Debbie Borkovitz
Boston University
This is the second in a series of four blog posts in response to the call: For many reasons, including AI, we had to adapt our teaching strategies and learn as we go this year. So let’s share what we found that was useful, promising, and/or positive in some way! Our audience is NE-COMMIT and anyone else curious about improving teaching mathematics.
The posts are ordered from those describing practices more resistant to AI to those describing practices more embracing of AI.
Here are links to the remaining posts: AI 1 Thinking Video Notes to my future forgetful self by Christine von Renesse, AI 3 Teaching Calculus III in the Age of AI by Ileana Vasu, and AI 4 Experimenting with Potential Ways to Incorporate AI into my Teaching Practice by Rebecca A. Norton.
For many years, in many courses, I’ve given involved writing assignments. Often students worked together to solve a complex problem, and then refined their solution and justification by writing individually. In more advanced classes, the assignments involved formal proofs. In the Fall of 2025 I gave an assignment I’ve used many times, and about a third of the class turned in identical solutions with identical variables. It became clear to me that these assignments didn’t work anymore with ChatGPT readily available – and maybe they never worked for some students. In the Spring of 2026, I taught three different courses, and I changed the writing assignments in all of them in ways ranging from tweaks to total replacement. Below are four changes that I found promising.
Mathematical Mixtape Assignment: For this assignment, I first explained to students in my Writing in Mathematics class what a mixtape is: how recording a cassette from various records took a lot more effort than making a playlist these days, and we often made them as gifts that expressed something about ourselves. Their assignment was to curate a “mixtape” of exactly five mathematical items, such as theorems, ideas, techniques, or tools, that represent their tastes in mathematics right now, with the audience as their actual classmates (not hypothetical students at their mathematical level, as I’ve described writing assignments in the past).
Students loved this assignment. They enjoyed thinking about their list, and they enjoyed reading their classmates’ mixtapes and thinking about the similarities and differences in their tastes.
I think there was some inappropriate AI use on this assignment, but I didn’t feel the tension of policing. I would make the comment, “This sounds like AI,” which led to some interesting conversations about the actual writing. Some students voluntarily rewrote parts of the assignment. Some said they didn’t use AI, and we talked about things like how replacing words or phrases with others that were less hyperbolic or more specific made the writing better. Some students said they used AI to brainstorm items for their list, and we just talked about whether that helped or not.
I initially got the Mixtape Assignment idea from prompting Claude to give me a list of ideas for personal writing about mathematics that was AI-resistant. The assignment aligned with some of the types of prompts in John Warner’s, The Writer’s Practice, which is a text for introductory writing courses that I read after we read his book, More than Words: How to Think about Writing in the Age of AI in our NE-COMMIT book group. The Writer’s Practice was written pre-AI and offers an alternative to formulaic five-paragraph essays and summaries. Many of his exercises ask students to express an opinion to an audience, which is not something I’ve done a lot in math classes. I loved the humanity of the assignment; how both writing and reading classmates’ papers made them think about math, their relationship to math, and how varied those relationships were throughout the class. Maybe in math we don’t leverage enough students’ fascination with each other….
A Print Magazine Also in Writing in Math students had the option for the last few weeks of class to either do more work on proofs or to create a math magazine. This was not a new assignment – I thought of it halfway through the semester the previous year, when I taught the class for the first time. One purpose of the Mixtape assignment was to use it as ideas for magazine articles. Nine out of 15 students chose to work on the magazine. What was different this semester, was that I used some extra funds I had to print copies of the magazine, with center binding like “a real magazine.” I was surprised at how motivating the idea of printing their work was. Students put a lot of effort into the magazine, and were proud of the result. When they came to pick up their copies, almost all were just giddy when they saw them.
I also gave students print copies of a different mathematical publication every week, including journals and Martin Gardner books. We reflected on the audience, style of proofs, and interesting articles or sections. Many students started their magazine articles by making outlines but then ended up with three-page articles with six sections, some of which were only one or two sentences long. So we pulled out some of the journals, and I had them look at whether they saw any articles with as many sections as theirs and just to pay attention to how authors chose to section the papers.
Many (not all) students told me that they liked reading math articles in print a lot better than digitally, that they could focus more and they thought more. One student started a habit of reading math before bed that he intends to continue. Many said they’d wanted to read more math articles but never got around to it until they had the print journals. So, I’m being careful about my stereotypes of digital natives – a lot of them like print!
