Is a hot dog a sandwich? More than a provocative conversation-starter at a party, this is the kind of question that invites a healthy scrutiny of our own assumptions and implicit definitions. Here’s a first-day-of-class activity aimed at challenging the sanctity of definitions, so that students can begin to take ownership of a more humanized mathematical discourse. Click here to jump to the activity.
“The best math questions all have the same answer: ‘It depends.'”
From a Twitter thread on telling the difference between an equation and an identity in the algebra classroom came this tweetstorm. For me, the question raises issues of our own expert blind spots, mathematical communication and tacit knowledge, and a way in which category theory can help us be more humble about students’ common “errors.” Continue reading “Equations, Identities, and #WhoSaysMath”
The older I get, the more time I wish I’d spent with combinatorics. That was true when I got tapped to teach our undergraduate combinatorics course for a semester in 2011 – there, I was rescued by the grace of a colleague and an excellent, inquiry-based text. And it’s true again now: I’ve got a counting problem in a research project that I just can’t crack. So I’m opening it up to the internet, here first and on MathOverflow later if needed. Continue reading “Of Cats and Combinatorics (Help!)”
This interactive video and set of resources was developed to support a faculty workshop offered by the Massachusetts Department of Higher Education in 2019. Special thanks to Robert Awkward, DHE’s Director of Learning Outcomes Assessment, for organizing and providing financial and logistical support for these workshops; and to Mary-Ann Winkelmes, Director of Teaching and Learning at Brandeis University, for co-facilitating the workshops by engaging participants in designing transparent assignments. Continue reading “Grow Up, Branch Out: Quantitative Literacy for the 21st Century”
Earlier this month, I did a preliminary assessment of Andrew Torrez’s speculation on the Opening Arguments podcast that the Roberts Court has ushered in a new era of polarization on the U.S. Supreme Court. The answer, looking at 20 years of history, seemed to be no. A wider view of 75 years of history, meanwhile, suggests the answer is… still no. The Roberts Court is not significantly more polarized in its merit case votes than any other Court in this history.
But, the data suggest two interesting trends in Supreme Court unanimity over the past 75 years: a steady boom-and-bust cycle about every decade, and a significant Roberts Court uptick in the second derivative suggesting that year-over-year, the consensus about consensus may be disappearing.