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Minding Machines is a podcast dedicated to fostering thoughtful, open dialogue about artificial intelligence. The show brings together educators, students, and practitioners to explore how these tools are changing the way we teach, work, and think. Our conversations focus on practical experiences, emerging questions, and diverse perspectives across disciplines rather than establishing rigid "right or wrong" answers or settling debates about AI.
Minding Machines is an independent podcast produced at Lawrence University, Appleton, Wisconsin. The views expressed are those of the participants and do not represent the university.
Background music - Relaxing Light Background (short version) by AudioCoffee (https://freesound.org/s/725615/)
[00:00:00] (music)
[00:00:02] Abhishek: Hello and welcome to another episode of Minding Machines, a podcast dedicated to fostering thoughtful, open dialogue about artificial intelligence. The show brings together educators, students, and practitioners to explore how these tools are changing the way we teach, work, and think. Our conversations focus on practical experiences, emerging questions, and diverse perspectives across disciplines, rather than establishing rigid right or wrong answers or settling debates about AI. Thank you for listening. I am your host, Abhishek Chakraborty, and I am an associate professor of statistics at Lawrence University.
[00:00:43] Abhishek: Our guest today is Scott Corry. Welcome, Scott. Thank you for your time. It's great to have you in the show. Before we begin, could you please tell us a little bit about yourself, your role on campus, and the focus of your work.
[00:00:58] Scott: Sure. Thanks, Abhishek. I'm the Patricia Hamar Boldt Professor of Liberal Studies and Professor of Mathematics here at Lawrence. I'm the chair of the Department of Mathematics, Statistics, and Computer Science. I myself am a mathematician, so I teach mathematics of all types here.
[00:01:18] Scott: And my research tends to focus on aspects of symmetry, which is a really nice aesthetic principle, but also turns out to be really important for all sorts of mathematics and physics. And beyond that, I like to read all sorts of things, including literature, philosophy, history, economics, science.
[00:01:40] Abhishek: All right, great. Thank you, Scott. Now you will have to face our icebreaker question. Okay,
[00:01:45] Scott: Okay.
[00:01:46] Abhishek: Scott, what is one thing you would happily automate away forever and one thing you would never automate, no matter how good technology gets?
[00:01:56] Scott: Hmm. Okay. Well, I think I'm lucky that my life and my job doesn't involve a lot of routine tasks that I mind doing. So the automation part, even though, you know, I think all of us thinking about AI are constantly thinking about automation, it's not actually the way I sort of fundamentally think about how it's impacting me.
[00:02:18] Scott: But maybe one thing, I only have to do this once a year. But as you know, Abhishek, once a year we all get in the room as faculty in this department, and we have to decide what courses and what times and what rooms we want to teach for the next year. And after that, I take a big spreadsheet that usually is a printout with all sorts of handwritten comments on it, and I have to enter it into one of Lawrence's systems that's kind of clunky and it's very error prone, and it's very hard to tell if you've made an error. And if you do make an error, it's very hard to fix the error. You have to redo the whole thing. And so if I could automate that, which I'm sure I could, I think maybe I'll take a stab at that next year.
[00:02:57] Abhishek: All right, cool. That sounds great. Yeah. So I'm getting the feeling anything tedious and time consuming or maybe error prone is probably something you would like to.
[00:03:10] Scott: Sure. And especially, you know, some things can be kind of tedious, but there is a benefit to doing them. You know, you feel that even though maybe looking forward to it, you think, boy, that's going to be tedious. But actually when you do it, you feel that you're getting some value from it. But I think that's the thing that I'm not getting a lot of value from, even though it needs to be done.
[00:03:28] Abhishek: I see, I see. Well, let's move on to our actual discussion. Scott, one of the reasons I'm very excited to have you on the show is I've always wanted to ask this question to a mathematician. My question is, so, the advent of AI has been very commonly compared to the rise of calculators that impacted math education in the past. I wanted to know your thoughts on that.
[00:03:59] Abhishek: Is that a fair comparison? Does that comparison break somewhere? You know, you are somebody who teaches mathematics, who has taught mathematics for a long time. You know, you've come through this period of controversy, let's say, and now you are still teaching mathematics in the age of AI. So what do you think about that?
[00:04:20] Scott: Yeah, that's a great question. So, you know, I think in a, at a first glance, there's an obvious similarity there. Right. So there was a time before calculators or computers where to do tasks like multiplying two large numbers together, you really had to do them by hand. And now, of course, we don't do that. And that's a good thing because multiplying two large numbers together is very error prone. And so that's a good thing. And now there are what AI is doing, LLMs are quickly becoming able to perform all sorts of cognitive tasks that go far beyond multiplying numbers together or manipulating numbers.
