Incorporating Ethical Discussions in the Mathematics Classroom

As mathematics, computational science, data science, and other tangential fields become increasingly involved in situations with large societal impact, researchers in these areas are beginning to recognize the need for sound ethical reasoning in their professions. Maurice Chiodo and Dennis Müller’s recent SIAM News article [3] about ethical questions in the context of COVID-19 modeling serves as an example. Our community is well versed in the ethics of scholarship, but our professional training likely did not address the ethical applications of our work. Here, I provide some tested resources to guide the incorporation of ethics-based questions and materials into existing classes or seminars.

Why Ethics Now?

Some fields (law or medicine, for example) have a formalized understanding of ethical standards, but mathematics does not. However, a number of professional organizations in the mathematical sciences acknowledge the need for such standards. Efforts like the Cambridge University Ethics in Mathematics (EiM) Project—and the two corresponding EiM conferences in 2018 and 2019—serve as flagship standards in working towards community-wide awareness. Of course, a simple “code of ethics” is not sufficient; ethical awareness should be integral to professional preparation. Many higher educational institutions recognize this necessity and are making ethics an explicit component of their curricula. Chiodo has been a continuing leader in this space for the last several years [2]. His webpages at Cambridge contain a wealth of resources, and several of the forthcoming examples stem directly from (or were inspired by) his course notes.

When we were developing a new data science major at Clarkson University, most of the coursework was already in place. As such, I told our administration that we only needed two new courses: (i) an introductory course in data science and (ii) a course in ethics. In addition to embedding ethics across the entire curriculum, we decided that the major would include a three-credit ethics course that is taught by a math professor.

The following exercises are student favorites from the aforementioned ethics course. Some provide background material and are appropriate for inclusion as part of a sequence (perhaps in a seminar course), but most are standalone items. Several can easily be incorporated into standard math classes. Many of these topics apply across multiple levels and might even serve as backdrops for larger faculty discussion.

Background Materials

For the Instructor: Bonnie Shulman’s “Is There Enough Poison Gas to Kill the City? The Teaching of Ethics in Mathematics Classes” [6] is a great starting point to help instructors design a framework that addresses ethical issues within mathematics curricula. This article is especially valuable for faculty members who are still exploring whether they want to include ethics in their teachings.

Background Definitions: The Internet Encyclopedia of Philosophy’s article about ethics provides an excellent summary of key terms in the field. I recommend equipping students with this standard terminology to inform their reading, ease discussions, and facilitate their consideration of multiple viewpoints (i.e., “That is the utilitarian argument, but how might your argument change if you take a duty ethics perspective?”).

Establishing a Professional Ethics Standard: The recording of Anna Alexandrova’s talk at the 2018 EiM meeting, entitled “How to Build an Ethics: Lessons for Mathematics from Other Fields,” presents an expert philosopher’s interpretation of an important meta-question: How can the professional community of mathematicians collectively move forward? Alexandrova notes that “No research, no matter how pure, is immune from social responsibility.”

Pondering the Impact of Abstraction: In “The Ethics of Mathematics: Is Mathematics Harmful?” [4], Paul Ernest argues that the standard method of abstraction—moving from the “real world” to mathematical equations, which is typical in math classes—may have adverse effects on mathematics students. This text can inspire some thought-provoking discussions about the profession as a whole. 

Single-Lesson Resources

Not Just “Avoiding Doing Bad:” There are many examples of “unethical mathematics,” especially in the context of data science, but fewer opportunities to highlight “good” behavior. Chad Topaz (Williams College) delivers an excellent talk about several projects at the Institute for the Quantitative Study of Inclusion, Diversity, and Equity. His October 2020 presentation at the Vanderbilt Postdoctoral Association Symposium offers an inspiring glimpse of the possibilities that emerge when one engages with the good side of ethics.

Laws and Ethics: Ethical behavior and legal behavior are not the same concepts, but some standards do become encoded into statute. On a day-to-day basis, mathematicians typically do not have to worry about the legality of their work. In the field of data science, however, this issue arises much more frequently. Patrick Hall and Ayoub Ouederni provide a short list of questions to consider with regard to the increasing scrutiny of the legalities of data-driven work [5].

