Analysis of Calculus Textbook Problems via Bloom's Taxonomy

Abstract

In calculus courses, instructors often use the end-of-section problems in a textbook in homework assignments or other course assessments. As a result, these problems influence the teaching and learning of calculus. In this study, we examine the levels of cognitive demand of these problems in a mainstream calculus textbook and classify them within the framework of Bloom's Taxonomy. We provide examples of the types of problems assigned to each of the six categories in this taxonomy and share some of the deliberations that led us to these assignments. Finally, we discuss the implications of our results for teaching calculus courses. We believe that our analysis will help calculus instructors be more cognizant of the cognitive demand of problems when assigning them for homework and, as a result, help them to appropriately support, assess, and enhance their students' understanding of the topics.

Keywords:

• Bloom's taxonomy
• calculus
• textbook analysis

Acknowledgments

The authors would like to thank the editors and the referees for their useful comments and suggestions on an earlier version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The cognitive domain is one of three domains the committee decided to investigate. The other two are affective and psychomotor domains.

2 One might think that plug-and-chug activity should be relegated to the knowledge category. However, Bloom et al. describe these two levels in specific language, and knowing a procedure or a process (knowledge) is not the same as knowing how to apply it in an abstract or concrete context (application). A learner displaying knowledge of a process might be to be able to list the steps that they have memorized, while the capacity to perform it as an application task might involve an actual context where the process needs to be used.

Additional information

Notes on contributors

Feryal Alayont

Feryal Alayont received her undergraduate mathematics degree from Bilkent University, Turkey, and her Ph.D. in mathematics from the University of Minnesota. She is currently a professor of mathematics at Grand Valley State University, where she also serves as the Mathematics Advising and Engagement Coordinator.

Gizem Karaali

Gizem Karaali completed her undergraduate studies at Boğaziçi University, Istanbul, Turkey. After receiving her Ph.D. in Mathematics from the University of California Berkeley, she taught at the University of California Santa Barbara for two years. She is currently a professor of mathematics at Pomona College where she enjoys teaching a wide variety of courses and working with many interesting people. She has most recently been involved with promoting the humanistic aspects of mathematics via her work through the Journal of Humanistic Mathematics. Gizem Karaali is a Sepia Dot (a 2006 MAA Project NExT Fellow).

Lerna Pehlivan

Lerna Pehlivan received her undergraduate degree in Mathematics from Boğaziçi University, Istanbul, Turkey and her Ph.D degree in Mathematics from the University of Southern California, Los Angeles. She held a Fields Institute Postdoctoral Fellowship at Carleton University, Ottawa and a postdoctoral position at York University, Toronto. She is currently a lecturer at the Faculty of Electrical Engineering, Mathematics and Computer Science at University of Twente, Enschede, The Netherlands.