Carl's Teaching Blog

A place to talk about teaching and learning

“You’re the DJ”: Thoughts from Teaching Social Justice using PBL #PCTM19

Thanks to everyone who came to my session today. We came up with a lot of ideas for projects and thought even more about how to actually teach them in your classroom. It was a great session and one that I’ll continue to think about and would love to talk about more in the comments or on twitter.

One of the questions that came out centered around the teacher, and the dual responsibility they have to 1) teach objective, unbiased information so as not to indoctrinate children and 2) prepare them for the actual world. Because the world is full of so much information, teachers need to select and choose and this selcting and choosing can be viewed as subjective. How do you decide whether something you are doing is subjective or objective?

Let’s say you want to teach a unit about public health in your stats unit during 7th grade. Some students may feel like public health issues should not be covered in math class, and the mention rankles their political beliefs while others believe these issues are too important to ignore and whose enthusiasm for change can push them to cherry pick data that supports their beliefs. If you’re that teacher you have quite a choice. As you plan the unit you may try your best to satisfy both students in what they will explore, but ultimately how decide whether it is safe to do or not? In the session we talked about walking the line between objectivity and subjectivity, and choosing whether to use the public health project. I answered the question, but it probably needs some elaboration. Here’s what @justinaion tweeted:

I swear this DJ reference makes sense. When I was a kid I loved DJ’d music, especially house music. My older brother Ray was in College when I was an 8th grader and he would bring down actual cassette mix tapes from actual DJs. I loved them, I played them into the ground and I still hum sections from those tapes from time to time. (Side note: Why do people call them ‘mix tapes’ if the songs play from start to finish without a dj making transitions. Isn’t that just called a ‘tape’? I digress.)

When I got out of college I thought I would try to teach my self to DJ like the tapes that I remembered from the 90s. With a computer I tried to capture the spirit of DJing house music without all of the physical labor required back then, and I got pretty good. I’ll rarely be prouder than when I mixed two songs together exactly like I heard it on an old mix tape after practicing non stop over a February break. My mixes weren’t as important as the fact that it was something I figured out thinking it was impossible for most of my life. I was just good enough to get paid, but ultimately couldn’t be as dedicated as the professionals who I respected and emulated. I decided to pour my energy into my actual job and my kids instead, but I often think about Djing. Especially when I think about things that are hard but I can do it if I just keep trying. I was thinking about DJing when I was getting ready for my talks that morning actually, so it makes sense that it came to mind during that session. Let me be more specific about the exact memory that came to mind.

I had offered my services as a DJ at a charity auction and someone won. I had to bring speakers and my equipment, but they told me I could play whatever I wanted. I convinced my girlfriend that accompanying me to this thing would be more fun than a typical night of board games and netflix with the ruse that I needed help carrying everything. Really I wanted a little boost of confidence. I was 100% confident these people weren’t expecting the house music I was going to play and I wondered whether they would hate it and tell me to pack up and go home early.

An hour into what would be my first, and only, house party gig where this guy came up to me who we can call Chaz. “Hey you should play this song next, I’ll totally get everybody dancing.” I saw that he knew the host of the party, and perhaps he would have more luck with getting people dancing, so I let him plug up his phone. This was nice at first because I could take a break and chat with my girlfriend who helped me lug all the stuff up there. Chaz starts playing music fresh off the radio that everybody is familiar with but no one really likes. After a while I ran out stuff to talk about with my girlfriend and found myself staring patiently at Chaz. “I’m the one that stayed up all night making this house mix playlist,” I thought to myself, “complete with transitions, rises, falls, and crescendos. I lugged all this crap here. This is my first chance to see if I can get people into this house music…” Chaz’s buddy brings him a fresh beer. “I should put my skills to the test and see if I can make this work. I should at least see if it will connect with people.” Chaz dances a little. He’s the only one dancing a little. I turned to my girlfriend and said “Dude has played enough of this garbage. If I’m the supposed to be the DJ, shouldn’t I just go put my songs on.” She looked at me like we were playing a board game and I spaced out and forget that it’s my turn. I told Chaz that I’m taking over after this song. “Ok cool I’ll go to the bathroom and get back on?” “No, I’m taking over for the rest of the night.” I jumped back into my playlist and tried my hardest to get this apartment party to vibe with this music that meant so much to me. Of course, no one danced the rest of the night, but in all reality no one was dancing when Chaz was on the decks either. They gave me a tip at the end, so I think that means they certainly saw some value in it, which gave me the confidence to keep doing it (just not at apartment parties).

