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What Would It Mean for Students to Bring Their Entire Selves to the Mathematics Classroom?

Ksenija Simić-Muller

In his influential essay “On proof and progress in mathematics” William Thurston 8 poses “How do mathematicians advance human understanding of mathematics?” as a fundamental question. We do not just do mathematics for our own satisfaction, we also wish to share the joy of doing mathematics with others. Thurston writes, “We are inspired by other people, we seek appreciation by other people, and we like to help other people solve their mathematical problems.” Those of us who love teaching love to share that joy with our students, to help them solve their mathematical problems. So why is it that so many of our students do not feel this joy? Why is their mathematical experience dehumanized?

To rehumanize our classrooms, we have to make different decisions than we have in the past. By rehumanizing, here I specifically refer to the recent conceptualization by Rochelle Gutiérrez. Gutiérrez 3 writes about the dehumanizing nature of mathematics classrooms: students are asked to leave their identities at the door and are taught mathematics as an exercise in compliance; and mathematics is decoupled from joy and play, and from authentic connections with the real world. While Gutiérrez primarily focuses on K–12 classrooms, her writing easily applies to college classrooms. She issues a call for rehumanizing mathematics (rehumanizing rather than humanizing to acknowledge ways people have long used mathematics in humanizing ways) and, much like Su 7, advocates for mathematics classrooms that focus on play and exploration; where students’ identities are welcomed, honored, and centered in the curriculum; and where mathematics is used not just to solve abstract problems, but to make sense of the world, including issues of power and oppression.

Gutiérrez 3, 4–5 identifies eight central traits of rehumanizing mathematics. All are important, and some are traits shared with active learning classrooms, for example, “Students collaborate and see each other as resources and authorities; the instructor is no longer the sole authority in the classroom,” or “Mathematics is a creative practice rather than consisting simply of rule following.” I have written about a few others in 6. Here I would like to focus on one trait that I think is particularly salient for sharing the joy of doing mathematics with all students: “Emotions have a place in a mathematics classroom; students are able to bring their entire selves to the classroom; and they should be able to feel joy when doing mathematics.” I am especially interested in the question of what it would look like for students to bring their entire selves to the classroom, particularly for students who are typically marginalized in mathematics classes, primarily Black, Indigenous, and People of Color (BIPOC) students, LGBTQ+ students, and students with disabilities.

I teach at a medium-sized private liberal arts university in the Pacific Northwest. I trained as a mathematician and retrained as a mathematics educator, and I teach a wide range of courses, from liberal arts mathematics to capstone, for majors and nonmajors alike. I am a white cisgender, heterosexual, able-bodied woman who immigrated to the United States from Eastern Europe in the 1990s. These identities are all relevant to how I show up in the classroom, engage with students, and work to rehumanize the mathematical spaces I occupy. Below are some strategies that I have found helpful in working toward the goal of cocreating with students classroom spaces where they feel safe bringing their whole selves.

Invest time in building a classroom community. Even though it seems that it is taking away from time spent on learning content, which is the primary purpose of a math class, time spent on creating community pays back generously in student engagement and commitment to the course. In my courses, we check in at the beginning of each class. I share relevant campus events, and sometimes students share events they are involved with. We almost always do warm-up activities. These are typically low-stakes, the types of activities where the focus is on mathematical discourse rather than correct answers. I especially like noticing and wondering, and especially about real-world issues 6. Students sit at tables in groups of 3-4, which has been one of the simplest and most effective ways I have been able to build community in the courses I teach.

Appreciate the students exactly as they are. Typically, we save our best interactions for students who are already doing well in our classes. We encourage them to take more classes, to major in math, to be a grader, or to apply for a scholarship. This seems like common sense. But we may find that the students who are doing well are those who look like us, who went to the same schools that we did, or who had opportunities to take more challenging math courses. We may tell ourselves we don’t have the time to catch up the student who is behind, don’t have the skills to work with the student with disabilities, or don’t need to accommodate the student who is working multiple jobs. And so we never know what potential we lost in the students we chose not to encourage. I yearn to give every student, regardless of how much math they know, or what grade they got in their previous class, the same amount of encouragement, faith, and respect. Even though I have a long way to go, I am most successful when I remember to enjoy the students as human beings, in all their quirkiness, insecurity, and confusion; when I connect with them as human beings first and mathematics learners second.

