Guest blogger, Erin Griesenauer (Eckerd College), shares how the COVID-19 pandemic led her to think about how to teach ethically and equitably, whether during a crisis or otherwise.
As I consider the interface between mathematics and ethics, one of the largest questions is what it means to teach mathematics in an ethical way. When I step in front of a class, I am accepting the responsibility of teaching the students there the material they need to know in the most ethical way that I can. As I think about how to accomplish this–also as I reflect on this summer’s international protests against racism and how I can bring the lessons of antiracism into my classroom–one thing I have come to realize is that teaching ethically requires me to teach all of the students I have in a way that actively helps all of them succeed. I need to recognize that my students bring different experiences and different strengths into my classes, and I need to work with all of them to use their strengths to accomplish the goals of the class. In a word, I need to realign my classes to value equity.
And, looking back on my experiences from this spring–when my students and I were forced out of our classroom and off our campus, and I was forced to find new strategies for teaching and learning–what I’m finding is that this push out of my comfort zone got me to try things in my classes that I wouldn’t otherwise have tried. And that these new strategies will be useful for students who might not have succeeded (or may have struggled more than others) in my past classes. So even though I have developed new teaching methods to address the exigencies of a pandemic, these methods will be good blueprints for future classes and will be instrumental in adapting my classes to teach more ethically.
This is appropriate, given the inequities that I was forced to confront this Spring. As we left campus, I had to acknowledge that my students were leaving campus to very different situations. Some wouldn’t have consistent internet access. Some didn’t have laptops or tablets. Some students had nowhere to go when campus closed; some returned home and took full time jobs; some had to drive an hour to have internet access; some were suddenly in charge of watching younger siblings—which resonated with me, as a parent of a preschooler suddenly left without preschool. As I restructured my spring courses with these students in mind, I made some changes that I plan to keep in recognition that, undoubtedly, these vastly different experiences are not suddenly erased when my students come to campus or into my classroom.
Below are some of the changes that I made and will keep into and beyond the uncertainties of the fall. None of these ideas are new—educators have been thinking about how to improve classes for a long time. However, now is a time to listen more closely and to really consider the needs of my students. This Spring, I was teaching two sections of Calculus I, so many of my thoughts right now reflect that class. However, I believe that these lessons can readily be applied to other classes.
Less is More: Of course, we should always consider what the core goals of our courses are and pare out the extraneous pieces that serve as distractions (at best) or roadblocks (at worst), but I was extra motivated to consider my core goals as I lost a week of classes, spent time reviewing after our two-week Spring Break, and learned to pace online instruction. I had to carefully consider what material could realistically fit into the time that we had.
At first, it may not be obvious why trimming out unnecessary topics contributes to equity. And this past Spring, my main motivation was time management, not equity. However, getting rid of extraneous topics
- removes roadblocks and allows me to form a narrative around the most important topics. Along with this, I can identify and potentially remove places where calculus relies on, and tests, skills from previous courses. This recognizes that my students come to me with different levels of preparation, and some haven’t been in a math class for several years.
For example, one of the challenges of optimization problems is finding x-values where the derivative is zero. But this challenge is unnecessary—it’s testing skills from algebra, not calculus, and it can be eliminated using a graphing tool like Desmos rather than finding the zeroes algebraically.
- gives me more time to use reviewing material from previous classes that I really want my students to know and bringing in other types of activities that I haven’t previously had time for, like building student intuition through manipulatives and other active learning projects. These activities have been shown to increase student success and support equity.
Provide the Material in Multiple Formats: I have always depended on lecture as the primary way to deliver information to my students, supplementing with other activities as time allowed. But when traditional lectures were removed as an option, I had to find other ways of bringing the material to my students. Recognizing that my students had varying levels of access to technology (some would be relying on their phones alone) and required different learning accommodations, I realized that I would need to present the material in a variety of ways. I used lecture videos, posted notes and slides, used the online resources that came with our textbook, online manipulatives, and found interesting articles to read.
Making and finding these materials was time consuming, sure, but now that I have them, I certainly plan to reuse them. I also found, talking to students, that they had a wide variety of preferences and approaches for using these different materials. Having information available to access remotely is important during normal semesters, too, for students who often miss classes because of chronic illness or jobs off-campus or athletics.
Use a Variety of Assignments: Related to presenting the material in a variety of ways, another strategy I found useful and plan to continue in the future is using a variety of assignments. Before the move away from campus, my classes had predictable assignments: homework, worksheets, quizzes, tests. But when we moved off campus, I was pushed to be a little more creative in the types of assignments I used. At the time, I wasn’t motivated by inclusivity, but by the knowledge that students working remotely would likely be more tempted to use on-line resources that were not approved (that is, cheat) and that it would be harder to detect when students did this. I wanted to make sure that honest students were not at a disadvantage.
So I added written explanations to quiz solutions—not just showing the steps, but writing an explanation about the method they used and why it was appropriate. I changed tests to more open-ended review projects (more below). I added forum posts and written reflections to go with review projects, virtual manipulatives, and online articles.
I plan to keep written assignments like these, along with more traditional assignments. What I found is that some students who are intimidated or frustrated by problem sets find writing reflections about their experiences easier and more enjoyable. Recognizing that some students prefer more traditional assignments, in the future I might also want to allow students to choose from among these different types of assignments so that they can best demonstrate their learning.
I also began relying on students more and added reading note assignments. These were worksheets where I asked students to read the book themselves and write down basic definitions and theorems. This was an effective way to include information that I didn’t want to spend time on in the lecture videos. It also gave students practice reading the textbook and finding information on their own, certainly important skills to learn. And, for some students, at least, these worksheets built a sense of independence and efficacy.