A Festival!: In my Math Explorations class I took away a paper assignment entirely and replaced it with a math festival. This course satisfies a general education requirement in Oral Communication, so the festival was actually more aligned with the class. The goal of the paper had been for students to spend an extended time period on one problem and use feedback to improve it iteratively. For the festival, I chose four activities; origami, a floor maze, and two puzzles; and students selected which they were most drawn to. Students spent about two weeks working in their groups, and a colleague from Math Ed. did a workshop for them on leading activities. The groups had choices about what version of their activity to share, what handouts to make, and how to introduce the activity. We had two class periods for the festival. In the first, students shared their activity with the other groups, and in the second, we invited people from outside the course. Afterward students wrote a reflection.
As with the paper, students spent extended time on one topic, and the iteration came in adapting what they said to different audiences. I used to teach mostly pre-service teachers, but now I don’t. I’m struck by what low-hanging fruit it is to teach any student, not just pre-service teachers, about things like wait time and asking open-ended questions (Eric Cordero-Siy, who led the workshop, joked that it was also dating advice). I know how much I learn about math, people, and communication from teaching using IBL pedagogies, and the festival was a chance to give students a taste of that.
We had perfect attendance both days of the festival, and students’ feedback was overwhelmingly positive, as was feedback from colleagues and others who attended the second day of the festival. It was fun for some of the math majors in the class to lead activities for their professors, and my colleague down the hall was impressed when he found out that the student who was confidently answering questions about the math maze was an International Relations major.
In-Class Writing Assignments: In Graph Theory I gave eleven In-Class Writing Assignments (ICWAs). These were strictly formative writing activities that usually took about 15 minutes at the end of class. In order to make time for them, I was stricter about having students message me if they were going to be late, so that we started our group activities as early as possible in the class period. I was surprised at how much students liked the ICWAs. I liked the rhythm of having quiet at the end of class after the bustle of having students in groups at the boards discussing problems. I also liked giving handwritten feedback from a comfortable chair away from screens, and I was usually able to return the (up to 35) papers by the next class.
At BU most of our students are very good at school, i.e. at performing learning to get good grades, which sometimes involves actually learning the subject at hand, and sometimes does not. The ICWAs were low-stakes and not announced in advance, so students never studied for them. I felt like I got a much more honest picture of their actual understanding than I would have had with a quiz they’d studied for. Often they got such a picture as well.
The content of the ICWAs was varied. Once I gave something that did look like a quiz. On a regular weekly survey, I asked hypothetically how they would do on an ICWA involving problems about negating mathematical statements and about converse, inverse, and contrapositive. Then on a whim, I decided to ask some typical quiz questions on the next ICW, and just marked each one correct or incorrect. Some students were very surprised, because they missed most of the questions, despite previous A’s on tests of the material in other classes, which provided a wonderful opportunity for them to reflect on the differences between getting a good grade and learning something deeply.
Many of the ICWAs asked students to write proofs. The very first proof was one from the book, “If a graph G contains a u-v walk of length k, then G contains a u-v path of length at most k.” As with all the ICWAs, I included definitions of all relevant vocabulary; the most important thing to note is that a path is a walk with no repeated vertices. I thought that most students would do the proof intuitively, e.g. to keep removing closed walks until there were no repeated vertices. I was going to follow up by comparing that approach to the book’s proof by contradiction.
However, a significant proportion of the class instead assumed that G contains a u-v path and proved that the path had length at most k. Reading those papers was intense for me, because I immediately understood why there was so much cheating on my formal proof assignments the last time I’d taught the class: I was very wrong about where many students were starting out, and even proofs that I thought should be straightforward for students were not going to be if they confused assumptions and conclusions and didn’t pick out the overall goal of the proof. Some dialogue with Claude told me that the issues I was having were common. I got articles from both Claude and from my Math Ed. colleague Eric. Mostly, I didn’t read these articles during the semester, but when the semester ended, I initiated this summer’s NE-COMMIT math led literature reading group on learning and teaching proof, so I could read and discuss some of them with others.
Since students all had the same amount of time for the ICWAs, I included choices or follow-ups so that everyone would have a place to start and something to keep them occupied for the whole time. Once I gave them three theorems from the book and asked them to choose one to prove (and to attempt more than one if they had time). I gave open-ended questions like, “Let G be a graph where all vertices of G have degree 2. What can you say about G? Prove as much as you can, as formally as you can.”
