So this week I attended two days of the NCTM 2018 Annual Conference in Washington D.C. I’m so fortunate because my school has a funder, PDT, that fit the bill. This was my first NCTM Conference — and I’m pretty sure that without their generosity there’s no way that I would have been able to attend.

While I was overwhelmed with the massive selection of workshops, thousands of people, and the dizzying amount of corporate sponsors, I did my best to stay focused. I narrowed my takeaways to two, one big and one small.

Well first let me just say that, naively, I was surprised by how lackluster some of the sessions were. None that I attended were horrible, but there were several that I was very unhappy about. This was true also for my colleagues that attended. What can I say, I’ve been spoiled by MfA — where the quality of PD is through the roof. After a while, I just started looking for sessions facilitated by folks that I knew and could bank on, like Sara Vanderwerf. She never ceases to inject me ridiculous levels of inspiration.

Anyways, back the takeaways. This school year, while I’ve adopted a more problem-based learning approach in my classroom, I’ve been crying inside at the loss of my standards-based grading structure. By pouring so much energy into reimagining my classroom, I sort of gave up on integrating SBG with PBL.

Well, with that being said, it seemed as if the entire the conference was screaming SBG at me. I attended a session with Dave Martin (he was incredible) on differentiating assessments and SBG and I walked out knowing that I have to find a way. My kids deserve meaningful, accurate assessment. There were several other sessions that also forced me to rekindle the love that I have for standards-based grading. This was the biggest and most impactful takeaway.

On a smaller scale, I went to a session by Chris Shore, the pioneer of Clothesline Math. I have played around with Clothesline Math once before after reading about it online, but this was an opportunity to experience it firsthand. It was awesome! Interestingly, his focus was on functions, yes functions, on the number line. It’s such an intuitive tool for building number sense. I’m definitely making plans to bring the open number line to my students before the end of the year. In fact, I hope that it can become a staple.

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.

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.