Date of Award

Summer 8-24-2024

Document Type

Dissertation

Degree Name

Ph.D.

Organizational Unit

College of Arts Humanities and Social Sciences, Psychology

First Advisor

Lauren M. McGrath

Second Advisor

Kimberly S. Chiew

Third Advisor

Michelle Rozenman

Fourth Advisor

Julia O. Dmitrieva

Copyright Statement / License for Reuse

All Rights Reserved
All Rights Reserved.

Keywords

Math, Multiple deficit, Multiple factor model, Neuropsychology, Numerical cognition, Structural equation modelling

Abstract

Recently, downward trends have been reported in U.S. children’s math performance following school disruptions during COVID-19 amidst longstanding concerns for instruction and curricula within the subject. In support of efforts to remedy these declines, the current work presents two studies dedicated to identifying cognitive factors that are most strongly related to math performance, and which therefore offer promising potential targets for assessment and intervention. Both studies use data from the Colorado Learning Disabilities Research Center, which includes participants ages 8 - 16 and multiple well-validated measures of all constructs of interest. Study 1 tests three alternative latent cognitive models of math performance including a comprehensive range of cognitive skills previously implicated in math. Results suggested that the best fitting model, which accounted for virtually all the variance in calculation and math problem solving skills, includes a quantitative pathway, verbal pathway, spatial pathway, and executive functioning/speed pathway. While all four cognitive domains were significantly correlated with math scores, both the quantitative and verbal pathways were uniquely related to math performance across age in this sample with all cognitive factors included in the model, suggesting that these skills may be particularly important to assess in screening and to target in interventions. To support such efforts at screening and intervention, Study 2 then focuses on identifying the component skills of the quantitative pathway that are most strongly related to math scores. In particular, Study 2 offers a novel approach to organizing and analyzing domain-specific numerical cognition measures by dissecting them according to their task requirements and examining their unique relations with math performance. First, a proposed four-dimensional model was tested, wherein tasks were organized based on the stimuli that they used (i.e., symbolic or non-symbolic) and the responses they required from participants (i.e., exact or approximate). This model was not supported by examination of correlations, nor an exploratory factor analysis, which yielded a one-factor solution. Given the lack of evidence supporting the existence of groupings/components of numerical cognition, math scores were regressed on all of the numerical cognition measures entered into the model together to explore whether certain measures were more strongly related to math scores than others. Higher scores on two non-symbolic exact number tasks were significantly related to math scores (β=.23-.43, p<.01) while approximate non-symbolic, approximate symbolic, and exact symbolic tasks were not related to math scores Overall, it was surprising that two non-symbolic tasks outperformed symbolic tasks in predicting math scores, given that math problems utilize symbolic values. This finding suggests that instruction using mixed symbolic and non-symbolic quantities may best support math learning. Taken together, these two studies indicate that a range of cognitive skills are implicated in math performance, highlighting the complexity of math learning. Within this context, the results suggest that special attention should be paid to language skills and numerical skills involving exact quantities and mixed stimulus representations (i.e., symbolic and non-symbolic) when designing assessments and interventions, given the unique relations between these cognitive domains and math scores.

Copyright Date

8-2024

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance

Rights Holder

Nina Anderson

Provenance

Received from Author

File Format

application/pdf

Language

English (eng)

Extent

149 pgs

File Size

1.1 MB

Download

Available for download on Sunday, September 27, 2026



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