Calculus Homework: A Storied Approach

Abstract

Storytelling has proved to be an effective way of passing on information from one generation to the next. Whether the information relates to history, culture, health, or morality, the story provides a framework so that complex ideas can be better understood and retained. In this article, we consider the role of narrative in the design and implementation of effective calculus homework. Focusing on three problems spanning first-year calculus, we examine how the elements of a good short story might translate into meaningful elements of a good homework assignment.

Keywords:

• Calculus homework
• storytelling
• tangent lines
• harmonic series
• comparison test
• geometric series
• narrative in mathematics

ACKNOWLEDGEMENTS

We would like to thank the reviewers for their many insights and helpful suggestions. Particularly, we are grateful for several excellent references shared by the reviewers which led to significant improvements to this paper.

Notes

1 Dr. Adam Spiegler of Loyola University - Chicago first introduced a version of this problem to one of the authors.

2 Hypernymy is the semantic relation between a more general word and a more specific word, (e.g., flower is a hypernym of zinnia), and hyponymy is the semantic relation between a more specific word and a more general word (e.g., zinnia is a hyponym of flower).

3 Actually, g is tacitly assumed to be three times continuously differentiable in this exercise. Such analytical details might cloud the main point for Calculus I students, but office-hour conversations are ideal for this clarification.

4 After designing this graph (Figure 1), we were surprised to find similar graphs in the literature, but in the more general context of “student challenge” (vertical axis) versus “teacher support” (horizontal axis). For example, see Mariani [14] and Hammond and Gibbons [9].

Additional information

Notes on contributors

Judy A. Holdener

Judy A. Holdener received her Ph.D. in mathematics in 1994 from the University of Illinois in Urbana, Illinois. Since that time she has taught mathematics at a wide range of schools including Harvard, Carnegie Mellon, the U.S. Air Force Academy, and Kenyon College. In recent years she has been spending increasing amounts of time crafting homework sets (which she titles “Gifts”) for her students. In her spare time she enjoys art, reading, gardening and watching her two red-headed boys play soccer.

Brian D. Jones

Brian D. Jones earned a B.S. in chemical engineering, M.S. in mathematics, and Ph.D. in statistics from The Ohio State University. He has taught at Kenyon College since 1995, and enjoys studying combinatorics, probability, and random structures of all kinds. His favorite academic activity is writing challenging and creative problems in mathematics and statistics. Out of the classroom, he enjoys music of nearly all genres, cooking, running, and juggling.