This paper extends work in the areas of quantitative reasoning and covariational reasoning at the undergraduate level. Task-based interviews were used to examine third-semester calculus students' reasoning about partial derivatives in five tasks, two of which are situated in a mathematics context. The other three tasks are situated in real-world…

Research on abstract categorical reasoning has shown that students with "A" grade point averages (GPA) have limited, better and often less, reasoning ability than students with lower GPA's. A similar effect was also found when testing "bright" and "dull" subjects. An analysis of this effect was conducted using the component model of categorical…