Student understanding of basic calculus concepts: Interaction with the graphics calculator

Abstract

The recent efforts to reform calculus have, in many cases, included increased use of technology. Several studies have explored the interaction between the use of technology and student learning of calculus. Our study seeks to build on this work by exploring the understanding of basic calculus concepts by students who are studying calculus in a graphics calculator-based environment. In particular, the purpose of the study is to developed descriptions of calculus students' understandings of function and limit, to explore the interrelationships among their understandings of these conceptual areas, and to identify instances where there is evidence that the students' understanding seems to have been influenced by the availability of the technology. Data for the study was collected through a series of clinical interviews with a small group of students enrolled in a first semester college calculus course and an advanced placement high school calculus course. The data was used to build descriptions of the students' understanding and the role the graphing technology might play in that development. Implications of these findings for calculus curriculum and instruction are presented.