There are some parallels between this and the question of objectivity vs. subjectivity.

The objective things are rarely objective, as our society is full of so many flaws and so much bias. To prepare teach kids to eventually inherit this world, they need to practice working on situations that might be subjective and making sense. Luckily math is the tool for making sense of things. Why not sharpen their ability with that tool by using it in situations where it is actually needed. If those two students are working on the health project, and they have criticisms, they should be able to use math to form their arguments. You could even plan for this kind of discord and ask students to present these math-backed arguments to someone else who decide whether something is subjective or not. If all of this or none of this happens, it’s probably better than the “objective” option. It’s better than Chaz playing songs off his phone.

If you’re choosing between taking the risk to do something new in your class instead of a more “objective” option, the first step is to put in the work. Do your best to learn pick a topic and a sequence of opportunities that are going to deliver the math objectives. Learn from the resources attached at the bottom of the google doc. Talk to other teachers, and people in your school to get feedback. Look for a low stakes place to put it into your scope and sequence. Make sure to actually be prepared to DJ with your set list and your backup songs. Don’t show up trying to play stuff off your phone.

Lastly, when it’s time to put your song on, put your song on. Do the activity, it’s ok if it doesn’t go well, it will go better next time. The important part is to try it, since anything is better than what I imagine would be in the textbook or whatever. When you don’t try it out, you miss out on the opportunity to get better at working with these kinds of tasks and the kids miss out too. The longer you wait, the longer Chaz will keep playing that garbage. Chaz has played enough of that garbage. You’re the DJ. Go put your song on.

Takeaway from my terrible cycle? Spend more time making kids comfortable.

Clogs have been in short supply this cycle, largely because things were going terribly. I think I know why. But first, let’s talk about what terrible looks like:

When we do VNPS, 5 of 8 kids don’t want to go to the board. When they do, 3 of 8 question why they can’t go sit back down. At least 2 or 3 kids per class will getting on their phone while their partner is writing. After a problem is announced students wait with blank stares until I go over to them, then when I get to them I feel as though I am moving a boulder. Spread this around the room and it’s like a field of boulders. Ok, ok, my classes are small, so it’s like a small field…perhaps ‘lawn’ is the right word. But it FEELS like a field of boulders, and it feels like I’m doing the heavy lifting.

There are reasons why. We had interruptions. I was out for the opening of the class, and we had break immediately when school got started. All students are new to this kind of class, some are new to the school. Many students had bad experiences with math. All of those were true last cycle. Let’s play the sitcom flashback music and talk about why last cycle wasn’t terrible.

Last cycle was amazing. 8/10 kids would go to the boards, start the problems and keep working without much trouble. Enough kids got started that even when we had the most complex problems there was enough work around the room that people could get started. Instead of blank stares, students would talk to each other, and seemed more willing to collaborate. It was like the boulders had grinded themselves down to billiard balls and they were already rolling around. I just had to direct them where to go. Visitors come in to my class and change their whole approach. This cycle if a visitor came they would give me a sympathy look and head back down the hallway.

What was the difference?
One difference with the first class was, and I didn’t realize this until the end, MAD Academy. I was visiting MAD Academy one day and saw half the kids from my class were there making music or designing murals.  All the MAD kids knew each other well. They were used to entertaining each others’ ideas, and encouraging each other to pursue their creative visions. When my class started, these kids were already comfortable talking, sharing, working and showing their ideas, all stuff that helps with VNPS. This comfort quickly caught on with a couple other kids, and it ended up being infectious with most of the other kids, outside of a few kids who had other stuff going on.

wearecityas Alum @franckstagram (class of ’94) shares his art processes and Native American-inspired symbol series with MAD Academy students.

The big difference is comfort. The kids were comfortable. Making kids comfortable made the teaching with the #thinkingclassroom as easy as rolling a ball across a pool table. So why did I ignore this important step?