[00:05:09] Scott: And so there's a way in which that's, those are tasks now that previously had to be done by hand or by humans that don't need to be anymore. But I think the, maybe the more useful way for me to think about this is the potential harm that comes to the educational process by both the calculator and the AI.
[00:05:32] Scott: So for the calculator, right, I think that it's undoubtedly helpful for students or for anyone to be able to multiply two large numbers together. But part of the problem is that the calculator doesn't help you understand when you're working with, in some context, with some problem of when you would want to multiply two large numbers together or two small numbers together, rather than adding them or manipulating them in some other way. And those two things don't need to be intentioned by any means. But I do think we've seen that the advent of calculators in early education, while certainly helping in some ways, has also made it so that some of those fundamental conceptual things about how numbers work, how they behave, how to think about them, how to use them.
[00:06:26] Scott: Many students haven't developed those ideas in a rich way and are overly reliant on the calculator. And we see that a lot as we, as we teach people mathematics at the beginning. And I think that one of my biggest worries about AI for the educational process is exactly the same thing. Right. These tools are extremely powerful. They allow us to do things that, that we previously thought maybe couldn't be done by a machine. Yet they risk the, they risk obstructing the development of some really foundational understanding and sort of a cognitive surrender. I think that people are using this term to, to the AIs that can do things and perhaps give the illusion of understanding.
[00:07:12] Abhishek: All right, that's. That's great to know. I just wanted to follow up recently. As you mentioned, there is a lot of talk about AI with the cognitive offloading piece, and it happened with calculators too, when they were coming up, and probably it still does. I was reading an article and it was very interesting to me that the author mentioned that there are two types of cognitive offloading, some things that you would actually want to offload. For example, when we drive, I guess pretty much everyone uses Google Maps. It's probably risky to use a physical set of maps when you're driving and Google Maps makes it easier. So that was the first time I came across that viewpoint. But of course, as you mentioned, there are things that we should not offload to any, any tool, no matter, or at least we should get the concept. We should understand the context before we offload. So in terms of calculators and AI, do you think that once students or once. If an expert uses them, then that's probably a better use of them than, you know, when you're entering into the field of mathematics?
[00:08:36] Scott: Yeah, I think so. I think we need to ask, when we choose to use, say, a calculator or an AI system to accomplish some task, are we doing it in order to have accomplished that task, so that that task is now completed. In the driving example, most of us, certainly when I drive, I don't particularly like driving for its own sake. I'm usually trying to get somewhere. And so for me, if I have the Google Maps on, even though that means I'm thinking maybe less about the region I'm driving through, which may be a loss, like it will get me there in a way that I can be confident in.
[00:09:22] Scott: And that is the goal I'm trying to accomplish. Sometimes, you know, say with a mathematical problem, say I'm about to teach a multivariable calculus course. We're going to be, among other things, computing integrals in that course, sometimes doing mathematics, doing engineering applications, doing all sorts of applied or theoretical work. You need to compute an integral because you are going to use that integral for some purpose. And at that point it may be very reasonable to use an AI system or a computational system to compute that integral.
[00:10:00] Scott: But if the purpose of what we're doing, say in a class is to develop familiarity with the idea of an integral, to understand what it is, how it behaves, and as a foundation for learning other things, then to just compute the integral or to have a machine compute the integral completely obscures that. Right. And so it's not just the type of task, I think it's the purpose for which you, as the user or non user of the AI or calculator is performing the task.
[00:10:32] Abhishek: Yeah, I see that point. And for our students, or for anybody else who is coming through the education phase, if that gap in concept remains, then it's a big challenge going down the line. It's very difficult to come back and recover something when you were supposed to be doing it like five years ago.
[00:10:50] Scott: Right.
[00:10:52] Abhishek: I'm also very excited to ask you this next question, which is more on the research side of things. So recently AI and math have been in the news together, I would like to believe for good reasons. AI has recently solved some age old math problems or proved some conjectures that have existed for decades. And these questions, you know, they were difficult and of course that's why they existed for decades. So I, before I ask you anything, I want to know your thoughts on that. Like what do you think from the, from the perspective of a mathematician and also from the perspective of a math educator.