Mathematics Provides Solutions: Our math majors really enjoy learning about differential privacy, which I introduce in the backdrop of its adoption by the U.S. Census Bureau [1]. Plenty of web resources offer varying levels of sophistication in their explanations, so I recommend that educators select one or two to tailor to their classes.

Case Study: Uber Surge Pricing: This topic—a class favorite—always generates hearty discussion among the students. I typically begin with a short news story that highlights the greedy side of surge pricing and encourages a certain viewpoint. Next, I present a 20-minute talk by Dawn Woodward of Uber about the underlying mathematical principles.

Industry Case Study 1: The Volkswagen emissions scandal, wherein the company installed “cheat devices” in their cars, inspires much conversation. I ask the students to think about how many people might have been involved and what levels of ethical culpability may have been at play. We consider whether some participants could have been “fooled” into going along, how others might have been willfully ignorant, and what ethical shortfalls are associated with such ignorance.

Industry Case Study 2: In the 1970s, a design flaw in the Ford Pinto resulted in an increased risk of explosion and fire in the instance of rear-end collision. Based on actuarial analysis of overall cost, Ford initially decided to pay settlements for the expected lawsuits rather than recall and fix the design. In this case, the mathematicians/actuaries did precisely what their job required. The company eventually made the recall, but only after this analysis became public and a judge awarded $125 million in punitive damages.

Milgram Experiment: Students often begin to think that when the ethical answer in a particular situation seems obvious, people should be expected to “do the right thing.” I show a short video about the Milgram experiment—the famous study at Yale University that asked subjects to administer shocks to other participants as part of a supposed “learning” exercise—to demonstrate people’s inclination towards obedience of authority.

Embedding Ethics Into a Calculus I Course: A final example, pulled directly from Chiodo’s notes, suggests the following problem: There is an oil rig in the ocean near a straight shoreline. Somewhere on the shore, there is an oil refinery. The rig is 100 kilometers (km) from the nearest shore point. You are asked to design the optimal route for an oil pipe from the rig to the refinery. The pipe costs $100,000/km under water and $40,000/km on land. Please compute the optimal route for the pipe.

At some point, students will likely indicate that they need to know the refinery’s distance down the shore. Give them the information and follow up with a conversation about the aspects that they might not be considering in their decision (as they will almost certainly choose to simply minimize cost).

Bringing It to the Classroom

Many mathematicians agree that we need more ethical understanding within our profession. To achieve an increased sense of ethical mindfulness, we must instill the rising generation with an awareness of ethical issues that they might encounter in the workforce. Consequently, the critical first step is making ethical discussions an important component of existing courses.

The aforementioned resources offer some “easy starts” for educators who are looking to explore ethics-based curricula. Hopefully these examples will provide a template for developing such modules in any course that focuses on applications. Just a few simple questions can help both students and teachers develop and flex their ethical muscles. 

References

[1] Abowd, J.M. (2018, August 17). Protecting the confidentiality of America’s statistics: Adopting modern disclosure avoidance methods at the Census Bureau. U.S. Census Bureau. Retrieved from https://www.census.gov/newsroom/blogs/research-matters/2018/08/protecting_the_confi.html.
[2] Chiodo, M., & Müller, D. (2018, November 1). Mathematics and ethical engagement. SIAM News, 51(9), p.6.
[3] Chiodo, M., & Müller, D. (2020, September 1). Questions of responsibility: Modelling in the age of COVID-19. SIAM News, 53(7), p.6.
[4] Ernest, P. (2018). The ethics of mathematics: Is mathematics harmful? In P. Ernest (Ed.), The philosophy of mathematics education today. (pp. 187-216). ICME-13 Monographs. Cham, Switzerland: Springer.
[5] Hall, P., & Ouederni, A. (2021, January 19). Seven legal questions for data scientists. O’Reilly Media, Inc. Retrieved from https://www.oreilly.com/radar/seven-legal-questions-for-data-scientists.
[6] Shulman, B.J. (2002). Is there enough poison gas to kill the city? The teaching of ethics in mathematics classes. Coll. Math. J., 33(2), 118-125.