Introducing Power Analysis in the Mathematics Classroom
By Carrie Diaz Eaton
Over the last several years, there have been a number of calls for us to understand and convey to students that mathematics is not neutral. Piper H’s Inclusion/Exclusion blog calling to #DisruptJMM, Belin Tsinnajinnie’s 2020 Hrabowski-Gates-Tapia-McBay Invited Lecture on colonialism in education and mathematics, and the NCTM position statement on the intersection of culture and mathematics are just a few examples.
I am so very lucky to be part of the Mathematical Association of America’s community, which values as part of its core goals the ideals of Inclusivity, Community, Teaching and Learning, and Communication. These pillars are not neutral - of course. But how do we actually bring these pillars together in action in our classrooms?
One method has been to focus on inclusive pedagogies and curricular structures that lead to success for all. A less discussed but emerging avenue is to openly discuss power and privilege in mathematics classrooms. This discussion is already a tradition in our community, in MAA FOCUS, at MAA MathFest, and privately in our mentoring sessions with students and colleagues. What might it look like or feel like to have these conversations openly in thousands of classrooms across the country?
I know that this is a time when inclusivity has become a partisan issue, and our ability to have some of these conversations in some states and institutions is extremely limited despite promises of academic freedom in higher education. However, not speaking - staying neutral - is already a statement and an action that maintains the status quo, which is active harm. Therefore, I would like us all to imagine for a moment what that might look like to speak about power and privilege our classrooms. Below I offer a few ways, from small to large, that could take us a little closer to a more inclusive future.
Take pride in how mathematicians question assumptions.
While our work as mathematicians across theoretical and applied disciplines varies dramatically, we have all been trained in the art of using our disciplinary techniques (logic, modeling, etc.) to prove, predict, or test the effects of varying assumptions on some outcome. In a previous post, I discussed one quick activity that I have used in my first-year seminar classroom to help uncover biases that we all may carry when defining terms like “best” when identifying an optimal solution. The process of examining assumptions is usually not “one and done”. Usually, we want to know how far our result can be extrapolated. Does this work for multiple dimensions? What if we were to relax this condition slightly? Of course, we already do all of these things in our mathematical process, but how much do we say this part out loud? Let's talk about how we conceptualize the world in general instead of associated with a specific theorem or model. We could share how we use mathematics as a tool of inquiry more broadly. We could share what we think are the most compelling problems facing our field and why. Unpacking this early and often would benefit all students. It wasn’t obvious to me that preliminary examinations were not about solving a particular problem, but rather to display a way of thinking. Perhaps unpacking the way we think for students may also signal to students the value of talking to others about how they view the world and how they inquire about the world. How could those ways help us see our work differently and how might those conversations expose assumptions we take for granted? It would also explain why diverse teams are so effective at problem solving.
Unpack the ecosystem of mathematical knowledge.
Higher education is a “good/service” bought by students. But tuition, housing, room, and board are not all they have to buy. Many introductory mathematics courses require textbooks, online homework system fees, and/or software licenses. Access to knowledge is not free. Research shows that students who use Open Educational Resources (OER) are more likely to succeed in their courses, particularly Pell-eligible students. Perhaps exploring the use of OER could be a meaningful change. It could also be an opportunity to talk to students about how education is commoditized, and how participating in the broader OER movement helps them and helps democratize access to education. As students mature into mathematical researchers, it is important to discuss how research happens. Who decides which problems are important? Who reviews publications, who submits publications, who are the publishers, and what does it cost? I have my students in my writing-intensive course conduct an audit of the authors that they are citing for an expository article on a topic of interest. What is the geographical distribution of the research represented - for example, does their article include research and perspectives from scholars in the global south? Why or why not? We could share the results of our own self-audits of our research or of our class readings. By talking with our students about how this system operates, we are actively discussing how power and privilege structure mathematics knowledge access and production.
Nurture students as knowledge creators.
One common assumption that students come to mathematics with is that all mathematical knowledge has already been created, and that knowledge is then transferred from teacher to student. However, the intention of all mathematics courses is to develop their skills for analysis and inquiry. This means that our goal is to nurture inquiry and knowledge creation. We know from many movements in inquiry-based learning and active learning that a carefully guided experience with support and reflection can help students develop a sense of self-efficacy. When we invite students to be mathematicians in our classes, when we see their questions, viewpoints, and investigations as important to help grow the knowledge of the whole class, we are re-imagining the knowledge ecosystem within the walls of our classroom. We are also disrupting the “knowledge bucket” model - questioning the very hierarchy that places the teachers above, pouring the knowledge into the brains of their awaiting student receptacles. Certainly, we have knowledge and experience to share, but so do students!
Humanize people in mathematics.
There are so many great projects which aim to tell stories from diverse mathematicians (e.g. Meet a Mathematician, Lathisms). Remember to tell your own story. Research shows that students benefit from understanding their instructors’ identities and paths, particularly those whose identities are underrepresented in the field (consider, for example, this study on LGBTQ+ identities). Tell your students about the mathematician who wrote your textbook or that theorem you are discussing. Each year I make small changes to better humanize my courses. Last year, I took the time to learn about Fermi, to better present Fermi estimation in my general education course. Fermi was an immigrant to the US who had a role in nuclear technology. But I also learned how he spoke out against the use of this technology for war, and notably at the Oppenheimer trials. When I teach correlation, I take the time to have students read about Pearson - whose contributions to developing the field of statistics have a much darker motivation. The development of mathematical techniques to measure difference and correlation were tied to maintaining White supremacy, and Pearson openly praised the eugenics movement and the US genocide of Native Americans. When I teach students about best practices for making figures and graphs, I have students learn of the early revolutionary work in data visualization by W.E.B. DeBois, who brought attention to the complexity of racial progress after the Civil War. When I teach the fundamentals of machine learning, I introduce Joy Buolamwini, “Poet of Code”, whose computer science research at MIT exposed bias in the popular commercial software for facial recognition and classification.
Many times when we think about how mathematics might intersect with conversations on social justice, we think about applications. This is also a wonderful thing to incorporate, but if our classes do not have an applied component, we might not know where to start. But all of the above examples - human assumption, cultures of knowledge, knowledge creators, our community of mathematicians, and our history - have shaped what mathematics is today, and none of it is neutral.
Carrie Diaz Eaton is Associate Professor of Digital and Computational Studies at Bates College and Executive Director of the RIOS Institute.