| Abstract | The chain rule, an important calculus topic, has received little attention in mathematics education research. It describes what one must do when taking the derivative of nontrivial or composite functions (e.g., sin(1/x), Pe-kt, etc.) and is closely connected to function-related issues that arise when there is a “function inside a function.” By understanding more about the difficulties calculus students have, calculus instructors can make informed decisions regarding the use of classroom resources to improve students’ understanding of this key concept. This poster includes results from an exploratory study where calculus students were given tasks involving the chain rule. These tasks contained functions with which students were familiar (polynomials and trigonometric), somewhat familiar (logarithm and inverse trigonometric), and not familiar (functions with names invented by the researcher names). Participants included Calculus I students in the spring semester (n=14) and fall semester (n=4) of 2007. The results of these two samples were similar; there were students from each group who successfully completed the tasks which involved functions they were familiar with in their calculus course. The students also had success with functions with which they were not familiar, although it was not to the same degree of success as the familiar functions. However, the students had the most difficulty with the functions with which they were somewhat familiar. In these tasks students replaced function composition with function multiplication. For example, even though students did not think of the function ln (-x3) as ln times (-x3) and use the product rule, when applying the chain rule they multiplied 1/x and (-x3) instead of composing them. This indicates that student have difficulties with function concepts that are specific to the context of calculus. Thus, incorporating function concepts throughout the calculus curriculum and not just as review material is both needed and beneficial for students. |
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