Provide opportunities for hands-on learning, regardless of the course content. During the past academic year, which was the first year since 2020 that felt almost normal, but not quite, I found hands-on learning especially beneficial for reestablishing some engagement skills we seem to have lost during the pandemic. When learning about symmetry in a course for future teachers, students made papel picado, a traditional Mexican craft made from sheets of tissue paper with designs (often symmetric) cut out of them. Then, for the remainder of the semester, I put out construction paper and scissors every day so that students could make other constructions, including paper snowflakes. We hung the art pieces on the classroom wall, where they stayed until the last day of classes, thus celebrating their creations and making the classroom more personable. In discrete mathematics and proofs classes, we began class once a week with a team building activity with interlocking cubes, where each student in a group gets a clue card, and all clue cards are needed to build a required object 1. This prompted groups to bond: there was often laughter heard, in addition to lively discussions about strategies for solving the problem. Most days I left the cubes on the tables after the warm-up activities. I never knew what elaborate structure I would find at the end of class. One day a whole family of ninja turtles appeared, on another day a family of ducks.

Allow different kinds of feelings in the classroom. In a perfect world, there would always be joy in all my classes, but this is not possible. My students are allowed to hate math, as many who come to my classes for nonmajors do, and with good reason, considering the histories they have with the subject; my job is to show them that they can do well in math and enjoy it, but not to force them to like it. They are allowed to be frustrated and to dislike whatever activity we are working on, though if this happens it is a clear message to me that I need to understand what it is about the activity that is not working and revise it as needed. Everyone is allowed to have bad days. If it is a bad day in the news, I acknowledge it and provide space for conversation. The world is always challenging for young people, but perhaps especially now in the era of climate disasters and attacks on rights and liberties that, at least for many of my students, are personal. Sometimes students really want to talk about issues. Sometimes they just want to work on math with their friends, and sometimes they want to work quietly on their own and listen to music. These are all valid, and I have learned to read the mood of the room and ask students what they need, then adapt.

Do not be afraid of difficult conversations, and learn how to facilitate them. I have difficult conversations with students, even though (or especially because) they are difficult. If there is a current issue that students want to discuss, I have learned to hold space for despair and for hope, and to find a balance between the two. I also make difficult conversations part of my curriculum. We use mathematics to analyze systemic racism, talk about the limitations of Western mathematics, and analyze the myth of the brilliant and troubled mathematician, among other things. There are now great curriculum resources available to address social justice-related topics 45, though I still often create my own. I have learned to have conversations about complex issues, related to the curriculum or not, from readings, professional development sessions, and conference presentations, as facilitating difficult discussions is not something most of us learn in graduate school. I have especially benefitted from participating in book clubs with colleagues.

Be more flexible. This is a complicated suggestion, as I know that faculty who are BIPOC, women, and/or trans, may not automatically get respect from students. However, in my experience, my willingness to bend allows students to be more comfortable being themselves, and fosters learning. Does letting students make animals from cubes during a proofs class negatively impact their learning? I have actually found that some students are able to focus better. And last semester, the student who built the most elaborate structures participated more in classroom discussions the more he was allowed to build with cubes in class. I have also learned that no pedagogical approach needs to be followed exactly. Even though learning is most meaningful in groups, sometimes students need to work on their own; even though research suggests that groups should be changed often and randomly, sometimes students just need to sit with their friends all semester; even though I think homework is essential, sometimes students have good arguments for why less should be assigned, and I listen to them (though grudgingly).

Do not sacrifice high expectations while being more flexible. While there are times when mathematics learning can briefly be put aside to deal with a timely issue, enjoy a side conversation, or just take a short break, learning always comes first. Nor is there a distinction in my classes between “fun” warm-up activities at the beginning of class and “serious work” afterward; all work should be equally joyful, challenging, fun, and frustrating. It is always a balancing of setting high expectations and not taking our classes too seriously. In my classes we play games, do a lot of hands-on activities, laugh, and listen to music; but I also remove myself from the front of the classroom so students can have more ownership, give honest feedback, keep pushing, and never let a student say they are not good at math.

Remember that you will never arrive at the final destination. I recently received grade data from the 15 years I have been at my institution. I was troubled but not surprised to learn that I do not give nearly as many As or Bs to Black students as I do to students of other races. It was humbling to be reminded that all the professional development I participate in and all the efforts I make to include all students are not sufficient to undo my biases and the impacts of living in a system that ranks and sorts by race, class, gender, sexual orientation, or ability (among others), as well as by perceived mathematical ability. It is easy to become discouraged, but we can also become curious, dig deeper into the data, pay more attention to our actions and student feedback, and keep learning.

Oftentimes we argue that we need to include previously excluded students in mathematics (particularly BIPOC students) because mathematics will benefit them, but we fail to recognize how mathematics itself will benefit from their perspectives. Even though written in 2002, this quote by Gutiérrez still resonates today:

The assumption is that certain people will gain from having mathematics in their lives, as opposed to the field of mathematics will gain from having these people in its field. In other words, most equity research currently assumes the deficit lies within the students who need mathematics as opposed to, or in addition to, lying within mathematics, which needs different people. Such programs seem to imply that the people being served by the programs need to improve but that the mathematics does not 2, p. 147.

