Transcript

Anna Stokke: Hi, I’m Anna Stokke and you are listening to Shifting Conversations, a podcast about dialogue and change in higher education in Canada where award-winning educators have conversations that help both raise and shift perspectives. In today’s episode, I speak with John Urschel, who is a mathematician and a former NFL player. We discuss parallels between learning math and football, math teaching and similarities between coaching and teaching, his journey from NFL player to pursuing a higher degree in math and many other topics. I really enjoyed this conversation, and I hope you do too. Before we begin, I wish to acknowledge that this podcast was recorded from the University of Winnipeg, which is on ancestral lands on Treaty One territory.  These lands are the heartland of the Metis people. I also wish to acknowledge that our water is sourced from Shoal Lake 40 First Nation. 

 

(Break) 

 

Anna: I’m Anna Stokke. I’m a mathematician and I’m a math professor at the University of Winnipeg and I am here today talking to Dr. John Urschel. He completed a PhD in mathematics from MIT in 2021. He’s a member of the Institute for Advanced Study at Princeton, and in fall 2022, he will be a Junior fellow at Harvard University. And I’m really excited to talk to John because he’s had a very interesting and rare career in addition to being a very accomplished mathematician. He’s a retired NFL player, he was an offensive lineman for the Baltimore Ravens and retired from professional football in 2017. And I just finished reading his book, which is excellent.  It is called Mind and Matter, a life in math and football. And he co-wrote it with Louisa Thomas. It’s an excellent book, and I highly recommend- 

 

John Urschel: My wife, I should add- 

 

Anna: That’s your wife? 

 

John:  Yes. 

 

Anna: It’s a very well written, excellent book. Really, really great. It’s a New York Times bestseller and I recommend reading it. So, before I get started, can you just explain what your position is right now? You’re a member of the Institute for Advanced Study at Princeton.  

 

John: So what does that mean, I guess?  

 

Anna: Yeah. 

 

John: That’s a good question. So, I would just describe it as a post-doctoral position. For listeners who might not be familiar with that in a lot of academic fields, it’s fairly standard. You get your PhD and if you, often if you have intentions to be a career academic, perhaps to become a professor, or lecturer at some point. Oftentimes, you’ll take an in-between position where you don’t have the full responsibilities of professor, but you still get to perform research and you get to sort of be a little bit more independent than you were during your PhD. And so post-docs, as we often call them are almost universal in math. Very few people straight from a PhD to a professorship. 

 

Anna: That’s true. And so, the next position at Harvard – you’ll be a Junior Fellow at Harvard, so that’s a similar position? 

 

John: Another fancy name for a post-doc. 

 

Anna: Okay. Okay. 

 

John: So, none of these places want to call them post-docs. But yes, I mean, it’s great. Although I should mention that I feel quite lucky to have both of these positions, both positions at the Institute this year and a position with the Society of Fellows next year. Because yes, it is a post-doc, but these are very unusual post-docs in that I have no teaching responsibility.  

 

Anna: Okay, right.  

 

John: Yeah. No supervisor.  

 

Anna: Oh, really?  

 

John: As a post-doc – you know this – but for people listening, either you’re a post-doc and you don’t have a direct supervisor. You have a lot of freedom. But you’re teaching, or you’re not teaching. It’s usually because you have a direct supervisor who’s paying for you. And so, you’re very much responsible for doing the work that your supervisor would like you to do.  

 

Anna: Okay.  

 

John: Also, it’s unique in that I’m my own boss but I’m also not teaching. 

 

Anna: That sounds great. So, who are you working with? You’re just working with people on campus or whoever you want to work with? 

 

John: Yeah, so working with people on campus. I have some collaborators from my time at MIT who I still talk to. I have some collaborators, you know, you make friends at places that are neither MIT nor Princeton. And also, while here, I would say Peter Sarnak would be the closest thing to a supervisor here. We have lots of interesting conversations. And we’re sort of mildly collaborating on some things we meet often sort of talk a lot.  

 

Anna: So yeah, that’s a really nice time to get a lot of research done and get prepped for an academic career. So, in the US, how long are people usually doing postdocs for before they move into a professor position? 

 

John: (Jokingly) Oh, don’t ask that question. 

 

Anna: Well, I know the answer in Canada? So that’s kind of what I am asking about.  

 

John: So yeah, in U.S. it varies. It really does. And in fact, sometimes it’s a little demoralising, I have to say. I think we can sort of say that the academic industry, the job market is not always the best. You definitely got a lot of people, not as many jobs as people. 

 

Anna: Right. Yes. 

 

John: And I would say, you know, hearing stories from professors of mine who got their first position in the 90s, or the 80s, it’s a very different world out there right now. And so, I would say it’s fairly standard that everyone does usually at least one post-doc for a year or two. Some people do two post-docs and I’ve heard of people doing three or four.  

 

Anna: Okay, yeah, yeah. 

 

John: What’s typical in Canada?  

