Improved Appreciation of Mathematics Through an IBL Liberal Arts Mathematics Course

Abstract

The author has taught an inquiry-based liberal arts mathematics class using the text “The Heart of Mathematics: An Invitation to Effective Thinking” by Edward B. Burger and Michael Starbird a total of 20 times since Spring 2001. The students in this class have almost all been in non-technical majors and many started the semester with negative or ambivalent attitudes toward mathematics based on their prior experiences. The author has gathered responses from students in this class that illustrate significant changes in their attitudes towards mathematics during the course. In particular, the responses gathered at the end of the semester are often eloquent about understanding the great ideas of mathematics that students confronted in this course and about seeing many more and varied connections between mathematics and the “real world” than they had previously realized existed.

Keywords:

• Inquiry-based learning
• liberal arts mathematics
• improved student appreciation

ACKNOWLEDGEMENTS

The author is indebted to Laura Bernett for pairing and typing the start and end of semester student responses of all 191 students and randomizing the resulting typescript so that the approved IRB protocol for “off the shelf” data could be followed. He appreciates the opportunity to have presented a preliminary report on the topic of this article in the MAA Session on Using Inquiry-Based Learning in Mathematics for Liberal Arts Courses at the Joint Mathematics Meetings held in San Diego in January 2013 and the particular encouragement of Phil Hotchkiss and Julian Fleron, two of the organizers of that session, who also suggested using student quotes to introduce each section of this article. He also thanks the referees, whose invaluable comments have helped enhance this article. In particular, one referee pointed out [1] and [4].

Notes

¹ Names used are not the real student names. They were randomly assigned from the list available at http://www.ssa.gov/oact/babynames/decades/names1990s.html

² The university had one eye on the US News and World Report college rankings, which included the number of small classes, defined by a cap of 19 students, in its ranking formula.

³ The “hot loop” theorem states that there exist diametrically opposite points on a variably heated circle that have the same temperature.

⁴ The “Hilbert Hotel” is an imaginary hotel that has an infinite number of rooms labeled by the natural numbers. Each room of the hotel can hold only one guest and all rooms are occupied. The first problem asks how to accommodate one additional guest. The second problem asks how to accommodate a countably infinite number of new guests who arrive on a so-called “Superbus.” The third problem asks how to accommodate the additional guests who would arrive on a countably infinite number of Superbuses.

⁵ Discovering the Art of Mathematics is the guest editing organization for this special issue of PRIMUS.

Additional information

Notes on contributors

Russell D. Blyth

Russell D. Blyth was born and grew up in New Zealand, receiving his undergraduate education at Massey University (Palmerston North). After completing a Ph.D. with a dissertation in group theory with Derek J. S. Robinson at the University of Illinois, he obtained a position at Saint Louis University, where he has been since 1987. He is a long-time advocate of active learning and makes extensive use of group activities in many of the classes he teaches.