JMM Workshop on ACT for teaching and learning
My name is Ted Theodosopoulos and I am a mathematician working at the Nueva School, an independent school for gifted students in San Mateo, California. It was largely as a result of the encouragement that folks at Topos offered me that I decided to propose a workshop on “ACT as a transformative, and impactful, paradigm for experiencing, sharing, teaching and learning mathematics” for next year’s Joint Mathematics Meetings, organized by the American Mathematical Society. I am happy to report that this proposal was accepted and the workshop will run on Wednesday the 4th of January, 2023, from 4–6pm.
My name is Ted Theodosopoulos and I am a mathematician working at the Nueva School, an independent school for gifted students in San Mateo, California. After several years in academia and industry, I transitioned to teaching at the pre-college level thirteen years ago, and this is my sixth year at Nueva, where I teach advanced electives in mathematics and economics.
My engagement with the Topos Institute began during the pandemic with a Zoom chat with Brendan Fong in April 2021. Since then it blossomed with significant positive consequences for my teaching practice. During my first visit to Topos in person last summer I met Paul Dancstep, who, over the course of this past Spring semester, visited Nueva on several occasions, meeting with students to present his Digital Abacus project, a category theory (CT) inspired interactive environment to explore compositional properties of algebra and geometry. These visits, involving a dozen juniors and seniors, have culminated in two concrete projects, pursued under the aegis of Research@Nueva, an innovative platform for collaborative, student-driven independent research experiences.
In the meantime, in early January, Paul had already partnered with David Spivak to deliver a student activity session, as part of Nueva’s 2022 Intersession, on compositionality in nature and AI. Doubtless this helped galvanize the growing student interest in Applied Category Theory (ACT), which was already apparent in the Fall, when I delivered a two-and-a-half-hour workshop on “Categories, Logic and Language” to a fascinated group of a dozen and a half students. This event was so popular I was asked to offer it a second time, in the Spring, attracting more than another dozen students.
By then, I had already reached out to Tai-Danae Bradley, partly at the recommendation of the folks at Topos. As a result of my acquaintance with her, I was able to incorporate a live-stream of her research talk at a recent workshop on categorical semantics, as part of my workshop with the students. The experience of listening in to a professional math talk, while being able to pause and dissect components of her setup that were of particular interest to them, was unforgettable for my students.
Even my classroom teaching was transformed this Spring, as a consequence of my involvement with Topos. Following a recommendation by Brendan Fong, I reached out to Tim Hosgood, who happened to be visiting the Bay Area for a few days, and who agreed to visit my Quantum Information and Computation (QIC) class for a guest lecture. The students were mesmerized by Tim’s accessible improvisation around the topics that we had been exploring. His engaging style resonated with them, as did his serendipitous introduction of diagrammatic methods, which inspired some creative future work for us. Later, in part through Tim, I reached out to Chiara Marletto, a leading researcher in QIC and constructor theory, who also agreed to visit my class, this time via Zoom from Oxford. My students truly felt an uncommon affinity with this burgeoning field of study, as a direct result of the personal connections they built with these two influential young scientists.
It wasn’t only my QIC elective that benefited from ACT. In January, I started my Linear Algebra class with a week-long dive into Eugenia Cheng’s recent “mathematician’s manifesto for rethinking gender.” My goal was to use this topic of great interest to my students as a venue to introduce a categorical perspective for linear algebra. This pedagogical experiment proved very successful, with students honing in on the unique power of CT as a language to consistently manipulate metaphors. They proceeded to deploy it creatively on several occasions during the semester. Before the end of the Spring, Tai-Danae was also able to visit my Linear Algebra classroom. She inspired us so much with her innovative work, bridging algebra and statistics in the context of computational linguistics, that we devoted one of the three culminating projects for our class on this very topic. A group of six students spent the last three weeks of class reading her recent research and exploring linguistic inferences using matrix encodings and partial traces.
In contemplating the classes I will teach next year, including Differential Equations, Graph Theory, Business Dynamics and Computational Biology, I find myself speculating about ways I can incorporate ACT perspectives to clarify my messaging and broaden my students’ experiences. But even beyond the classroom, my engagement with the folks at Topos have enriched my professional development as a mathematician. I am a probabilist by training, and had practically no exposure to CT in my formative years. While I have significant experience modeling stochastic processes, particularly in biology and economics, I only began exploring CT six or seven years ago, through the work of John Baez, with whom I was acquainted since my student years at MIT. It was largely as a result of the encouragement that folks at Topos offered me that I decided to propose a workshop on “ACT as a transformative, and impactful, paradigm for experiencing, sharing, teaching and learning mathematics” for next year’s Joint Mathematics Meetings, organized by the American Mathematical Society.
I am happy to report that this proposal was accepted and the workshop will run on Wednesday the 4th of January, 2023, from 4–6pm. The format is informal, without pre-planned talks. Instead, people can contribute ideas for short share-outs, in a survey link, and we can accommodate spontaneous, improvised brainstorms as well. I envision it as an active, participatory working meeting. The goal of our workshop is to bring together researchers and practitioners from different fields to jointly explore ACT as a paradigm for refreshing the experience of learning mathematics. Here is a link for further information and how to attend. See you in January, in Boston!
I look forward to continuing my fruitful collaboration with the Topos Institute over the coming years.