Haha, I was going to write PCMI 2022 Day 1, but I know I absolutely wouldn’t be able to keep up blogging every day. It’s 8:22pm, and I’m just getting back to my room after leaving it at 7:15am, and golly gee, I’m spent. For those not in the know, PCMI stands for Park City Math Institute and it’s a 3 week summer professional development, and the teacher program is called TLP (Teacher Leadership Program). The information for the teacher program is here, and the constantly updating webpage with the materials we’re using this year is here. I did it two times in the past, in 2010 and 2011, and both were transformative for my teaching, and allowed me to meet and make some amazing math teacher friends around the country! So if you haven’t heard of it, and you want a recommendation from someone who is super critical about most professional development, this is me saying that it’s worth it.

One of the things that happened in the pandemic is that I stopped truly engaging online with other math teachers. Partly, was drowning with trying to figure out how to teach in a totally new way (remote and hybrid), partly I recognized there was no real way for me to teach effectively and I was constantly comparing my teaching to what I had done in the past, and partly my soul was crushed. It was hard to go online and see all the positivity and innovative things that people were implementing when I was just barely keeping my head above water. So I just stopped engaging by blogging which was my form of reflecting (what, a blogpost about how I started doing a bit more lecturing and became less engaging while teaching online? how depressing)… and stopped reading other math teacher tweets.

I’m hoping at PCMI to start blogging again here and there, even if each blogpost is just a mishmash of stuff. I even started engaging with some math teachers again online, and it reminded me why the online math teacher community can be so powerful and why I loved it so much. Here’s an example… one of my two working groups is on how to 3D print. My school has 3D printers. But I have never had any great ideas about how to use them in my classes (except for calculus, which I haven’t taught for a while, but I see lots of connections there). So in my working group, I was learning the basics of tinkercad (which is how you can create basic 3D things to print). But I realized as I was learning the tool, I didn’t know what the motivation was for learning it. In Geometry/Algebra 2/Precalculus, what is a concept that students learn where 3D printing would actually enhance student learning of mathematics — like they would understand the concept better because they learned to 3D print it? And so I threw the question out on twitter:

Math T question: for high school math teachers of anything other than calculus, do any of you do any 3d printing? If so, can you explain how or send me some links to things? I'm trying to see if there's a way to enhance student/conceptual understanding (1/2)#MTBoS

— samjshah2 (@samjshah2) July 18, 2022

It was amazing to see people reply! And share links, and ideas! I haven’t yet gotten to look through all of them, but it seems to me like there are probably two or three classes of things: (a) things that kids will make and be proud of and appreciate but didn’t actually enhance their understanding of the math (but would bring them math joy), (b) manipulatives or demonstration thingies that a teacher can make to illustrate or play with ideas (but the making of the manipulatives wouldn’t be so powerful), and (c) the thing where the actual building of the 3D model develops and enhances a kid’s sense of an underlying mathematical concept or idea (where the time spent doing the building is actually worth the payoff in understanding, rather than just using pre-created manipulatives).

So that was fun to re-engage with twitter! And when we saw that Eli Luberoff (founder of Desmos) was coming, it was fun to be able to tweet him to say everyone seemed excited!!!

I also really enjoyed starting to get to know the teachers here in person. I was actually pretty nervous about coming because I honestly think I’m going to just be alone and no one is going to want to hang out with me. But of course that’s never true, but it doesn’t make that fear any less real! (I grew up with no friends when I was younger, so I think that has just scarred me in this respect!) And to find people who want to share groan-worthy math jokes they make in their classroom while we’re eating dinner, or to talk about why someone took the leap to go from 20 year veteran classroom teacher to principal over our breakfast oatmeal, or (fill in any number of conversations here), reminded me how much I love hanging out with math teachers and geeking out.

In the morning, we do fun collaborative math problem-solving. My table (SHOUT OUT TABLE 3) spent a ton of time on this opener:

We found patterns, codified them, refined them, checked them, broke them, fixed them, posed our own questions about them, etc. It was cool because we all had different approaches and styles, but that also made it challenging. I have my kids reflect a lot about how they work in their groups — what they bring to it, what they think they can work on, etc. And so I think that in some ways we were very strong: there was a lot of idea sharing and excitement and conjecturing. But this is a wondering: I wonder if everyone felt like we were all working together to create collective knowledge. Something I tell my kids in my class is that when they’re working in groups, the goal isn’t individual understanding (that they can build at home)… it’s to build collective understanding. And so everyone has to be as invested in the thinking of others as they are in their own thinking. And I’d say that on that metric, there was a lot of interest in the thinking of others, but not for us to build some sort of group collective understanding, but rather to fill it bits and pieces of our own individual understanding. My whole thing about individual understanding versus collective understanding in my classroom… I don’t think this is actually part of the PCMI morning group philosophy, but I think it would be interesting to see if a group I was in all agreed to go in that direction and what we could accomplish both socially and mathematically. I think it would generate some really rich question-asking that would refine our own thinking and understand other people’s thinking, but also help us sortwhat we were having a surface level understanding (more pattern recognition) of to deeper conceptual understanding of (an ability to say why something worked). 

Okay now I’m really lagging, but I want to briefly talk about our “Reflecting on Practice” session. Our focus is going to be on assessments, and I think it’s going to tie into many conversations we’ve been having at my school about grade inflation. Because one of the things we’ve been talking about at our school is “what does a grade mean”, and it’s clearly an artificial construct that flattens a multidimensional thing but is super important in the larger scheme of things because grades matter (at least to my students, for a variety of reasons). And so it was interesting to think about what is “knowledge” and “how do we know that we know something” — because our leader said — we can’t really think critically about assessments until we delve into some of the philosophical underpinnings. We got some reading on assessments from NCTM’s Principles to Action which reminded me if we as teachers reframe and expand our definition and purpose of assessments, they can be much more useful in our teaching practice. 

I also went to a lecture on cryptography which was beyond my level of understanding, but the speaker was excellent and though I needed time to understand the details, I could see the larger argument and zoomed out bigger picture view of what she was sharing. 

With that, it’s 9:10pm, and I am flagging. So tired. So night night I go!