by Daniel Chazan, University of Maryland; William Viviani, University of Maryland; Kayla White, Paint Branch High School and University of Maryland

In 2012, 100 years after Henri Poincare’s death, the magazine for the members of the Dutch Royal Mathematical Society published an “interview” with Poincare for which he “wrote” both the questions and the answers (Verhulst, 2012). When responding to a question about elegance in mathematics, Poincare makes the famous enigmatic remark attributed to him: “Mathematics is the art of giving the same names to different things” (p. 157).

In this blog post, we consider the perspectives of learners of mathematics by looking at how students may see two uses of the word tangent—with circles and in the context of derivative—as “giving the same name to different things,” but, as a negative, as impeding their understanding. We also consider the artfulness that Poincare points to and ask about artfulness in mathematics teaching; perhaps one aspect of artful teaching involves helping learners appreciate why mathematicians make the choices that they do.

Our efforts have been in the context of a technology that asks students to give examples of a mathematical object that has certain characteristics or to use examples they create to support or reject a claim about such objects.¹ The teacher can then collect those multiple examples and use them to achieve their goals.

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by Sarah Hagen

Recently as a graduate student I taught a week-long boot camp for incoming mathematics graduate students at Oregon State University. It was my first foray into teaching under the active learning model and it was a completely transformative  experience for me as an instructor. The change in my own attitudes towards teaching and pedagogy were so abrupt, so all-encompassing, that I felt compelled to immediately record my thoughts on the experience. Continue reading →

By: Matt Stamps, Yale-NUS College

When Yale-NUS College reviewed the curriculum for its Mathematical, Computational, and Statistical (MCS) Sciences major in the autumn of 2018, I spent several weeks reading about mathematics programs at similar institutions.  A common learning objective among many of the programs was a variation of “preparing students to become lifelong learners.” I really like this goal because, among many other reasons, it reminds teachers that students are human beings who have lives beyond their studies, and it reminds students that learning is not confined to the early years of one’s life.   As I reflect on my life of learning thus far, I cannot help but notice how significantly the way I learn has changed since I was a student.  Some of these differences arose naturally with changes in my circumstances over the years, while others could have been addressed while I was still a student.

In this post, I want to share some observations about how my approach to learning has changed since I started working as a professional mathematician, and how I have changed my approach to teaching with the hope of helping my students develop more effective and relevant learning strategies earlier in their mathematical journeys.

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Interview with Ari Nieh, with commentary from Yvonne Lai

Like many of us, I began teaching online this Spring. Unlike many of us, I began doing so at the start of the semester. I am co-teaching a class at Michigan State, and I live in Nebraska. One of the most useful conversations I had in preparation for this assignment happened in 2013, well before the current coronavirus epidemic. The math department at the University of Nebraska-Lincoln had been considering a synchronous online version of a mathematics course, for rural teachers. I chatted with Ari Nieh, then an instructor for Art of Problem Solving, about what it would take to teach online, especially via chat forum technology. (Ari then became a lecturer in Writing, Rhetoric, and Professional Communication at MIT; and now he is a game designer at Wizards of the Coast.) In the end, that course was run asynchronously (and in many ways consistent with the advice given in a previous post). Nonetheless, much of the advice I received 7 years ago aged well. With Ari’s permission, I share snippets of our conversation in this post, edited for readability, and with commentary from present-day me.
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