 

Anna: Lately, I’ve seen four- or five-years post-docs. So yeah, it’s a tough job to get into. But, we love this. That’s why we do this. 

 

John: I can assure you being an academic, it’s very fulfilling and getting to do research, getting to work on things that interest you. Getting to mentor and encourage young people, teach young people, but the job prospects in industry are definitely more lucrative.  

 

Anna: True, but this is a great job. So, here’s another thing. You were born in Winnipeg, I’m here in Winnipeg, this is this is where I live. So how long were you in Winnipeg?  

 

John: For like, barely a minute. I was there- 

 

Anna: Okay. Just a minute. 

 

John: …until I was three, perhaps? 

 

Anna: Oh, okay.  

 

John: So, I’ve been I’ve been back to Winnipeg, you know, a couple times, but I don’t have any fond childhood memories of Winnipeg.  

 

Anna: Yeah, and you grew up more in Buffalo. Is that right? 

 

John: Yeah, part Buffalo, part Niagara-on-the-Lake. So, my mother lived in Buffalo. My father lived in Canada.  

 

Anna: Oh, I see. Right. And so you came back to see- 

 

John: So back and forth and then often I’d spend a good chunk of my summer visiting my dad’s family in Calgary. 

 

Anna: Oh Ok. Oh, so you’ve spent a fair bit of time in Canada? 

 

John: Yeah, I should say that, you know, some parts of Calgary, in particular. Canmore, very much does feel like home to me.  

 

Anna: Oh, wow. Yeah. Canmore is beautiful.  

 

John: Yeah. My grandfather has a log cabin there.  

 

Anna: Oh, wow. That’s awesome.  

 

John: I used to spend every summer you know, you can walk into town, yeah, it’s beautiful. 

 

Anna: Oh, that’s great. So okay, so Buffalo and then you went to Penn State.  

 

John: Yeah.  

 

Anna: That’s pretty exciting. And I wanted to ask you about something – when you were in high school, you had a coach, and you talked about this in your book, that the coach was really encouraging of you. You know, you have great talent, you’re going to be able to play in the Big Ten, et cetera, et cetera. But maybe from your point of view, you thought you had more talent in mathematics and science and the teachers weren’t saying this to you? 

 

John: In hindsight, I can say I definitely can recognise that I had more talent in math, than I did football. 

 

Anna: But the teachers weren’t encouraging you to become you know, a mathematician or a scientist in the same way that your coach was encouraging you to become a football player. What were your teachers encouraging you to do? 

 

John: Yeah, that’s, I mean, this is an observation that’s really stuck with me. And to some extent, I should say that it’s easy to just make this observation and sort of like, make a direct conclusion from this. But I should say that, in some sense, the way a coach’s job is measured, in the way a teacher’s job is measured, is very different. In the sense that if you’re a teacher, very often, especially when you’re teaching, let’s say, high school or below, let’s you know, avoid, you know, talking about teaching university, you’re very often measured by your worst performing students. If you have students who are not passing your class, this is a problem. Right? In high school? I would imagine. You have a couple students who are amazing, and who seemed like they have a lot of talent in this and you’ve really helped them a lot. If you have a bunch of students who are not doing well, then your performance would be measured as poor, in some sense, right? Perhaps? Whereas as a coach, no one cares, how well you coach up your worst 10 players. 

 

Anna: Ok. 

 

 John: No one cares. But your best five or 10 players, these are your most important players. So, in some sense for coach, I’m fundamentally, this coaches most important person in high school, because they’re measured by wins and losses, and wins and losses are most influenced by your best people. I go to some to some university like Penn State, my coach can say, “look, I coach this person there at Penn State. This is why you should come here and play for me.” This is this is these are sort of very helpful things. Whereas for a teacher, I’m in math class, I’m getting hundreds on everything. I’m not really paying attention. And in some sense, “oh, I don’t have to worry about John. John knows what’s going on. He’ll hand in all his homework. He’ll get all the questions right on the test. I don’t even have to worry about him. He can just stay there and do whatever he wants.” So,  in some sense- 

 

Anna: You completed the curriculum. So you’re good, right?  

 

John: Yeah. So yeah, I would say yes, this is true. And yes, this is something I definitely observed. But in some sense, I understand and why it is a little different. Although I do think that I would encourage teachers to try to encourage your strongest students and try to sort of push your strongest students, I would encourage teachers to try to set high goals for your students before they set high goals for themselves. Which is something that coaches are constant in. 

 

Anna: Okay. Oh, that’s interesting. I guess I hadn’t thought of it that way. I mean, some of the things I often hear is that when students are good at math and science, they’re usually encouraged to go into engineering. So, you know, very practical thing, which makes a lot of sense, right. But you know, oftentimes, that’s how we end up with students in math, kind of like with you, you went to Penn State, you actually were enrolled in the engineering programme there. Largely because your mom wanted you to do it, right? 

