Wednesday, August 26, 2026

AI 4: Experimenting with Potential Ways to Incorporate AI in My Teaching Practice


Rebecca A. Norton, Ph.D

Massachusetts Maritime Academy


This is the fourth 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 2 Changing My Writing Assignments by Debbie Borkovitz, and AI 3 Teaching Calculus III in the Age of AI by Ileana Vasu.


Using AI to help students prepare for class


Several years ago, I started asking students in my Applied Calculus course to prepare for their upcoming classes by “reading” a section in the eBook and answering a “Getting Ready for Class” question. I thought asking them to do some preparation (in addition to their problem sets), would accomplish a couple of things. First, I thought it might make things more equitable for students who had not previously taken Calculus. Second, I hoped that students would learn how to access and use their eBook.

In recent years, as you might suspect, students began to use AI to respond to the questions without ever opening their eBook. I gave students’ zeros and started requiring page and paragraph citations in their answers, but I quickly grew weary of “policing” their work. I still liked the idea of students preparing for class, though, and I was curious to know how to use AI to help students learn. So, I designed an assignment that asked students to paste the “Getting Ready for Class” question into an AI tool of their choice, and then answer some questions about the response that AI provided them. I implemented the new assignment via Blackboard in the Spring 2026 semester, and throughout the semester I made tweaks to the questions to try to get students to read and reflect on the information that AI provided them. Students completed the questions on Blackboard, so it is difficult to share the assignments with you, but below is a fairly typical exchange that a student had with AI when completing one of the assignments. The questions are numbered with the students’ response below each question. I kept the formatting the same as how it appeared in the student’s submission.


Directions: The following question comes from a "Getting Ready for Class" (GRC) assignment in your eBook. Read the GRC question and then complete the questions on the form below. NOTE: It is okay to copy and paste the question into an AI platform, but make sure to also include the designated prompt that is given in question 2.




1. Which AI tool(s) are you using?

chaptgpt


2. Prompt your AI tool to give you an answer to the GRC question without a lot of calculus  jargon. Copy and paste the response it gives you below (include the entire response): 


            \(f(x)=ln(g(x)) \)

            and 

            \(f(x)=e^{g(x)} \)

            are similar because both use the chain rule. In each function, there is an “inside

            function” \(g(x)\), so after differentiating the outside function, you multiply

            by the derivative of the inside function, \(g'(x)\).

            For \(f(x)=ln(g(x))\)

            \(f'(x)=g(x)g'(x)\). For \(f(x)=e^{g(x)}\):

            \(f'(x)=e^{g(x)} \cdot g'(x)\) In both cases, the derivative includes \(g′(x)\), which shows

            that both functions follow the same chain rule process.


3. After reading the AI tool's response, think of a good follow-up question that would help you clarify your understanding of the topic.  Do not use AI's suggested follow-up questions; think of your own follow-up question based on the answer AI provided.  The follow-up question must be directly related to AI's previous response.  Paste the prompt you give AI here:

how come for the ln problem, you have to divide compared to multiply?


4. Paste the AI tool's response to your follow-up question here:

            For logarithms:

            \(d/dx[ln(x)]=1/x\)

            So when the inside is \(g(x)\), the chain rule gives:

            \(\frac{1}{g(x)} \cdot g'(x)\) which is the same as:

            \(\frac{g'(x)}{g(x)}\). That is why you divide.



5. What is one thing that you learned in AI's initial and/or follow-up response(s)?  Be specific, and use your own words.  (Do not copy and paste from the AI tool's response(s).

I learned that the reason you divide is because it's actually 1 over g(x) times the

derivative of g(x) which is the same as dividing.


6. What is one thing that you think AI could have done better to help you understand the topic?

I feel like it could have answered the questions in a shorter, more simple way.

For my last questions when I asked why I divided, there was a long complex

explanation, but when I asked again it gave me it in a simple sentence.


7. OPTIONAL: Did you find any errors in any of the AI tool's responses that you pasted above?  If so, explain what the mistake was.  If Dr. Norton agrees with you, you'll earn an extra point on the next quiz.  If not, type "N/A".

NA




Overall, I think using AI made for a better assignment than I had been giving in

previous semesters. There were still some students who were “gaming” the

assignment and not putting much effort into learning anything by completing it. 

There are others who I think found it helpful.  As a first adventure into using AI

in my classroom, I think it worked fairly well. Here are a few positives I observed:


A) More students were completing the AI assignments than they had been in my

previous classes where I used the original prep assignments.  They seemed more

willing to read the output of an AI model than they were a section of an eBook.

