Off-campus UMass Amherst users: To download campus access dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.

Non-UMass Amherst users: Please talk to your librarian about requesting this dissertation through interlibrary loan.

Dissertations that have an embargo placed on them will not be available to anyone until the embargo expires.

Author ORCID Identifier


Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Joonkoo Park

Second Advisor

Adam Grabell

Third Advisor

Jennifer McDermott

Fourth Advisor

Darrell Earnest

Subject Categories

Cognitive Psychology


Math anxiety, or a sense of dread related to performing mathematics, affects a wide population of students and adults, but we do not fully understand how math anxiety comes into being. One possibility is the Reduced Capacities Theory, which suggests that natural variations in numeric/spatial capacities are a causal factor in math anxiety. To understand how these numeric capacities relate to math anxiety in adults, this work focuses on three areas that remain underexplored. Chapter 2 focuses on performing operations on nonsymbolic quantities, which has not yet been tested in relation to math anxiety. We tested the hypothesis that performing addition and subtraction with dots using the Approximate Number System would relate to math anxiety. We asked participants to complete a math anxiety survey, two measures of working memory, a timed symbolic arithmetic test, and a non-symbolic “approximate arithmetic” task, in which participants performed addition and subtraction on dot arrays. Using Bayesian analysis and multiple regression, we found evidence for there being no relation between approximate arithmetic performance and math anxiety, suggesting that difficulties performing operations does not constitute a basic number ability linked to math anxiety. In chapter 3, we measured the relation between number and letter ordinal processing and math anxiety. In separate blocks, we asked participants to determine if triads of numbers and letters were in order (e.g., 4 5 6) or out of order (e.g., C E A) to measure response time and accuracy. Participants also completed a timed arithmetic test to understand the relation between ordinality, arithmetic, and math anxiety. Several hypotheses were assessed including the specificity of math anxiety to numbers (comparing number ordinal trials to letter trials. We found that there was no relation between math anxiety on any measure except that high math anxiety related to slower responses to number ordinal judgement, and that math anxiety mediated the relation between ordinal judgement performance and arithmetic. Together, these data suggest that ordinal processes are unlikely to be a causal factor for math anxiety, despite being critical for early mathematics learning. In chapter 4, we assessed responses to counting sequences and inhibitory control in relation to math anxiety. We developed a modified Go/No-Go task in which we manipulated trial length, whether they responded to completed vs “violated” (e.g., 21 22 23 vs 21 22 24, respectively) sequences, and distance (violated being +1 or +4, between subjects). Participants also completed a math anxiety survey. We assessed response time, and accuracy to understand counting sequence representation’s relation to MA, and false alarm rates to understand inhibition’s relation to MA. We found that the high MA group was significantly slower to respond when number to respond to was not consecutive. There were no relations between MA and any other measure. When viewed together, these data suggest that the Reduced Capacities theory may not be a viable framework for understanding the origin of math anxiety, as all results can be more easily explained by the effects of anxiety on performance. However, because these data were all collected with adults, it remains plausible that children who go on to develop MA may struggle with these capacities during early schooling and see equal gains as their low MA peers. We end by suggesting several potential avenues of research related to MA, focusing on students’ and adults’ emotional interpretation of their math experiences.


Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.