When I planned this class I was convinced that it wasn’t the comfort that MAD Academy had built, but that it was something else. This attribution error made me put even less emphasis on comfort building and more on getting started sooner. Big mistake. Failing to make sure the comfort was there for all kids, regardless of their background, or whatever else is going on outside of school crippled everything else I tried to do this cycle. After spending most of the cycle moving boulders all day, I am going to think hard before I do that again. Instead I want to be more effective at building rapport and comfort with each class.

Comfort was rarely a focus when I started a class. As a management-challenged young teacher my focus was the opposite of comfort, in hopes of keeping kids ‘in-line.’ This stance has shifted, as I include more icebreakers but only after I walk through the syllabus and all the rules. I’m sure this is as effective as websites that make you read the terms of service, and so I’ll space the rules out across the first few weeks of class anyways to make more time for comfort building. I also tend to rush through the icebreakers too as if there was is trophy for how quickly I could get kids to start “doing math.” This is a race to see how quickly I could start lifting boulders. Instead I need to spend my first days sanding those boulders down by doing some activities to get kids comfortable sharing and being vulnerable together. If you have any ideas for what those activities might be, let me know in the comments.

Making Connections Across Math’s Changing Landscape

One of my co-workers was saying that she has no where to talk about what she is learning and how she is trying to grow as a teacher. She said that she is reading a lot of books, and trying a lot of things, but doesn’t have anyone to share it with or have a lot of time to process it. This was exactly the kind of thing that I talked about in my talk at #OAME2019 a month ago about why teachers need to connect online.

The basic premise of my talk was that teaching is constantly referenced in relation to the factory model which was the hottest economic opportunity as compulsory schooling went viral. Unfortunately, the factory model wants workers to follow the instructions to carryout precise and scripted movements to produce widgets, while schools need teachers who are able learn and grow in order to plan and implement innovative and dynamic lessons with students. The professional and emotional support that turn of the century factory workers need is vastly different than that for teachers. The kinds of support teachers need for this job may exists in patches, subject to grant funding or the shifts of political winds or under the eye of visionary administrators, but for many it doesn’t exist. Schools may make the shift, but the regulations and rules that allow schools to exist are essentially carved into stone and require loads of legal action for change. While it’s good that education’s importance is underscored by it’s inclusion in laws and regulations, it’s not good that people have to wait for change. Luckily we have the possibility to construct our own support network through the internet. We can write and share about things we are doing to learn and grow. By sharing we open ourselves up for feedback and perhaps provide writing that others can learn and grow from. 

Here are the slides from my talk:

It was great being in Ontario and giving this actual talk. Thanks to Sam Shah, Laura Wheeler, David Petro, Cal Armstrong and everyone else who was attended. If you were there, or if you weren’t and just think my slides are valuable let me know what you think in the comments. Better yet, let me know when you start sharing stuff on line!

Clog: Big questions to answer as I ask the #thinkingclassroom to dance again

Our school is beginning the 4th term. This means all new classes, all new kids and another fresh crack at the #ThinkingClassroom. I was debating about trying a different class this cycle, but the planning for this new class failed to materialize as I spent too much mental energy prepping for #NCTMSD2019. Repeating the class is important to me because the cycle ended in a way that felt unresolved.

A more deliberately comfortable classroom

Two very different students kids struggled from the beginning last cycle. It seemed like they didn’t know how to say they felt uncomfortable. My best guess was that the source of their discomfort could be one of three things:

  1. The whole VNPS routine
  2. Being in a math class in general
  3. Other things going on in their lives.

With the first two, a warm vibrant environment and lots of interesting math problems should be enough to win kids over. With the third, it seems like a larger effort for making the kids feel valued and competent would be useful. For the two students who struggled, their parents or their social worker made very clear that they had some other things going on in their lives, and no one had an easy answer for any of those things. Ultimately they both struggled with all 3 of those possibilities, and neither was able to gather enough momentum for the magic of the Thinking Classroom to have the same effect that other students were experiencing.

With more time, the discomfort may have gone away, but our block-scheduled, 8-week cycles made it hard for kids to really lock in. Instead students who aren’t excited to share or work with the group, a strong desire to ‘finish’ and get back to their seat, and frequent trips to the bathroom, college counselor, nurse, etc. One of these two kids stayed in the class a little more than the other, but they both struggled mightily on the final project. By the end of the last 8 weeks it was pretty clear that the uncomfortable students missed out on the practice of solving a lot problems, understanding the quadratic vertex form among other big mathematical ideas of the class, and a lot of the relationship building to support them as they finished the class. One of them scraped by and passed, the other did not.

