How I Got Into Teaching
April 24, 2010: Without any post-graduation prospects. Received this email.
June 2010: Interviews and model lessons in DC and NYC. Future wife informs me that it’s probably not a good idea for me to move to DC. So! NYC it is.
Rational Expressions (2010 – 2015)
My first blog. It was all over the place, in terms of what I wrote about. I retired it when I needed a fresh start.
Math Mistakes
Summer 2012: With help from Dan Meyer, I start mathmistakes.org. I also make a youtube video about Khan Academy.
Global Math Department
Fall 2013 – Spring 2014: On Global Math Department board.
Fall 2013 – Summer 2015: Coordinated speakers for Global Math Department
April 2014: Along with the other folks of Global Math Department, created the GMD newsletter.
Summer 2015 – Summer 2016: Chair of Global Math Department
Complex Numbers
I spent a few years thinking a lot about complex numbers. I experimented with a few different ways of sharing more sophisticated perspectives on complex numbers with kids. These experiments culminated in a project with Max Ray-Riek. We developed curricular materials and shared our approach in an NCTM presentation in 2015.
The big idea: most approaches to teaching complex numbers rely on a purely algebraic motivation (“What’s the solution to x^2 = -1?”), often citing history to support this approach. This is false history; complex numbers only gained mathematical respectability when people married a geometric and algebraic perspective on them. This approach is rarely shared with students, leaving students without a good understanding of their importance, meaning or uses. We developed a transformation-centered approach. All of our materials are here.
Feedback
I’ve thought a lot about feedback during my teaching career. I used Standards-Based Grading during my first three years teaching, and wrote about my issues with the system. Grades undercut good feedback — for this reason, SBG falls short as feedback.
I wrote a series of blog posts about feedback in 2014. I gave a talk about hints at ShadowCon in 2015.
I’ve continued to write about feedback on this blog, though I formulated some of my ideas most clearly in Beyond “Better-Luck-Next-Time” Feedback. In short, I no longer think that the important part of feedback is the comment. In fact, those are usually optional. The best feedback experiences in my classroom have come from responding to student work with a whole-class activity that sets up an opportunity for students to revise their work.
Cognitive Load Theory
I wrote an essay on Cognitive Load Theory. I felt frustrated by how little I understand of an area of research that is controversial in math education, so I started to read about it. As I read more and more of the original papers, I realized that there was a fascinating story to tell about how the theory had evolved from its early days. I wrote this essay to capture what I learned.
I’ve continued to blog about the theory since writing this essay. The piece that I’m happiest with is Cognitive Load Theory and Why Students Are Answer-Obsessed. It captures my view that the theory ought to be of interest to a wide variety of educators, even those who don’t see themselves as “traditional” educators.
Other
2014 – 2016: Member of the first Heinemann Fellows cohort.
June 2016: Organized a mini-TMC conference in NYC.
Teaching With Problems 