[00:11:46] Scott: Yeah, well, this is an exciting time from my point of view. These advances, these results have been truly stunning. And so maybe one thing I'll say is I think many of us in the mathematical community are just trying to keep up with the news, and it's fascinating and a little bit unsettling for sure. But what I would say that, you know, one thing to mention just as an observation, is that many of the breakthroughs, certainly the most prominent ones, the ones that are getting all the news, are actually the construction of counter examples to lots of very long standing conjectures. So this is a situation where there may be, for a century, for half a century, for longer, there's been a, a belief, a conjecture that a certain mathematical statement is true.
[00:12:39] Scott: And these things are often established by leading figures in mathematics for good reason, right? They have reason, whether it's sort of the collection of lots of data, sort of examples where it does hold true. Very often there are aesthetic reasons or heuristic reasons to think that this might be true. But we don't have the proof, which is the gold standard in mathematics. And many people spend, whole fields of mathematics come up around developing techniques to try to investigate these claims.
[00:13:11] Scott: And what's happened recently is that some of these things, that many people, without knowing whether they were true or false, but most people tended to believe they were true, LLMs have now come up with, with examples showing that some of these things are in fact not true. And so I think that's an interesting thing to think about. And I think in, in hindsight it's maybe not a surprise that these AI systems have an advantage here in the sense that to come up with counter examples it would really help to have a vast knowledge of the entire literature, which the LLMs do in a way that no human can have read all the papers to know all lemmas and all the approaches. And second, they have a real persistence. They don't get tired, they don't get bored, and they don't particularly care about spending a long time on their career going down a path that might not be the path to actually try to disprove something rather than prove it, which is a common technique in mathematics, is to spend some time investigating maybe the thing you're proving is not true.
[00:14:17] Scott: So people do this, but it takes a lot of energy and time to do that, whereas the LLMs have a lot of capacity for this. So I think that this, this has been interesting to see that the exam that, the construction of these, these examples.
[00:14:35] Abhishek: All right, that's, that's, that's a good viewpoint from what, what you're thinking. Oftentimes when things like these happen, like if, if a machine solves an age old conjecture or gives a counterexample, the question about creativity comes up, the question about novelty comes up. And if whenever it has come up to me, I ask a follow up question, what does it mean by, what does it mean by creativity? Like what does it mean for that person? So from that perspective, and also from the perspective if I, if I think of mathematics as an art, what is your view on if somebody says the LLMs are becoming creative?
[00:15:26] Abhishek: And also from a practical standpoint, are these solutions, counterexamples, proofs, are these actually novel? Or could they be just attributed to possessing a vast amount of, let's say, knowledge?
[00:15:46] Scott: These are good questions and they're tricky to think about. I mean, for me, I would say that certainly the word novelty can be applied in the sense that these. We have seen the LLMs present new novel examples and approaches to things. And also I think that what almost always what counts as novel, even in human production, is the new synthesis of prior things, the new combinations of things that have come before. This is why it's so important in mathematics, but in everything, to read old things, to read old papers, to read old books, to read old novels, to read old philosophy, to look at old sculpture.
[00:16:28] Abhishek: And that's why PhD takes time.
[00:16:30] Scott: Right. It takes time. And you know, just as a person, you know, whether you have a PhD or not, I would say to remember that there is a lot of things that have been thought about and there's there those things are continuing or continue to be worth thinking about because they do inform what we do. And the more you can know about what came before, you can combine in interesting ways. So I actually think that a lot of what novelty is in going back to mathematics, certainly in mathematics, is combining some approaches or some examples, maybe from two different fields or even in the same field, two different sub areas or problems to make progress on something. And I think, as I was mentioning before, I think the LLMs have a certain advantage in this because of how much of the literature they have available to them.
[00:17:22] Scott: Creativity, I think, is a trickier thing because I think that when we use the word creative, that is very much something we tend to apply only to humans. And so it is difficult there therefore for us to think about whether we want to extend that to a machine. And I think we may see over time a certain kind of narrowing of what we're willing to call creative as a way of protecting the human. I think I may be less interested than many people of drawing a firm line between what is creative and what is derivative, because I think that so much creativity does involve the creative novel use of prior things.
[00:18:04] Abhishek: I see. And what do you think is the future of mathematics research. Now that the LLMs are doing these things, is it time for us to really assess what it means to be human in, in a research field? Like what do we do now? If this is, this is being done by, let's say, machines, which they are, where do we come in?
