Students in math classes often treat math as a set of rules or procedures to be memorized, and do not see it as a creative and powerful way of modeling reality. In this episode, we examine how combining dance with math instruction can help students develop a deeper connection to mathematical concepts while also building human connection among the students. Thanks for joining us for Tea for Teaching, an informal discussion of innovative and effective practices in teaching and learning.
This podcast series is hosted by John Kane, an economist... ...and Rebecca Mushtare, a graphic designer... ...and features guests doing important research and advocacy work to make higher education more inclusive and supportive of all learners. Our guests today are Manuela Manetta and Lori Teague. Manuela is an Associate Teaching Professor in the Department of Mathematics at Emory University. She is the recipient of
a 2023 Emory Williams Distinguished Teaching Award. Lori is a choreographer and Associate Professor of Dance and Movement Studies at Emory University. They are co-developers of the initiative Mathematics through Movement, and they have taught different types of courses integrating movement into mathematics instruction at Emory. Welcome Manuela and Lori. Thank you. Thank you for inviting us. Today's teas are:... Manuela, are you drinking any tea today?
Yes, I'm drinking a wild sweet orange tea. Oh, that sounds lovely. How about you, Lori? I am drinking an Organic Chocolate Super Berry Burst. Wow. That sounds flavorful. Yeah, it's a special day. And I have a ginger peach green tea today. A nice favorite. I also have a favorite John. I have an English breakfast tea today. Very good. So we've invited you here today to discuss your mathematics through movement initiative. Can you tell us how this collaboration came about?
During a review session for a final exam, my students were struggling with understanding the geometric properties of a system of differential equations. They were just staring at the graph on the board trying to make sense of it, but they were completely lost. So I tried something unusual. I stepped back from the board, I paused, and then I walked towards it, saying, hey, look, I'm walking along the curve. I have past time beyond my back, the future in front of me,
and as time goes on, I get closer and closer to a straight path. So as I approached the board, I saw that something clicked in them. They could finally see it. And so it was amazing to watch the transformation in their faces. And most of them nailed this topic on the final exam. So then something else happened during office hours. I got an email from the college with this chance to
teach a sidecar course. So a sidecar course is an interdisciplinary class that is taught by faculty from different departments when they can find a unique connection between their subjects for a single semester. Since I've always loved to dance, I thought, what if I could bring math and dance together? And right then, there was a student with me, and I shared this dream with her, and she said, “Oh, you know what? I'm in a dance class right now, so I just know the right
professor for you.” And soon after, I invited Lori over to the math department. I showed her some of my course graphs that represent the solutions of differential equations. She looked at those shapes and curves, and something just clicked for her. She saw the connections with dance language. So we decided to make it happen. And we brought students in my differential equations class and our move improvisation class to work together in a sidecar course.
Well, I just remember this same student that we shared walking up to me and saying, “Hey, my math professor wants to work with you.” And I was like, “Me? Why me?” But again, when I went over to Manuela's office, I'm definitely kind of a “yes” person. So I’ve been teaching at Emory for so long, I thought, well, let me just see where this is going to go.
And we did call the first iteration of what we did, Dancing Dynamical Systems, and it was really triggered by Manuela's description of what's called population dynamics, predator and prey systems, and she tried on her computer to explain this to me through the visuals that she typically uses in class. And I just will say that as a choreographer, I'm always in the unknown. We don't know the outcome. All of our dances are experiments.
And so I agreed to do this because I thought this would be exciting to see where it would go. And I think the other thing that is part of this initial piece is people have a lot of fears around dance as well. They think they can't dance, just like people think they can't do math. And we're all movers, but some people don't identify as movers, and we've had a very eclectic group of people take our classes. Some people have studied dance, they're an athlete, and some people have
no real body knowledge at all. And I think we're helping them articulate the knowledge they hold in their bodies in a cognitive way, via the body, because movement research is founded in the body, sort of a reverse process of what math does. I love this collaboration so much. Since you began this initial collaboration with the sidecar course, have you explored other classes that blend math and movement together? Yes, we did. So most of the classes were set as directed research classes.
