Who are our students?

By: Edwin O’Shea, James Madison University

In Marilynne Robinson’s Gilead, Reverend Ames testifies that each person in his flock has “a kind of incandescence in them… quick, and avid, and resourceful. To see this aspect of life is a privilege of the ministry which is seldom mentioned.” I think this is a privilege of the educator too. But our flock’s life cycle, the fourteen weeks from the cradle of the first day syllabus to the grave of the final grade, has a different rhythm to that of a liturgical calendar.

In a semester where I have over 100 students, witnessing each student’s luminosity is challenging, and by the time I get to know even half of them the semester is likely to be halfway through. So I ask my students to help me to see them. I ask what their values are, to tell me about the work they’ve done and are about to do, and to share their hopes and aspirations as people.  I ask them about the concrete challenges that they might face as the semester progresses and what they wish previous mathematics teachers understood about them.

I do this because understanding my students holistically aids in my support­ of each student individually and can cultivate active learning communities. I do this because if the semester gets rough on my end ­— it invariably does — I have a wealth of prior empathy and insight to fall back on so that my students succeed in their goals. I do this because knowing only their placement scores and/or GPAs is not enough! There’s also a body of research supporting that when students’ values are affirmed in STEM [i], they are more likely to succeed in that course and continue as a STEM major.

I ask for their help on the first day because it is most expedient and it is the most important day of the semester [ii]: Consulting my students on that first day establishes a framework for the class, that we are starting a dance between the content of our discipline and the context from which each person comes; and in this dance both partners matter equally and each will have their turns to lead. The first day is also the liminal space between their previous experiences in mathematics and what this new course promises to be, so it provides an opportune time to reflect and to project, to celebrate and to prepare.

 The Questions

The questions I will discuss below are intended for junior/senior math majors but can be adapted for other populations of students [iii].

What was your path to becoming a math major? Do you identify as a ‘math major’? How is this choice perceived by others and how do you respond to these perceptions?

These questions are general yet typically elicit responses about formative experiences, far beyond what I originally anticipated when I first put this questionnaire together. Students tell me if their confidence is low, if they have a passion for physics, if their vocation is in teaching. They let me know if college was not the expected path for their family members, or if it was absolutely expected, each of which exerts its own distinct type of pressure. Students also tell me about their perceptions of local and global mathematics culture and how they situate themselves within it; in doing so they invariably tell me about their values.

Students also share personal issues outside of the major. Some will say they are holding down a full-time job and then I know that they might need some flexibility on deadlines [iv]. Others might be returning from some time away from college necessitated by mental health, financial, or family concerns: I tend to pair these students with partners who are more collaborative than competitive. For example, my typical Quantitative Finance or Engineering students — not inherently, but culturally, competitive — tend to be a poor match for someone who needed a break from school for a period of time.

The responses allow me to tailor my interactions with my students but also to customize some of the content of the course.  For example, when I am assigning projects in the second week of Abstract Algebra, I can assign a reading project on matrix groups to the student who is very interested in physics. Similarly, if the class has future teachers then I will assign a project on transformation groups relating to isometries and how that relates to the state’s high-school mathematics curriculum.

The next questions ask the student to reflect on their time at university. It asks for a self-assessment of what courses went well, why they are here for this course, and the extent to which they have learned from positive and negative past experiences in collegiate mathematics. These questions are implicitly asking the students to transition from values to responsibilities, to a sense of ownership of their education. The questions also give me a very practical insight into their mathematical motivation and the gaps in their existing knowledge we might need to address.

What’s your favorite area of mathematics? Your favorite ideas/results? What course do you wish you could have avoided? What course do you wish you could take again? What would you tell yourself if you could travel back in time and talk to your freshman self?

My final questions concern mentorship. Knowing my student’s values and motivations, how can I support my student’s future plans? ­­­The responses can also be used to calibrate the course’s emphases to where they can have the most impact.

What are your future plans in terms of vocation? Do you hope to enter into a job in industry? Are you preparing to be a high school teacher? To go to graduate school? To run for the hills, join a commune and live off the land?  What non-math skill do you wish you were better at?”