B) AI’s responses do not include body language, tone of voice, or negative words

that may discourage students from asking questions.  Plus, it never tires of

questions or runs out of time.  In that way, AI can serve as a valuable and patient

tutor or study partner, and students in my class seemed to be comfortable

interacting with AI.

C) My students were exposed to different ways to prompt AI, witnessed the results

that followed based on different types of  prompts, and reflected whether AI’s

response was helpful.  “Prompt engineering” is something that I have personally

gotten much better at compared to when I first started using AI; I think my students

may have learned a little about that, too.

D) Finally, on a personal level, I learned more about which AI tools my students

were relying on, which was something I was curious about, and I also saw the

differences in how the different tools answered the same questions.  ChatGPT

was the most popular model among my students, but there were a variety of

different models that students used.  ChatGPT is the most verbose in its responses.


Here are a few negatives:

A) Though AI seems to be fairly reliable in explaining topics related to math, it still

gets things wrong, and sometimes hallucinates.  It seems to have difficulty creating

graphics.  I saw a lot of confusing and inaccurate graphs/diagrams in students’

submissions. Here’s an example:





B) Very few students took me up on the last question to earn extra credit if they

found something wrong with AI’s response.  That worried me because it means

that they were not recognizing when AI was telling them something inappropriate.

C) Certain models, especially ChatGPT, provided “tips” for students about what

they should write for credit.  For example, it would say something like, “If you want,

I can give you a super short one-sentence answer that you can write on a test."  It

was as if the model had been trained on providing students shortcuts instead of

helping them to learn the concepts.


Despite what my students may or may not have learned by completing these

assignments, I learned a great deal by reading the responses, and I grew much

more comfortable with knowing what to expect from AI.  I am debating on whether

I want to use this type of assignment again with my students.  On one hand, it

would be easy to do, because all of the assignments are set up in Blackboard

ready to be used again.  On the other hand, based on some additional experimentation

I did with AI over the summer, I think I have found a more useful way to use AI to

help students prepare.  I write about it in the section below titled “Creating a ‘Study

Buddy’ bot for students to interact with.”


Trying to get AI to evaluate students’ homework assignments


At the start of the Spring 2026 semester, I decided not to use the online homework

system that was associated with the eBook I was using in my Applied Calculus

course.  Based on my own observations and discussions with other professors in

my department, I realized that even though students were completing the

assignments, they were not getting the practice they needed.  It was too easy to

cut and paste homework problems into AI and get the answer for the problems on

the assignment.  I thought that if I asked students to turn in a written assignment on

Blackboard that even if they ended up using AI to complete the problems, they would

at least have to write the work down, and that would be more helpful than just cutting

and pasting answers online.

  

Fresh from the winter break, and not thinking carefully about my time commitments,

I thought that if I used a rubric to grade the homework assignments, I’d be able to

turn them around quickly enough to provide relevant feedback to my students.  As

the semester progressed, however, I got behind in grading them, and found myself

at the bottom of a grading hole.  Since grading is tedious, and it is difficult to motivate

myself to do it, I started experimenting with AI to see if it could help.


I began using an AI platform called BoodleBox because my school had bought a

license for the Spring semester for faculty to experiment with. The platform is

designed for educational settings.  It claims that it somehow provides access to

different AI agents without allowing those agents to collect information about the

interactions that you have with it.  I am skeptical about that part, but I took my

chances and experimented anyway.  I wanted to see if I could teach it how to apply

a rubric to my students’ submissions and provide an appropriate grade.

 

I provided the AI agent with my rubric and an answer key for the relevant problems,

and without any other input,  it did a decent grading job.  It applied the rubric a little

differently than I did, though, so I created a flowchart to guide the AI agent to apply

the rubric in a way that it would arrive at the same score as me.  That took some

effort.  I tweaked the flowchart by doing several grading runs where I compared

the scores I assigned using the rubric versus the scores that AI assigned.  I also

added in some steps based on the feedback that the AI agent gave me so it would provide me with more reliable results.  Here is a link to the flowchart I ended up with.


In general, I was happy with the way AI implemented the flowchart;  I was definitely pleased with how quickly it could apply it and format the output for me.  It turned out, however, that the whole process was not as efficient as I had hoped.  AI often had difficulty with students’ handwriting, or finding all of the problems within a student’s submission, or being unable to read the problems if the student submitted a photograph of poor quality.  In those cases, it would grade the assignments based on what it could read, and then flag it for me to review.  When I looked at those cases, it rarely provided the appropriate grade.  In its defense, it gave me some advice to help improve its ability to score the submissions, but its main suggestion was that I ask students to format their homework in a specific way.  Since the students had already turned in the assignments, I was not able to implement the advice it gave.  Additionally, based on specifications with the BoodleBox platform, I had to upload the students’ work in batches and that really slowed the whole process down.

