Mathematics Doubt, proof, and what it means to do mathematics Throwback post from 2013 on a way of thinking of mathematics as the interplay between belief and doubt.

Teaching Building Fall 2021: Discrete Structures A work-in-progress report on my Fall 2021 classes, one month before launch.

Academia The semester that was, Part 2: A 3x3x3 reflection on Modern Algebra Another 3x3x3 reflection on my Winter courses, this time my Modern Algebra class.

Academia The semester that was: A 3x3x3 reflection on Calculus What I learned, what surprised me, and what I still don't know about the Calculus class that just finished up.

Course design What I learned from an open-technology policy in my classes In the fall, I instituted an open-technology policy in all my classes. I'm not going back.

Mathematics Four things I used to think about calculus, and what Iâ€™ve replaced them with Throwback to a 2009 article on changing conceptions of Calculus teaching -- with updates for 2021.

Academia Building Modern Algebra: Assessments More on the upcoming Modern Algebra class: The big ideas of the course and how I'm assessing those.

Course design Building Modern Algebra: Learning objectives The first post in a series on building a Modern Algebra course starts where the course build process starts: with learning objectives.

Course design Building Modern Algebra First in a series where I describe the course build process for a new course, Modern Algebra.

Teaching The power of student-generated examples in mathematics Why don't we have students generating their own examples more often? And how might such a strategy of student-generated examples look in practice?