Carl's Teaching Blog

A place to talk about teaching and learning

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Beyond Linear #NCTMAnnual 2017 Presentation Materials

So the time came for my #NCTMAnnual talk in San Antonio. I had been thinking about it for weeks, telling my co-workers and family about it, and furiously touching up my slides. When the time came there was no one in my room. Not even me. I was in a cab travelling uncomfortably fast towards the conference center a full 25 hours after my planned arrival in the city. At that point I was already aware that I wasn’t going to talk, and it was pretty disappointing (and the cab driver going 80 was not helping). The NCTM was hit with a fortuitous wave of cancellations and a slot emerged at the end of the day Wednesday where I could give my talk.

My talk was a 30-minute burst so it began like most bursts, with a quickly paced race through as many ideas as time would allow. This talk is about a way to think about quadratics that I have been thinking about after the work in my school. At a transfer school, students will enroll in your class at any point of the year. Like, right after you had your really great introduction to functions, for example. Or perhaps right before you teach your unit in quadratics. I began to think that I should teach quadratics with the same focus usually reserved for linear equations. We focus on starting with exploring places where quadratics exist naturally, and taking students thoughts about those patterns and connecting them with the graphical, tabular, and equation-al(?) representations of quadratic equations. This is different than the last textbook I used which opens up the quadratic unit with F.O.I.L.

The session was moving along pretty smoothly until I gave the participants the washing dishes problem in the slides below. The problem was meant to be a quick taste of a strategy to offer kids a genuine chance of interacting with a quadratic pattern that arises from a real-world scenario. There was nice hum of thinking mixed with frustration in the room. I moved to cut it short as we were already 25 minutes through my alloted 30 minutes and prepared to post up the “answer” on the slide. When I got everyone’s attention and told them “we’re going to have to move forward” everyone looked at me like I was blocking the television during the fourth quarter. “I really want to hear what you guys are thinking,” I said, “but we are about to run out of time. It’s a burst so it’s only 30 minutes.” Someone in the crowd was said “No, let us keep going…” another said, “Just finish… there’s no talks after this, and we have nowhere to go.” I was floored.

We worked more about on the problem longer while I looked around for an interesting approach to highlight. It became a team effort as we all worked to make most out of our extended time together. Sadie helped me figure out how to focus the document camera and we talked as a group about Janet’s example of work that she ripped out from her notebook. Then I showed a way that student might approach the problem if they followed the linear approach I was describing earlier. Then a full 20 minutes after I was supposed to finish I began talking about another problem that fits this mold, and how these kinds of problems can be created to help kids make sense of quadratics. Janet left saying “I’m going to think about examples that I could show my kids.”

This 50+ minutes of my 30 minute talk has been the highlight of a conference full of highlights. I was honored and excited to have a great group of people to do math with. I’ll have to write more at a later date about the actual math in my talk, but I wanted to write about my experience giving the talk. Thanks to all of the people who came, our 50 or so minutes together totally made up for the 25 or so hours I had to spend behind TSA security the day before my talk was scheduled.

 

Handout:

Download (PDF, 323KB)

Some quick thoughts about Finance and Math

I haven’t written a blog post in a while, so I figured this tweet is as good a prompt as any to get back in to it.

I taught a math econ unit for a few years now and I have a few things that I do. I did a Global Math Dept talk once, but it was the only one ever that the audio recording dropped out on (sad face). Here are the slides from that.

In this talk I pretty much list all of the tricks I have, some of which include:

  • Giving kids credit card applications is always a good time. I’ve collected a box of those mailers that they send me, but you could find some of them online. Then you can make a task where the kids use exponential growth to see if they can manage life with a credit card. Here’s what I’ve used in the past.
  • Stock market games are always fun, even though there isn’t too much math involved unless they are doing some next level modelling and regression and what not. I had kids go to Marketwatch and play a game with the rest of the class to see who can make the most of their $100,000 investment.
  • My co-worker has a bunch of projects he uses for a lot of the formulas that use exponential growth for financial purposes.
  • Speaking of Exponential Growth here is a little lesson on exponential vs. linear growth that is a play on that whole “grain-of-rice-on-the-chessboard” thing:

Is this helpful? Let me know your thoughts in the comments.

How this political atmosphere is changing me (and this blog, and my twitter)

This Sunday feels like a good time to write about what’s happening on my blog. I haven’t written as much as I would have liked over the past few weeks, so I feel a little explanation is due.

We have not had any actual classes for the past few weeks so there has been any actual teaching since my last class log. Most of those class days were spent floating around the room helping kids, so there wasn’t much to blog about earlier in January. There was also a lot of administrative tasks needed for the individual scheduling for students. (It’s a super cool network of google spreadsheet that I may blog about later on my other blog). … Oh and it was my wife’s birthday. So we had our first baby-sat date night at Olmsted, which was really nice. I plan to write more with the start of February, where I won’t be inhibited by my lack of classes to talk about, my administrative demands, or my frenzied last second search for birthday presents. So I guess that’s the only thing that’s going on with this blog about teaching and learning.

