For three and half days this week, I had the opportunity to participate in the Exeter Math Institute.
It took place at the Spence School, an illustrious independent school on the upper east side. I’ve visited the school on a few different occasions, and it always makes me gasp. From carpeted classrooms, busts of historic figures, marble staircases, and a grandfather clock in the welcome hall, in many ways it feels more like a museum than any school that I’m accustomed to.
Getting past my awe, I quickly learned on day 1 of the institute that this would be very different than any other professional development that I’ve experienced. The focus isn’t so much pedagogy or even math pedagogy. The facilitator, Gwenneth Coogan (who I later learned is a former Olympic athlete), was set to immerse us in a Harkness mathematics classroom for three-and-a-half days. Harkness is problem-based, so that meant that I was going to be doing a lot of math — which was actually the whole point of attending. I feel that I negatively impact my students by not mathematically challenging myself on a regular basis. Plus, I’ve heard nothing but rave reviews of the Exeter problem sets. (We worked on Mathematics 2.)
*Notes about Gwen: She had no slides. We used Desmos from time to time, but at no point did she even think about using a projector. This was refreshing as she moved us to be in the moment. Flow, anyone? Also, I found her to be incredibly personable and welcoming. Through all my struggles she provided a warm smile and wholehearted encouragement.
An unexpectedly pleasant aspect of the PD was the fact that I got to collaborate with both public and private math teachers. Rubbing shoulders with them, listening, and sharing stories was so helpful. I now wonder why more PD doesn’t cross over these public-private boundaries. Interestingly, despite Harkness being typically found in elite private schools with class sizes of 8-12 students, I learned from Gwen that Exeter’s goal is actually to develop Harkness in public schools (whose class sizes, to say the least, are not 8-12 students). With that said, there were only 8 of us at this EMI, an intimate little group. Admittedly, this helped the conversations get deep and stay deep. Call me crazy, but by the end of the institute, I thought of asking my principal if we could host an EMI at my school next summer. Why not?
Knowing very little about the Harkness method, being immersed in it taught me a lot about how it works and why it can be successful. Through independent exploration and group communication, students use problem solving to explore and learn mathematical concepts. The teacher isn’t the focus, as they’re just another person in the room who helps spur discussion. The mathematics and the interdependent nature of the class are everything. There are no prescribed notes or detailed lessons, just carefully planned problem strings that help unlock mathematical ideas for students. There is a sequence for the course (I think), but there are no units, per se. Concepts are interwoven into problems and uncovered by students little-by-little over the course of the school year. The result is unbelievably high levels of student ownership of learning. Experiencing it firsthand, it was truly liberating.
I do have a couple reservations. First, how the heck am I make work for a class of 34 students? Putting motivation aside (like, yeah), a rich class discussion is what truly makes Harkness thrive. Having high expectations is one thing, but to what extent can my 30 students have discussions at the same level of sophistication as a class of 12? I’m on board with PBL and Harkness, but that worries me. Second, selecting problem sets is critical in Harkness, and many Harkness teachers actually write their own. I may be the minority, but writing my own problems is not realistic — especially the type of problems that have a variety of solution pathways and generate real learning based on integrated mathematics. And thanks to the Common Core, I know that I can’t use the Exeter problem sets straight up. Lastly, I have a feeling that by shifting to a nonlinear problem-based approach (instead of unit-based, which is more linear), may throw my standards-based grading system for a whirl. What do I do???
Like much of anything we do as teachers do, much of my implementation of a Harkness- style of teaching and learning will rest on lots of tweaks and adjustments over time that will make it effective for students that I teach. I’ll start small and hope for the best. Geoff’s PBL curriculum might also be a big help.
A closing thought. In a Harkness classroom, there are boards all around the outside of the room. A powerful feature of the class — and one that captures the heart of what Harkness represents — is a message that Gwen relays to her students early and often: the boards are you for you, not me. In other words, the board space is used strictly for showing student thinking. It encourages students to be vulnerable, to get things wrong. I made progress in this area last year with VNPS — PBL and Harkness seem like a natural next step.