Carl's Teaching Blog

A place to talk about teaching and learning

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How to make the most of the 2023 NCTM Annual Meeting #NCTMDC23

For the past 2 years I’ve been working as committee chair for the NCTM Annual. I’m excited to get to see everyone and to see if everyone can take advantage of the opportunity to gather and learn from each other. The committee and I have worked to come up with a lot of new features this year, but because it’s been a while since people have gone to a big conference, I wanted to try to share the features. This Tuesday I did a little Instagram live with @TheMathGuru talking about how to get the most out of the NCTM Annual Meeting in DC. I thought it might be useful for people to see what we talked about in blog form. so I can include the things I forgot to mention. So I hope you find this brief guide valuable, and if not, let me know if there is anything I can do to make it better:

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Dance Parties, Fortnite, and not Knee Injuries

OPEN STREEETS!!!! Open streets is a summer activity in my neighborhood where they clothes the streets for child-friendly activities, and grown-up beverage consumption. This inaugural event had a performance from the band Brass Queens, the crosswalk outside our cupcake shop transformed into a full on dance party.  People of all ages were getting down. Even I got out there, unfortunately hurting my knee in the process. This post isn’t about me being injured, however, it was what was going on in the child dance section.

My kindergartner was dancing around with about 5 of my friends, but I was curious about the deliberateness that another girl applied to dancing. This 4th-5th grader was doing something that I see lots of kids doing at weddings and other dancing events. As the crowd around moves and grooves spontaneously songs, this kid was stayed in one certain spot, immune to the rhythem, cycling methodically through selections of the fortnite dance moves (emotes?). You’ll see kids do the floss, then do the dance move with their hands and knees going back and forth, and then back to then floss again. Allday. It was hard to not contrast the Fortnite approach the with group of kindergartners that my daughter was a part of. They went from trying to coordinate some kind of congaline, then ran to a different part of the floor, then followed along what the band was doing. They broke into groups, then got back together. They’d all mimic one persons thing, then all go do their own solo thing. Izzy begged me to pick her up, then ran away as I grimaced while grabbing my knee. But, again, this isn’t about me being injured, it’s about thinking.

Dancing, for me at least, isn’t about thinking. It’s kind of a spontaneous space where in you look to see just what you and the people around you can do with the beat and the melody that you’re being given. It’s not a time for strategy, or practice. This is what it seems like for my kindergartner. She’ll frequently have dance parties in the house that feature only fresh, unrehearsed moves or move combination. These dance parties don’t require recalling a sequence of moves that she learned earlier, pausing awkwardly upon finishing, and starting into another shortly after as if the music wasn’t related to her movements. These dance parties connect to a primal part of what it means to be human, and might resemble what our ancestors were doing around a campfire a few short millenia ago.

One of the girls with my daugther was from her ballet class. In class she is learning very specific movements like plie, releve, and arabesque and will give us formal descriptons of each. There is a focus on reproducing the moves correctly, and a whole larger context that these moves live in. Spontaneity and creativity don’t mesh with these formal sessions, at least not at first.

As my daughter ran into the dance party with this brass band with her friends, the group would casually break out moves they learned from ballet. The training from ballet gave my daughter a new set of skills that she could call on intuitively whenever the moment came on the dance floor. It wasn’t part of a rehearsed sequence. It was fluid. The ability to flow into and out of these dance moves while being in the moment seemed starkly different than seeing the Fortnite girl carrying out one full procedure after another. Because the moves also became part of her natural movement, it seems likely that my daughter would be able to retain these moves. She’ll probably flow into her ballet moves when she has kids of her own, and subsequently injures her knee on the dance floor while trying to pick up her 53 pound daughter like an idiot. But, seriously, this piece isn’t about me. It’s really about math.

Solving a problem is a natural and spontaneous thing. Students and adults figure out problems, craft approaches to find a solution, and verify their work constantly through life. For example, figuring out how many ice cubes to put in the ice pack, how much Aleve to take, what angle of elevation relieves swelling in your leg are all problems people must solve. When we see these problems we go about solving them as spontaneously as we do dancing at a dance party. As we learn math, however, that math knowledge can flow into the problem solving naturally. We won’t just carry out procedures regardless of what the problem entails, like the Fortnite approach. We’re not just going to try and throw any quantities we find into a proportion, for instance. The math we learn is to augment our primal natural problem solving process with new, fancier capabilities so you can flow into and out of different strategies as the situation demands. After my daughter started ballet the spontaneous dance parties were markedly more graceful, and powerful. Hopefully my math students will be able to have graceful and powerful problem solving skills after my class, whether they are facing subtaction, proportions, exams, or even the problem of finding an orthopedist that takes their insurance.

