"The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational fluency, numeracy skills, fraction knowledge, understanding of equivalence, and algebraic reasoning skills, and the cognitive abilities of spatial... Show more"The current study investigated college students' content knowledge and cognitive abilities as factors associated with their algebra performance, and examined how combinations of content knowledge and cognitive abilities related to their algebra performance. Specifically, the investigation examined the content knowledge factors of computational fluency, numeracy skills, fraction knowledge, understanding of equivalence, and algebraic reasoning skills, and the cognitive abilities of spatial visualization, crystallized intelligence, and fluid intelligence. A multiple regression analysis found that while controlling for gender, the highest math course taken, and the number of years since an algebra course, fraction knowledge and the spatial visualization ability of spatial imagery were statistically significant predictors of algebra performance along with the control variable identifying whether or not participants had taken at least one calculus course. In addition, cluster analysis identified six content knowledge and cognitive ability profiles, with varying levels of both content knowledge and cognitive abilities observed across the six clusters. The six profiles - characterized as Low All, Moderate-Low All, Moderate-High MASMI, Moderate-Low Spatial, Moderate-High All, and High Spatial - varied somewhat in terms of their algebra performance scores. In particular, the participants in the High Spatial cluster group and participants in the Moderate-High All cluster group had similarly high algebra performance scores, which were significantly higher than performances scores observed for participants in the other cluster groups. Additionally, the participants in the other cluster groups exhibited similar low algebra performance scores to each other except for participants in the in the Moderate-Low Spatial and Low All cluster groups. Participants in the Moderate-Low Spatial cluster group had significantly higher algebra performance scores than participants in the Low All cluster group. The differences in algebra performance scores among cluster groups suggested that the observation of higher algebra performance occurred when participants had strong spatial visualization skills, strong fluid intelligence skills, and high content knowledge or when participants had strong fraction knowledge, numeracy skills, algebraic reasoning skills, and spatial imagery skills."--Pages ii-iii. Show less