 

John: Yeah. I mean, I majored- started out in aerospace engineering. Mom told me, I was going to major in aerospace engineering. I said, okay mom. I mean, I didn’t even know what a mathematician was until I got to college. I didn’t understand like, what is it as a profession I didn’t even understand like, people just did math for a living. Like, I thought there were math teachers. But, I knew nothing about the idea of like someone researches mathematics. This is a concept I’d actually never heard of, until I got to college. 

 

Anna: Yeah, I guess I probably could say the same thing. I definitely hadn’t heard of it. But yeah, I went to university. Actually, when I went to university, I had no intentions of majoring in math either. But actually, I thought I’d be a lawyer. That’s what I was thinking I do. And I was doing philosophy. And I was doing math. And I ended up in math, just because I like it and it’s challenging. And I had a good, a good Prof. Right? You always have a good prof who kind of nudges you into the profession. So yeah, I mean, I don’t think many high school students would know what a mathematician is or what they do. But certainly, we end up with a lot of students in math in that situation, who went to become engineers, and then they decided they liked their math courses, or here at my university, it’s usually they come to study computer science, and then they end up doing a double major, and finding out ‘Oh, math is what I actually really love.’ 

 

John: It seems like it’s really exclusively one of those things. Like it’s either there are computer scientists, they’re double majoring. Or they’re a physicist, or they’re a mathematician, but they’ve been going through math camp since they were in high school. And they’re very much 100% on the math track. Meaning they sort of knew they were going to be mathematicians, since they were young. You know, they’ve been doing math, competitions, math, things, all the way through high school, maybe their professors or parents or academics. And then you have this third group, which I think you and I fall in, which is people get to college, they start out in something else. And maybe they have a very positive experience with a professor, very positive experience with the class. It makes them say, “Hey, let me go look at this math major. Let me get some more of this.” Somehow, it’s only these three things, which is kind of, which is strange. I think we must have bad advertising.  

 

Anna: And maybe we do? I don’t know, no, yeah. Okay, so what about parallels between getting good at football and getting good at math? Do you see any parallels? 

 

John: Oh, that’s… let me think. So, getting good at football is a lot I would say- it’s tough. I can talk about it for me, personally. And then I can tell you sort of why it’s tough for me to sort of connect them. So, for football, why do we want to get good at football? Well, football is all about competition. Every single day, every single play of every single practice, you’re competing. And either you’re winning or you’re losing. And the whole idea of football, is to compete and try to win as much as you can. And so, in general, the motivation in football to improve in football, is to win. And in some sense, losing is a very negative thing that motivates you, supposed to motivate you to keep doing better and better and better. It’s this desire to win. It’s this need to constantly win and sort of like the unacceptability of failure, like the strong hatred of losing,  

 

Anna: Right. 

 

John: All of these things sort of come together. And in math, I would say that for me personally, it was less like the strong hatred of getting a math problem wrong, but more the desire to sort of understand. Desire to be able to answer the question why? The desire to see an interesting problem and have cool tools and techniques to try to solve it. Yeah. So, I would say the math side is very much more curiosity and more motivated by sort of fun and play and beauty, whereas the football is very much motivated by like winning. 

 

(Break) 

 

Anna: I mean, I often say to students when they’re struggling well, you do have to do a lot of practice, right? So, you can’t get good at math unless you do a lot of practice. And there’s a whole sort of ladder thing like if you can’t do a limit am it because you can’t factor. So, you have to be able to do the things all along that ladder. And so, there’s a lot of practice involved. And I mean, I don’t play football, obviously, I’m not nearly big enough for one thing, but I don’t play football. But I play the piano a bit, right? So, I’ll often say it’s like that, you know, if you’re if you want to get good at playing a musical instrument, you do have to do your scales, you have to do your practice. And eventually you get really good at it, and it becomes really easy. So, I kind of wondered if there weren’t sort of parallels like that?  

 

John: Yeah, I think football I would consider football more like a piano in some sense. You know, you’re doing certain movements, certain motions, there’s certain fundamentals. you have to get very, very good at. And it’s perfecting these sort of like, simple things. That makes you great at football. Whereas math, yes, you know, you have to learn how to factor. But you’re not perfecting factoring for a year. You to learn something more complicated and do something more interesting. And yes, math builds on itself. But in some sense, it feels like there’s much more going on in math… you learn something and there’s diminishing returns to just perfecting that one thing. The cool thing about math is if you know I’m learning to factor, let’s say, I see it for the first time I do it a bunch of times, I try to understand like what’s going on here, what’s fundamentally happening. And then after that, I can move on to something else. And I can use that, yeah, build something sort of bigger. And so in some sense, I think like the learning math or getting good at math is like so much more fun than learning piano, so much more fun than getting good, you know, getting good at football so many fresh, they’re constantly seeing something new. Every single day that’s building on itself. It’s like you’re building a house, and it’s just getting like higher and higher. Whereas in football, I’m doing you know, as a football player, the drills I’m doing in high school, I’m functionally doing the exact same drills in college and pro football. I’m doing them every day. Yes, I’m much better at them, because I’ve been doing them for a long time. But I’m fundamentally doing the same things. But no, I agree. Like, fundamentally a love of what you do is really important. Interest in especially in things like math, where things constantly build on themselves. A curiosity, I think is like one of the single most important things. 

