2023 Theses Doctoral

# On Mathematical Expertise, Inhibitory Control, and Facets of College Students' Psychoeducational Profile: An Empirical Investigation

Although the importance of problem solving as an essential component of mathematics learning and doing has consistently been recognized, recent research has only just begun to identify and describe the complex set of variables influencing the endeavor. Therefore, the aim of this study was to empirically investigate the relationships between several of these variables: mathematical expertise (as measured by the advanced nature of the mathematics courses students have taken, and are enrolled in), the cognitive ability known as inhibitory control (the ability to inhibit or suppress an immediate response to a stimulus, and engage in deeper, more reflective thought), and facets of college students’ psychoeducational profile (e.g., academic habits of mind, future orientation, self-limiting beliefs), which provide information about the nature of college students’ learning and development.

In this study, one hundred and thirty college students, enrolled in different levels of mathematics courses (from introductory courses to major courses in mathematics) were administered a modified version of the Cognitive Reflection Test (an instrument designed to measure the ability to activate one’s inhibitory control capacities) and a survey instrument designed to measure domain-general and mathematics-specific psychoeducational facets of their academic profile. Information about membership to other subgroups (e.g., gender, academic major, mathematics courses taken in high school) helped to further contextualize the findings.

The majority of all participants did not correctly solve any of the problems of the modified version of the Cognitive Reflection Test which required inhibitory control. However, those with a greater level of mathematical expertise (i.e., those taking more advanced mathematical courses) performed significantly better than their peers on these problems and exhibited more desirable responses on the psychoeducational survey instrument. Responses to items of the survey instrument that measured behaviors, habits, and experiences that limit students in their conception of, approach to, and engagement with mathematics indicate the presence of a psychoeducational facet specific to mathematics that cannot be sufficiently explained by domain-general facets also under measure. These limiting characteristics related to mathematics were also significantly related to students’ performance on the modified version of the Cognitive Reflection Test, indicating a potential relationship between such characteristics and problem solving success on inhibitory control tasks. Considering the measures of mathematical expertise utilized in the current study, the social nature of mathematics learning may help explain the development of both inhibitory control ability and limiting beliefs in mathematics.

The current study extended the methods utilized in previous research to examine the relationships between inhibitory control and mathematical expertise in college students while also investigating these in relation to particular psychoeducational variables known to influence learning and development of college students. The findings of this small-scale empirical study provide a modest step forward in these areas of research by providing another lens through which to view several phenomena already being extensively investigated by other researchers.

## Subjects

## Files

- DarrowJr_columbia_0054D_17631.pdf application/pdf 1.61 MB Download File

## More About This Work

- Academic Units
- Mathematics Education
- Thesis Advisors
- Karp, Alexander P.
- Degree
- Ph.D., Columbia University
- Published Here
- January 11, 2023