So those are kind of research labs where we let the students lead the collaboration among them and basically design their own learning experience, especially when we asked them to come up with projects where, basically we asked them to be the teacher and explain math through
movement. Then we participated also in an initiative of the college that's called LINC, which really means learning through inclusive collaboration, where the goal was to connect, again, two classes in the college with different goals, different experiences, and we decided to connect my partial differential equation class and Lori's dance literacy class, and we basically had like a different setting, in the sense that we had four meetings total in the semester,
and they were based on a theme. So we chose waves, and it was a lot of fun to bring my 40 students in partial differential equations into a dance studio. You can imagine that mathematicians, or like people in applied math, don't feel like dancers at all, and so we threw them in a dance studio, and it was very fun to observe as the situation unfolded. But at the same time, we basically brought the dancers into our math classroom. You must have seen their faces when
they saw all the equations on the board. But then we let them lead an activity in class to basically represent waves even if the students were sitting in their desks. So it was a very fun experiment. Then I let Lori speak about another experience that we had that is a freshman seminar. Yeah. And also just want to reinforce that I think that it was very important for them to be in each
other's spaces. We're recognizing that there's a prescribed, I guess, type of learning style or approach that one would take in a studio type class, a creative type class, very interactive with the professor and classroom where students are sitting at desks, and so when we went into the math class, they are in desks, and the space doesn't have a lot of room to move. How do we use the space? So that problem solving was kind of fun, and that project was more choreographic in
terms of showing waves as a choreographic little entity. Then we did a freshman seminar, and that class has a prescribed amount of students. It's usually 12. I think we ended up accepting 19, because the topic was attractive to freshmen. It met one day a week. Well, the other ones met one day a week. Freshman Seminar met twice a week, and it allowed us to test all of these lesson plans that we had started doing again. I think it was really fun for the students. We
also recognized we had a mixed level, I guess, of math skills. So people who had high math skills sort of helping someone who had not low, but maybe struggling with some of the concepts, not remembering algebra or calculus concepts from high school. So returning to those things and as always, moving into the body in a way that maybe people who'd never taken any kind of dance class, all of that would have been new to them. Can you describe some of the ways in which the
math and dance are combined in course activities? Can you illuminate what a particular activity might have looked like? You've hinted at some of these things are. But it might really help for folks that maybe have never been in a dance classroom, or maybe have never been in a differential equation classroom, to see what some of these things might look like.
Exactly. I have never been in a differential equation classroom. I still don't completely understand everything that I'm looking at, and so I'm going to say this is a true collaboration. I need her. I cannot do this class. I don't understand high math the way that Manuela does,
and it's been a long time since I've taken a math class. My approach, or our approach, is that we're looking for, like, parallels, different correlations, shared imagery, just material that you introduce to the students to invite them to reinvestigate the concept or explore a component of the equation. So it's not a direct like by moving, they're going to completely get it. It's just that by moving, there's a part of the equation they can understand more
fully. One example, we have these physio balls. They use them in movement therapy. We have them in dance classes, and they really are a great way as a prop to understand physics concepts.
So on a physio ball, you may be on your back or your belly, and there's a particular equation that Manuela has aligned with this, but you're finding different points of balance from your center of gravity shared with that ball’s center of gravity, like if you were lying on your belly, trying to raise your arms and legs and finding that maintaining and finding that balance point.
