Carl's Teaching Blog

A place to talk about teaching and learning

Category: Uncategorized (Page 1 of 18)

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.

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?

What to do, now that the election is over

The election results have now had enough time to sink in and the results, are probably “permanent”.  “Permanent” is a relative term, of course, as this is 2020. A truckload of absentee ballots could be found inside an a shipping container in Ohio, Pennsylvania or Florida, and trigger more media speculation and delay. But for the moment it is time to wrap your head around the fact [Joe Biden|Donald Trump] will be President for the next 4 years.

Certainly there are lots of immediate geopolitical, and national consequences. Our participation in global climate change efforts will probably [lead to a boom in solar and electric|mean the world leaves us, and our fossil fuels, behind]. National efforts against the Coronavirus will be [bolstered by a coordinated national response|reduced to crossing our fingers and waiting for a vaccine]. It will be nice going forward to not be inundated with election ads and twitter posts, but it seems like reports of [Donald Trump not participating in, or being capable of, a peaceful transition|Donald Trump not participating in, or being capable of, working with a Democratic house and senate] are part of the political news in the months ahead. At this point, I’m [happy|disgusted] with the results, but glad this election is behind us. Whatever mental capacity I’ve gained now that it is over, is quickly being co-opted by all the work left to do in our schools after the spring.

A lot happened last spring. As Covid-19 shined a harsh light on the inequality that exists in the vulnerable parts of our society it was clear that the shadows of those inequalities are cast on our education system. At the same time, the brutality of our policing system demanded system-wide reform, which requires changes in schools. Schools are certainly part of the criminal justice system, and harm is caused to students through direct acts of  violence, and the normalization of silence. These things are pervasive nationally, but won’t have a national solution. Our national education secretary can’t be expected to come in and address this now because [their appointment will take months|she’s awful]. Furthermore, the constitution prevents the federal government from making sweeping change in education. To address these things, we are going to need that action to come from a place closer to home.

At this immediate point in history, when people around the country are are [reeling in jubilation|ill with disgust], it’s nice that we’ll have some certainty for a change. Yes, history is will be watching to see if [Joe Biden |Donald Trump] will bring about the change they seek, but now that they are in place, what are the changes that you can bring about? What are the books you could be reading, lessons you could be trying, feedback you could be seeking out? How can the values you want to see in our democracy, live in your classroom? Now is the time to go work with social workers to support students in need, or work with the deans at your school to have a more restorative discipline process.  Can you advocate for school policies more equitable and anti-racist? And can your students help? It may feel selfish or myopic to focus on your classroom and your own development in the midst of national chaos. Really it’s the first step towards sustainable long term change in our schools.

The election results are definitely [relieving|revolting], but they are also helpful, because now we can focus on things we can control. The problems that have been made so clear could be addressed with things that are within inches of our grasp. Those problems might still be around in the next election cycle if they fall off of people’s radar. This is still an important opportunity to push for the things that our students and our schools need.

Responsive School Design For Pandemics

Our school is doing remote learning, like every school I know whose year hasn’t ended. With the end of this year comes urge to move past hastily planned system we have been running since March, and look forward to the fall. Most people are postponing thinking about the fall because every time the mayor or governor holds a press conference they can’t say what the fall will be. The truth is, we already have all the information we need to start planning, and the first step is in looking real hard at this remote situation that many of us our mired in.  Uncertainty about next school year will loom from now until it September, and will be a constant through June. Luckily, the design of this web page can help to provide a clear idea of how to plan around uncertainty.

Web Page Designs Drastic Shift

For the last decade, web designers have struggled to build websites that deliver content and look beautiful, despite companies constantly creating new devices to view the site to on.  Modern websites instantaneously adapt to screen sizes as wide as a smartboard and as skinny as a smartphone. To see this in action, try experimenting with the size of this window. As you decrease the width of your browser window, the image of the 4 devices at the top stays perfectly sized for your window. Shrink it enough and you’ll notice menu icons appear. When it’s as small as the width of a smartphone screen, title of my site snuggles down next to the menu icons, conserving screen real estate, the font is easier to read, while the image at the the top still fits in the window. Websites didn’t always do this.

Comparing the ESPN website from 2010 and 2020 shows that actively adapting websites weren’t always around. Advances in technology created a litany of web-ready devices, so website developers had to build the  adjustments to the big screen, the small screen, and every screen in between. Having a website solely for a full-screen computer was as typical for ESPN and other companies as the 7-period school day is for NYC educators. The consistency and predictability of web design was unmoored by Apple’s 2010 invention iPad, as neither the desktop or iphone sized sites really good on the really popular device. How they addressed the needs in these website issues maybe have some valuable lessons for schools looking to address the litany of fears surrounding this pandemic.