[00:18:35] Scott: That's a great question. Well, I just want to lead by saying I'm a real optimist about this in the sense that I don't think that mathematics is in any way over for humans. And this goes, you know, I think for all fields. Right now mathematics is kind of on the, the bleeding edge of some of these results because it's a context where claims can be verified sharply and distinctively. But what I would say is that maybe it's worth thinking about what mathematics is.
[00:19:08] Scott: I think in the popular imagination there's maybe two broad ways that people think about mathematics. One is maybe in some ways the most common is that it's a set of tools for supporting progress in science and technology and engineering and in other technical subjects. And that's certainly true. And on the other, there's this sort of part of mathematics that is culturally valued and sometimes shows up in the newspapers as these really hard abstract problems that are solved by people and those people kind of gain the glory of solving them. They win the Fields Medal, they and that and that.
[00:19:56] Scott: Those are kind of the two things. There's this very practical aspect of mathematics some, most people think about a lot. But then there's also this very intellectual glory seeking part of problem solving. But actually for most mathematicians, the work is in, the discipline is somewhere in the middle.
[00:20:13] Scott: Mathematics is a subject filled with rich ideas that have strong interconnections. It is filled with esthetic delights and it is a extremely useful and powerful way to train the mind. So we're now at a place where, yes, the AI, in collaboration with human mathematicians, seems to be able to produce new mathematics and to make progress in mathematics at an increasingly fast rate. But I think if anything, this will lead to more need for humans to think about the meaning of these results, to see what's really going on and to explore the interconnections. There's more for us to understand rather than less. And I think that sort of phrasing it as well. Now the LLMs are stealing all the glory from these problems is the wrong way to think about what's happening in mathematics.
[00:21:10] Abhishek: I see. And we can, if we come with the belief that the LLMs are machines, then we can leverage their use of having possessing a huge amount of knowledge and literally at our fingertips.
[00:21:24] Abhishek: I want to change direction and I wanted to ask you questions from your profession as an educator, as a math educator. What challenges have you seen with the advent of AI in math education? What challenges do you see in your own classrooms? What have you noticed in your colleagues' classrooms as well, from discussions?
[00:21:54] Scott: Yeah, this is a great question. I think it's, it's very, certainly very live for me. I have to say that six months ago I was not particularly interested in AI. I hadn't personally looked too much into it. I kind of was thinking of it mainly as a new way for students maybe to, for lack of a better word, cheat.
[00:22:18] Scott: Right. To sort of, instead of doing the work themselves, writing their problem set, writing their paper, they could have an LLM, produce something. And my knee jerk reaction at the time was largely we should, we should try to encourage them not to do that and figure out how to forestall that. As I mentioned earlier, I'm still very worried about that sort of cognitive surrender. But I've now spent the last six months trying to learn something about AI and starting to use it for various things myself.
[00:22:49] Scott: And I think now my experience last year with students and going into this year we will see is that more and more students are using LLMs. And I think many of them are not using them to cheat, or at least that is not their intention in the sense that more like I would say last year was the first year that I routinely had students come to my office hours and say quite forthrightly and openly, oh, I was talking to Gemini or Claude or Chat about this. And very often I thought that was a reasonable use in the sense they didn't seem, at least in that moment, to be using it instead of doing their problem themselves. But they were using it as another tool to understand and sometimes prompted the fact that they didn't understand something that Gemini had told them, then allowed us a conversation.
[00:23:43] Scott: And my approach going into this year is to try to take that seriously and realize that our students are going to be all over the place. I think we are definitely going to have students who have no interest in using an LLM at all. And we have others who will maybe overuse them and use them for everything. Right now we probably have students everywhere in the middle who are interested in it. My faith is that largely students here at Lawrence are here for the right reason. They do want to get a good education.
[00:24:12] Abhishek: I do believe that.
[00:24:13] Scott: Yeah. And so it is, I take it as my primary job to create a structure in which that desire can be fulfilled. And I think that that's, as educators, that's actually maybe the most important part of our job. Even more than being an expert in certain areas of mathematics and being skilled, I think what we're really here for is to create a structure that just doesn't exist out there in the wild that can get the best work out of a student.
[00:24:39] Scott: And so that. That means some real rethinking of the way to approach AI. And so I'm literally, right now, we have a week until classes, a little less than a week, I'm thinking about how to talk to my students about inappropriate and appropriate uses of AI and to try to make kind of a structure where I basically say, I know some of you will be using this, and if you are going to, here are some models for how to use it in a way that doesn't obstruct your learning, but actually can enhance it.