This movement will help you find what is called constant solution of a differential equation, and you're also kind of recognizing physically what your challenges are in your body, just as you would, what were the challenges in solving the equation. Another way we work a lot… so they have a lot of experiences where their own individual… how they sense something, or how they feel it in
their body, is unique to them. And then we do a lot of things where we work in pairs, and those are maybe more choreographic that this trajectory is interacting with this parabola, like the shape of that in space and time. That's maybe more graph assignments. And then we work in small groups, also to solve problems, and that's where they discover a little bit more choreography
in their own movement choices. When we do vectors and eigenvectors, there's a prescribed behavior for a vector and an eigenvector of what it can and cannot do, and that's very similar to choreography in terms of applying restrictions to the body to get a different dynamic behavior and stage that for us is just esthetically pleasing or communicates an idea, and for Manuela,
or in math, it's to solve the problem. So one thing that I want to add to what Lori said that she needs me to kind of come up with the activities, because she doesn't have, like, a strong math background. I need to say that I need her so much because my training when I was young was in ballet, so I always thought that dance was like a strict set of rules. Same thing that people think about math. There's a strict set of rules, and, oh, that's it. You want to
do your choreography, you want to execute it as well, and that's it. But Lori opened my mind to a pretty new world where improvisation… I was so awkward in it at the beginning. I was like, why am I in a dance studio? What am I doing? I don't know what I have to do here. So it is really like the collaboration, a key point of our work. And even when we are working together in the dance studio, most of the times, we are picking on students’ ideas and we consult and
we go ahead and try new things, even if we've not planned them. One activity that I want to talk about that is about differential equations is an experiment that we call competition game. We basically propose it all the time because it's fun for the students, and it represents something that I cover towards the end of the differential equation course, when we introduce
the predator-prey model and the competition model. And I noticed that the students have a hard time not really understanding the equations at that point, because they've trained a lot from that, but understanding what is the behavior of a solution, what is the biology application attached to it? And connect those points for them is really hard. So basically, what we do is we don't reveal what we're going to achieve in the game, but we ask them to select their strongest asset and move
according to that. So one fun fact is that during a semester, a student chose hair, and so it was just flipping his head the entire time. I think he lost the game. In the end, hair did not work. So what we do is we usually mark a small region on the floor with tape, and this will basically represent the limited resources that these populations have. And as we go on into the game, we try to limit the space
making the area smaller and smaller and smaller. And so eventually the students need to leave this area. And so this could basically represent the fact that they lose in the competition. Yeah, I do remember there was a student that, kind of remembering her choice, but let's say that you said, “Oh, I think a real asset of my personality is that I'm adaptable.” And when the space gets smaller and smaller, a person who can change levels, move in those
tight spaces. being the most adaptable, often wins honestly. So it's not the strongest or the tallest. It was this woman that had that quality I remember, who succeeded in our first game. So I imagine one advantage of this is you're pushing students quite a ways out of their comfort zones, for both students with backgrounds in dance and math. What are the main benefits to students of participating in this combination of activities?
So one thing that I've noticed, especially after COVID, is a big shift in students’ approach to learning. So more than ever, they tend to focus on memorizing everything, almost word to word, and repeat back exactly what the instructor says. It's like they're playing it safe, relying on notes, videos, and any resources that they can get to make sure they're prepared. But what's interesting is they're not as concerned with really digesting or understanding the material,
and they're focused on having the right notes and information just to pass it down. So it's becoming basically more about reproducing what's given to them, rather than exploring ideas for themselves. And so when we combine math and dance, the movement based activities force the students to step outside of the typical problem-solving approach they're used to in math. And so instead of following a set of instructions, as I said before, like they do for a math problem,
they have to focus on the concepts themselves and think more creatively. So these activities require them to engage deeply with the material, often in ways that go beyond the usual analytical methods. And then when students are asked to embody mathematical ideas through movement, they're forced to make those connections and think in new ways and figure things out on their own without the right answer. There's no right or wrong answer for us, so they actually feel free to speak up,
even if they leave their comfort zone. They're not afraid of asking the math professor that question that can be a dumb question for them. So in that sense, including dance or movement in math can also kind of get them closer to the math instructor and to their peers. One big difficulty that I have in my class is to make them work together. I try every semester to organize group work. It doesn't work. It just doesn't work. They don't talk to each other. They don't know each
other. They have no willingness to make friends in a math classroom. They just want to work on their own. And so, in this setting, we change all of that. They start collaborating. They interact with each other, and even the quieter students who usually hold back in a traditional math classroom, they feel comfortable contributing. It almost seems like the extreme discomfort that probably all of them are facing is like, “Well, we at least have this in common.”