Reconsider Tests: When we moved to remote learning, I knew right away that I would replace our tests with some other assignment. This decision was based on my belief that, no matter what restrictions were put in place, I would not be able to prevent students from cheating. What I was stunned to find, though, was that without tests, the class didn’t fall apart.
Instead of tests, I had students complete “Unit Review Projects,” where students effectively wrote a test themselves and submitted their own solutions. Because of the stress that my students were under, I structured these assignments to be as simple and straightforward as possible: I gave them an outline of the topics that we had covered in the unit, and I asked them to come up with one question for each topic and write out their solution with all steps.
Students seemed to enjoy this assignment—certainly they enjoyed it more than a test–and I believe it was a good way to review the material before we moved on. I was especially impressed by the creativity the students showed for topics with word problems, like Related Rates and Optimization.
In the future, when we are back together on campus, I plan to offer students the choice of taking an in-class exam or completing this type of review assignment. That way, students who prefer a traditional exam can do so and students who suffer from test anxiety or prefer not to take the test for other reasons can do this instead.
Focus on Motivation and Affect: To me, motivation used to mean choosing examples that related to students’ interests every once in a while. I still think this is important, but teaching through a pandemic has taught me that it’s not enough.
The emotional toll of the pandemic—the anxiety and uncertainty felt by both my students and myself—made me appreciate that it is also important to address students’ emotions and help them overcome negative emotions that might be evoked by a math class (or outside circumstances). Obviously, I’m not a counselor and I’m not trained to help students facing severe problems. But giving students tools to overcome their feelings of stress is something I can do.
I found the two topics where students needed the most help to be general stress and procrastination.
- Stress: The main lesson here is that self-care and personal wellbeing can’t be ignored. Some students need to hear that it is important to eat well, exercise, and get enough sleep. Hearing a professor say that these things take priority over studying for a test or completing a homework assignment carries extra weight. Many are also surprised to hear that they’ll actually learn better if they take a break and get more sleep. Beyond that, I also shared some suggestions for self-care and relaxation strategies that I have used.
- Procrastination: The first step is to recognize that procrastination is not about laziness. If students are procrastinating, it is usually because either they (1) don’t know where to start or (2) have negative feelings about the task that they don’t want to confront. Helping students recognize these two causes gives them a first step when they find themselves procrastinating: why am I putting this off? Once they identify the cause of their procrastination, they can take steps to address it.
That being said, overcoming the habit of procrastination is hard. I hope that I will have more luck persuading students to face their habits of procrastination on campus than I did remotely. This is a topic that will need to be revisited throughout the semester if we’re actually going to see change. One useful thing to keep in mind is that a new study has shown that waiting for an experience that you’re looking forward to is a mix of positive expectation and negative feelings about waiting, but putting off an experience that you expect to be negative (that is, procrastinating) is only bad—negative expectation and negative guilt about putting it off. To overcome this, you have to stop putting it off. Admit that you’re not looking forward to doing whatever it is (homework, studying for a quiz, etc) because it will be hard or confusing or frustrating. Then do it. This will minimize the amount of negative feelings you experience.
Build a Predictable Schedule: For students who have a lot of responsibilities, being able to plan and schedule in advance is important. When we moved off campus, the need for a predictable schedule was even more important. I posted a schedule that listed the assignments that were due and the new work for each day. I had this mostly filled in by the time we began remote work, and updated it as needed. I know that students found this helpful, so they could plan their week in advance.
Keep in mind, though, that the goal of having a predictable schedule is to help students as they organize their schedule. The point is not to enforce a rigid schedule just for the sake of having a schedule. The other side of recognizing that my class is just one part of a student’s life is the ability to be flexible, to give students the ease they need to fit my class into all of the other demands they are facing. Which brings me to my last point …
Be Flexible: Really, the biggest takeaway from an unexpected shift to remote learning is that it is important—and possible—to be flexible in how I teach. Given students’ various circumstances, it was important to be flexible with deadlines, with how students submitted their work, with how I communicated with students. Flexibility is about more than that, though. This spring was a hard lesson in flexibility, and the idea of flexibility underlies most of the other changes I’ve mentioned. Identifying the main ideas for my class let me be flexible when deciding how much time to spend on each topic and which topics to leave out. I was forced to be flexible in delivering the material, and learned that it was easier than I expected. I’ve learned to be flexible in my conception of what a math assignment looks like and what sorts of work count as “doing math.” This flexibility has helped me identify individual students’ strengths in a way that I wasn’t able to before.
Reflecting on my experiences this Spring is just a first step in learning to address the ethical mandate as a teacher to help all of my students succeed, by identifying their individual strengths and emphasizing equity in my classroom. There is a wealth of information out there, and the next step for me is to learn more. Here are some resources that I am planning to read to educate myself:
Harriet W. Sheridan Center for Teaching and Learning: Resources on Inclusive Teaching
Rethinking Mathematics, edited by Eric Gutstein and Bob Peterson
Mathematics for Social Justice, edited by Gizem Karaali and Lily S. Khadjavi
Journal of Urban Mathematics Education
Erin Griesenauer, Assistant Professor of Mathematics, Eckerd College
 | Professor Griesenauer conducts research in Operator Theory and Mathematics Education. She is interested in integrating ethics into her classroom, using service learning, and recently teaching a course in Mathematics of Sustainability. |
Ethical Mathematics 