The purpose of this study is to examine the mediating roles of critical thinking disposition and mathematics anxiety between cognitive flexibility and academic achievement. A cross-sectional study was held to observe and compare path coefficients among latent and observed variables across 662 university students studying elementary mathematics education. In concur with grade point average scores, Cognitive Flexibility Scale, UF/EMI Critical Thinking Disposition Instrument and Math Anxiety-Apprehension Survey scores were utilized for structural equation modeling analyses. The results of this study indicated that freshman students experience the greatest impact from cognitive flexibility on academic achievement, while sophomores experience the least impact. Additionally, with the exception of the model for sophomore students, the mediating effects of the critical thinking disposition between cognitive flexibility and academic achievement were positive and statistically significant. Additionally, none of the models’ estimations of how mathematics anxiety would mediate between cognitive flexibility and academic achievement were statistically significant. Last but not least, for junior students only positive and statistically significant mediating effects of critical thinking disposition and mathematics anxiety between cognitive flexibility and academic achievement were found. This study put forth evidence to investigate cognitive flexibility, critical thinking disposition and math anxiety in higher education and to show the total, direct and mediating effects on academic achievement.