That's right, and it was even true for me, right? So when we did our sidecar course and I had to move in front of students and in front of the dance professor. That was awkward for me, that was embarrassing for me as well, and I think it helped me a lot in my growth as a human being as well. I just want to add that this is not territory that's hyper familiar to dancers, either. Manuela talked about her own ballet identity, and that's a prescribed form that is a lot about perfectionism.
And then many of our students grow up doing competition dance in studios, and that's also about being exact and competing and winning. And the kind of dance in our program at Emory is not that at all. And so they're introduced to improvisation. Dance is a very social form, and so our class sizes are smaller, and we are used to moving, of course, in front of them,
because that's what we do. So I think those two things are different from the get go, but I do see a similarity, that it's unfamiliar territory for dancers as well, until they get to college, and then dance in college is different from what they've grown up doing. So we saw the collaborative nature of class. They were laughing a lot, but they were willing. And we actually asked them that at the beginning. I know this is going to be different, but you just have to have
a willingness to experiment, and that's going to make a big difference. And I think the other thing that I remember… it was between classes, and I said, I think we should really share with them our discomfort and that transparency, I think, helped as well. We talked about when we were in high school, I was shy. I didn't want to raise my hand and admit that I didn't understand something. So I hope that helped. We felt like it did, just to say we get it,
but you have to ask questions if you are lost. So I have to say that in this. I identify so much… like in Italy, I studied my whole life in Italy, and in Italy you have like this distant relationship with your professor, and so I never raised my hand to ask a question, even in college,
I didn’t wanna ask a question in front of everybody to a professor. So I really relate to the students in this sense, even though I try to make my classes engaging and let them share as much as they can with me and be nice or whatever, be friendly, but there's nothing like as a dance studio to make this happen, rather than a math classroom. It really sounds like this collaboration and the opportunity for these groups of students around this discomfort has taken down a lot of barriers.
You've started talking a little bit about how students have responded. I'm sure the response shifted over the course of the semester. Perhaps at first, it maybe was about shock, and probably evolved. You talked about students laughing in the studio and things later on in the semester. Can you talk a little bit about how students responded at the beginning and how you ease them into this space? Because I'm sure you had to do some onboarding, and then how maybe that
evolved over the course of the semester? Yeah, so there's a bit of hesitation at the beginning. So some students were distressed or in discomfort with the movement aspect often and unsure about the space at first, but Lori would take the lead of this in a beautiful way. So one thing that was memorable is that she made us introduce ourselves with pronouncing our
names and associating with our names a movement. I usually in my math class introduce everyone the first day of class, and some of them, they're afraid to speak up, even if they just have to say their names and why they're there, which is usually because of a requirement for the major. But anyways, that experience of associating a movement with their names was memorable, and everyone had to echo the movement and repeat their names. And I think this is not only like a
way to get acquainted with one another, but also to remember the names. Because if you associate a name with a movement, you most likely remember the name. I do, because when you have three classes, I've got to learn about 60 something names every semester. And there's a lot of different ways that we learn. And I will see someone on campus, and I will remember their movement, sometimes easier than I can, sometimes, their name. And then
it takes several weeks, and I can integrate both things. But again, in a beginning level class, Modern I, which is where this shared student we had was, we all do, we just call it the name game, and it's very effective. It kind of breaks the ice. And I will say, in terms of the progression that we feel over a semester, we repeat things, warm ups, they're not prescribed, but we continue to repeat some of the same material of body awareness techniques that are somatic,
that they get more and more comfortable with. I'm not correcting anyone, it's just an experience to be in the body and be present to learn, and then when we get into improvs, and that is a course that I totally love teaching at Emory, and I'm in my silly self, I think, when I teach improv, it's about the potential of anything to go in any direction, and it is about breaking rules sometimes. And once you charge an environment or a room with that kind of energy, it's just
