By Tim Chartier, Davidson College

In October 2021, Hortensia Soto was announced as the next President-Elect of the MAA. Tensia has a long association with the MAA. Most recently, she was Associate Secretary, planning the virtual MathFests and Joint Math Meetings. Soto is a professor of mathematics at Colorado State University. In this article, we get to know Tensia for her research and scholarship.

Chartier: First and foremost, congratulations on being elected to serve as the next President of the MAA!

Soto: Thank you. I am happy, honored, and humbled.

Chartier: In this interview, we are going to concentrate on you as a researcher. You work in Math Education and focus on embodied cognition? Can you help us understand that field and how embodied cognition plays a role in teaching and learning mathematics?

Soto: Embodied cognition is a lens that hypothesizes that learning is body-based. This means that we learn by moving and implies that generally our body enacts a mathematical idea before we can utter it verbally. Thus, in this field we pay attention to utterances such as gesture, body-movement, facial expressions, eye movement, etc. that may or may not be used in conjunction with verbiage as a source of evidence for the reasoning that may be occurring. Some say that utterances such as gestures are the first sign of intuition.

Chartier: Now, let’s focus on your research. What types of questions have you explored and what types of questions does your research focus on right now?

Soto: For the past decade my research has focused on the teaching and learning of complex analysis where my research participants have been pre- and in-service teachers, undergraduate and graduate students, and mathematicians. With my colleagues, we have explored how these various populations reason geometrically about arithmetic properties, function behavior, and analytic concepts like differentiation and integration. In my research I document utterances such as those listed above to support how a research participant might be reasoning about a concept geometrically.

I am currently working with six newly minted Hispanic PhDs as part of the NSF-funded project Latinx Mathematicians Research Community: https://aimath.org/programs/researchcommunities/lmrc/ As part of our project, we are exploring a mathematician’s spontaneous gestures as they teach complex analysis.

My post-doc Jessi Lajos and I are working on two new projects related to the teaching and learning of abstract algebra. The first project is about intentional (not spontaneous) gesturing that is conveyed to students and how it may impact students’ learning. For the second project we created environments where the research participants engaged in physical activities to explore Cayley diagrams, cosets, and normal subgroups. We are interested in how the activities might provoke intuition about the concepts. As part of these activities some participants had an external view, such as holding an object, and other participants had an internal view where they were part of the object. We hope to also create an augmented reality activity and are collaborating with faculty from the computer science department to help us code and create the environment. That will hopefully be next fall.

Chartier: How does your research impact your classroom teaching?

Soto: My research and teaching feed on one another. I get ideas for research from my teaching, and I integrate what I learn from my research into my teaching. For example,

• I pay attention to my students’ utterances as they convey concepts. This is particularly important as students are in the process of learning a concept because generally students can convey an idea with gestures before they can express it verbally. My job is to help them put words on their gestures and then help them mathematize their words.

• I frequently ask students to put their pencils down and look at my hands because I might gesture a concept, I might try to bring a diagram to life with my gestures, or because I attempt to connect a geometric and algebraic representation with my hands by simply pointing. The important piece here is that I am conscious of my gestures, and I intentionally try to help students be cognizant of them also and the mathematics behind the gesturing.

• I ask students to revoice and regesture other students’ verbiage and gestures.

• I create learning environments in the physical world where students act out the mathematics such as Euclidean transformations or stereographic projections. I also create dynamic geometric environments where students explore concepts. Sometimes the environment can be in the imagination via a thought experiment where I say “imagine that …” In all of these environments, the students convey ideas to one another via gestures based on the experience and I ask questions that help the students formalize their ideas.

• I integrate metaphors and encourage the use of metaphors especially for abstract notions where there are no diagrams.

• I am famous for saying, “you have a look—is there something you want to share?” I say this when I believe a student has an idea or a question but might be too shy or afraid to speak up. Some students laugh and respond, “how do you know?” Some students say, “no, I don’t” and after I ask, “are you sure” they say, “well, I was thinking/wondering/ …” Basically some students think I am psychic. Students’ gestures and facial expressions provide me with insight into what they are thinking, which helps me to teach.

• Mostly, this makes my class more interactive and fun (at least for me).

Chartier: I have a feeling you see the next question coming, but how can the rest of us benefit from embodied cognition without being an expert like you in the field? Are there ways we can use embodied cognition in our teaching?

Soto: I hear this question quite a bit and the answer is really pretty simple. Be cognizant of your gestures and of your students’ gestures. Becoming aware of our own gestures and making our students aware of our gestures can serve as another form of communication of mathematics. Some students need this and if we can help one more student then I believe we are making progress. From my own teaching experiences, I have found that when I introduce a topic from an embodied perspective, students generate several of the big theorems related to the topic. My job simply becomes to help the students symbolize and formalize their ideas. It also gives them insight into the proof. Too many times our lessons consist of writing a theorem, proving it, and doing some exercises and then repeating this again for another theorem. This works well for some students, but not for all.

Mostly, I think most mathematics instructors integrate embodied cognition into their teaching, but they aren’t cognizant that this is what they are doing.

Chartier: Is there a resource or place to turn, beyond you receiving a flood of emails, to learn more about embodied cognition and how we can use it in our teaching?

Soto: I am part of the Embodied Mathematical Imagination and Cognition group and we have a website. Here is the link https://www.embodiedmathematics.com/

Chartier: Finally, you are, of course, going to be President of the MAA! What are your hopes and visions for the MAA?

Soto: The MAA has gone through some major changes for the past few years that are good for the organization. These changes required difficult decisions and reorganization. Thus, I hope that the MAA can begin to stabilize and transform simultaneously. This may sound like an oxymoron! I mean that after MAA HQ moves to its new location, (which I believe is the last big change for a while) I hope the MAA can begin to transform to address the second component of our mission statement which is to advance the understanding of mathematics and its impact on our world. Currently, the MAA is doing an excellent job of advancing the understanding of mathematics through its programs such as the AMC program, Project NExT, meetings, webinars, and through activities directly related to its core values. I wonder how we might use our understanding of mathematics to address issues that impact people around the world; issues such as those that are poverty-related like homelessness, hunger, fear for one’s life, etc. I envision the MAA community using our mathematical knowledge and our generosity for inclusivity and community to pave this road.