 

Anna: Yeah, definitely. So, I’m, I’m extremely impressed with you. Because I know how hard it is to do research mathematics, it’s very hard. And it requires a lot of concentration. And you know, there’s a lot of stops and starts and things don’t always work out. In fact, most of the time, they don’t work out and you just kind of have to keep at it. So, I really find it just amazing that you were able to do a master’s degree and published three papers, like in good journals from your master’s degree, while at the same time playing football for Penn State. And I mean, I don’t I don’t know how you did it? Right. So how do you think you were able to be successful doing these two things at the same time? 

 

John: It’s a good question. I think I often get this question. And I want to make sure that I do student athletes justice. Because I think student athletes, particularly student athletes, at top universities, this is a tough job. This takes up a lot of time. And I want to stress that if I wasn’t a math major, if I majored in, let’s say, History or English, there is not a chance in the world, I could have been nearly as successful as I was academically. There’s just not enough hours in the day. Because you know, you’re working this job, I don’t know where I would find the time to read everything I would need to read or sort of, you know, go through everything I would need to go through. The beauty about math is that homeworks are short, the amount you have to read is not very long, often. Like, you know, in a in a history class, they’ll give you a 400 page book and say, have this read in two weeks in a math class, you know, you have a whole semester to cover 100 pages in a book. Now, of course, the 100 pages are much denser. You know, there’s less problems on the homework, but the homework, you know, requires a lot more thought it’s more complicated. But the thing that really helped me was being good at sort of the major I was doing, if I chose a major that perhaps I liked, but I didn’t feel like I was fundamentally you know, had some advantage in, it can be very tough to do quite well. Just because of the amount of time it sort of takes and I can say from my time at Penn State, I was trying my best to sort of be the best football player I could be in putting in you know, lots of hours in football and really the majority of my academic time was spent on research it was spent reading sort of outside of class spent on doing things not related to my classes, and I would spend, I would say of the academic time I spent all the way through my undergrad. When I was doing my Masters, I was taking some PhD coursework at Penn State. And obviously, you know, these classes were quite involved. But during my undergrad, I would say I spent 80 to 85% of my like, academic time, on research. On reading things that were not for classes, I took. Like, my very first research project. I did this all day, every day sort of offering my free time. And I spent, like, I spent the bare minimum on my actual like, classes, just because I was so- One, I was so interested in mathematical research. Two, I just had such little time. One of the things that I’m very grateful for the past, sort of four or five years and having more time, is that, yes, you know, I’m still productive doing research. But I have so much more time now to just sit back and learn about tangential things, go to more talks, listen, read more papers, do more things that is not like directly related to what I’m trying to finish right now. And that’s been something that’s enjoyable and that’s something that, like, I think I unfortunately missed out on as an undergrad. 

 

Anna: Okay, well, that’s good. I mean, that’s good to hear you say that. I kind of wondered how it would feel to have so many intense things going on, like you’re a football player, or you’re, you’re doing PhD in math, and then to have one of those things be taken away. Personally, I thought, well, maybe it’d be great if you had these two things. Because if one wasn’t going well, you could say Yeah, but I’m doing this other stuff, right. I too, like too busy. So, you know, if I didn’t get to my research, and I wasn’t something wasn’t working, working out. You can blame it on the football.  

 

John: Now I just blame it on the children. 

 

Anna: Children. Oh, right. Yeah. Yeah, that’s true. Children take up a lot of time. Yeah. Yeah, I use that as well. Definitely. Always the children. 

 

John: My daughter’s had such a busy week, I’ll get that. You know, I’ll write that proof up for you by next week, just wait till next week. 

 

Anna: Exactly, exactly. You always need some sort of excuse. So yeah, okay. So, you’re playing football in the NFL. And you decide you want to do a PhD in math. And you get into MIT. And you’re kind of doing both –  going there, I guess in the offseason – but registered full time or whatever. What were the other NFL players doing? PhDs in English? Geography? I mean, what were they doing? Is this normal to be doing something like a PhD when you’re an NFL player? 

