of math scores were performance on the incongruent Stroop trials and the inconsistent decimal comparison task, both of which involve inhibitory control. While more research is needed to determine which of these two factors is more significant, the results suggest that domain specific measures of executive function may be better predictors of math ability than domain general measures.

A better understanding of which executive functions predict math performance and learning can be used to design interventions that will more effectively improve math performance. Rosenberg-Lee described a study that she conducted which looked at students who placed into remedial math classes when entering college. Studies have shown that 80 percent of students in remedial math classes fail and that students who have to take these courses are much less likely to graduate than their peers. To deal with this issue, many colleges and universities have been developing “bridge programs” for students to attend in the summer before freshman year. The programs give students an opportunity to fill gaps in knowledge, improve academic skills, and gain a supportive community before starting college.

Rosenberg-Lee’s study examined a specific “bridge program” that was developed at Rutgers for students from low-income backgrounds. The researchers tried to determine whether the program caused improvement in student math scores and to explore which specific cognitive and non-cognitive factors predicted initial math performance and learning. In the study, 54 entering undergraduates were given an Accuplacer math test before and after the bridge program. They also completed executive function tasks including a Stroop test, a backwards spatial scan task, and a task switching exercise, as well as non-cognitive assessments on math anxiety, math attitudes, grit, mindset, and social support.

Overall, Rosenberg-Lee found that the bridge program seemed to be effective: many students’ arithmetic and algebra scores improved, and some placed into higher math classes after completing the program. With regard to the cognitive assessments, Rosenberg-Lee found that students’ performance on the backwards spatial scan task predicted their initial math scores. This suggests a connection between general cognitive skills and math performance.

Additionally, Rosenberg-Lee found that performance on the incongruent Stroop trials predicted which students’ math scores would improve the most after completing the program, indicating that inhibitory control plays a role in math learning. However, high scores on the math anxiety questionnaire negatively predicted learning: students who were most anxious about math tended to improve less. Thus, it is worth exploring how interventions to reduce math anxiety, such as expressive writing, could be incorporated into curricula.

Rosenberg-Lee’s talk shed light on some of the research that is being done on the cognitive processes that underlie math performance. A better understanding of these cognitive factors will allow researchers to develop interventions that will more effectively help students improve their math skills.