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Award Winning Teachers: Benjamin Braun, Mathematics

Award Winning Teachers profile, photo of Benjamin Braun, mathematics professor

By Elizabeth Varnado
February 17, 2020

As the nominations for the 2020 Outstanding Teaching Awards are submitted this month to The Office for Faculty Advancement, I sat down with Benjamin Braun, associate mathematics professor, who was a recipient of the award in 2019. Ben has taught math courses at UK since 2007, and currently teaches advanced courses in the topics of Algebra and Mathematical Composition and Communication. Ben finds connections between math education and other disciplines within his teaching, using the history of mathematics and creative writing assignments to strengthen math learning. In our interview, Ben discussed the benefits of engineering a classroom environment where learning (and failure) are public, allowing all students a chance to find their strengths and build resilience in academic settings.


What are some of the challenges of teaching in your discipline?

At all levels, from early childhood all the way up to graduate education, many people have a lot of feelings of guilt and shame about their mathematical abilities. It's not uncommon for people to say, "I'm not a math person, or I was good at math until blank and then I became bad at math." You don't typically hear people say things like, "Well, I was good at reading until the books got to be 30 pages long and then I stopped being good at reading!” People don't talk about literacy in the same way as math. In mathematics somehow, there’s a feeling like, if you don't have complete and total mastery, in some sense, then you're a failure.

The typical person who walks into our classes has mathematical knowledge sort of like Swiss cheese: they know some things really well, each at different levels, but there's a bunch of gaps. If they really knew their stuff up to a certain point, then we could just meet them and pick them up from there... Instead, everybody's got this unique set of things that they don't quite understand. It makes it really hard to have a coherent, consistent response to try to help everybody. And I think that's something that you don't necessarily always see, say in humanities or social sciences.

You know what a masterclass is in music education? You stand up at the front of a room with somebody who really knows what they're doing and you play for them. And the intention is that you’re going to screw some things up, and then they're going to tell you and everybody else in the room about them. Really the only way you can get better is to let a lot of people hear you and then get feedback about what you don't know. We don't have a practice like that in mathematics, in general, and we would really benefit from it. Students, and math teachers at all levels, haven’t had an authentic mathematical experience where they felt comfortable just laying out the things that they don't know. And the only way that you can figure out what you don't know is to make mistakes in public and have people correct them.


Interesting. Do you have a system in your class where you make this space for people to fail at math, in a nice way?

When I have my own smaller classes, like the composition communication course and the matrix algebra course, I teach those with an inquiry-based learning structure. With IBL, the primary activity that goes on in class is students discussing and collaborating and working in small groups. To a large extent, the purpose of that is so I can walk around and listen to these discussions and look at people's notes and see what they're doing. Then, the way that they're doing mathematics becomes public to each other, and to me, and I can give feedback. Not just on their knowledge, but on their process: ...if I hear them say, "Oh, I'm an idiot!", I can respond like, "By the way, you're not an idiot, or you wouldn't be in this class," like, “You made a mistake, and that's reasonable.” It's easier to set cultural norms about failure in the classroom, if all of the intellectual and behavioral and emotional functioning of students is in the mix, publicly.

In the case of our large calculus classes…they are a bit of a machine. But, I also know that in the recitations, the students are put in small groups and they work together on a worksheet given to them by each graduate TA. So I may not be the one doing it, but as part of the team that's teaching, the students are getting time to do some of that public exploration.

If you're going to do math, you're going to make mistakes. Some students, they make a mistake once and then they're just like, "ah....I'm out." They lose all their steam. So you’ve got to be able repeatedly take an intellectual punch and keep going. And that's really just about like how you respond to your own emotions. And students need some guidance about how they respond to their emotions like that, and failure also needs to become culturally normative, right? As an instructor, you have to make sure that people know that's a normal thing.

So…Sometimes we don't do quite as much content in a class like this. But the idea is that you're making space for people to develop practices that help them become better practitioners and more highly proficient. All the studies show that these types of teaching techniques are generally better on average, for people who are typically excluded or marginalized or mathematical spaces… Latinx, Black, Hispanic students, Indigenous students, LGBTQ students, first generation students, students with jobs…I mean, I’m sure you can make a list of all the people who typically don't feel safe or welcome in mathematical spaces. So...part of this approach is really trying to build a community where people are able to find the way that their authentic selves can find a place where they're valued. And again, if you don't make room for their voices, then they're never heard and you're not able to figure out what they're capable of contributing.


How do you feel your teaching philosophy has changed in your years of experience?

I would say that three major things that have changed: first, is the importance of small group conversation. I did a lot early on of whole-class discussion, having everybody sit in a circle and talk about mathematics, based on things they've done. And then I kind of realized, partially from reading the literature and partially just from testing things out, that people don't like to talk in front of 30 people. Math faculty don't either! ...I mean, if you go to a faculty meeting in any department anywhere, if there's 30 people, nobody wants to talk. It's just a human thing, right? Or at least...maybe there's two people who like to talk right, but most people are never gonna speak up. But if you say, “Hey, turn to the people to your left and right and have a conversation,” then all of a sudden, the room will erupt with conversation, right? Again, this is just a human thing, has nothing to do with math. So I think really carefully about the environment where students participating. Is it within a small, local community within the classroom? Is it individually? Is it as a listener to me? Is it in dialogue? Who are they in dialogue with? ...things like that.

The second thing I think about a lot is the idea of teaching as a team, especially in these large courses for first year students that we teach. I don't have to do everything. I really need to work carefully to develop a better training relationship with the TAs, to make sure that we're all clear about what we're doing. The third thing is just to de-center myself. Early on when you're teaching, it's natural to think: What am I going to do to teach today? You frame the experience in the classroom from your perspective, as a leader of the classroom. But I’ve strongly reframed that as: When I think about teaching, the thing to absolutely put first is the experience are the students are having. How am I engineering an environment in the course? How am I providing guidance and scaffolding to create the experience that is going to help students learn the best? This is really de-centering me as the focal point of the classroom and centering that around the students’ experiences.

…When we talk about what we are going to cover in class, it’s always a list of topics. But really it should be some balance between the list of content that we want to cover and the list of behavioral practices that we want students to develop: independently learning mathematics, collaboratively learning mathematics, communication skills… and then, how they learn to navigate their own emotional responses to things, like failure.


What is an example of your favorite teaching strategy?

This is really simple, but, the first three to five classes of the semester, I always start by having the students introduce themselves to people sitting next to them. Whether it's the big calculus class, or whether I have students in groups or whatever... You know, we're at a big school, and a lot of times, it's very daunting to try to figure out who you can talk to. I think knowing people’s names and making connections is really important, and so one of the things that I really try to do in all my classes, especially in my large calculus classes, is engineer the environment to build a community. The TAs in their recitations also give students a chance to learn names and interact doing math with a good number of their peers in the class within the first two or three weeks, and that way, hopefully, they can figure out some people that they get along with, mathematically at least... And then after a few days, I just publicly make a point to say, “By the way, if you find people who you really like working with, you should swap cell numbers and do your homework together.” And, sometimes, again,...people are hesitant, but then once you give them an excuse to do it, it's normal. I don't understand all the psychology of it. I don't know if anybody does but... giving that kind of guidance really helps. I'm talking about very small interventions, that seem to make a big difference, at least in my classes, before and after I started doing them.

I think of it as the difference between reporting and communicating. When you say your name just in sequence (like when we “go around the classroom and introduce yourself”) then you're just reporting your name. When you're turning to someone and actually talking to them, and exchanging actual conversation, then you're opening up communication. So that's probably my favorite. That's one I tell everybody about.