 

John: Definitely not normal. Also, in hindsight, and I say this to anyone who will listen, definitely not recommended. This was not my this was not one of my best decisions. This was not a good decision. I can say in hindsight. And yeah, I mean, NFL players have all sorts of interesting sort of things that they do are interested in, outside of football, like, you know, I have friends who are serious fishermen, or hunters. Or they like sculpting like what sculptures or dealing with cars. So, people have a lot of diverse interests. But I can say being a full time PhD student at MIT, so during the fall, I had coursework. I had to read, you know, do the problem sets, I had to send my solutions in via email, this was just too much. I mean, as much as I said, you know, I was able to manage playing football at Penn State while taking coursework and doing research. I felt like I had enough hours in the day, of course, I didn’t have time to sort of aimlessly be creative, as much as I would like. But when I was doing pro football and the PhD at MIT, it was too much. It was just I had no free time. I was constantly stressed. I was constantly overworked. My then, fiancée at the time, she like almost never saw me. I mean, I went through a whole season, I took three classes at MIT, I am playing in the NFL, the season ends, semester ends, I have three weeks before my qualifying exam. And I haven’t been preparing at all because I’ve been busy with classes and busy with the season. And I pretty much locked myself in a room for like 15 hours a day for like three weeks to prepare for my qualifying exams, and I just go out for food and go to the bathroom. And that’s it. And so, it was just, I can say like during the fall, and in particular that month before my qualifying exams. This was, this was just not pleasant. It was not enjoyable. It really was not. I do not miss doing the PhD and playing in the NFL in the fall at the same time. 

 

Anna: No, that would be pretty rough. 

 

John: I think it’s important to sort of to say these things because it’s important to recognise we only have so many hours in the day. And there is something as too much. 

 

Anna: Yeah, for sure. Yeah.  

 

(Break) 

 

Anna:  One chapter in your book that I found really stressful was the concussion chapter. I mean it is a dangerous sport.  There’s a lot of head injuries and that sort of thing. And so, you had this concussion and what I found stressful about it was that you couldn’t think like you normally were able to thank you couldn’t keep the definitions in your head and that sort of thing. Were you afraid that you might not recover from that? 

 

John: No, I felt pretty confident that everything will come back like this, like the history of people who get concussions. Also, I got a concussion in high school previously. Just experience, like, you know, as a football player, you have a lot of experience with head injuries, you have a lot of experience with friends who get head injuries. And so just from everything I had known from science, I felt pretty confident that I was going to bounce back from everything. 

 

Anna: So you’d educated yourself about it. 

 

John: Yeah, I mean I, you have a lot of experience, My high school concussion was actually not football, but a car accident. But ah, yeah.  

 

Anna: Oh, no. 

 

John: I feel I should mention, but yeah, I felt fairly confident, you know, things would come back. The main thing is, I was just extremely frustrated because I can’t do mathematics. And I also like, can’t play football right now. And so, my two favourite things like I just can’t do. It was just a very, very frustrating time.  

 

Anna: Yeah, that’d be awful. Okay, so you’re not teaching in your current position. Right. And you won’t be teaching at Harvard in the fall, although I’m sure the students would love to have you. But ah, 

 

John: I enjoy teaching. 

 

Anna: Yeah, me too I love teaching and so you’ve taught a few classes, you taught a couple at Penn State, and then you taught a class at MIT. First question, What classes do you most want to teach in the future? 

 

John: Okay, that’s a good question. For some reason, I feel like my preference is like, somehow at the extremes. I would either be extremely excited to teach a topics class. So, you know, let’s say at MIT, it would be, you know, a class, maybe topics in numerical analysis, or topics in spectral graph theory, whatever it may be. And the idea is, it’s a one-off class, I teach whatever I want. And I’m teaching very, very advanced concepts. So, this is like cutting edge things. We’re moving fast. And we’re covering sort of like the I’m getting people- everyone in the class is a PhD student, and I’m getting people up to the state of the art and we’re learning about very recent developments. That sounds like a lot of fun. Yeah, for sure. Yeah. But also, just be really excited to teach introductory classes. I enjoy getting a broad group of students who aren’t necessarily all, let’s say math majors…sort of knowing they’re going to be research mathematicians, and even getting people who sort of know they’re going to do something else. And just getting a chance to interact with them. Make sure they have a positive experience, possibly positive last experience with a math class and just try to you know, positively impact their lives. Like for instance, I think a topics class, or probably like, a first linear algebra class would probably be my favourite classes to teach. 

 

Anna: So, a linear algebra class – like vector spaces?  

 

John: Oh, so nothing like- not like a fourth year. The second class that a math major, or a computer scientist, or physicist, or an engineer would take.  

 

Anna: Got it.  

 

John: So like, at MIT, it’s 1806. Yeah, at Penn State, it was Math 220, I believe.  

 

Anna: Okay, well, that’s good. Well, I like to teach intro calculus, the differentiation class. Kind of for the reasons that you said. So, I like to teach a group of students that just came out of high school, and it’s their first experience with university. And they’re from all sorts of different disciplines and don’t necessarily want to continue in math. Just to give them a good feeling about math, so I like to teach that group and then my other favourite course to teach is, well, I like linear algebra as well. And I really like to teach group theory. So those are my two favourites. 

 

John: Gotcha. So, it sounds like somewhat similar. You like getting a broad group. But then you also like teaching something very specific. And like what you’re really interested in mathematically. 