Despite having the most positive experience I’ve had in years, I could only think about these kids as I looked to teach this class agian. They didn’t succeed with the math, which was disappointing, but they also didn’t succeed with this method. The primary reason I adopted the Thinking Classroom was to repair their negative relationship with math, but the last cycle seemed to just confirm that relationship. That doesn’t mean it didn’t work! I’m confident that I need to be more explicit about the kids relationship with math and look to find ways to help kids jump back in to the class despite their absences. I’ll hopefully be able to get some feedback on my improvements this time around as well as the student who failed last cycle signed up to take my class again.

Some new tweaks

To launch the thinking classroom, I decided to spend more time trying to explain the model to students. Today I decided to spend more time explaining why we are going to learn this way, and even made a space for talking about the class and it’s structure on the note sheet.

This time the note sheet will be different as well. I am going to make it a daily point to collect notes, and some kind of feedback about the class, and then get in the habit of the responding to what students say. Opening a space for conversation with kids will be good, and I can try to download them towards some positive note-taking habits so they don’t have to learn the hard way. The notes will hopefully be for them, but hopefully they will also be a space for students to let me know if the class isn’t working for them and where I can suggest strategies other than leaving class.

We teach 90 minute classes, which is too long to do VNPS all class, so I will break the class up into different acitivities. Today I took the chance to do a proper icebreaker in the middle of class. This gave a chance for everyone to get to know each other. We did a speed dating activity, which would be about half way down this powerpoint, after which kids worked in groups based on who they partnered with in the activity.

Going forward I’m going to ask the kids to read about math and what their thoughts are. I’m going to give them my ignite talk, make clear that we are taking time to play with math, and ask them to write about the research about some of the Thinking Classroom ideas (VRG, VNPS, etc) as it’s always good to include some literacy, and it may help the kids who are uncomfortable find more reason to engage.

Open questions

As this first class ended, I’m realizing that many parts of the thinking classroom work is still a work in progress. Here are some questions I still have.

I am pretty unresolved about how to deal with kids who are uncomfortable, or who may have anxiety or other conditions. How do I get those kids who are uncomfortable to be involved and invested?

It also seems like however the groups share out, the male students end up dominating the conversation and the ideas. How can I structure the tasks, and the class time to make the female students feel empowered?

The Thinking Classroom structure gives a lot of opportunity for the teacher to tailor activities for each of the students at the different boards. In trying to help any student in my class, there is space for me to provide scaffolding in real time that can support or push students as needed. It’s a great idea, but… How do I actually use my questioning and my question-answering to make sure all student are staying in flow?

Lastly, I think my struggles with the last class was that I assumed that this new approach to teaching would create a new classroom culture, like uploading a fresh new operating system on to the computer. In reality, the thinking classroom is really like an app and the larger operating system is what the kids and I think math class really is. If I am not doing the work of deliberately creating the environment, communicating expectations, and building relationships, I’ll basically be allowing all those old ideas and mindsets about math remain operating in the background. It’s like trying to upload the newest version of photoshop on an old Compaq that is running Windows ME. So I need to upgrade my classroom culture. How do can I change the culture of my class in order to help the students change their relationship with math?

All of this is going to have to be pretty difficult to do given my school and everything that comes with it (8 week classes, kids who are uncomfortable with math, project based classroom). I’d love any ideas you might have, feel free to leave any thoughts you have in the comments!

Ignite afterthoughts

I did an ignite talk yesterday!

It was pretty scary. Having to speak in front of that many people, getting introduced by Matt Larson, having to come after all of these people you respect and not getting to control when your slides change. It’s impossible to just not think about the people. If you’re doing one of these, begin by choosing an idea that keeps you up at night. Make sure it’s a good one. You will definitely be nervous, no idea can fix that, but knowing that you are about to say something important will help you push forward. Especially if it is something that needs to be heard, and that won’t get heard any other way. I had a bunch of ideas which boiled down to the talk above, but I thought it would write a little extra about what I might have said if I had more time.

