Sandwiches and the Ontology of Definitions

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 PDF activity. Update: Phil DeOrsey made an interactive Desmos version!

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Equations, Identities, and #WhoSaysMath

“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”

Of Cats and Combinatorics (Help!)

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!)”