Adapt Respond Overcome

After COVID-19 forced a blunt introduction to remote learning this spring, schools now can expect a fall where being able to slide into remote learning is a new normal. Schools will be expected to dust off the Google Classroom and Flipgrid if next year brings a second wave, or some families decide to stay in quarantine, or an outbreak happens in school. This experiment has been difficult and unfamiliar, but likely to return in the fall if the pandemic is still going. How can you map out any calendar for the year if your school will still be in the building, remote, or doing some kind of hybrid? With vaccine deployment expected in second semester at it’s most optimistic, your school can expect to snap in to a significant portion of time. It would be nice if we could switch between the old  model and this new remote thing, flexibly, right? Almost as flexibly as a … Reposnsive website?

Responsive Web Design was born a few months after the iPad in an influential blog post by Ethan Marcotte. In that post he provided an example of a responsive website that now looks standard, but was like a Back 2 The Future Guitar Solo at the time. He writes:

This is our way forward. Rather than tailoring disconnected designs to each of an ever-increasing number of web devices, we can treat them as facets of the same experience.

Wouldn’t it be great if next year could feel like one coherent experience? The news of a positive test hits your school community, in mid-October, not only does your school know how to shift the learning, but the clubs, events, and all other parts of the school experience know how to shift as well. Following some of the ideas of the web design, we could try to create a responsive school experience, in the hopes of ensuring for more equitable education in the face of these challenges.

Remote First

The first step for planning for next year should be to think through a remote learning approach that fits your values. Returning to remote learning in the fall is as appetizing as returning to that nightmare I had where I was surrounded by pirahnas. However if a second wave is remotely probably for the fall, returning to it with a plan you feel good about would be like returning to the pirahana dream, but with live preservers, or better yet a boat. Tightening up this step might involve the following:

  • Reflect – How was this spring? What headaches were caused for teachers, students, parents and staff? What worked? What things were absent in a way that made you sad? For those of us (still) working in June, you may want to send out surveys, and collect artifacts to enhance your reflection.
  • Tighten – Figure out ways to make the remote learning better.
  • Extend – Make a plan for a whole year of remote, not just something that could work for a couple of months. Make the ship, not the lifeboat.

Planning “Remote First” is key because it has the most restrictions. The phrase “Mobile First” has been the ethos at Google since 2010 because after tackling the challenging restrictions of mobile computing there is also great opportunity for the future. Once these most challenging problems have been tackled, it is now possible to build more amazing experiences everywhere else.

These are some big remote learning questions (that I wish I had answer to, and would appreciate thoughts in the comments)?

  • How do you have useful discussions?
  • How can students meaningfully collaborate?
  • How do you build community?
  • How do you support students with special needs in all of the above?
  • How can you monitor student work?

With the remote plan figured out, it is now possible to go to the opposite end and think through the completely optimistic full-year building plan. It’s not quite as simple as taking what was supposed to happen this year, since the building plan needs to avoid contradicting the remote plan. If the remote plan is using some app to build community, use it the building too. If the remote plan can’t include that super awesome hand-on project, don’t include it here. Better yet, figure out how to do remotely, update the remote plan but add the full-glory version to the building plan. Having the two plans mapped out should eventually look like two trains running on parallel tracks. This is key since there is probably going to be some jumping back and forth between trains through the year. Starting with the constraining remote plan first will ensure a coherent experience for people no matter which train they are on. Deciding when to jump trains is the reason from breakpoints.


Website designers use breakpoints to define where a website needs to change for given the size of a users window. For example, if the width  of this window gets smaller than than 1000px the sidebar disappears. If it gets lower than 784 the navigation changes. The breakpoints continue until at 500px the full mobile layout takes over.  These breakpoints are aligned where the major device screen sizes would be and the designer made sure to plan which elements of the mobile layout and the desktop layout would be the right amount at each breakpoint.

A Breakpoint for a school might be an hybrid where some people are remote, others are in the building. For example, one positive test result could send a whole group of students into self quarantine. A breakpoint here would be helpful think through. These students’ teachers would know to move their instruction to the remote train, and in thinking through this breakpoint, maybe some letters home were drafted to communicate this to parents. A similar breakpoint could involve teachers being out on quarantine in such number that coverage is unmanageable. Then the classes can convert to computer labs, essentially, and students who are in the building can work remotely with the staff that are left. Throughout the summer and during the year, if it seems like a lot of people move between the remote plan and the building plan, it would be good to stop and think through how that would work, and call that a breakpoint.

Adapt, Respond and Overcome

The leap from old rigid websites of 2010 to the flexible ones we have now invovled lots of little steps. We still don’t have a lot of information about the way school will look in the fall, but we certainly know two ways it can look. We know what the remote learning looks like, and we can plan to make that better. We know what the building learning looks like, and we can adapt that so it is more responsive. With the two plans in hand, we can take little steps to handle whatever gets thrown our way, and in the process make our schools more adaptive and flexible.

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