 

Anna: So, I was thinking about how you’ve experienced different types of, of teachers in a way. So, you’ve had basically the highest level of football coach, right. Like you were in the NFL, you had NFL football coaches. On the other hand, you know, you went to MIT. How could you draw from both experiences to become a great math teacher? 

 

John: That’s a great question. I think the thing that you take from football coaches, particularly in the NFL, or even more so in college, I think is getting the most out of people. Finding ways to get the most out of people and finding ways sort of how to motivate each person uniquely.  

 

Anna: Right, ok. 

 

John: That’s a big skill of a college football coach.  

 

Anna: Ahh ok. 

 

John: Like the motivation aspect is the big thing. When I think about teachers I’ve had at MIT or at Penn State, the thing that I’ve learned the most from professors at MIT is more things like how to teach a topics class, which we talked about before. But I don’t think the thing that you learn a lot about is how to teach a broad class. Because just because someone’s a professor at MIT, you shouldn’t assume that that means that they’re an elite world-renowned teacher. You should ah, you shouldn’t assume this. 

 

Anna: No, no, you absolutely cannot.  

 

John: You absolutely cannot assume this 

 

Anna: I completely agree with you. Yes 

 

John: Throughout my career – I don’t want to talk about specific institutions I’ve been at – but I want to say more broadly, if you talk to just about any math major, and you know, this, or any person who got a PhD in math, they just have a laundry list of stories of math classes they took, where the teaching was non-existent, there are so many issues. And too often you have this situation where people are very much researchers first- 

 

Anna: Right, Right Right. 

 

John: And they sort of have to teach, yeah. 

 

Anna: Yeah, and so you’re gonna decide based on those experiences that’s going to tell you what not to do-  

 

John: But no, I think, I hope, at least that during my teaching career, I’ll be flexible. What I mean by flexible is, I’ll have some ideas about what I think I should be doing. And then I’ll try to learn and try to say, ‘Oh, I did that. But maybe that wasn’t so good.’ Or I get feedback. And I say, ‘Oh, maybe I should do it like this.’ And so, I should say that I do have some ideas about how I like to teach. But those ideas are very much open to, you know, other, they could change. But in general, I’ve sort of found that the things that I try to fundamentally do in my classroom is sort of, first of all, just let people know that I want to be there.  

 

Anna: Exactly. 

 

John: Sounds like such a small, tiny thing 

 

Anna: I completely agree. 

 

John: So often, yeah, I’ve been in so many classes, where you can just tell the professor does not really want to be there, they’re not really prepared. They’re not excited about the material. It’s sort of like, ‘I have to do this. And now I’m going to once I’m done, I’m gonna get back to what you know, when I really want to do,’ and so just acting like you want to be there, I think is really important. The other thing is that I like to try to create an environment in my classes, which welcomes engagement and really de-stigmatises sort of incorrect answers. And what do I mean by this? I constantly want to try to create some environment where people feel comfortable talking without fear of looking like slightly less intelligent or without fear of getting things wrong. And this often comes for me personally, through me making mistakes, and sort of saying- Oftentimes, I’ve noticed, you know, a professor makes a mistake. And they just try to erase it as quick as possible, and sort of do things but recognise that I will make mistakes when I’m sort of writing things on the board. When someone answers a question, but their answer is wrong. Still thanking them for answering the question, thanking them for their insights, focusing on the insightful parts of their question and just generally trying to make sure that when people talk or when people are engaged, that you give them positive feedback.  

 

Anna: Yeah for sure 

 

John: You know, in some classes, as crazy as this going to sound, sometimes people ask questions, and they get faced with quite negative feedback. 

 

Anna: Sometimes people don’t ask questions or encourage participation at all. So yeah, I agree with you. It’s really important to encourage a lot of participation. And it’s really important to make sure that students feel comfortable participating and that they feel comfortable giving wrong answers. Right? So yeah, definitely. So do you think any of your coaches would have made good math teachers if they if they had the math chops? 

 

John: Yeah, yeah, I’m sure I’m sure they would have. I think so. 

 

Anna: Yeah. And so, the whole pep talk thing, you know, like, I watched Friday Night Lights, the series which was great. 

 

John: I never saw the series. I saw the movie. 

 

Anna: Oh, you didn’t? Oh, okay. Yeah, I saw the movie too. Yeah. So, I watched the series, and there are a lot of pep talks. So that’s something that I guess happens a lot in football? 

 

John: Yeah. Yeah. I mean, I think yeah, I think especially the coaches who are more technical, I think, I think they’d be quite good math teachers. I mean, they’d have to, they’d have to clean up some things, but I think they should be good.  

 

Anna: How about the other way around? Do you think any of your math profs can be football coaches? 

 

John:  Yeah, I think so.  I mean, a lot of football is sort of doing very simple things and doing them very well and doing them very precisely. And so, I would say, you know, if you have a math teacher who’s very good at getting people to be able to do very specific technical things like getting someone to be able to factor. I wouldn’t say that this is like the so different from techniques that I’ve seen from some coaches getting a kid to be able to do a certain technique like a certain run blocking technique or a certain pass blocking technique. It’s practice. 