I do not think that mathematicians can advance human understanding of mathematics if they are not willing to let humans rehumanize (and therefore advance) mathematics. Our courses are better and we are better when every student has the opportunity to contribute in meaningful and authentic ways. I still do not know what it would look like for all my students to be able to bring their entire selves to my classroom, especially as this is not something I can determine on my own without student input; but I think I get occasional glimpses. Like when a future teacher and a “Swiftie” writes a fantastic lesson about the inequities involved in buying tickets for Taylor Swift concerts. When a student solves a problem while bobbing his head to a tune in his head, confident in his knowledge, and content to be working on math with his group members. Or when a student who was never successful in a math class excels in a probability unit partly due to her being an experienced Dungeons & Dragons player.

Whatever work we choose to do to create more equitable classrooms, departments, committees, research teams, and universities is indefinitely ongoing. It is also full of joy even when/because it is incredibly hard. Our humanity is intertwined in the humanity of others, and the project of rehumanizing mathematics necessarily includes rehumanizing ourselves.

References

[1]
T. Erickson and R. Craig, Get it together: Math problems for groups, grades 4–12, Lawrence Hall of Science, Berkeley, CA, 2018.
[2]
R. Gutiérrez, Enabling the practice of mathematics teachers in context: Toward a new equity research agenda, Mathematical Thinking and Learning 4 (2002), no. 2–3, 145–187, DOI 10.1207/S15327833MTL04023_4.
[3]
R. Gutiérrez, Introduction, Annual Perspectives in Mathematics Education: Rehumanizing Mathematics for Black, Indigenous, and Latinx Students, National Council of Teachers of Mathematics, Reston, VA, 2018, 1–10.
[4]
Gizem Karaali and Lily S. Khadjavi, Mathematics for social justice: Resources for the college classroom, Classroom Resource Materials, vol. 60, MAA Press, Providence, RI, 2019. MR3967051,
Show rawAMSref \bib{KK1}{book}{ author={Karaali, Gizem}, author={Khadjavi, Lily S.}, title={Mathematics for social justice}, series={Classroom Resource Materials}, volume={60}, subtitle={Resources for the college classroom}, publisher={MAA Press, Providence, RI}, date={2019}, pages={vii+277}, review={\MR {3967051}}, }
[5]
Gizem Karaali and Lily S. Khadjavi, Mathematics for social justice—focusing on quantitative reasoning and statistics, Classroom Resource Materials, vol. 66, MAA Press, Providence, RI, [2021] ©2021. MR4390800,
Show rawAMSref \bib{KK2}{book}{ author={Karaali, Gizem}, author={Khadjavi, Lily S.}, title={Mathematics for social justice---focusing on quantitative reasoning and statistics}, series={Classroom Resource Materials}, volume={66}, publisher={MAA Press, Providence, RI}, date={[2021] \copyright 2021}, pages={vii+287}, review={\MR {4390800}}, }
[6]
K. Simic-Muller, Noticing and wondering to rehumanize mathematics classrooms, PRIMUS 33 (2023), no. 4, 431, DOI 10.1080/10511970.2022.2073624.
[7]
Francis Su, Mathematics for human flourishing, Yale University Press, New Haven, CT, [2020] ©2020. With reflections by Christopher Jackson, DOI 10.2307/j.ctvt1sgss. MR3971543,
Show rawAMSref \bib{Su}{book}{ author={Su, Francis}, title={Mathematics for human flourishing}, note={With reflections by Christopher Jackson}, publisher={Yale University Press, New Haven, CT}, date={[2020] \copyright 2020}, pages={x+274}, isbn={978-0-300-23713-9}, review={\MR {3971543}}, doi={10.2307/j.ctvt1sgss}, }
[8]
William P. Thurston, On proof and progress in mathematics, Bull. Amer. Math. Soc. (N.S.) 30 (1994), no. 2, 161–177, DOI 10.1090/S0273-0979-1994-00502-6. MR1249357,
Show rawAMSref \bib{Thurston}{article}{ author={Thurston, William P.}, title={On proof and progress in mathematics}, journal={Bull. Amer. Math. Soc. (N.S.)}, volume={30}, date={1994}, number={2}, pages={161--177}, issn={0273-0979}, review={\MR {1249357}}, doi={10.1090/S0273-0979-1994-00502-6}, }

Credits

Photo of Ksenija Simić-Muller is courtesy of John Froschauer. Copyright 2021 Pacific Lutheran University. All rights reserved.