Carl's Teaching Blog

A place to talk about teaching and learning

Category: Uncategorized (Page 1 of 12)

Clog: The circles keep going

We did our fourth circle in the cycle, and things are now rolling right along. These circles, which are covered in an earlier post, involve me and the kids sitting around in the circle talking to each other. The kids are all pretty used to the routine, and I keep coming up with ways to relate it to what we are learning. It isn’t going to stop any time soon, so what better time for a little update!

Structure

Each circle begins with a chairs in a circle, a talking piece (a ball or something), and each kid has a white board, a marker, and recently erasers. I sit near a piece of chart paper for to writing down the results of each students question to the group.

My prompts have involved kids asking questions of each other. So far I have done:

  • Week 1: What is a yes or no question you want to ask everyone, and predict whether 5%, 15%, 50%, 85% or 95% of the people will say yes.
  • Week 2-3: What is a question on a scale of 1 -10 you want to ask everyone, and predict what number people will say the most.
  • Week 4: What is a question on a scale of 1 -10 you want to ask everyone, and predict the distribution: skewed left, symmetric, skewed right.

These simple prompts lead to authentic responses. The questions asked are genuine in that they are from the people in the room, and the answers are genuine because they are from the people in the room. When it is time to work with other data, it helps to be able to pull examples from the chart paper that we all had a part in creating. Today for example, when I talked about the z-score, it was nice to use a question from the circle as an example instead of ‘dinosaur femurs’ or whatever.

Strategies

I have done this enough now that I am starting to get some strategies that help. One thing is that I want to control who all is talking a lot. Having the talking piece let’s kids know who is supposed to be talking. After everyone shows the results, and as I am writing on the chart paper, I’ll pick someone who had the highest or the lowest number and ask them why they said what they said. I can also use this as a way to have some kind of equity in who controls the airspace. I’ve also had a bunch of sample questions on the wall so that when kids inevitably say they don’t have a question, they can just pick one of the other ones. The question I was using were from the Census At School, since we are going to eventually use that data.

Next steps

So the thing that I want to work on is how to keep expanding so that at the end the circle will be a way for people to share their final projects and get feedback from their peers. For that I need to figure out a number of things like making sure the kids are comfortable listening to each other, and responding respectfully. I’ll also need to finish making my project. 

The other big thing is how much class time this takes. Seeing up the room so that we can get right into the circle is important. When we’re finished kids should quickly transition out of the circle and back to their tables. To make transitions quicker I have students pick up their folder or laptop or the next activity as they leave the circle. Another struggle is also writing the data and also facilitating the group. Maybe a student could keep track of writing the numbers that are produced after each question, but without making that kid feel left out. The white boards also seem like a ripe opportunity for student creativity, and currently all students do is write one number, and then erase it.

All in all, it’s going pretty well. I look forward to writing another follow up at the end of the cycle. If you have any ideas or thoughts, please let me know in the comments!

Clog: Suddenly a math argument breaks out

So I always want to try to get kids to have big mathematical discussions in class, but it doesn’t always happen. Today a VERY lively mathematical discussion broke out in class. There was a point where like 3 kids were up at the board, vigorously gesturing at the models that were written at the board, while the rest of the class waited breathlessly for one of them to be conferred as “the answer”. It was out of hand.

Now this didn’t exactly go well. I’m not saying a bunch of kids screaming at each other is ‘productive discourse’, but that’s to be understood. The class was actually a class I was subbing and it was the second day the class had ever met, and a huge chunk of kids missed class on the first day. Class started very quiet as to be expected from a new group with a sub teacher, so I wasn’t really emphasizing turn-taking and sharing, which I would later regret.

Here’s the problem that the class was working on:

Draw a diagram 1:

There’s a softball league with three teams, The Alligators, The Bears, The Crocodiles, The Dolphins, The Eagles, The Foxes, The Grizzlies. Each team plays each of the others 3 times. How many games are played?

I asked the students to read the problem as a group. It would have been nice to stop after the first sentence and do a Notice, Wonder, but instead I asked a few questions to make sure people were interpreting the question right.

  • “What’s important here?”
  • “7 teams, 3 times”
  • “What’s a game?”
  • “When two teams play each other.”

They started working, and when they did I made sure I only commented on their process, and I didn’t confer if anything was right or not. Anyone who thought they were done I asked them to explain their process further, or to draw the diagram that the teacher requested. At this point the class was pretty low energy, and seemed to be convinced that they had the right answer.

The was a quiet girl in the middle of the U shaped tables whose method I wanted to talk about first. She literally listed out all of the games, and the rest of the kids just immediately started multiplying. The Elmo didn’t work, and the class was pretty low-energy, so I started by writing what I heard her say, which also allowed me to organize the work slightly (re-writing student work isn’t ideal, she should have done it, but it made sense given the context). Once all the games were up there, grumbling started.

  • “What happened after the AG team?”
  • “Why is there no BA game?”
  • “Why doesn’t G play any games?”

