EPaDel Fall 2024 Section Meeting

Benjamin Gaines
Iona University
Playing (And Winning) the Game of Cycles

In the Play chapter of Mathematics for Human Flourishing by Francis Su, he introduces the Game of Cycles, a combinatorial game played on a graph consisting of vertices, non-overlapping edges connecting those vertices, and the two-dimensional cells enclosed by those edges. Players take turns marking arrows on edges, with the goal being to surround a cell with arrows all oriented the same direction. The only catch- players are not allowed to create any sinks or sources with their move. In this talk, we will describe how this game is played, the winning strategies that have been found for some families of boards, and some of the work that continues to be done on boards where a winning strategy has not yet been found. We'll also share how this game can be used to introduce mathematical ideas to interested students of all levels, with minimal background knowledge required.

Dr. Benjamin Gaines is Associate Professor and Chair of Mathematics & Physics at Iona University.  He is also Treasurer of the MAA Metro NY section, and the recipient of Iona’s 2022 Brother Arthur A. Loftus Outstanding Student Research Award, and the MAA Metro NY Section’s 2024 Distinguished Teaching Award. His primary research interests include combinatorial games and math education, particularly on questions involving writing in mathematics.  In addition to teaching courses throughout the math curriculum, from Mathematical Thinking through Abstract Algebra, he greatly enjoys working with students on research questions in games and statistical data analysis.  He is very interested in helping learners of all levels overcome the perception that they are "not math people".

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Steven Greenstein
Montclair State University
Thinking With Things About Mathematical Things

As mathy people, we like to think about mathematical things. As a math educator, I like to think about how things shape our thinking about mathematical things. Things like physical manipulatives – tangible objects with pedagogical purposes – have a long history in math education. Recent research is contributing to the discussion by affirming that our thinking is not confined to the head. Rather, it is fully embodied. Even further, it’s extended through our interactions with material things. As the theory goes, the knowledge we have arises from our engagement with the full sensations of these embodied and extended experiences. In a very real sense, making sense is that which we make of our senses. In this talk, I will express some of these ideas through activities that invite the audience to make sense of mathematical ideas through their engagement with original manipulatives designed by future elementary teachers as part of their mathematics teacher preparation coursework. These experiences aim to demonstrate that manipulatives can provide the experiential context for activities essential to students’ learning of mathematics, and at every level of mathematics. And as far as objects-to-think-with go, they can be fun-to-think-with, too.

Steven Greenstein is a former high school math teacher and currently an Associate Professor at Montclair State University. He likes to think about mathematical things… and how people think about mathematical things. Steven is interested in enactivist theory and the phenomenology of mathematical experience; the design of tools that mediate it; cultivating creativity for radical change through qualitative mathematics; and issues of education and social justice. Through teaching and research, Steven wants his work to support the practices that democratize access to legitimate mathematical activity that honors the diversity of learners’ mathematical thinking and that is guided by agentive inquiry, mathematical play, and the pursuit of wonder-ful ideas.

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Ranthony Clark
Duke University
Quantitative Justice: Using Math to Change the World

Quantitative Justice research comprises the mathematical, computational, and statistical investigation of real world problems related to social inequity. In this context, mathematical tools can be used to quantify notions of ‘fairness’ in a given domain, generating both new mathematics and impacting society at large. In this talk we will introduce this emergent field of interdisciplinary research. In particular, we will use computational redistricting as a motivating example to show how math like statistics, metric geometry, and topological data analysis is being used to shift societal systems.

Ranthony A. Clark is a National Science Foundation Ascending Postdoctoral Fellow, Phillip Griffiths Assistant Research Professor, and Computational and Mathematical Science Fellow for the Center for Computational Thinking at Duke University. She earned a PhD in Mathematics in 2018 from the University of Iowa and her research interests include applied algebraic topology, data science, commutative ring theory, math education, and the history of Black mathematicians. Dr. Clark is deeply invested in quantitative justice, that is, using mathematical tools to address societal issues rooted in inequity. Her current work in quantitative justice involves applications of mathematics and data science to electoral redistricting. She was a Berlekamp Postdoctoral Fellow for the Fall 2023 Semester program on Algorithms, Fairness, and Equity at the Simons Laufer Mathematical Sciences Institute (SLMath) and currently works with the Quantitative Gerrymandering Group in the Department of Mathematics at Duke University.

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