So the time came for my #NCTMAnnual talk in San Antonio. I had been thinking about it for weeks, telling my co-workers and family about it, and furiously touching up my slides. When the time came there was no one in my room. Not even me. I was in a cab travelling uncomfortably fast towards the conference center a full 25 hours after my planned arrival in the city. At that point I was already aware that I wasn’t going to talk, and it was pretty disappointing (and the cab driver going 80 was not helping). The NCTM was hit with a fortuitous wave of cancellations and a slot emerged at the end of the day Wednesday where I could give my talk.
My talk was a 30-minute burst so it began like most bursts, with a quickly paced race through as many ideas as time would allow. This talk is about a way to think about quadratics that I have been thinking about after the work in my school. At a transfer school, students will enroll in your class at any point of the year. Like, right after you had your really great introduction to functions, for example. Or perhaps right before you teach your unit in quadratics. I began to think that I should teach quadratics with the same focus usually reserved for linear equations. We focus on starting with exploring places where quadratics exist naturally, and taking students thoughts about those patterns and connecting them with the graphical, tabular, and equation-al(?) representations of quadratic equations. This is different than the last textbook I used which opens up the quadratic unit with F.O.I.L.
The session was moving along pretty smoothly until I gave the participants the washing dishes problem in the slides below. The problem was meant to be a quick taste of a strategy to offer kids a genuine chance of interacting with a quadratic pattern that arises from a real-world scenario. There was nice hum of thinking mixed with frustration in the room. I moved to cut it short as we were already 25 minutes through my alloted 30 minutes and prepared to post up the “answer” on the slide. When I got everyone’s attention and told them “we’re going to have to move forward” everyone looked at me like I was blocking the television during the fourth quarter. “I really want to hear what you guys are thinking,” I said, “but we are about to run out of time. It’s a burst so it’s only 30 minutes.” Someone in the crowd was said “No, let us keep going…” another said, “Just finish… there’s no talks after this, and we have nowhere to go.” I was floored.
We worked more about on the problem longer while I looked around for an interesting approach to highlight. It became a team effort as we all worked to make most out of our extended time together. Sadie helped me figure out how to focus the document camera and we talked as a group about Janet’s example of work that she ripped out from her notebook. Then I showed a way that student might approach the problem if they followed the linear approach I was describing earlier. Then a full 20 minutes after I was supposed to finish I began talking about another problem that fits this mold, and how these kinds of problems can be created to help kids make sense of quadratics. Janet left saying “I’m going to think about examples that I could show my kids.”
This 50+ minutes of my 30 minute talk has been the highlight of a conference full of highlights. I was honored and excited to have a great group of people to do math with. I’ll have to write more at a later date about the actual math in my talk, but I wanted to write about my experience giving the talk. Thanks to all of the people who came, our 50 or so minutes together totally made up for the 25 or so hours I had to spend behind TSA security the day before my talk was scheduled.