After first thinking that she made a mistake, I encouraged the student to defend her work and explain that after we counted the first ‘AB’ game where The Alligators played The Bears, we didn’t need to count The Bears playing the Alligators. Grumbles.

One of the students who disagreed offered to describe what he did. He said that The Alligators are going to play 3 games against The Bears, 3 games against The Crocodiles… and thus they would play 6 games 3 times, or 18 games. So then the rest of the teams would play 18 games. So then a bunch of people agreed with that, but there were now contrary grumbles about the games being double counted. Around this point people stated asking me what the answer was. I said that’s your job to figure it out. If it’s the answer you should be able to defend it. THe students kept talking about it and as they talked I came up with representations to write on the board to show what they were thinking. I drew a table with ABCDEFG along the side and the top and wrote the number 3 in all the spaces so people could see all the games. As people began to question the number of games, I wrote out the decreasing cascade of games 18+15+12+9+6+3+0 as the student in the back who listed the games began a more vigorous defense of her ideas. The main student opposed to this still had questions and offered to come to the board and draw his own diagram. I stepped to the side. Suddenly 3 students were up there having a screaming match and the rest of the class was following along vigorously. One student had defined “playing” as both hosting a game, and travelling to play a game, and so he was counting the double-counted games. I explained how this misunderstanding of the problem led to his different understanding, and if that is the way it was defined, then the problem would have a different answer. The kids were still wanting me to pick an answer, but I think if you understood the problem differently and can explain your work, then that would be your answer. The class quieted down and everyone said their brain hurt.

Why is it so darn hard to push ‘Send’???

Many people say, I’m talkative. People rarely describe me as quiet either online or in real life. Despite my 100+ blog posts and my 3000+ tweets, I feel like frightened every time I hit that blue button that spreads my thoughts all over the internet. I’ll still read some tweets and then think about replying for minutes, hours, maybe days only to decide not to send anything at all.

Why shouldn’t I just hit send already? Well some of the typical reasons that float through my head are “I don’t really understand enough to comment on this” or “I already know so much about this, that they couldn’t really care what I think.” or “I have a pretty good response, but it’s not JUST right. Besides, this person basically said the same thing I said.” These are excuses are pretty thin. Too thin to hide behind, infact. The reality is these excuses are just proxies for the general fear that goes along with any kind of public exposure, be it twitter, a college party, or my 9th grade student council elections.

Today I spent a lot of time thinking about my inability to hit send after reading this tweet from Dan Meyer:

Now I didn’t reply to Dan’s tweet, but not because I wan’t interested in it. There are lots of reasons people question posting something, more than just whether it’s “ok.” Possible replies rolled through my head all day but, naturally, nothing congealed into a 140 character response. In the moments before I made the choice not to hit ‘Send’ here, as per usual. Specifically I thought:

  • Did somebody else already post this somewhere else?
  • Is this conversation still active?
  • Do I actually know enough to add to the conversation?
  • Are my thoughts too big to fit into a tweet?
  • Are my thoughts too small to justify a blog post?
  • Is there something better I should be doing then sitting here vacillating about whether or not to hit ‘Send’?

Is that just me? I do have weird brain chemistry after all, it’s hard to gauge what’s normal. If these do float through your head that’s good, they are valid. They haven’t gone away for me, and the reality is, they’ve been there when I don’t hit send, and also when I do. These thoughts are always going to be floating through one’s head before they put something out, but that d0esn’t mean people should hide behind them. These kind of thoughts should be considered, and used for improvement, but not render you to silence. Let me just go through and respond to these thoughts so you won’t have to next time (You’re welcome).

  • Did somebody else already post this somewhere else? – Well, this isn’t as important of a question as “Did YOU post about this yet?” YOU are the only person in the world working in your context, with your population, and your ideas matter.
  • Is this conversation still active? – If you’re saying something relevant, a new conversation will start. If not, you just got the last word.
  • Do I actually know enough to add to the conversation? – If you don’t, the best experts in the world may read your tweet and point you in the right direction. Besides, if that’s your concern, not posting means you’re just going to be stuck there with your ignorance.
  • Are my thoughts too big to fit into a tweet? Are my thoughts too small to justify a blog post? – Well, write the post and tweet it. Or, write a bunch of tweets and put it on your blog.
  • Is there something better I should be doing than sitting here vacillating about whether or not to hit ‘Send’? – Nope. If it’s important enough for you to think about it for this long, it’s only going to help your brain to continue thinking about it with friends on the internet.

Hopefully this will might help others who hesitate before tweeting and blogging. I was in the middle of hesitating about writing this, but then I started watching this video about a guy who was hesitating about posting a song to soundcloud, but then he did and it ended blowing up. Sure this guy was a talented artist, and he made a really good song. You can hear his doubts in between the rants of Gary Vaynerchuk who owns the youtube channel. Gary V is a social media guru and one of the big things he talks about is the importance of just putting your stuff out there and letting the world decide. Seemed relevant.

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.

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