By Lew Ludwig
When I first started this column over a year ago, I naively named it "There and Back Again: A Mathematician’s Tale of AI Exploration," a nod to Tolkien that I thought was a clever pun. I expected to explore generative AI and report back, complete with generating fun, Hobbit-esque images in a Shire-like math landscape. How challenging could it be, I wondered?
Thirteen posts later, some did provide this bird’s eye view of my exploration, including how to code with AI, how skilled students can productively interact with AI, and how students might use AI as a tutor instead of just an answer machine. My recent posts have shifted from pure exploration to a more focused dialogue with the MAA community, expressing my concerns about how AI is reshaping our classrooms. I discussed the need to engage with this technology to make informed decisions about when and when not to use it, and a piece on how we should stop blaming our students but instead help guide them along this potentially dangerous path.
Reflecting on the past year, I now see my experience as mirroring Peter Jackson's interpretation of “The Hobbit: An Unexpected Journey.” This unexpected journey took a new turn last week with over 150 attendees at my MAA webinar, "From AI Wary to AI Wise: Becoming Empowered to Make Informed Decisions." The feedback was illuminating; we collected over twenty suggestions for topics to explore in future webinars or through this column. This feedback has been transformative, shifting this column from a one-way communication into a more dynamic and interactive dialogue with the MAA community, enriching our shared exploration of AI.
Given the open-ended nature of these suggestions, I began by organizing them. Not surprisingly, I turned to AI, specifically ChatGPT 4o, the free model from OpenAI, which your students most likely use (holding 60-70% of the market). If you're curious about my process, you can follow my exchange at this link. Although it managed to categorize the topics, the organization was less impressive than I had hoped. Undeterred, I attempted to load the pages of my “There and Back Again” pieces to see if it could suggest relevant past articles. This attempt was an epic fail; half of the recommendations were from Devlin’s Angle, not my posts.
Frustrated, I shifted gears and opened a new ChatGPT window, aiming to use the more powerful “reasoning” model, ChatGPT o1. To my surprise, I was invited to try the “even more powerful” (if you subscribe to the AI hype cycle) ChatGPT 03 min model. You can see this exchange here. This version was notably more effective, adeptly handling the complex task I set out. It even paused to point out inconsistencies in my prompts—some suggestions were missing, and others were duplicated. This level of responsiveness was impressive, but this series of interactions highlighted both the capabilities and the ongoing limitations of AI.
While I aim to address most of your invaluable suggestions, this post will concentrate on three specific areas:
- Evolving Teaching Practices & Preparing Students for an AI-Driven Future
- AI-Enhanced Assignment & Assessment Design
- Empowering Student Engagement with AI & AI-Powered Tutoring
Let's focus on the third topic. In my previous post, "There and Back Again: Of Tails and Tubes," I explored how students in a real analysis course could use AI to deepen their understanding of complex subjects, not just to get answers. This semester, I had hoped to utilize NotebookLM as a tutor for my linear algebra class. I uploaded the OER textbook chapters, the course reading notes, and the practice quizzes, then began interacting with the bot. Unfortunately, it turned out to be just an answer machine—spitting out correct responses with minimal input from me. I pushed it further by asking it to complete the reading notes I had shared. It did so in excessive detail! This attempt was a significant setback; instead of the AI tutor I envisioned, I encountered a chatbot capable of doing the students' work for them—clearly, it was back to the drawing board.
I value the second group of suggestions, as they offer opportunities for me to provide practical examples in my next post. Meanwhile, I outlined several entry-level activities in my recent MAA webinar, starting around the 29th minute. You can access the recording here.
Continuing our unexpected journey, let's address the first group of suggestions: Evolving Teaching Practices & Preparing Students for an AI-Driven Future. This is a crucial area moving forward, but there are no easy answers. As I mentioned in the webinar, strategies that work for me and my students might not work for you. You are the expert; you understand your context, content, and students best. Therefore, you will need to engage with this technology to discover what it can and cannot do and how it might help—or not help—your students.
In a recent AI session for faculty at Denison, a colleague expressed frustration, saying, "I barely know how to use these tools myself; how am I supposed to incorporate them into my classes and teach my students?"
This comment made me reflect. Although I have been using AI for more than two years, I seldom utilize it in the classroom—I'm simply not ready. If you share my colleague’s frustration, give yourself a moment of grace. Take a deep breath! You do not need to master generative AI overnight. You can't teach what you're still learning yourself. Tackle AI at your own pace, ensuring it doesn't overshadow your expertise or dictate what is best for you and your students.
But suppose you've tackled all that and are eager to go deeper and exchange ideas with others? Fantastic! Following a successful Special Session on Generative AI for Improving Instructional Productivity at the Joint Math Meetings, Feryal Alayont, Rachael Lund, Bevin Maultsby, and I are developing a virtual community of practice for college and university math educators. This community will focus on using generative AI to enhance teaching, learning, and student engagement. Keep an eye out for this group on MAA Connect.
As we continue this unexpected journey, it’s clear that the path is neither straightforward nor predictable. Yet, the promise and challenges of AI in education compel us to forge ahead, equipped with the lessons learned and insights gained. Our shared experiences in this community have not only deepened our understanding but also broadened our perspectives. I invite each of you to join this ongoing dialogue, contribute your unique experiences, and help shape a future where AI enhances our teaching and enriches our students' learning. Together, let's explore the new territories AI offers with curiosity, caution, and an open mind.
What’s New
With all the advancements in generative AI models, it's challenging to stay updated. Ethan Mollick’s recent blog post, "Which AI to Use Now: An Updated Opinionated Guide," provides a comprehensive overview as of late January 2025. It includes a discussion about the new DeepSeek model from China.
For a continuously updated summary of the available tools and their applications, José Bowen’s AI Ecosystem website is an excellent, if lengthy, resource. It covers the latest generative AI models and API (Application Interface Programs) — user-friendly interfaces that utilize large language models.
Further down on his webpage, José also offers some sample prompts you can try to see what these “frontier” models can do. As always, remember that the free models are not as robust as their paid counterparts. Additionally, with many "free products," you often become the "product" yourself, as the system collects data and behavior patterns from you.
Happy exploring!
Lew Ludwig is a professor of mathematics and the Director of the Center for Learning and Teaching at Denison University. An active member of the MAA, he recently served on the project team for the MAA Instructional Practices Guide and was the creator and senior editor of the MAA’s former Teaching Tidbits blog.