Students' Understanding of Functions in Calculus Courses

Abstract

This paper is based on a study of student responses to two types of questions on final examinations in calculus classes, one of which requires only Pointwise understanding and the other of which requires Across-Time understanding. The results of this study show that these two kinds of understanding are clearly distinguishable. But, more crucially for teachers, they show that, at least in simple situations, students have a confidents and secure Pointwise understanding of functions, but even at the end of the first or second quarter of calculus-when we tend to assume they have already acquire this abilit-they are still struggling to see functions in an Across-Time manner.