My Discovery-Based Math Elective: Different Things Become Difficult (Part 11)

This is part 11, of a 15-part series of posts detailing how I developed and piloted a discovery-based high school math elective. The first, introductory, blog post for this series can be found here [Introductions]. The goal of this post is to describe a couple of the biggest ways teaching this class felt different from a traditional class, primarily from a planning/prep perspective.

Teaching this class was a very different experience. Some things were much easier. Some things were much more difficult. Here are a few of the biggest differences, in terms of what it was like teaching the class.

• Why does it feel like I'm doing less prep?
• I'm the kind of teacher who often feels the need to make my materials at most a day or two in advance. The making of the materials is a part of my planning process, and so in making whatever materials I need, I am able to prep myself to teach the class the next day. Sometimes I'm able to go an afternoon without having to prep anything for the next day, but not often.
• As a 3rd year teacher, I have enough background with my content, students, and routines that I can whip up a good enough lesson in not that much time. I can always sink more time to make lessons better, especially if I'm experimenting with something. But I don't always have to. I don't even always want to--I'm not trying to burn out any time soon.
• The prep load for this class was very different. This year, the first one teaching this course in its entirety, I made the first half of the PSets for this course during the summer. Since the only materials I really needed for the first four days of the week was the PSet itself, that meant that during the first few months, I did basically no material creation. It honestly felt a little weird being able to go multiple days not really having to prep anything. In fact, the time spent outside of class was so much freer than any other class I ever taught:
• Sunday: 30 minutes reviewing the PSet, tweaking and polishing it
• Monday: One hour, after school, grading notebooks (I taught one section of 28).
• Friday: 30 minutes before school prepping for the discussion.
• And that was it. Sure, around exhibitions there was much higher time demand, but that was only for a couple weeks, once per quarter. I definitely could have improved the class by reviewing notebooks in the middle of the week, providing written feedback. But overall, the class went pretty alright. It felt like I was getting away with something. Until the first Sunday morning when I realized I hadn't already made the PSet for the next week.
• Let me tell you, one whole Sunday has never felt so short. Trying to write a whole PSet, with all the layers that I want it to have, that does the job and doesn't suck, is super complicated. And some parts of it I couldn't just research and come up with an answer to. So much of the math in these PSets is there because at some point in the last five or six years I stumbled across it on Twitter, PlayWithYourMath.com, or Numberphile or something. And I couldn't really force that to happen. Needless to say, that PSet was less good than the others.
• This is all to say that this class doesn't necessarily have less prep than other classes I've taught. It just pushes the material prep work to the summer and breaks, when I actually have the time to sit down and think through a whole PSet, peruse all my different archives of interesting problems, and play around with things. In particular, trying to create content threads that wander and braid meaningfully across multiple PSets requires a huge amount of focus and time to do with any kind of intentionality. I actually have to build the PSets in one big document, because there is (ideally) a bunch of interplay between PSets.
• The heightened demand on content knowledge
• Similarly, this course, as designed, puts so much of the scaffolding into the hands of the teacher, who has to differentiate, scaffold, prompt, and redirect in real-time. Sure, we have to do that in all our classes already. But with so many options, legitimately telling students to feel free to pick whatever questions and paths that they want means that the teacher could have literally thirty students doing as many different problems, needing as many different scaffolds.
• This means that the teacher has to have some really strong content knowledge. And while I wouldn't ever recommend it in any classroom anyways, with this course it is basically impossible for the teacher to just be "one week ahead" of the students. This is especially important, since so much of the content isn't the kind of math that many of us learned in high school.
• The teacher of these PSets needs the perspective on the whole landscape of problems, their full depth and connections. I wrote these PSets, and I wouldn't even say I have 100% understanding, but every shortcoming in my content knowledge is a point where I am needlessly limiting students. This challenges was made easier for me because I was the one writing the PSets. So I was able to build PSets that reflected my own experience as a math major, #MTBoS teacher, PROMYS for Teachers alum, recreational math hobbyist, Numberphile fan, and colleague of some math teachers who shared some truly awesome backgrounds.
• My goal is that it is useful to have already packaged this course as series of pretty complete PSets. Teachers to whom this content is unfamiliar can experience this as an authentic and fun opportunity to do some interesting and developmental math. Hopefully, by presenting all of these written PSets, in one big package, that frees up teachers to take some time and be students again--do the PSets. I wouldn't ever tell a kid they needed to do all the problems, but the teacher? Go for it. Play around. Map the mathematical landscape. Try to find the narrative threads throughout the PSets. If a kid asks for help, we have to have a solid vision at the ready, because this course places a lot demand on efficiently conferencing and circulating.