[00:25:08] Scott: Because I think that going back to the calculator question, a thing a calculator can't do, it can multiply large numbers for you, but it can't really help you with that phase of, why am I multiplying these together? But actually, the LLMs can not only perform a lot of reason through a lot of mathematical material problems, but can also serve as a good interlocutor for understanding the choices. Right. And. But. But they have to be used that way. Right? And they have to be. They can make mistakes, of course. And so.
[00:25:43] Abhishek: But that's why. That's why you need a human to realize what the mistakes are and whether we should be even doing or where we should be using the LLM. Right.
[00:25:52] Scott: That's right. Yeah.
[00:25:54] Abhishek: Sorry to interrupt.
[00:25:54] Scott: No, no. And so I think, you know, the question of how to deploy that in the classroom to help students both realize that, yes, this may be a tool that they want to explore using and how to use that so that it heightens their intellectual and learning experience rather than detracting from it. I think that is certainly possible. And I think that, you know, in the past six months, using it for my own intellectual exploration, often outside of mathematics, it clearly can do that. It clearly can be a very powerful way of heightening your intellectual experience, but it does require a certain type of use, and it has to rest on some prior understanding of what you're trying to do. And so using it as kind of a ladder to progress on, I think is something really exciting, but something that all of us here at Lawrence, and I'm sure everywhere else in the world are trying to figure out.
[00:26:48] Abhishek: I do want to digress a little bit and come back to something that you mentioned. And I think the reason why I want to come back to this. I hope that some of our listeners will find it helpful. As you were talking about your experiences of AI in the classroom, you mentioned that six or eight months back you were not really paying attention.
[00:27:14] Abhishek: I want to know if you could tell our listeners, I want to know what did you do? Like, what things did you try out? Was it just. And what was your path towards learning a little bit about how AI works and then thinking about how to incorporate it into our classrooms? I think some of our listeners will definitely benefit and hopefully be encouraged if you can mention some of the examples from your own personal journey with AI.
[00:27:45] Scott: Sure. So I have not to say we'll sort of see how, what we do. So honestly, what, what brought. The first time I systematically used AI for anything that wasn't kind of a lark was in last winter term, I was teaching a course called Math 103: Preparation for Calculus, which I taught many times. And one thing I do in that course, and especially I wanted to, to redo that time I was teaching the course, was to construct worksheets for every day that students would work on in class so that they, you know, the class period was the students had read some material coming in. I would give some amount of a short presentation, lecture, discussion, and then, you know, students would be let loose to work through some relevant problems. So every day a worksheet needed to be made and constructed. And this is the thing, sort of thing that we've been doing for many, many, many years. Usually the way you do this is some combination in the past of writing down problems out of your own head and then seeing how they worked out. Often those are bad problems. They don't work right. They're too complicated. The answer is messier than you want. So you fix them.
[00:28:59] Scott: Or going to textbooks and copying various problems from textbooks and selecting them, or finding materials that maybe a colleague has used and adapting from those. And so it occurred to me, well, maybe this is a good use case. I never really used to use something like Claude to try to construct these. And so I did. I started a workflow where I would have Claude propose, you know, construct a simple worksheet based on topics I gave it.
[00:29:26] Scott: And I started to learn that Claude is very good at doing this. Right. And that was important for me. You know, I would get something from Claude and then my next step that I would do is I would do the worksheet and I would eliminate problems that I didn't like and I would change them. And so it was by no means a sort of just an automation.
[00:29:44] Scott: Right. It was. Here's a draft that kind of got rid of some of the work of going to various books, looking at other sources, making up things off the top of my head, to having very quickly a nice packet of material that I then cut down and changed to have good materials for the class. And what I can say is that that workflow was much more efficient and led to better products than I necessarily would have made because of the time savings and because of the sort of effort I could spend more of my mental effort on actually curating the problems and seeing. Where do I want this worksheet to start? Where do I want it to end? What do I think about the timing? And so I think I can say without a doubt that I taught that class better than I ever have because of this somewhat light use, but substantial use of AI to help me construct a certain type of material. So that was my first, first use of AI and I really didn't know anything about it, except with this idea that maybe this would be a way for me to start to explore whether this is a useful technology for me or not.
[00:30:48] Abhishek: Yeah, that's a great example. And you were supervising the entire process all throughout. So even if the AI did make any mistakes
[00:30:59] Scott: which it did, but I caught it, right?
