The article reports on additional data collected during interviews for a project investigating the different ways rate may be experience by pre-calculus students. It evaluates the participants' understanding in a specific rate context. Insights into perceptions of rate in several different representations were provided by detailed analysis of the video record of each participant's interview. The article also presents the Victorian Essential Learning Standards (VELS) expectations with respect to the concept of rate.
The author recommends teaching integration first, and move on to differential calculus only after a sound understanding of integration has been attained. A rationale for teaching integrals before derivatives in a first calculus unit intended primarily for engineering students at the University of Ballarat is presented. It is concluded that students fail to see the connection between getting the right answer and understanding what they are doing. It is noted that the formal manipulations required for high school differential calculus questions are simpler than those for integral calculus.