Student identity modulates calculus proficiency and calculus self-efficacy

We assessed changes in calculus proficiency and calculus self-efficacy occurring during the second semester of calculus-based introductory physics, which covers electricity and magnetism. We found that both final course grade and student gender were linked to changes in both quantities with women displaying larger gains in calculus proficiency than men and men showing larger gains in calculus self-efficacy. When combined, these data suggest that student identity may modulate the correlation between a student’s calculus abilities and their perception or self-evaluation of those abilities. These data may thus also indicate a potential contributing factor to gender-related differences in physics self-efficacy as well as the complexity of addressing those differences. Finally, both principal component analysis and network analysis of the data generated this same conclusion while also indicating an inverse relationship between student proficiency solving pure calculus exercises and calculus exercises in the context of physics. This is consistent with previous reports detailing that mathematics transfer to physics is difficult.