[00:31:01] Abhishek: Absolutely, yes, yes. And the next thing I wanted to talk about is you said of having. You were thinking, or you might have done previously as well, of having, like, open communication with your students. Right. I think, I think that is really valuable. And it doesn't necessarily need to be about AI. It should be about everything that you do in your class. Because I see the syllabus as sort of an agreement, as a contract between you and the students. And it's good to be open from, especially from the instructor side of things.
[00:31:35] Abhishek: When you mentioned about the syllabus, I wanted to ask you. I have heard about instructors having a syllabus policy on AI and typically they would denote it by colors. Red, yellow, green, which is full use, yellow, which is moderate use, red, absolutely no use. Have you used that kind of strategy for, for any of your courses?
[00:32:03] Scott: So I haven't used the color coding strategy until this year. So all through last year, all the courses I taught, I still had a blanket policy in my statement saying just, you know, for any work you turn in in this class, you cannot use AI for. And I explained why, you know, that I thought that again, that these assignments are designed to build really foundational skills and that at the time I thought using. I don't see how using AI can be compatible with that really. Although I left open the idea that, you know, like as I said, you might chat with a large language model about the course concepts or something, and I saw that students were doing that.
[00:32:47] Scott: You know, I think that, you know, I'm not naive. I think that certainly over the past year I saw that some of the work that I was spending time grading, maybe a lot of the work was in fact pretty produced or at least substantially enhanced by a LLM. Right. I can just tell. I've been grading papers for 20 years and suddenly a much higher percentage were written in a way the beginning students of mathematics don't write mathematics.
[00:33:13] Scott: And this didn't necessarily change the performance on exams and quizzes, say. So you start to see sort of a divergence between the work and the effort you're putting in to provide feedback. And so this is something I've. I'm thinking a lot about as I go into this year and I know many colleagues are as well. And my current approach as I go into this is to start to think about a system where, first of all, traditional work, homework, writing things is still really important, but the amount of the actual grade that will be worth will be less, because I think I just want to be open about the fact that there are many ways that this is necessary practice. There are many ways to get feedback on that work, which is really important and I hope to sort of promote various ideas and have students select and encourage what they want. Attendance at office hours, I think is one of the most high impact ways you can get feedback on a work. Right? You write a problem, you're not sure if it's right, you think it was right, it wasn't right, you're confident it was right, no matter what.
[00:34:16] Scott: Going to talk to someone, your instructor about your thoughts about that are great. Going to talk to peer tutors is great. But also this is the opportunity I'm going to try to be open with my students about is that if students are using LLMs, which I think many of them will be to help write or completely write their solutions, they should at least know how to do that well in a way that the LLMs can actually scaffold that learning rather than completely obstruct it. And, and so I'm literally this week thinking about how to make that an option again. The amount of course credit that will be obtained from that is very low.
[00:34:55] Scott: Right. And so everything will be around using this opportunity of writing solutions as a way of enhancing the learning that will then be evaluated in other ways where the AIs won't be available. But I'm kind of flipping the, I'm trying to flip the conversation from one of, I've set the rules here and you just need to either not use it or use it, or use it a little bit to sort of talk with students about how they are tempted to use it and to make a course structure that allows for students who don't want to touch AI at all, to students who do want to learn to use it in powerful ways to enhance their learning.
[00:35:31] Abhishek: And I can add to that. I sometimes use analogies from sports. For example, you mentioned practice problems. So I was, I keep telling my students that, you know, practice is important, obviously it's important, but you are mostly assessed on how you perform on match days. You can be great at practice games, but if you don't perform well for some reason, for whatever reason on match day, then you're not the greatest player, right. So I see that point.
[00:36:05] Abhishek: I wanted to know, because you teach a wide range of courses from the intro level to, you know, we have upper level courses, how are you adjusting your AI policies or how, how are you thinking differently? Or are you actually thinking differently for these courses? Because a lot of our intro students need to take those courses. But of course the, the people that take the upper level courses are taking it based on their own interests. Right? They're, they're probably math majors. So how are you adapting your AI strategies? And I, I was also curious to know, do you see any difference in student perceptions of AI in the intro level versus the advanced level?
[00:37:04] Scott: I think I'm going to learn a lot this year on this question. And so for instance, right now, the fall that I'm going into, starting in a week, as I said, I'm teaching multivariable calculus, which is a 100 level course. And I sort of started to describe there some of the things I'm thinking about. I am also teaching a very advanced course for upper level students, our topology course. And as you said, that's a different audience or at least an audience at a different stage of their education.