different than having to get to a concrete outcome. It's very explorative, and the freedom, I think, is what you feel more than anything, To speak more about the students’ response about the course, I think that we had such a positive feedback. Some of them at the end of the semester said that they like to start with a movement-based activity before introducing the math concepts. And I think this is what the students like, and I do also. I always ask Lori, let's start with a
movement hook, because to start with an equation, it's always hard to get their attention. I do that in my classes already. I don't want to do that in a dance studio. And some of them have also said that this basically is a new study technique for them, that they're going to associate movement to what they're learning, and then I guess what they see the most is the visualization of the
mathematical concept. So we think about embodying it and experiencing it in the body, but I think that, for them, it's more about really seeing, not only in themselves, but seeing in the other
students as well. And one thing that I’d like to add on this is that we had also two students, Luoran and Ruishi, working on theses for math and movement, and basically they took the lead of one of the courses in one semester, and one of them studied the pedagogical side of math and movement, and the other one took the assessment part, so she developed questions and surveys and everything to see if this course was beneficial to the students, and they turned this experience into two honors
theses for their graduation. And now we're working together in trying to publish their results in a nice paper, hopefully, that we get out soon. That's great. That's a great experience for students. It was and it was inspiring to me that they wanted to do an honors project in it, because that means that this really resonated in them. They both graduated with highest honors, I will say as well. We weren't collecting empirical data at
all. We were just allowing this thing to be free for many years. And one of the things that we did, though, is we have the students reflect and so after class, we said, “How do we know what really happens? Is this sinking in? How are we going to know if what we're doing is working?” And I did go back, because I don't want to try to paraphrase what I'm remembering, these light bulb moments sometimes for students, we don't know when they happen. Is why we need them to write it in a
reflection journal. But we were doing a class that was physics concepts, really, so like resistance, velocity, momentum, Newton's laws of motion. And this is something that one student said, “I physically felt the resistance of air molecules as my body moved through the atmosphere. It was eye opening. It provided a tangible connection to these abstract concepts. I descended through the atmosphere. I keenly felt the drag force exerted by the air molecules, this resistance or drag
I felt in my arms and my legs.” And so I think again, in science classes, which are so different from classes in the humanities, where people discuss and write a lot, it was also helping these students describe feelings, really, sensations, that they were having in the body when they were exploring these mathematical concepts. Manuela talked a little bit about how dance maybe lit up some math. Lori, can you talk a little bit about how
maybe dance students saw math differently? Well, we really don't have that reverse scenario, because in those first years, we had two dance students, we had four TAs, and two were in math and two were in dance. And these were two people, one was a dance major, the other
was a dance minor. They were very interested in doing this, and they were my demonstrators a lot, but typically, I would say most of the time, the people that sign up for this are in math, so the crossover really hasn't happened, even though, in our field or at Emory people double major. So there's plenty of people who are biology or chemistry and dance and
they take math classes. I think that this will unfold over time, but I would say that we've designed this for math students to introduce movement to them, as opposed to the reverse. Still too scary for dancers to get to math. Yeah, back to fear. Yes. Well, it sounds like you've conquered fear in one direction… Yeah. …so it shouldn't be that hard to conquer it the other way. That’s right. It does take a bit of work though to get to the level of differential equations.
That’s true. Oh, my goodness, yes. So I can see how connecting mathematical concepts to dance provides students with some additional cognitive hooks, ways of connecting what they're learning to other experiences, which can make it quite a bit more memorable. Could you imagine this type of approach of embodied learning being applied to other disciplines? For example, if you bring some people in from music, might you have a course called Hamiltonians or something. That's great. I get it.
