Defense Date

Summer 7-20-2017


Immediate Access

Submission Type


Degree Name



Counseling, Psychology, & Special Education


School of Education

Committee Chair

Ara J. Schmitt

Committee Member

Elizabeth McCallum

Committee Member

James B. Schreiber


Math Fluency, Cognitive Abilities, CHC Theory


Math fluency, which refers to the ability to solve single digit arithmetic problems quickly and accurately, is a foundational mathematical skill. Recent research has examined the role of phonological processing, executive control, and number sense in explaining differences in math fluency performance in school-aged children. Identifying the links between these cognitive abilities and math fluency skills has important implications for screening, assessment, and intervention efforts in schools. As extant mathematics research in the context of Cattell-Horn-Carroll (CHC) theory has evaluated either broad mathematics performance or math calculation skills, little is known about the specific relationships between math fact fluency and broad and narrow cognitive abilities. The present study investigated the relationships among Math Fact Fluency performance and the CHC theory-aligned broad and narrow cognitive abilities using a child-age subset of the Woodcock Johnson IV standardization sample. Results of the path analyses indicated that General Intellectual Ability (GIA) exhibited significant direct and indirect effects on Math Fact Fluency performance. With regard to broad cognitive abilities, Processing Speed had the greatest direct effect on Math Fact Fluency. Likewise, in the narrow abilities model, Perceptual Speed was most related to Math Fact Fluency, after accounting for GIA. Contrary to initial hypotheses, Working Memory, Phonetic Coding, and Attentional Control did not significantly contribute to Math Fact Fluency. Finally, the inclusion of Math Problem Solving within the cognitive abilities model resulted in a moderate direct effect on Math Fact Fluency performance. These findings are discussed in terms of directions for future research as well as implications for clinicians and educators.