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Calculus: An Active Approach with Projects

Stephen Hilbert, Diane D. Schwartz, Stan Seltzer, John Maceli and Eric Robinson
Mathematical Association of America
Publication Date: 
CRM Series
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Susan D'Agostino
, on

Calculus: An Active Approach with Projects provides calculus instructors with advice and an impressive collection of classroom activities and out-of-class group project assignments for a one or two-semester calculus course. Developed from the authors’ experiences teaching calculus at Ithaca College, the book is intended to supplement rather than replace a calculus textbook.

The authors’ premise is that students learn better when they are actively engaged in discovering and developing the ideas of calculus. For instructors who are new to including activities and projects in their calculus classes, the authors provide a fairly substantial question-and-answer section concerning implementation. Some of the questions they address are: How can using projects and activities improve my course? How do I grade the projects? How will I have time for the activities? How do quizzes and exams relate to activities and projects? How do you teach the logical and theoretical aspects of calculus? In addition, the authors provide a sample curriculum illustrating how the activities and projects may be integrated into a typical calculus course.

The book has two broad objectives. The first concerns 91 different in-class activities which vary in length from 5 to 50 minutes. The second concerns 23 different out-of-class projects that instructors may assign to small groups of students. Both the activities and the projects may be may be photocopied to hand out to students in class as long as the copyright notice appears. The idea is that students will be prepared to assume responsibility for the larger, more involved out-of-class projects after working on the smaller, in-class activities.

Most of the activities set the stage for students to discover a single calculus concept on their own. For example, in a fifteen-minute, open-ended activity called “Gotcha,” which features a newspaper article involving a state trooper’s confidence concerning the speed of a car as it drives between two painted lines, students develop the ideas behind the Mean Value Theorem. Each activity is presented as a worksheet with space left for computations. There is also a detailed set of instructor notes identifying the topics of each activity, summaries, background assumed, time requirements, threads and notes.

The topics of the projects include standard calculus applications, including roller coasters, taxes, drug dosages, satellites and topographical maps. What distinguishes the projects is the way in which they provide early previews of calculus concepts. For example, according to the sample curriculum, the project titled “More Tidal Flows” may be assigned as early as week five in a thirteen week semester. In this project, students gain a preview of the Fundamental Theorem of Calculus long before the theorem is introduced as part of the curriculum in week twelve. As with the activities, there is a detailed set of instructor notes for the projects that include summaries, background assumed, threads and notes. The authors also provide guidance for the instructor concerning the optimal number of projects to assign, the number of students to include in a group and a particularly ingenious method for identifying students who are not fully engaged in the projects (see item #8 on page 304).

Calculus: An Active Approach with Projects is offered as an e-book and a print-on-demand book. Unfortunately, accessing the e-book means running an executable file rather than opening a readable document such as a PDF. This creates a security risk, since running an executable file, and in fact one that does not carry a digital signature from the publisher, opens up a real potential for malware. Prospective e-book readers may want to verify that their schools do not have IT security policies that forbid the running of unsigned executable files.

Fortunately, the print-on-demand book bypasses these concerns. The print-on-demand order I placed (not identified as from a reviewer) appeared in my mailbox within a week. In terms of quality, the book is indistinguishable from other high-quality, soft-covered, non-print-on-demand books on my bookshelf.

Overall, I heartily recommend the print version of Calculus: An Active Approach with Projects. Though I have not yet experimented with such a broad implementation of activities and projects in my calculus classroom, Calculus: An Active Approach with Projects certainly provides concrete tools, helpful suggestions and the inspiration to try.

Susan D’Agostino is an Assistant Professor of Mathematics at Southern New Hampshire University. Her essays have appeared in The Chronicle of Higher Education, MAA Focus and Math Horizons. She is currently writing a math book for a general audience.

The table of contents is not available.