Oh wait. I actually didn’t mention that other thing that happened towards the tail end of January. Technically it was a November thing, but most of the work that I took on didn’t start until mid-January. I really underestimated just how much time I would need to devote to this. What I had to do for this thing was curl up into the fetal position on my couch/floor/classroom, scroll through the as much internet news as I could, and try to convince myself that the world wasn’t imploding. This has been taking up pretty much most of my time for the past two weeks. It started just around the time that my colleagues and I watched the inauguration during lunch.

My colleagues and some students watching the inauguration during lunch

Since the inauguration my attempts to figure out what is going on have been voracious but not necessarily successful. I’m diving into all the political news I can handle, both to try to harvest any optimism from news of the resistance, and to try to make sense of a Trump voters view point. Finding actual information is really hard. There are active disinformation campaigns, information that isn’t made public, and my need to parse through boring information so I can know about typical government procedures. This frustration would make me give up. In the past I’d ignore political news and go about life assuming all is well. I can’t do that now. Partially because of the switch that flipped on election and the healthy paranoia I’ve developed about the world around me around me (I think I learned this from my dad, who listened to Rush Limbaugh on the ride home after work every day even though he hated Rush Limbaugh). The other reason I can’t bury my head in the sand is genuine interest. I really do want to know what all of us Americans thinks about America. Why is it so hard to figure out what prior actually think?

https://twitter.com/JustinAion/status/822848618881306624

The day of the Womem’s march I was slated to teach saturday school. The trains were crazy, so I took a cab with a particular chatty cabby. I asked him whether the march was causing traffic problems, and he replied with “Women! Why are they marching??? They already have everything!!!” To which I replied with a swift punch in the face a heavy-handed discussion of places where male privilege operates. When I got out of the cab I was a little disgusted. I was also struck by how little conversations like this happen. This was the only conversation I had about any political issue with someone I didn’t agree with in maybe 8 months, and it was an election year! Even though I’m off of Facebook, apparently I’m still in the echo chamber that prevents me from understanding what’s driving the people outside the chamber.

Over the past few weeks it’s become clear that I am going to need to develop more faith in America if I am going to be my normal, optimistic, not-paranoid self. I also have learned that the media isn’t helpful, and if it is, it will be very hard to find. But at the same time, I’m surrounded by Americans who perhaps help me restore that faith, or at least help me understand exactly how much further we still need to go. Maybe the next step for my own sanity is to start talking about politics. (*gasp*)

Which brings me to my blog, and my twitter. Both of these are venues to have conversations about America, Democracy, and the political actions that shape them. While I am an educator, and am only interested in this blog and the twitter for developing myself as an educator, I can’t ignore isolate my profession from the world we work in. Education is indistinguishably intertwined with the needs of the public and the way that public is governed. We as a people must democratically decide how to fund our schools, where to build them, and what to teach in them. When students arrive, we must show them how this democracy works, give them experience operating within a democratic system, so they can grow up to lead our democracy into the future. This is a lot of work, more than can be handled in a civics class, work that math teachers can and should be sneaking into their classrooms. This could be modeling what it means to be an active citizen. It certainly means having active discourse about important ideas, and finding ways justify those ideas and defend arguments. It means pushing students to see things from multiple perspectives, cooperating on meaningful tasks, and communicating that work with others. This is all just good math teaching. With only a slight lateral shift, we can help students apply these principles while discussing current events, systems of iniquity, or even the ideals of democracy and in the process make our mathematically proficient students into mathematically proficient citizens.

As educators it seems that we should be sharing strategies to live up to these ideals. As grateful as I am to lean on my extended network for real world contexts for multiplying binomials, I am now also grateful in hearing how to talk about the inauguration, or talk about immigration, or whatever the next executive order will be. Learning what they think helps me to gain more perspective, and will increase the usefulness of a class conversation if students want to have a discussion about these things. Posts like Michael Fenton’s recent one are encouraging. As I try to figure out how to inject more democracy into my teaching, my work with teachers, and my work as an administrator, it will be invaluable to have honest perspectives around these important issues as a part of my time line. Thinking about these things regularly helps inform my thinking, and prepares me to facilitate a conversation about an issue if it comes up in class, or in a parent meeting, or one-on-one with a student.

https://twitter.com/MyMathscape/status/824762528110608386
On Thursday I had such a meeting. A student who disappeared for months returned to school to enroll for this semester. This student is not a citizen. I remember a few years ago he was worried about not being able to go to college. Who knows what his worries might be. Based on what I have been reading, however, I knew that New York City was a sanctuary city, and our mayor was prepared to fight against deportation. I told him that there are a number of resources I could share, resources which I have seen shared across my personal network. The student relaxed, signed up for a full program, and is on track to graduate by June.

