Carl's Teaching Blog

A place to talk about teaching and learning

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.



How do we pull kids out of these rabbit holes?

This is going to start like a political think piece, but I swear it’s about math curriculum and pedagogy.

Next to ‘THE TELEVISION’ in my high school textbook is a picture of Kennedy and Nixon having the first televised debate. At this debate Nixon showed up sort of

JFK and Nixon at 1960 debate

prepared, looking hot and sweaty, and perhaps a little rattled by the appearance of his opponent. As my teacher told the story, JFK spent weeks prior at Martha’s Vineyard relaxing and preparing for the debate. He showed up looking relaxed, tanned and screen-ready. He even had a makeup crew! JFK was prepared for the new medium of television and because of that he won the debate, and a lot of popular opinion. His control of that medium, led to control of the white house and the establishment of presidential debates as a critical part of any campaign.

If my daughter grows up to be a history teacher, she will probably have a section to teach about ‘THE RISE OF SOCIAL MEDIA’ they will probably have one of  Trump’s tweets. Trump is the figure here, because he is probably the first person to really master that medium, and hopefully no one will ever manipulate the public in that way again. Trump shoots off tweets faster than the fact checkers could keep with him, which I’m sure his followers loved. At the same time, Facebook, Twitter, YouTube and other platforms were directing people to more and more content using machine learning algorithms. Delivering people things what they want from the universe of content on their platforms helped these companies sell more ads. As shown in the Social Dilemma, the technology can push people down rabbit holes, some of which can be dangerous and toxic. As the new technology helped people find more and more about his message, aided by targeted campaigns from Russian and Cambridge analytica, Trump shocked the world with his 2016 win. The rabbit holes kept burrowing deeper conspiracies like Pizzagate and QAnon continue to snare Trump supporters.

Today after math class a group of students started listing a group of conspiracies they heard online, too many for the teacher to counter. It sounded as though the students were delivering outrageous claim after outrageous claim, but could only back it up by saying “I saw it online”. These teenagers had been pushed down the same rabbit holes that are leading to much of the political extremism of our now polarized country. When faced with an actual argument, an actual opposing view, it sounded like the students faltered. Perhaps this is where math class comes in.

If we do it right, math class could address the problem of students we are losing to social media. In math class we talk about communication, argumentation, and proof from Pre-K to PhD with an emphasis on applying it in new situations with fluency. Often schools skip this work and focus on computation, but that is dangerous. Students deep into social media get fed post-after-post of things they agree with, where they may stop expecting ideas to proved with logical arguments. If we want schools to teach students to logically pick apart an argument, ask questions, write out proofs and to do it all with speed and fluency, then math is subject to teach it. Math class is be the place where students build the muscles to apply, analyze, and support what they learn in History, Science and other classes or at least it could be.

How envisioning the future helped us work together

As I write this we are all waiting for the results of the election. For me I’m trying to do something between waiting with bated breath for to update. While I wait I will extend a little 3 day streak for blogging in the month on November. The thing that I keep thinking about is the activity we did to open a recent staff meeting.

Envisioning the good life

A lot of time was spent planning this particular staff meeting because we knew there was tension and anxiety in the air because, well… [gestures broadly at everything]. What was proposed to open the meeting was a visioning exercise that we each did mentally before engaging in small groups. We were each envisioning a future where our work has flourished, making positive contributions to our community and an overall good life. To fully imagine this we had to close our eyes and get relaxed and really try to immerse ourselves in the sights and sounds and smells of this future. After some time to think about that we brought our awareness back to the room and talked a little bit about it in small groups.

When our group got together to talk about this future it was one of the most interesting discussions that we have ever had in the school. We talked honestly about the things we were hoping for, but people also were able to discuss the things that we should change in order to really serve our students. The positive vision was so valuable that there was no resistance to the internal shifts we would have to make in order to move towards that vision. As we moved to the rest of our agenda, that future perspective pulled our discussion towards what matters and held us together even as contentious issues were brought up.

The interesting thing of thinking about that future was that no one described what they saw. We talked about how students would be their full selves, and how we effective we could be, but no one sketched out a game plan. Our tight schedule prevented us from describing what our futures with the color and the detail that a kid would if they were explaining what their ideal homecoming date would look like. This means that we were all talking about different futures, and that was ok. Trying to move towards all of our futures helped us all work together.

As I’m writing this and we are currently unsure of how this election will work it seems like taking a minute to think about a better future can help how I approach whatever news I get tomorrow morning. What will 10 years from now be like? How will my efforts to the communities that I’m a part of make our work more significant? How does what I do tomorrow impact that future?

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