A Baker, a Decorator, and a Wedding Planner Walk into a Classroom
By Lew Ludwig
Baking, Decorating, or Planning: What Role Are Your Students Playing?
Are your students learning to bake the cake? Are they learning to decorate the cake? Or are they acting as wedding planners so they can outsource the cake so they can focus on the other stuff? This analogy, shared by Maha Bali in a recent podcast, sheds light on how students might utilize AI. Are they crafting the fundamental elements themselves, enhancing pre-existing frameworks, or orchestrating larger projects by delegating specific tasks?
From Scratch or Pre-made: How Do Your Students Approach Calculus?
For example, consider the application of this cake analogy to integration in an introductory calculus class. Should students calculate a Riemann sum to determine the area under a curve, akin to baking a cake from scratch, which demands considerable time and understanding? Alternatively, might they simply use the Fundamental Theorem of Calculus to find the area under a function—essentially using pre-existing frameworks as the base cake and then enhancing it to produce a result, similar to decorating a cake? Or are they engaged in an economics application, using integration to compute consumer surplus, focusing on the strategic implications rather than the intricate calculations, akin to a wedding planner who coordinates the event but delegates specific tasks to experts?
Depending on our student population, we may adopt different teaching approaches. For an engineering-focused course that might lead to a subsequent course in numerical analysis, understanding Riemann sums is crucial. For most students, however, learning to apply the Fundamental Theorem of Calculus (FTC) suffices—akin to the cake decorating analogy. Ultimately, our goal is for students to transfer the principles they learn in calculus to other areas, such as economics, similar to how a wedding planner oversees various aspects of an event.
The Real Bake-Off: In-Class vs. Online Performance
While this is all well and good, according to my online practice problems last semester, all of my students were professional bakers—earning 100% on the formative practice I would give them. However, the in-class assessments (the real bake-off?) exposed a different reality: many attempts were underbaked and bland, while others were seriously burnt. This discrepancy highlights how students, adopting a wedding planner approach, outsourced their practice to AI, only to falter when faced with actual testing conditions. However, this issue isn't new. Even before AI, my students weren't exactly professional bakers; rather, the advent of AI has simply intensified their tendency to offload tasks they perceive as busy work—specifically, my online homework.
Revamping the Recipe: A New Approach to Assessment
This semester, I implemented a new approach. The traditional online problem sets were removed, and instead, every Tuesday, students receive a "pre-quiz" assignment consisting of questions similar to those given before AI integration. Students have a week to work on these pre-quizzes. The following Tuesday, class begins with students working in groups to review and correct their pre-quiz answers, facilitated by Socratic questioning from my TA and me. After this collaborative review, the class concludes with a brief individual quiz based on the pre-quiz content.
This approach sets it apart from online exercises by making it apparent to students how directly their grasp of the pre-quiz material impacts their success on the in-class quiz. Additionally, because the pre-quiz is not graded, students are less inclined to rely on AI, promoting more authentic learning.
Leveling the Playing Field: Group Sessions as Equalizers
Previously, I had concerns about the inclusivity, accessibility, and equity of timed assessments. This semester, however, I've found that the group sessions before the quizzes serve as an effective equalizer. During these sessions, more advanced students have their understanding challenged by peers who are still grasping the material, fostering a more collaborative and supportive learning environment. This dynamic not only enhances the learning experience for stronger students but also provides an opportunity for those less advanced to solidify their understanding by engaging with complex ideas. True, my alternative grading colleagues might argue that this approach still heavily leans on extrinsic motivation. However, the real proof is in the pudding—or should I say cake? At least I am not sampling as many stodgy or crumbly cakes.
The Proof is in the Pudding... or the Cake?
In this evolving educational landscape, Maha Bali's cake analogy provides a compelling framework for rethinking our instructional strategies. Historically, we in the math community have often aimed to mold our students into bakers, equipping them with the skills to construct mathematical concepts from the ground up. However, considering that for many of my introductory calculus students, this will be their only math course—a requirement they need to fulfill for graduation—it's crucial to focus on what will truly prepare them for their future careers. Instead of insisting they all become expert bakers, we can empower them to leverage AI tools effectively as decorators who elegantly apply formulas or as wedding planners who strategically manage complex projects. By adjusting our teaching methods to suit the diverse needs of our students better and incorporating the strategic use of AI, we can more effectively prepare them for the varied challenges they will face in their professional lives.
What’s New?
For this edition of 'What’s New,' I want to share a book that, despite my initial reservations due to its provocative title, proved to be a pleasant surprise: “AI Snake Oil: What Artificial Intelligence Can Do, What It Can’t, and How to Tell the Difference.” Authored by Arvind Narayanan and Sayash Kapoor of Princeton, this insightful work offers a well-balanced and thoughtful examination of AI’s capabilities. The authors are particularly hopeful about the potential of generative AI technologies like ChatGPT, while they critically assess and debunk myths about other AI applications. AI Snake Oil is an essential guide for anyone looking to understand the effective use and the often overstated capabilities of AI across various sectors. It also features an accompanying website filled with additional resources to deepen your understanding.
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.