 

Anna: Yeah! So when you talk about near the end of the book, you’re talking about thinking about retiring from football, you talked about working with African American students, and sometimes they expressed to you that they felt shut out of math. That they maybe didn’t feel like they belonged. And I’m wondering if you can talk a bit about that, like, talk about your experience, and why you think that some students would feel that way?  

 

John: Yeah, yeah, of course. So, for me, personally, I think, Well, I think and I’ve come to feel very strongly about this, that in some sense. So, first of all, I’m an African American mathematician. But in some sense, my experience as an African American mathematician, I think, is actually like, quite atypical, in a sense. In the sense that, you know, never once in my entire math career, have I ever sort of like taken a step back and felt like, I don’t fit in here. I don’t belong here. What am I doing here? Never in my math career, have I ever, like taken a step back and like, doubted myself, or doubted, like ‘should I be here?’ And I think that that’s actually a very atypical thing. And I would say the reason why I never felt like that is because in some sense, who I was, or like, you know, how I valued myself never really had anything to do with like how well I was doing in math. And I never felt isolated. Because as an undergrad, I had my entire football family. I mean, these are like all my best friends in the world, like my best friends like today, are all the guys I played college ball with. And so, in some sense, these are the guys I lived with, these are the guys I ate with, you know, I hung out with, and I didn’t really have any friends in the undergraduate math major. I didn’t talk to anyone, the undergraduate math major. I didn’t even know until I sort of got to MIT, I didn’t realise there was even such a thing as like study groups. I didn’t realise people did piece sets of groups. I didn’t even know this existed until very later on and I never felt, I guess I never felt isolated because I really had this family built in, in football. But, I can say that, you know, through interacting with, let’s say, other African American researchers, or let’s say PhD students at MIT, that my experience is very much the exception. And I think it’s often rooted in sometimes being behind other people in the classroom. I mean, okay, unfortunately, you know, race, in some sense, by not being a certain minority correlates with socio-economic factors, and quality of education. And I think that feeling of being behind, that feeling of also not being able to relate to people in your class. That feeling of mild exclusion. For instance, when people are pairing up to work on problem sets together, no one asks you to sort of work with them, like things like this can really sort of can snowball.  

 

Anna: Yeah, definitely. 

 

John: My experience with this is through the MIT Black Graduates Student Association. 

 

Anna: Oh ok. 

 

John: It’s seeing experiences of my peers. 

 

Anna: Okay. So what do you think the solution is? 

 

John: Well, first of all, a race and like socio economic status, ideally, should not be like correlated really, at all, is one thing. Like, it’s sometimes the fact that these things depend on each other like the problem. The second thing is obviously just, you know, increasing quality of education for all.  

 

Anna: I agree with you. 

 

John: obviously related to my previous point. And then the last thing is just trying to make sure that, you know, classrooms are welcoming environments, and to make sure that we as mathematicians represent our sort of our discipline. Well, I don’t know, maybe we are representing it correctly, but represent mathematics as a discipline that’s welcoming of people from sort of, like all backgrounds and all different perspectives and all experiences.  

 

Anna: Absolutely. Yeah.  

 

John: So that’s what I would say. And I mean, me personally, I’m, very much I’m very much a research mathematician first. I mean, if you ask me, yeah, what do I do? Why do I do math? I do math because I like solving beautiful problems. And seriously what I enjoy. I like teaching other people, math and sort of sharing the gospel of math, but a secondary thing that do care about is trying to encourage people in math trying to sort of show people how cool math is, and particularly increase the participation in math of people from underrepresented groups. 

 

(Break) 

 

Anna: And you’ve worked in a programme at MIT, Primes MathROOTS programme. Oh, was that with high school kids? 

 

John: So much fun. Yeah, high school kids. I in fact, I was. Yeah, I was just doing some stuff from MathROOTS before I hopped on the call, yeah, I love it. So nice, fantastic program. It’s been going since like 2015. I’ve been involved in it since like 2019. And the whole idea, I just enjoy it so much. The whole idea is we take 20 kids from high school aged kids over the summer, who for some reason are from sort of like some underrepresented background and don’t have access to high quality mathematics education. What do I mean by ‘high quality? So this is very much like a talent accelerator, we’re getting people. So, this is sort of like one area of a large regime, which needs help. But I think this area also needs help. We’re getting people who are good at math, we’re getting people who love math, but we’re getting people who are good at math and love math, but don’t have access to high quality mathematics, which is a very niche group. But it’s a fun group to work with. So, the idea is, if students who are good at math, good SAT scores, good, whatever it may be good grades and math, but their parents aren’t academics. They aren’t, you know, taking advanced college classes at their local university, maybe there’s no strong local university where they live because they live in a rural area. The idea is we take students like this, they come to MIT and we’re just having a math party for two weeks. It’s awesome.  

 

Anna: Nice! 

