Abstract:

Given our culture where students are expected to be familiar with more and more in each course, it seems that not enough time is provided to them to practise and hone their skills in one area before moving onto another. Often times by the end of a first semester Calculus course, many students do not fully understand the very important technique of effectively using the method of substitution to integrate functions. Can this be traced back to a lack of good differentiation skills, not clearly understanding the chain rule, or simply not having enough time to practise?

Assuming a combination of these we hypothesize that, the earlier the formulae of differentiation are introduced in the course, the better the chances are that students will learn them well. Tendency to mix up differentiation and integration formulae will be lower, and hence lead to a better understanding of the techniques of integration.

In this paper, we outline an alternate approach that we experimented with in a first semester Calculus course recently. Based on the above hypothesis, this approach seeks to increase the amount of time available to students to study and improve their differentiation skills, before the topic of integration is even introduced to them. This means straying from convention and introducing topics in a slightly different order and manner, so as to enable familiarization of differentiation formulae very early in the semester. Limits are studied next, which allows for the study and appreciation of the theoretical aspects of the derivative, followed by applications of the derivative. All along, opportunities to practise the rules and formulae of differentiation are provided to students before integration is introduced to them.

In this paper we also present a comparison of student performance using this new approach versus the conventional approach.

Keywords:

Calculus, first semester, improve differentiation skills, student performance.