First-year in an Undergraduate Mathematics Program: the function definition and the local/global duality of Calculus concepts

Abstract

Drawing on research on understandings of differential calculus concepts conducted with first-year undergraduate mathematics majors enrolled in a Brazilian public university, the article highlights the local/global duality as one of the essential dynamics to be exercised and explored when dealing with concepts like differentiability in a context of a first-year undergraduate mathematics program. Moreover, it suggests that the exploration of a particular definition of function “ more suitable for the educational demands in such a context “ could contribute to decrystallize and broaden perceptions formed during high school, stimulating fluidity in the aforementioned dynamics. Keywords: Understanding. Calculus. Differentiability. Function. Local/Global Duality.