Initially the graph below was going to be my first slide but it’s too complicated. It’d take 3 slides at least to explain what google ngram is (a search of words and phrases in all the books that google has analyzed since 1800), I realized that this might eat too much time to include, but it’s still really interesting;

This graph shows how often the term ‘mathematics test’ appeared in books published in english over the last 200 years. ‘Mathematics test’, and similar terms like ‘math test’, ‘arithmetic test’, and ‘math assessment’ all seem to be non-existent until the mid-1920’s, implying that math tests weren’t part of school math education earlier. This means the engineers who built the railroads, engineered clocks, and laid out cities, were probably taught math without seeing a published ‘mathematics test’. The mathematicians before that time did their work with no one insisting they score a certain percentile on a collection of multiple choice items. It’s quite a contrast to the measuring stick mentality where math is only the test. If the only reason to take math is to prepare for the test that assures successful passage on to the next level, then we’ve turned this beautiful subject into Candy Crush.

What’s worse about this graph is the historical backdrop of the increase in mathematics testing. America was still unsure how all the recently freed slaves were going to integrate in society. At the same time racial hierarchies based on pseudo-science were being adopted by some as a way to reorganize society. This is also around the time that the eugenics movement was gaining prominence. Some of these tests were popular because they affirmed people’s beliefs that some races were better than others. Go read about the guy who made the SAT. These tests have a legacy of assigning privilege to certain racial groups, while making claims to be objective. Tests are probably better now, but given this legacy, and the outcomes, maybe it’s time to explore the idea that the tests might be the problem. However, there is a lot to unpack in the history of testing, and I only had 5 minutes to do this ignite so the ngram got scratched.

Pedagogy has also changed a lot since then. When I looked around for resources about why certainly been influenced by testing, and also by the need for matehematicians to outfit cold war defense contactors. The “traditional” or “Skill and drill” way of teaching that results is pretty sad. Paul Lockhart a lot about this in lockharts lament. It was long enough that it could be an ignite by itself, but just read the first bit if you haven’t.

Download (PDF, 391KB)


If I had more time I’d talk about the compound benefits of cutlurally relevant teaching. Learners need to connect new information to the world around them. The brain learns through connection, not isolation. It’s literally a huge mesh of neurons and learning connects those neurons or strengthens those connections. If we are actively connecting the math part of the brain, to student’s culture and identity, when they are going to be more likely to think about math outside of the classroom. So if we can get kids to think about fractions when they are making empanadads or california rolls or bratwurst, they are more likely to master the concept than if they only think about it on test prep worksheets.

The idea of homework is really popular, We talk about flipping the classroom, but if we want kids to engage in mathematical thinking when they aren’t in our classrooms we should start by telling them connect math to things that they are already doing. Ask students to talk to the elders in their community about the math they use and bring that back in the classroom. Have students think about recursion when they go to get braids Put their world to work for mathematical thinking. This could be a whole other talk too. but I didn’t really have enough time.

Bethany Lockhart’s Shadowcon talk really connected with me especially the part about facing your fear. After her talk I worked her hashtag onto one of my slides.

Changing the way we talk about tests, bringing beauty, culture, and kids identities into the classroom is scary. To make progress we all have to face our own fears around these topics, often alone. Facing their fears and making a bold move is the only way to move past the problems caused by the measuring stuck mentality and the lack of culturally relevant teaching. Being scared will have to take a back seat to moving forward if we are going to change the way we think about math. Of course, I don’t know the right scary thing is for each person. People need to figure out what things are just outside of their zone of proximal development and do that, particularly in the form of CRP, particularly as it relates to changing kids relationship with math, andparticularly with changing the testing culture. What I would have loved to gone into more in my talk, and what I think Bethany did beautifully, was letting people know that the teachers are the ones to take risks and try new things.al

One more thing. #mathphoto18 was useful in coming up with the pictures that were used to visualize real world math connections. @erricklee did a great job facilitating that last year and I hope #mathphoto19 will be even better. Thanks to the following for taking the pictures that helped me make this talk: @alfgoralo, @MrsNewell22, @MNmMath, @carodumas29, @nadine1osborne, @debboden, @pinn,@ccampbel14,@mr_davis_math, @sagold, @BonnieUMontana, @wmukluk, @TheErickLee

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