Being aware of the political concerns of others, and coming up with ideas for ways to help students understand political issues is now ready important to me. I am really glad to have people on my feed that post more than just math. In fact, I hope people could organize their talks about the intersections of math, politics and democracy into some kind of hashtag or regular chat. That’s a pipe dream, right now I’m going to keep trying to figure out what’s going on, and being really grateful to all the people sharing what they learn on the web. 

If that, or any of this sounds interesting to you, PLEASE let me know in the comments.

Clog: Last Day of Class & the Class Survey Project

Monday’s class was the last of the cycle, and probably the class that felt the best. Yes, I know that this is kind of cheating. With the marking period’s end bearing down on kids, it’s kind of hard not to have a productive class. My constant thinking about Work Time over the past few classes set the stage for a outburst of productivity.

After announcing that this was the class I told the class that I will meet individually with each student. Once everyone knew what their next steps were, I was able to float from table to table for the rest of the period. Some kids were calling on me for help, some others were getting help from their neighbor, and everybody seemed to make progress. No students got lost, or seemed distracted, or battled the other ills that plagued the work time at the beginning of the project. All in all it worked out pretty well. At the end I handed out the last page of the project, which was also a little reflection about how the project went.

Class Survey Project (Modular Project FTW!)

The big thing that I think made this work out well was that the project itself was really easy to understand. Some of my previous projects, like the road trip, are sequential. They’re like movies, complete with plot twists and everything. If you come in the middle, you’ll need to have a lot of things explained to you. The Class Survey Project was modular. The different steps were broken into parts that can be done independently. Students could enter into the project at any place as long as they understood the question they wanted to analyze. This was kind of like re-runs of a sitcom. You can watch whatever episode is on that day, as long as you know about the main characters. It also helped that students could choose whichever module they want. This allowed students to reason about the choice of the strategy they were employing, while allowing me a chance to scaffold their work on that section. With the sequential projects, the story-arc tells students what strategy to use, removing the students agency in choosing their approach. This was the first time I’ve done the project this way, so please check it out and leave me some feedback in the comments.

Download (PDF, 501KB)

 

Clog: Unfortunate start, unexpected finish

Class Begins

I had a cute exchange with my kid right before last period class on Friday. The kid was talking to a girl, and tried to appear tough, and then I appeared tough back, and he backed down, but it was cute. I walked down the hall and into my class and he went down the stairs and cut class. This student spent two weeks away from school to celebrate Christmas and he has yet to get started on the project after break.

Another kid asked me for water. “You know,” I replied, “last class you went for water and didn’t return.” “So do you want to me leave, like, collateral?” “Yeah leave your gloves on the table and get water.” I looked back 10 minutes later and her seat was empty and his gloves were gone. This student has missed a lot of class and has yet to start the project.

Rocky Start

For all of this week, and all of next week students are going to be working on their projects, so there will be a lot of independent work, which means Work Time. Today’s class began with self reflective questions on the board about the project. After Wednesday I began to form a plan to make Work Time as productive as possible. The plan for today was to was to precede work time with these questions to quickly assess needs. Unfortunately, timing is everything, and by the time I got all of the questions up on the board, laptops were out and projects were started. Kids were too distracted by the prospect of making progress, and their individual questions around that, to want to start on those questions on the board. I tried to get everyone to start it. Then one girl said, “Hey. Let me ask you a question about the data table…real quick.” This led to her neighbor asking a follow-up. Then a kid across the class verbally wondered why they can’t also ask a question. And so on… At this point it was like a bunch of kids sitting there saying “Let me eat my vegetables!!!” and I kind of caved on the questions, except to point people to them when I walked around.

Around the time I caved on the questions it became clear that the monster at the drinking fountain swallowed the student from above. My plans for structuring Work Time is precisely for those kinds of students. She had missed the last two classes, and had no clue about how to get started on the project. Theoretically she would have answered the questions, and in the process gone down the list of things she would need to do to be on track. Instead I’m assuming she walked in, saw everyone working and gave up. Perhaps actually writing the questions on the board takes too much time, I should make an actual handout that can help people go through the parts of the project, but not feel super redundant for kids who have been there the whole time.

One of the kids who have been there the whole time was still struggling with the project. This student was super focused today for some reason though. Once the class devolved into the typical work time set up, I spent a lot of time near his table answering questions and clarifying the project. I kind of feel like a crutch for students who aren’t truly independent learners. Given the kinds of math phobias students have before they come to me, it’s clear to see why they might need a crutch. The questions don’t help this student, because this student probably wants a much more specific and detailed sets of questions than what was on the board. What the student probably needs is a whole new conceptualization about himself as a math learner. This is something I have to figure out I guess.

Class Ends

After class was over the student above asked what the next part was. I said, “you make a histogram with that data.” He quietly walked over to the table where the project components were laid out. He then headed back past his departing classmates and sat back down at his desk and picked up his pencil. He worked well after school to start and finish this histogram. We worked for a full half-hour after school had ended. ON A FRIDAY. Oh, and all the while we were working, another student who also stayed working on her project. It was certainly unexpected, and inspiring to see students rising to the occasion.

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