Cognitive Factors' Influence on Fraction Development in Students of Varying Ability Levels

The aim of this study was to evaluate the relationships between student attention, nonverbal reasoning, math achievement, and a variety of fraction outcomes, and to examine how those relationships vary for students of differing ability levels. This study provides initial evidence of the influence of nonverbal reasoning on conceptual understanding, estimation, and word problem set-up of fraction problems, and provides evidence that nonverbal reasoning may not be significantly linked to fraction calculation. This study also found that a more direct measure of student attention was significantly linked to all included fraction outcomes, though the relationship was not as strong as those found in previous studies using teacher ratings of attention. Furthermore, teacher ratings of student attention and results of the d2 Test of Attention explained very little of the same variance on fraction outcomes. The influence of cognitive factors seemed to hold steady across participants in all three ability groups. Participants with school identified disabilities showed significant deficits in the conceptual understanding of fractions even when controlling for general math ability. Essentially, students with identified disabilities separated themselves from those with math difficulties in their weak conceptual understanding of fractions. Students with math learning disabilities also scored significantly below their peers with math difficulties in nonverbal reasoning and word problem set-up.