Clog: Solving the problem of ‘Problem Solving’

This cycle I’m teaching a problem solving class with some pretty high stakes. In the past I would teach the problem solving class as almost a diversion, or a a path away from the Algebra-Geometry-Trig avenue that students expect. After the pandemic the pressure around going through content has lessened, and the focus has shifted to let students ‘Do Mathematics‘. It’s kind exciting! I’m reminded of that Halloween where my Mom said I get to eat all the candy I want! Of course, a couple hours after my Mom’s announcement, I was in the bathroom sick to my stomach. Planning this cycle has not involved anyone getting sick, and only moderate amounts of candy, but it hasn’t been exactly exciting. The increased pressure around a thing that used to be a fun little diversion has caused me to look at my planning differently. Here are some of things that I have done so far that has made the class work or are still a work in progress.

Go with what you know

Initially I decided that I need to do things totally different. I thought that I needed to rethink the entire class from the ground up using one of the previous times I taught it as a guide, but largely throwing everything out. As I got just a little bit into this re-design it became clear that we are still in a pandemic, our school has a lot of stuff to do, and I didn’t have time to anything other than print out the old stuff. We use a few units from Crossing Rivers with Dogs that focused ofn Drawing a Diagram and Systematic Lists. This ended up making so much sense. Relying on the muscle memory of something I’ve done a bunch of times reduced mental stress, and as I go through it with the kids I notice a lot of ideas for fixes. Now I can gather all the ideas that I would want to improve so we can give it a quick overhaul before the next time we need to teach it.

The Thinking Classroom remains undefeated

One of the reasons I wanted to overhaul the class was because the old curriculum wasn’t optimized for Peter Liljedahl’s thinking classroom, which I have been working on. If these old problems were broken into smaller pieces to make it easier for students to try it, I thought it could make for a better thinking classroom sequence. There wasn’t time for the overhaul, however, so there wouldn’t be time for the thinking classroom…or so I thought. Yesterday I had decided to make VRG (visibly random groups) and doing VNPS (vertical non-permanent surfaces) because there was a level of independence around creating ideas just wasn’t happening. It went really well despite not doing norms or even really talk about what was going to happen, and also a bunch of kids came in late group sizes were wonky. The task was really heavy, but it was great for people to say, everyone did it a different way. Not everyone even got it right, and everyone was ok with it. Lesson learned. Next cycle of problem solving I’ll have the whiteboards up at the beginning of the term.

Escaping the ‘curse of the undone grading’

For each class session of the last 3 weeks I’ve lugged all of the folders for all of the students down 3 flights of stairs to my desk, only to lug them back up the same stairs before the next class. Why do I do this? Because I keep telling myself that “I’ll grade these before next class. Kids need feedback. There will be some time tonight and it won’t even take that long.” Lies. Why do I tell myself this? Well it’s not all a lie, the kids really do need feedback and if I am not giving the clear ideas of what a well-solved answer looks like, they might think they can just hand in something that they pulled out of photomath (this happened on Tuesday). I want students to use their brain and think, but it seems like they don’t want to get invested in the problem solving process if they think I am ultimately going to tell them it’s wrong. My idea of feedback isn’t to tell them they are wrong, but to give them a clear picture as to what may be wrong and how it could be right-er. This entials me giving each student a full detailed breakdown of each of their homework problems, pointing out all the possible avenues for further elaboration and actionable steps for what can be done. As I type this, that doesn’t sound feasible or even useful.

If  a student is going to receive a giant stack of feedback on some of the classwork from weeks ago, it will place a lot of stress, emphasis and pressure on the wrong place. In those assignments, students are to be practicing their problem solving skills. As it is practice, it’s expected that they can make mistakes and foibles. Students who see that this formative work is placed under the magnifying glass could leave students feeling like they don’t have a safe place to grow their skills. I thought of Grading for Equity which says how decreasing pressure around the homework lets students have a place to practice. A place to make mistakes. Perhaps not going hard with the red pen was actually a good thing for students.

I was sitting downstairs after Fridays class with a noticeably lighter load and realized I had forgotten the folders. I’d have to go upstairs if I was going to get the folders, but realistically there wasn’t going to be any more time to grade it today than there was the days before. Before actually continuing to repeat this feedback cycle, I asked Lavonne, a science teacher who happened to be nearby, about how she did feedback. Lavonne regularly gets creative work back from her students so she was a good person to ask. She described a feedback practice more focused on giving students the information they need about the work they are doing in the moment, instead of waiting until later. Imagine going around to students and letting them know this is what they are doing and this what they need to know. She had no stack of grading to carry home, nor any intentions to gather folders from three floors up. I decided that I was not going to do that either! Instead I was going to figure out how I am going to try to give feedback for now and in future classes.