 

John: So, pretty much the way it goes is. I, So I’m the Academic Coordinator. So, I teach all the math classes, I run all the homeworks, I run all the problem sessions, I run all the like office hours. I scheduled all the sort of like guest speakers and we just do math for two weeks. And we start from basics, because we don’t want to exclude anyone who you know, is good at math and loves math, but perhaps doesn’t have sort of the prerequisites. We don’t even assume calculus. All we assume is, you know, a background up to like, Algebra pre-calc. And we do a sort of two-week curriculum that starts off with basics of mathematics, the idea of mathematical proof. And going through really, what is college math curriculum. So pretty much like two weeks of introduction to proof, things like number theory, things like graph theory, things like polynomials. And yeah, we, we just do this all day, every day and we sort of like, it’s a very fun time. The students get a lot of time to work on sort of problem sets that are very much built around sort of having fun in the joy of solving things. You know, there’s no grades or anything. It’s just learning, getting more comfortable with doing math getting more comfortable with seeing math and the important thing is interacting with- it’s staffed like the mentors, the academic mentors, my academic staff, are all MIT PhD students who are really passionate about the work and so yeah, it’s a really, it’s really fun.  

 

Anna: That’s a really great programme. 

 

John: I can’t express enough how much I enjoy it! And in fact, I have a, I have an undergraduate researcher. At MIT, we have these UROPs like Undergraduate Research Opportunities program. I think it is,  

 

Anna: Right, yeah. 

 

John: I actually have an undergrad who was in MathROOTS as a high school student. 

 

Anna: Wow! 

 

John: Who did research with me, which was really fun.  

 

Anna: That’s awesome! 

 

John: And what I just found out, and I didn’t even know this until so, there’s a guy who’s a PhD student of Peter Sarnak’s at Princeton, who I had met, I met him I gave a talk, I gave a colloquium at Princeton Applied Math, and he was there – Henderson’s his last name. And, you know, we talked, we hung out, you know, a couple days after. African American mathematician, PhD student at Princeton, and I just realised, like, 15 minutes before I came on this call, I’m 99% sure he was a student back in 2015. For the MathROOTS program. 

 

Anna: Really?  

 

John: Yeah, yeah.  

 

Anna: Wow! That’s really impactful.  

 

John: That’s really cool.  

 

Anna: So that’s really great. 

 

John: Yeah, I need to ask him about it. Talk to him about it. I mean- 

 

Anna: That’s excellent. That sounds so good. That’s great that you’re doing that. Okay! So, I just want to ask a couple more questions. Is your mom happy with your career choice? 

 

John:  As a mathematician?  

 

Anna: Yeah. 

 

John: Yeah, she is. She’s quite happy.  

 

Anna: Good. Yeah. She got over the whole engineering thing? 

 

John: Yes. She did get over the whole engineering thing.  

 

Anna: Okay. Okay. And so what’s next for you?  

 

John:  Oh, more of more of what I’ve been doing.  I’m just looking forward to doing more math, eventually being a professor at a university, doing research, getting to teach getting to inspire young people, and you know, just hanging out raising a couple kids. 

 

Anna: Sounds great! Last thing. Do you have any advice for people who want to pursue math? 

 

John: Yes. I would say the best advice I can give you is be curious and make sure you are in charge of your own math education. That’s what I would say. I think too often people who are interested in math are majoring in math or like math or studying in high school. They’re constantly depending on the teacher or the lecturer to teach them things. And if you’re constantly dependent on that person, then you could be in some trouble depending on who you have. And you know, you’re very much at the will of that person. Whereas go buy a math book and go, go read it on your own and go try to, you know, take control of what you learn when you learn it. And I find that lecturers can really complement the things you learn. But it’s best when math is personal. It’s best when it’s you sort of actively engaged in that. 

 

Anna: Yeah, well, that’s great advice. Well, I’ve really enjoyed our conversation today. I learned a lot. And it was really interesting to talk to you. Sorry if I didn’t talk about football enough.  

 

John: Oh, no, we could talk about football even less. I came for the math. 

 

Anna: Okay. Okay, good. But yeah, I really enjoyed our conversation. And thank you so much for joining me today. I really appreciate it. 

 

John: Yeah, absolutely. Thanks for having me. I really, I don’t know, I feel like a Canadian mathematician. And so, I liked I liked having the chance to come on. 

 

Anna: Shifting Conversations was created by the Society for Teaching and Learning in Higher Education, or STLHE 2021 cohort of the 3M National Teaching Fellows, with the expert guidance of Judy Bornais and Srini Sampalli. This project was made possible by STLHE with the generous support of 3M Canada. Special thanks to the team at STLHE, Jay Adamsson Natalie Smith, Tanya Botterill and Debbie Brady. Project management and technical support from Craig Fraser, social media support by Aysha Campbell, additional support from Meghan Tibbs. Original music composed by Hope Salmonson and performed by Ventus Machina. You can find more information on our website www.stlhe.ca/podcasts.