Articulating our Assumptions: A short math classroom exercise

By Carrie Diaz Eaton

Hi friends! This semester, for the first time, I am teaching a first-year seminar course. Many small institutions may have this sort of course, where first semester students can gain an introduction to the college and also to an interesting topic at the same time. The first-year course I am teaching is for STEM Scholar students interested in STEM, generally, so I have a mix of math, biology, chemistry, and physics prospective majors. But they are also passionate about other things, too, like art, the environment, and social justice. Because STEM Scholars is part of our HHMI Inclusive Excellence program, we discuss building STEM identity, learning about and researching contemporary issues in STEM, and building a community of care for each other.

I recently tweeted about a small “math” exercise I did in class as a discussion on bias and positionality in science research, which students had just read about prior to class. They also took one of the Harvard Implicit Bias tests and reflected on the results. Students sorted into groups and we discussed these readings and ideas a bit, realizing that bias can be both conscious and unconscious, and what we might do once we have knowledge about our own biases.

Then I announced to all students that I had a quick “math exercise”: I was going to give them 60 seconds. I asked, "How much does it cost to get from here [Bates College] to New York City?," and gave them 60 seconds to come up with a number. I said they could use their phones or computers, estimate, etc. I made it a point for them to feel rushed, and I scrutinized my watch to emphasize the time.

When time was up, I asked students to compare answers with others in their group—asking “Are they different? How and why?" After a small chat, I said "Okay, let's report out—I don't care about the cost; what I want to know is what assumptions did you make?"

The first volunteer mentioned it was free to walk, to which I replied, “Okay, but what assumptions did you make?” They responded, "I assumed everyone had two legs."

This may sound like a simple response, but this is a big assumption. Certainly, we could observe that everyone in this class "has two legs"—but my mom does not have two legs. So this opened the door for us to discuss ableist assumptions that we may make, especially at Bates, where not all buildings are handicap accessible. We also discussed how this may affect transportation options other than walking, such as subways without handicap entrances or walking between stations.

And what about the disabilities and challenges we can't always see—that aren't as obvious as using a wheelchair or missing a leg?

The next person said “I assumed I was on a very small budget.” This led us into reflecting how that might change the mode of transportation you are thinking about. Perhaps where you live, busses are seen as the least expensive mode of transportation, so that’s where you immediately went.

Another student said they just assumed they were driving—which makes other assumptions about vehicle ownership, accessibility, and having a driver's license. Others went right for flight schedules, requiring familiarity with nearby airports, confidence about meeting identification requirements (not all states will issue DACA students a Real ID), etc. The point is that a quantitative problem is not necessarily independent of our social positioning.

I closed with reading a portion of DataFeminism (pg. 82-83), which a colleague recommended:

“Sandra Harding, who developed her ideas alongside Haraway, proposes a concept of strong objectivity. This form of objectivity works toward more inclusive knowledge production by centering the perspectives — or standpoints — of groups that are otherwise excluded from knowledge making processes. This has come to be known as standpoint theory. To supplement these ideas, Linda Alcoff has introduced the idea of positionality, a concept that emphasizes how individuals come to knowledge-making processes from multiple positions, each determined by culture and context. All of these ideas offer alternatives to the quest for a universal objectivity — which is of course an unattainable goal…. Rather than reviewing these positionalities as threats or influences that might have biased our work, we embraced them as offering a set of valuable perspectives that could frame our work. This is an approach that we would like to see others embrace as well. Each person's intersecting subject positions are unique, and when applied to data science, they can create and generate creative and wholly new research questions.”

I was inspired to do this activity by a GAIMME workshop several years ago. We were talking about constructing open-ended modeling projects and there was a problem, something to the effect of:

“An employee is late to work in an eight-story building with 1000 employees. They blame this on the elevators, even though they are in the building early. Could this be true? If so, how could you help?”

Anyone who has been to a JMM conference may have experienced this elevator issue at the hosting hotels. However, I remember thinking that my born-and-raised undergraduate Maine students may have never encountered this issue—and may need help even imagining the situation. The group of educators at my table and I noticed there was an implicit cultural assumption made in this problem (for context, the discussion of culture and positionality as intersecting with SATs was a contemporary issue at this time). One tenant of a universal design for learning approach is to think about accessibility more broadly as cultural accessibility. We thought perhaps showing a video, incorporating this experiential approach, may help students with the modeling process.

For my STEM Scholar audience, students who face barriers to success in STEM because of their positionality (first generation, race/ethnicity, gender, sexuality, income, ability, etc.), the activity I designed and the reading I chose was intended to guide students to confront their biases and their positionalities. I wanted students to reflect on how they may carry axes of both privilege and marginalization, and to rethink their positionality as an asset. This is important, because I want my students to feel empowered to lead science and mathematics into the next frontier. Data Feminism as a text excerpt worked well, because it emphasized how knowing one's positionality is important to acknowledge and frame, and we should appreciate how it enriches science and mathematics. We closed by sharing some challenges or thoughts, first in small groups and then together. The main takeaway from their discussions was how much more important it is to be part of science and mathematics, because of the unique new perspectives that we bring, new exciting questions we could generate, and new directions we could take the field.

Some instructors might use the travel or the elevator problem to have a short discussion of a subset of correct and algorithmically obtained solutions. Instead, I posit that mathematics classrooms are uniquely positioned to facilitate these conversations about implicit bias, cultural assumptions, and positionality. Questioning assumptions in mathematics (and STEM) is an important skill that is also a core value of mathematics discipline and to the teaching of critical thinking more broadly.

References

D'Ignazio, Catherine, and Lauren F. Klein. Data feminism. MIT press, 2020.