 

In the end, I don’t think I saved any time in grading my assignments for the Spring 2026 semester.  In fact, I may have spent more time trying to tweak things with my flowchart than I would have if I had just graded the assignments.  It wouldn’t have been as fun, though!  Plus, I’ll be able to use what I designed in the future.  Now that I know what the model needs in order to process the students’ submissions accurately, I can require that students complete their work in the required format.  I will also consider using a homework folder on BoodleBox, which is another suggestion the platform gave to me, because then it could check to see if a student’s submission was acceptable and require the student to resubmit their assignment if the model was unable to read it.  Plus, having the student upload it directly to BoodleBox would keep me from having to transfer the files between Blackboard and BoodleBox, which was the biggest time consumer in getting AI to grade the assignments.

 

Overall, I learned a lot about how to interact with an AI agent in a productive way.  It felt a bit like having a teaching assistant.  As I noted in the previous section, AI never gets tired and it is not possible to hurt its feelings.  So it is perfectly “happy” to make adjustments until you are satisfied with the outcome.  It is important to be explicit in your instructions, though, because it will assume things that may or may not align with your own philosophies.  In coming semesters, I plan to implement the lessons I learned during the Spring 2026 semester and continue to experiment with asking AI to apply rubrics to help grade student assignments.



Creating a “Study Buddy” bot for students to interact with


At the last minute, I was asked to co-teach a summer course called Introduction to Python for Business Data Analysis.  I did not have much time to prepare.  It was not a course I had ever taught before, and it was not a course that my school had offered before, so I didn’t have anyone else’s materials to borrow from.  Plus, it had been a while since I’d really done any programming myself.  So, I knew I was going to have to leave myself lots of planning and thinking time to make sure I was prepared to teach the classes, especially since each summer class was the equivalent of a week during a regular semester.  

I wanted to make assignments that provided students with some feedback, but that I would not have to spend much time looking at or commenting on myself.  I had learned my lesson trying to collect and look over my students’ homework in my Applied Calculus class during the Spring 2026 semester, and I did not want to dig myself into any more grading holes!  So, I tried to design a bot within BoodleBox that specialized in the material that we were focusing on.  I named it “Python Study Buddy”.  You may have to sign up for a BoodleBox account, but if you do, you can try it out here:


https://box.boodle.ai/a/@PythonStudyBuddy


Last I checked, BoodleBox was giving two-month free trials.  If you do call up the bot, the first thing it will ask you is what chapter you want to work on.  Tell it a chapter number between 7-14; those are the chapters in Part II of a book by Lee Vaughn titled Python Tools for Scientists.  Students were required to buy a pdf version of the book.

In between class meetings, students were assigned to interact with the bot.  At the end of the session, students would ask the bot to print out a transcript, and then upload the transcript to Blackboard.  I then reviewed the transcript and assigned a grade based on a rubric.  The rubric included four categories: Topic, Productive Interaction, Demonstrated Learning, and Time-on-Task.  As an aside, I had AI create the initial draft of the rubric based on a description I gave it. 

I considered this use of AI to be a success.  The bot acted as an assistant that condensed the information that I needed to give students the proper grade and allowed me to apply my rubric quickly.  Additionally, at the end of the course, several of the students mentioned how helpful they had found Study Buddy and that they used it as their main study tool because it helped them decipher the information within each chapter in a conversational way.  I will definitely continue to experiment with similar tools in my upcoming classes this fall. 










A3: Teaching Calculus III in the Age of AI

 

Ileana Vasu

Smith College


This is the third 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 2 Changing My Writing Assignments by Debbie Borkovitz, and AI 4 Experimenting with Potential Ways to Incorporate AI into my Teaching Practice by Rebecca A. Norton.


 This year, I made a deliberate choice to redesign parts of my Calculus III course around the reality that AI tools are now part of how students work. Rather than treat that as a problem, I built it into the course intentionally, leaning on two frameworks I keep coming back to and am genuinely grateful for: Tara Yosso's Community Cultural Wealth, which treats students' backgrounds and lived experience as assets rather than gaps to fix, and Francis Su's Mathematics for Human Flourishing, which asks what math is actually for beyond right answers. A colleague and I worked on two projects together this year, and I was genuinely glad to have someone to think this through with. I'll just be discussing one of them here. Here's what came out of that work this year: the parts that felt genuinely useful, promising, or just good, and the parts that reminded me why I love teaching this subject in the first place.