With math I want students to take ownership of their problem solving which has been associated may mean being ‘less helpful’. When kids say “is this right?” I say “How can you find out?” because I want to remove myself as a thinking crutch and build their math confidence. At the same time, students need direction that they are on the right track if they are doing anything. If I continue to not give students the right answer, I could at least try to support the process of documenting their problem solving efforts so expectations are clear about what is needed in our final projects. I’ll try to figure out how to build more formative assessment around open-ended problem solving. If you have any idea how I can do that, let me know in the comments.

Looking towards the future

We had a bunch of kids who got in big trouble. NYPD trouble. Having to spend the night in jail kind of trouble. When they came back to school we had to address it because it was related to school, but we also wanted to to be supportive because those kinds of interactions can be traumatic.

So we’re sitting in the room with all the kids, lots of individual meetings with parents have happened, or have been scheduled, but we are still going to meet with the whole group as a whole one last time. The other administrators go in hard with the fact that they need to stay out of trouble and what life is like with an NYPD record, especially one without a high school diploma. Then everyone finished and there was a clear chance for me to jump in. What should I say?

Here’s what I came up with…

“Alright kids, we’ve done a lot of talking to you, but you haven’t said anything, let’s go around and hear from you. Let’s have you say these three things:

  1. How many credits you need to earn in order to graduate
  2. What you plan to be doing 5 years from now
  3. What class gives you the most trouble.

And pay attention to what each other is saying because there will be a quiz. ”

The kids went around, awkwardly at first saying off there things. “12 and a half, I think. I’m supposed to be done in April, that’s all I know. I want to be in College. Math…” Then after that I said…

“So now let’s see if you’re listening, Jonathan, do you remember any of the three things that walter said…” We went around again, less awkwardly giving everyone a chance to say what other people’s big 3 are.

“Ok great, now why am I asking you to do this before you’re allowed to go back and attend your classes?” They started to fidget so I quickly answered my question. “Well you guys are lucky to have found a really good group of friends, so you should use your relationship to support each other. The next time one you starts trying to do something dumb you can jump in and say ‘Walter, you know you have 12 and a half credits left, you’re not going to be in college if you keep cutting math class.'” This was met with some laughter. “For real, if there is any positive thing that came out of your whole situation it’s the fact that you have a good group here. Lots of people walk through halls or through the neighborhoods and don’t have anyone. If you guys can figure out how to help each other look towards the future you can do anything.”

Then I might have gone into something about that book the pact or something. Actually, no I would probably have just cut it there.

Ok actually I didn’t say any of it. When it came for my turn to talk I just sat silently and agreed with what everyone else was saying. I wasn’t really sure that I would have a chance to chime in or when it would be and then the moment was gone. Everything I wrote after “Here’s what I came up with…” was what I came up with at 4:48 in the morning and decided to write up here. On the chance that this group gets in to trouble again, I’ll see if I can use this and I’ll come back here and comment on how it went.

Face-To-Face Registration: Losing more Than Time

Today the entire school was working as a focused whole on creating student schedules. It’s more to it than that, but essentially the purpose that Registration serves in our school. It’s an important purpose because of our internships, as it allows for face-to-face placement. Underlying that is a period where all parts of the school can grow stronger through face-to-face interactions of all kinds.

Figuring out all the factors that will build a schedule that’s a good fit for students is hard. If efficiency is the only concern, we can boil it down to a school’s typical system of requests and course grids. Going through the process more deliberately allows slight adjustments to be made but most schools have a limit to what customization student’s can achieve. Those limits are built into a scheduling process that carries the school to an efficient and optimized solution in whatever time frame matters.

What has happened at our school for as long as it’s been open is the schedule building process is put entire in the students hands. Each student has to come through the school and align their classes and internships for the next term by sitting down and talking with a teacher, or multiple teachers. This means students who didn’t do what they were supposed to do last cycle might have to sit in front of the teacher who was expecting work from them. Any lingering issues between the two have to get worked out so that we can get this process going.

At the end of the day, students have a schedule, and they also have agency. They now can feel proud of the collection of classes they put together and can articulate why it will move them towards their desired future. The school community also benefits from issues being resolved, or at the least having a venue for resolution. Doing things in this big mishmash at the start of the school year always invites people to ask why we can’t just create a smooth bureaucratic process for this. However the time-efficiency gains might not be worth the losses that would also come with the alluring bureaucratic process.



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