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 activity.

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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”

Grow Up, Branch Out: Quantitative Literacy for the 21st Century

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”

The Visual Syllabus (2019 National IBL Conference Poster)

“If my teaching is ‘different,’ my syllabi should be too.”

About three years ago, concomitant with my wholesale switch to standards-based grading, I also set aside the well-worn course syllabus template that I’d used for all my courses and set out, from a blank page, to design a syllabus my students would find worth reading. The result is a colorful, four-page visual syllabus that is now the key artifact of my teaching. Continue reading “The Visual Syllabus (2019 National IBL Conference Poster)”

The Infinite Series Sorting Hat

Looking for a way to keep all those convergence tests for infinite series straight? Looking for a cultural reference that some of your calculus II students will still find timely and relevant for a few more years? Look no further than the infinite series sorting hat.

Get the printable versions:

(Thanks to the many folks on Twitter who gave me suggestions to improve the original version!)