Teaching Integration: How Certain Instructional Moves May Undermine the Potential Conceptual Value of the Riemann Sum and the Riemann Integral

Abstract

Past research in calculus education has shown that Riemann sum-based conceptions of the definite integral, such as the multiplicatively based summation (MBS) conception, can have important value in interpreting and making sense of certain types of definite integral expressions. However, additional research has shown that students tend to not draw on the MBS conception, even in situations where it would be advantageous to do so. In this study we examine how introductory instruction on integration, in which explicit attention is given to the Riemann sum and Riemann integral, may be related to students’ tendency to not use the MBS conception. In particular, it appears that some calculus instructors may make instructional moves in their classrooms that directly undermine the time the instructors had spent developing the Riemann sum and Riemann integral concepts. In doing so, students may perceive these concepts only as calculational procedures, rather than as a potential source of conceptual meaning.