You are here

Calculus Mysteries and Thrillers

R. Grant Woods
Mathematical Association of America
Publication Date: 
Number of Pages: 
[Reviewed by
Jeremy Case
, on

Calculus Mysteries & Thrillers provides eleven standalone calculus projects, each embedded in a fictional story. While not for everybody, the book is a good resource for those instructors who assign and write group projects for their calculus classes.

The stories involve a fictional consulting team who, armed with the tools of calculus, solve problems involving pool sharks, pirates, hockey coaches and kidnappers. Despite the whimsical tone, the problems are not trivial. A typical calculus student could not solve these problems without working in a group over a two week period.

Assigning any group project is a gamble since projects take so much time and effort for both the student and the instructor. If the project is too hard or unclear, the attempt to engage the student may backfire. On the other hand, if it captures the student's attention, then he or she will supposedly work harder, take more interest in the course, and gain more depth of the material.

What should the appropriate project be? Using real data or real applications such as found in Project CALC or Applications of Calculus (MAA, 1993; ISBN 0-88385-085-0) seemingly would be the best approach. However, I have difficulty finding such a project with minimum prerequisites which illustrates the topics I want to cover. The use of fictional stories allows more freedom to create appropriate material.

Obviously, the stories in Calculus Mysteries & Thrillers are unrealistic situations where calculus could be used. Yet, as in good fiction, being untrue does not mean inapplicable or useless. I believe they still have pedagogical value illustrating the power of calculus. In some ways, the stories return the spice to textbook problems whose flavor has been boiled away for space considerations. According to the author R. Grant Woods, "Students take the stories for what they are, as a means of humanizing what is perceived as a cold and hard subject."

In Calculus Mysteries & Thrillers, while I did not find the projects condescending, I could see where some would object to its "cuteness." One has to decide if it fits one's personality and course objectives. However, one benefit for this book is that teachers can modify and reproduce the material to fit one's style (as long as it is non-commercial). I appreciate anything which alleviates my conscience with regards to the murky copyright and academic honesty issues.

Another book which has a similar policy is Student Research Projects in Calculus,by Cohen, Gaughan, et. al. (MAA, 1992; ISBN 0-88385-503-8). A good starting point for those using projects and the inspiration for the book under review, Student Research Projects in Calculus provides 103 ideas for projects and more detailed suggestion on how to use projects. By contrast, Calculus Mysteries & Thrillers provides much more of a story to each of its eleven projects. Whereas a project idea in Student Research Projects may run a page, the story provided in Calculus Mysteries & Thrillers averages about 4-5 pages. Both books provide a difficulty rating and a list of mathematical requirements for each project.

The author of Calculus Mysteries & Thrillers suggests that his book could be used in a technical writing class or at least by those interested in improving communication and writing skills. Students must sift through the problems presented in everyday language to analyze the relevant facts. Solutions are then to be submitted to a client whose knowledge of calculus is minimal. At the same time, the report must be accompanied with detailed mathematical analysis thereby requiring clear thinking and communication. The book provides a solution for each project which I found very helpful, not because the answer was given, but because it helped in seeing how a solution might be written. While my students may never approach their quality, the provided solutions provide a guide with which to help.

According to its preface, two themes which occur in each project in Calculus Mysteries & Thrillers are the setting up an appropriate coordinate axis system and thinking about the domain of functions used. I found careful consideration must be given to distinguish between variables, parameters, and constants. Issues which arise in related rates problems will arise here. Most of the projects call for a general solution for varying parameters and also a special case numerical solution.

I wish that some of the problems were more open-ended so that students could make and test their own conjectures. Often during the story, the fictional consulting team claims to have solved the problem and gives hints as to how they solved it. While perhaps necessary for beginning students to gain confidence, I found myself trying to figure out what their solution was rather than exploring my own solution. Furthermore, the stories are almost always resolved by the end. For example, by the end of one story, you know the character escapes kidnapping by pirates. My tendency would be to make the students turn in the correct solution before letting them free. (In my weaker moments, I have wondered where such pirates could be contacted).

For the most part, technology is not emphasized, which is understandable but unfortunate. Students could take more ownership of their learning by experimenting with the help of the computer. However, to accommodate the different computer packages would be a tall order. I should add that when I assigned one of the book's projects in my Calculus II class, one group could not algebraically determine a curve, and used the computer to numerically plot the points on the curve. This suggests that students may bring in technology on their own. It also shows that one consequence of using projects is that grading becomes more challenging.

Overall, I would suggest Calculus Mysteries & Thrillers to those instructors who use and write projects in their calculus classes. While some may find the stories condescending, I found the book to be an excellent resource. The projects are ready made with solutions and most have been field-tested. However, the greater benefit for me is that it has sparked some new ideas on how to present projects.

Jeremy Case ( appreciated his participation in Project NExT for expanding his ideas of mathematical instruction. He enjoys reading fiction when he is not performing other duties such as teaching mathematics at Taylor University in Upland, Indiana. These days he reads fiction in many different ways as his baby daughter wants the same Dr. Seuss stories read again and again.