I distribute these questionnaires on the first day of class and ask the students to return on the second day of class with their responses. At no point do I make these responses public. The questions demand vulnerability on the student’s part so I am compelled to reciprocate by trusting my new students with my own answers to these questions. I do so by responding verbally to these same questions on the first day of class. I answer as I think my twenty-year-old self would have and also how my middle-aged self understands these responses today. I worry that I’ll look like a fool but it never works out that way.

On Affirmation

For an “active learning”[v] context, where vulnerability and play are partners of discovery and rigor — a joining of many dialectics in the hopes of achieving a synthesis — the affirmation of students’ values may be yoked to their success in the class.

Miyake et al. provided evidence that when women in an introductory physics class “wrote about their most important values” twice in the semester, the discrepancy between male-female outcomes reduced substantially. Further, that “the benefits were strongest for women who tended to endorse the stereotype that men do better than women in physics.” In a different STEM context, Jordt et al. examined the discrepancy between underrepresented minority students and white students in introductory biology classes and concluded that the relative “underperformance of URM students could be mitigated” by a similar values intervention. The biology education lab of Sarah Brownell has more investigations along these lines.

I would suggest — as an axiom rather than an empirical finding – that the more a person feels affirmed in class the more likely they are to wholeheartedly participate in groups with others: the more likely they are to trust, the more likely they are to take risks. Indeed, group work without intentional individual affirmation is more likely to promote a tepid conformity — the “just get it done” treatment of the worksheet that defers authority to the student perceived as the group’s strongest or, failing that, the instructor — rather than the form of radical consensus that we as instructors wish for. The type of consensus I mean is one where each participant seeks to hear the other and where students’ collective achievements surpass their individual struggles with the material. It’s my suspicion that if we sincerely engage in an active learning practice without paying attention to individual affirmation, we risk cementing real and perceived hierarchies among students and, in doing so, exacerbate the very types of privilege and status quo that we might be trying to supplant — not just in our class but, more broadly, in our discipline’s culture. This is why affirmation matters.

Returning to Gilead, the epistolary work referenced in the introduction, Ames writes with the urgency of a dying father anticipating who his young child will be and what he will need from the world. He professes a nuanced and practical faith with decency, introspection, and a transparent and messy imperfection. For the teacher, the stakes are lower than those in Ames’s letter but the exercise, imperfectly anticipating the world as a young person might experience it, requires Ames’s same sense of optimism leavened with a dusting of realism and the acceptance of frequent futility.

To help our students navigate the outer world and the universe of our discipline, we can ask them to share what they think of as their true north, their stars within and beyond our discipline, the terrains they’ve passed through. We can ask which mountains they want to climb and let the contours of our courses, our programs, and our discipline’s culture be influenced accordingly. But if we want to know the answers to these questions, we have to ask our students. And honor the trust they place in us when they answer. In doing so we give our class a greater chance to become a community in which everyone is affirmed as a person, where collective risks are more likely to be taken, and where opportunities are increased for every student to join our discipline fully.


[i] Setting aside my deep reservations about the use of the term “STEM”; I’d prefer if we called it “MASH,” dumping engineering and technology for the arts and humanities, cf. https://sententiaeantiquae.com/2018/11/28/science-and-humanity/

[ii]The importance of the first day is in Chapter 2 of Geeky Pedagogy: A Guide for Intellectuals, Introverts, and Nerds Who Want to Be Effective Teachers, by Jessamyn Neuhaus. West Virginia University Press, Morgantown, West Virginia, 2019.

[iii] The questions I ask for introductory classes like Precalculus can be found at my website: http://educ.jmu.edu/~osheaem/teaching/who-are-our-students.pdf

[iv] Art Duval advocates for flexibility too in “Kindness in the Mathematics Classroom,” (this blog, Feb 2018). Duval’s main question is in response to Francis Su’s essay on “grace” in the classroom, how does one practically implement Su’s vision for mathematics praxis?

[v] As expected, “active learning” is quite the broad church. My own style emphasizes the centrality of reading outside of class, some elements of flipped classrooms and IBL, and mastery-based assessment.  See “What Does Active Learning Mean For Mathematicians?” by Benjamin Braun, Priscilla Bremser, Art M. Duval, Elise Lockwood, and Diana White, Notices of AMS, February 2017.

[vi] Thanks to Cynthia Bauerle for pointing me to some of the science education literature on affirmation.

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