[00:37:36] Scott: And I think there the stakes are different and the motivations are different. One thing I'm going to do for sure is to spend time at the beginning talking to those students about how they're using AI, how they want to use AI, and what their goals are for the course. One thing I've thought about, and this is still very much in progress, is that in a subject like topology, where it's a, it's a beautiful subject, it's an important subject.
[00:38:04] Scott: It's a subject that has a sort of core in a course, but then it goes in many, many, many different directions that become more and more advanced. And seems to me a good use potentially of an LLM for students in such a course is to try to commit to a workflow that doesn't really use LLMs except in a way that might sort of talking to you in the same way you might talk in office hours to someone, but to practice those skills of fundamental problem solving for the core course material, but then to use LLMs to sort of go well beyond the course material and start to learn about more advanced things once you have, or as you build that foundation. I don't know exactly how to structure this, and I think this is something that I want to talk to my students about. But just as I've always recommended to my students, you know, this is a bit of a tangent, but in mathematics, I think I've often found that the typical student, even the typical very strong student, tends to think, well, you know, this material, I'm studying this course, that's the material. And it's not that common to see students then reading a second book in the subject at the same time, or in the summer afterwards, or extending.
[00:39:23] Scott: Whereas I think that that isn't so true. You say, take an English major who takes an advanced course in a certain type of fiction. It's likely, I would think, that they would then be inspired to read lots of other novels in that area. Maybe that's my imagination, but I've always encouraged my students. If you're serious about learning mathematics, just like any other intellectual pursuit, you should be excited about this and you should seek out other things to read and to ask about that go beyond the course material, either during the course or after the course. And I think that a powerful use of LLMs is to use them in this way to explore further intellectual developments using what you are learning as a springboard. So I'm hoping to kind of model that, which is, again, how I'm finding value in it in my own life.
[00:40:08] Abhishek: Great. I like this perspective. I've heard a lot of Instructors say that AI or LLMs have given us the opportunity to demand more of our students and to go even beyond our courses. And I like that perspective.
[00:40:26] Abhishek: I know we are short on time. I definitely think we have to have you back. But for this episode, I wanted to ask you a couple of things that has been on my mind. And this goes back to you teaching intro classrooms, intro math classrooms. We get a lot of students who have math phobia who probably would skip the course if they could. I just want to know your first viewpoint that comes straight to your mind. Do you think AI could be helpful in alleviating math phobia or building necessary support structures for these kind of students?
[00:41:16] Scott: That is an interesting question. You know, I think. I don't know. I think. I mean, I guess I hope it can. Right? I hope it can. And I think that, you know, what do I think help such students? I don't know. It's complicated.
[00:41:28] Scott: I think, you know, math phobia, meth anxiety. The cultural space of mathematics is something that I think is valued in some ways, but is a subject of terror for many, many people. I think it's a complicated psychological thing that people are experiencing. So I don't pretend to know exactly how to combat it, but in my own life it's been to sort of be cheerful and enthusiastic about mathematics and hopefully a compelling person to hang out with and talk about mathematics and hopefully make people feel like that perhaps doing mathematics can be a different sort of experience than possibly some negative experiences they've had in the past. To the degree that LLMs, talking with, using LLMs can support that, to sort of take away some of the mystery or to heighten the mystery, actually to make it seem more interesting than you, or to reveal that it is more interesting than you thought in the past, or to reveal a certain kind of simplicity that maybe the explanation of an LLM, if prompted correctly, could help someone.
[00:42:27] Scott: Maybe the context of sitting with an LLM, even though that is kind of a not human thing, but maybe some anxiety comes from the social space of classrooms. Maybe these things could be helpful. I think that it is probably highly dependent on the, the particular person, but I have hope that perhaps these things could be used.
[00:42:49] Abhishek: Well and we could discuss about this more when we get together again.
[00:42:53] Scott: Sure, I'd be happy to come back.
[00:42:55] Abhishek: What would you suggest to (a) our colleagues in a liberal arts landscape? And I'm coming from the assumption that AI is here to stay and it will get better, not, not worse. What will be your suggestions to our colleagues? And I know you have already provided one example from your own personal journey with AI. And what would be your suggestions to upcoming students about AI and how to, how to figure that entire landscape when it comes to education?
[00:43:37] Scott: Yeah, so the story I told about my first real use of AI was. I told it because it was my first, but actually it sort of, although it wasn't pure automation, it did have this flavor of sort of a task that I made somewhat more efficient for myself and therefore I think a better outcome. But that's actually not the way that I'm finding the most value in AI. So what I would maybe say to colleagues, of which I have many who are skeptical, I think for good reason of AI who are resistant possibly to AI, who are scared about AI, and similarly for students, maybe even more so as young people coming up in a world that is rapidly changing.