I mean, the short answer is yes, because I think movement relates to everything personally. But I can give you an example that was eye opening for me. So in 2023 there was a conference at Emory, hosted by the Center for Mind, Brain, and Culture, and it was called Minds and Movement: Prospects for the Study of Embodied Cognition, and Dietrich Stout, the director of that, initiated the whole conference, and he had heard, I think, our article had been written about us in the Emory Report,
and he was like, “huh, movement and math, let's bring them into it.” But it brought together these researchers in different disciplines: psychology, neuro/brain, behavioral biology, anthropology… a lot of anthropologists… who believe that cognition is grounded in the body sensation and movement, but the disembodied models from AI were starting to produce or suggest another outcome or another
theory. So, the question, really, that was asked at the conference, the overarching question. was: “has embodied cognition run its course?“ Like, how do we use our bodies in learning, and how could it foster applications in human health, therapeutic practices, all kinds of things. And the conference was fascinating. Everyone had, like, 20 minutes to present, so it was really lectures all day long, or mini-lectures, and I was like, we can't do what we do in 20 minutes, so they gave us a
two-hour workshop. It was at the end of the day, and I thought, “My goodness, they're not going to come.” I was skeptical. I was like, they're tired, they're going to want to go home and eat. But we brought them into a dance studio. They did all come. They were participating, just like our students, and laughing and sweating and interacting very playfully, and it just opened that door again, a huge door, asking questions that stimulated discussions about
how movement could be in any of these fields. But one of my takeaways was just this man that looked at deep sea divers and the reflex, the skill building, in the body of free diving, or the embodiment of reflex. Another person, her research was the neuro-mechanics that sculpt differences in our movement. There was another woman, I think she taught at Georgia State. Her paper was called “The Mindful Dynamics in Architectural Design.” So the body is part of
everything, and it's just kind of our awareness or your entry point into that. Mine is dance, but people use movement to research all kinds of disciplines or interact with other disciplines. One thing I'd like to mention is that this reminds me a lot of some of the work
that Susan Hrach has done. She was on a past podcast, and she has the book Minding Bodies, we'll include references to that in the show notes, because much of that discussion relates to this concept of embodied learning, and I think they compliment each other very nicely. Yeah, I'd love to look that up. I'd love to connect with her. So we always wrap up by asking: “what's next?” We have been working through research labs and
initiatives and things that have been going on in Emory. But finally, we got our course approved from the college, and it's a lab attached to my differential equations class that is optional for the students, and it's called “Differential Equations through Movement,” so we're going to offer this 50-minute lab every week to the students, and every week we're connecting with the classes that have been taught during the normal sessions of differential equations.
And sometimes we're going to use that lab to kind of reinforce the ideas. Sometimes we're going to use those labs in order to introduce new topics for the next week. So for instance, we've seen that with population dynamics, those games have worked beautifully. So we are gonna use those games to introduce population dynamics before I cover those in a analytical fashion. Since we haven't done our research in collecting data and our case study, we're going to do that
too. So we are now designing assessment tools so we will have pre- and post-tests, surveys, video interviews, observations in class, and students’ journals and reflections, so that we can compare all students in differential equations with the students that take the lab and see if this is effective or not. And now we have another dream, but I’ll let Laura speak for that.
Well, I think that, even in our initial design, I think of this partnership, how do we share it with other educators, to empower them to find new ways to help students learn, and we both have presented in our own fields at conferences and things like that. As Manuela said, we're working on a paper that will be shared, and that's another way that it moves out into
the world. But a more imaginative, perhaps creative, way, is that we're thinking of creating either a film, which would be some type of dance performance and/or a live performance, where you could use technology in terms of the set design or background screen, where someone would be seeing mathematical concepts in some way, maybe abstract or creatively expressed, and to create choreography with professional dancers, not students,
that would help share concepts in math, and we're not sure when that's going to happen, but we talk about it almost every year, and it's really about finding the time to do it. And now you've said it out loud on a podcast, so maybe it'll be real. I know. careful. That's right. That's how you turn dreams into reality. Thank you. This has been an interesting conversation, and it's nice to see people doing some creative things to help students make connections and to learn more deeply.
Yeah, that sounds really fun, and a great class for people to observe. Thank you. Thank you. If you've enjoyed this podcast, please subscribe and leave a review on iTunes or your favorite podcast service. To continue the conversation, join us on our Tea for Teaching Facebook page. You can find show notes, transcripts and other materials on teaforteaching.com. Music by Michael Gary Brewer.