For the last ICWA, after some definitions and preliminary questions, the prompt was, “There are 5 non-isomorphic connected cubic graphs of order 8. Find as many as you can,
and indicate whether each is planar or not. If you find them all and you have time, try to
prove that there are no more.” I was a little dismayed that this late in the semester, a few students ignored the definition of a cubic graph that was written right there, and instead assumed a cubic graph was a graph that “looked” three-dimensional. I was even more dismayed that one student clearly cheated with AI during the ICWA and gave a complete, incorrect answer with no pictures, which alerted me to the possibility that some LLMs would get this question wrong.
I gave the problem to Claude Haiku, which got it spectacularly wrong. It made a table of five graphs and three of them were different names for the vertex-edge graph for a cube. One had 16 vertices. It said that one planar graph was not planar and gave the wrong reason why another graph was not planar. I ditched the next day’s plan and spent the next class having a whole class discussion about the AI solution, which was a very engaging activity.
I followed up other ICWAs in different ways. Sometimes I incorporated them into the next class’s group activity, other times I made videos about common solutions or mistakes, and sometimes there was no follow-up. I was pretty discouraged for a while, but about halfway through the semester, I realized the students’ proofs were getting better.
I am also definitely going to use the ICWAs next time I teach Graph Theory and also in the fall when I’m teaching Discrete Math again. I loved the freshness of them, that the writing really conveyed students’ current thinking. Giving feedback was interesting and varied, and it felt like I was being much more helpful than I often was on larger assignments. I am also looking forward to changing other things about how I approach proof, based on some of the literature we have been reading.
Here’s how student Lee Ferris described the In-Class Writing Assignments a few months after the course ended, “I never thought I’d say this but the in-class writing activities were my favorite things to do. Proof writing was one of my weaknesses, so these weekly activities helped me to attempt a proof and receive feedback on how I could strengthen my argument and apply it to the next week’s assignment.”
I started out completely avoiding AI, due to environmental and ethical concerns, which I still have. I resented having it imposed on me, often by people whose values are very different from mine. After the fall, I decided I had to use it myself to understand it better, since so many of my students were using it. Sometimes I like it. Just lately I am starting to have the thought that this is actually an exciting time to be teaching – not because I’m excited about AI, but because no one knows what’s going to happen, which is always true, but often we can pretend we know and right now we just can’t. So we have to be present, and being present is required for both learning and good teaching. In reflecting on last semester, I am surprised at how positive I sound, because I often did not feel that way in the moment, but I think the presence of trying new things, engaging with students, and working with faculty who are also trying new things is actually something I feel pretty good about.
Coda: More on Being Present in Class
No Devices for Distraction: In the fall, I grew weary of constantly entering a room where every student was on their phone or laptop, and where conversation before class mostly happened when a group of students had all taken the same test earlier in the day. I’m not one to complain about “kids today,” but I do think that my generation had to figure out how to deal with a lot of awkward situations that students now use their phones to avoid. I suspected that many students were on their phones just to avoid awkwardness, not because of what was on the screen. I also was frustrated during group work at the board, where students would take pictures of the assignment sheet and read it from their phones rather than talking about the problem statements together, and where some would look things up to avoid potentially productive struggle.
In all my classes I instituted a “No Devices for Distraction” policy that started when they entered the room. I was clear that they could stay in the hall if they needed or wanted to be on their phone or laptop before class started (and they could also pop out during class). I did not require them to talk to each other before class; it was fine to review notes, work on a math problem, or otherwise engage individually with something related to the class (one student played with a Rubik’s Cube most days, then did his final project applying course material to solving cubes). If students did want to talk, they could talk about most anything, as building community was an important part of the class. Sometimes I suggested prompts if students looked especially awkward, e.g., “You could ask a neighbor what they did over the long weekend…” and then the classroom immediately started buzzing.
On the first day of class we talked about “Focus, Friction, and Community” and how they related to learning. Before activities at the board, I gave guidelines for device use. Often the only permitted use was for the student designated as the reporter to use their phone to take photos of the boards. I reminded students that they weren’t in a race: a little friction in making sense of the problems was good for learning, as was trying to talk about a definition someone forgot or an unclear concept, rather than looking it up. On other days, we used devices for tasks related to class, such as working from online textbooks or writing in LaTeX.
The policy was a pain to enforce; I had to ask students to put away their phones in virtually every class period I taught the whole semester. However, in the end students were overwhelmingly positive about it. Many talked about how the policy helped them stay engaged and focused in class, as well as helping them make friends and build community. I like the framing that when we are in the class space, we should be present in the class space. In our current context, where so many are actively scheming about how to draw even more of our attention, I think it makes sense for instructors to set some boundaries to make it more possible for students to focus and be together. I hope that a nuanced policy like this one can also help students make more informed choices about when to use their devices and when to set them aside.
