Last week I attended a workshop led by Dan Meyer, hosted by the NYCDOE. This was the first in a series of three that I’ll be fortunate enough to attend with him this school year.
The focus of the session was to diagnose what Dan referred to as the paper disease. It’s the idea that learning mathematics through paper (like a textbook, for example) restricts not only how students learn mathematics, but also how they’re thinking about mathematics.
He demonstrated ways to use technology to open up problems to a wider audience of students. Of course Desmos was a focal point, but his oh-so simple method of using white rectangles in Keynote me struck me even more.
Here’s how it works: take a problem, any traditional problem typically found on a state exam or textbook, and screenshot it into a presentation software (keynote, PowerPoint, whatever). Start removing information given by covering up some of the info in the problem with a white rectangle. Repeat this process until you have something that can spark curiosity and give access to a far wider range of students. You’re basically deleting part (or most) of the problem, which may include the question objective itself. Less information equals greater access; it allows for students to formulate questions and make inferences about the info in the problem before even attempting to answer it.
The other huge takeaway for me was his development of informal v. formal mathematics. This could be interpreted as meeting students where they are, but I feel that it’s much more than that. Getting kids to think informally about mathematics during a lesson – especially at the beginning – requires far different planning than simply leveraging prerequisite knowledge. It’s more about how students are engaging with mathematics rather than whatever content they already know. Informal math also feels a hell of a lot different than formal math. When students are immersed in informal mathematics, they don’t even realize they’re doing mathematics. The same can’t always be said for formal mathematics.
Closing the loop, Dan argued that learning mathematics through paper flattens informal mathematics onto formal mathematics…instead of using one as a bridge to the other. This act injects our students with the paper disease.
I left the workshop wondering about how I’ve made math a highly formalized routine for my students. I left wondering how I would begin using the white rectangle. I left wondering about the unit packets that I create for my students, that together form my own textbook and how they’re impacting my students learning of math. I left wondering about the power of estimation. I left wondering how less is actually more.