[00:44:19] Scott: I would not try to convince them of any particular position on AI. But what I would say is that I agree it is here, it is improving, it will affect us, it's going to affect all of us. So I recommend that people start exploring in whatever way they think, like how it could be useful to them and not necessarily because they can automate something that they find tedious. But I actually think its biggest use for me is heightening intellectual experience. I think it really can do that. So I would recommend for people, rather than thinking about, you know, doing their homework for them or writing their lecture for them, or making their powerPoint for them, all these things undoubtedly it can do, and there are dangers there.
[00:45:05] Scott: But think of something that you've always wanted to know more about. Think of a novel that you've always wanted to read but found to be a little bit intimidating and you're not sure you have the background for. Think of a collection of poetry you'd like to read. Think of a period of history that you'd like to know more about. An art style that you wish that you knew something about.
[00:45:27] Scott: Anything. It can literally be anything as long as you care about it. And ask an LLM advice for how to get started thinking about that thing in a scaffolded way. Explain to the AI who you are and what your background is and what you're interested in and the types of things that you would like to know. And ask for sort of a high level suggestion on how to approach this subject and then specific recommendations with sources and maybe a workflow, depending on what it is, of how to scaffold next steps.
[00:46:02] Scott: I think that people who haven't played around with AI will be impressed with what they get back and then take it from there. Right? You don't have to follow up on that plan, but I think the people who use it in such a way may find that a whole world of intellectual riches that is always there, right? You can go look at anything you want already, there are books. But these systems can very powerfully tailor recommendations to you.
[00:46:31] Scott: And you don't just have to take them at face value. You can end up in a back and forth, you can push them on some of the recommendations and they will change. And I've done this many times with various things. And what I would say is one of the one most pleasing things is first of all, it's allowed me access to a variety of things that, that I have struggled with in the past. And second of all, it has often led me to dig deeper into traditional sources like the Lawrence University library than I have in years.
[00:46:57] Scott: Right. I'm in there recently checked out a book on Florentine Renaissance politics for something I was doing and another that I had to track down a PhD dissertation that was out of print from the 1960s that I got through interlibrary loan. These were things I discovered and were recommended through an LLM that I was working on at different intellectual project. And so it doesn't have to be sort of an abandonment of things that many of us value like libraries and books. I'm actually reading more than I was six months ago. And part of that is my engagement with these LLMs. So I would encourage people to explore in something they care about and see what they think.
[00:47:37] Abhishek: All right, that's great. I mean, and to our listeners, that, that is actually Scott, for you, like, you know, who likes to read and he has figured out a new way to collaborate with LLMs to read more. Right. All right, thank you so much for your time. I would like to close this by just asking, and I'm curious, maybe you've already given us the answer. What's on your mind these days? I know we are, we are a week away from the start of the term, so possibly that. But is there anything that you're looking forward to in the next year or so in your own journey as an educator?
[00:48:16] Scott: I mean, I think the big challenge certainly for me, and I think for everyone is thinking about this AI in education. You know, basically there's just the delight every year of getting back after the summer and meeting students and working with them, which is, you know, why I do this job. So I'm looking forward to that. The big task ahead of me is that I'm teaching a new linear algebra course that I'm creating with help from our colleague Alex Heaton in the math department that is specifically designed for the new data science major. And this is some of the mathematics that among other things does underlie the architecture of LLMs. And so, that's work I need to do. But I'm excited about thinking about that, thinking about building a course and then teaching it for a new audience.
[00:49:03] Abhishek: All right, thank you so much, Scott, for your time and for sharing your thoughts and experiences. And we have to figure out a time to have you back on the show.
[00:49:13] Scott: Be happy to come back. This has been a blast.
[00:49:14] Abhishek: Thank you to our listeners, thank you for tuning into Minding Machines. Full show notes, resources mentioned in this episode, and a complete written transcript will be available on our podcast page. If you have an idea for a future topic, a question you would like us to explore, or if you have suggestions for guests, whether they are educator, colleagues or students, please reach out through our feedback form linked in the show Notes. Until next time, stay curious and keep prompting thoughtful questions.
[00:49:44] Abhishek: Minding Machines is an independent podcast produced at Lawrence University. The views expressed are those of the participants and guests and do not represent the university. This podcast is also separate from my teaching and research roles at Lawrence University.