Document Type

Report

Publication Date

5-2026

Abstract

The following portfolio is a representation of the course MATH 1060, Calculus I, taught at Clemson University. The contents can be broken down into 3 major components.

• The first being an analysis of the students who may typically be in the course, the prerequisites required to take the course, and what paths students have after completing the course. This analysis is based upon the course curriculum at Clemson, and as a result will likely not align with that of other universities

. • The second major component is a map of the concepts discussed in MATH 1060 as well as the various misconceptions students may have about these concepts. The diagram shows how the topics of the course are interrelated and thus can be useful for both instructors and students. The outlined misconceptions, supported by current research, identify how the misconception appears and identifies the root cause.

• The final component, and perhaps most useful for instructors, is two lesson plans each addressing a major misconception identified in the course. The first lesson plan is aimed to be a second lesson of the chain rule. The focus is on helping students differentiate between when to use the product rule, chain rule, and both in conjunction with one another. The second lesson plan is an introduction to u-substitution. This lesson aims to show the connection between u-substitution and the chain rule as well as determining whether a certain substitution is viable for computing the integral.

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