Math isn't neutral, so I do not teach it that way

I believe math has never been the culture-free, purely objective subject it's often presented as, and this year I tended to this belief in the Calculus projects. I built a surface from six parameters (two for each student in a group of three) drawn directly from each student's birthdate. Plug in your birthdays and out comes a genuinely strange equation, and when graphed, an equally strange bumpy little landscape, nothing like the tidy paraboloids in the textbook, and nothing any other group has. Students find critical points, analyze gradient fields, and then name their surface and write a short narrative describing it as a landscape. It's been lovely to watch students light up over a shape that's theirs. A surface built from your own birthday isn't something AI can meaningfully do for you. It doesn't know your surface exists until you build it. Of course, the math was not tidy, so students had to use Mathematica or Matlab, or Python to visualize their surface and its critical points, but they were free to use AI in learning how to use the software as long as their explanations were documented and their learning thorough.

Documenting AI use, instead of policing it

Every project includes a short, required section: what AI tool you used, what you asked it, what it gave you, what you had to fix, and what you learned from this interaction about mathematics, or coding. This one change did more for honesty than any detection software could. Students stopped hiding their AI use and started reflecting on their learning, often with real curiosity. The most common thing they discovered on their own: AI produces confident, plausible-looking code that is sometimes just wrong, and you only catch that if you understand the math well enough to check it. That's was the habit of mind I want them building, and I loved seeing them arrive at it themselves.

Multiple pathways, and room for real strategy

For the vector calculus portion, groups choose two of three options - gradient field analysis, directional derivatives, or flux integrals, based on their own strengths. This wasn't originally designed as an AI response, but it turned out to matter for the same reason: it shifted the emphasis from "did the AI produce the right output" to "did your group make a smart, thoughtful choice about how to approach this." That kind of judgment is much harder to outsource than code is, and it also felt like an honest nod to Yosso's idea of navigational capital, students strategically working with the tools and constraints in front of them, rather than following one prescribed path.

Creative narrative as a window into real understanding.

Every project ends with a short story describing the surface as a landscape: naming it, describing its features, weaving in the actual mathematics. One group named their surface "The Twin Comet Highlands," describing an origin story where  locals had a story that two comets had created the landscape and checked back with geological data to actually figure out whether the story matched reality or not.  Reading things like that has genuinely been one of the joys of my teaching year. It's also turned out to be one of the clearest windows into real understanding I've had in years: hard to fake, and just a pleasure to read like the one below:

Long ago, two comets are said to have grazed this land in the same season, one burying itself deep enough to raise Comet’s Crown, its ejecta pushing the ground up to 5.46 units above the plane, still by far the tallest point for miles. The other struck lighter, near the origin, and left only Whisker Ridge, a modest rise of 0.43 units that locals will still proudly call a mountain if you let them. Between the two impacts runs The Crossroads Pass, sitting at the exact center of the map,elevation zero. Every trade route through the highlands passes through here, because it is the only way across without a serious climb.  A visiting geologist, on hearing this legend, is said to have sighed and pointed out that a real comet strike leaves a crater with the peak rebounding up from inside it, not a lone summit rising out of open ground and that nothing in their surface is quite symmetric enough to have fallen from the sky in one piece anyway. The locals thanked her for her time and kept telling the story the old way….and the story continues

AI as an unexpected equity tool

I was not sure if AI might widen the gap between students who already knew how to code and those who didn't. In practice, it narrowed it somewhat, and that was a genuinely happy surprise. Students with no programming background could get a working starting point instead of staring at a blank file, then actually learn from modifying it. Not a level playing field, but a less tilted one, and a small, practical example of building on what students bring rather than what they lack.

The bigger takeaway

The adaptations that worked shared one thing in common: they made the mathematics personal enough, and the reasoning transparent enough, that AI became a tool students used rather than a shortcut around the point of the assignment. None of this happened by accident. It came from deliberately redesigning around the reality that these tools exist, and from a belief that mathematics was never neutral to begin with. Between the personalization, the storytelling, and paying closer attention to what students actually bring into the room, this was the year I felt calculus held a little more room for human flourishing, AI and all. I'm grateful to have gotten to teach it this way, and grateful, too, for a colleague willing to build alongside me.


AI 2: Changing my Writing Assignments

 

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.



AI 4: Experimenting with Potential Ways to Incorporate AI in My Teaching Practice

Rebecca A. Norton, Ph.D Massachusetts Maritime Academy This is the fourth in a series of four blog posts in response to the call: For many...