Carl's Teaching Blog

A place to talk about teaching and learning

Category: Clog (Page 1 of 8)

Clog: Launching the #ThinkingClassroom again

So my thinking classroom may have just given the best math class interactions I’ve ever had. More on that later. First let me get up to speed with this experiment.

Last cycle I had a good experience with the Thinking Classroom. I’ve written a few blog posts about it, including one about my plans, another about my awesome and excessive randomizer, and another about kids taking notes. The experiment ended in January because the marking period closed, but I decided to reboot it with a new kids on a different schedule. It’s really great having a second chance to go over the norms with a fresh group and get more practice on-boarding them. Having a bank of problems to use is an added bonus. So far, we have been doing  visual patterns, including my new favorite visual pattern lesson for VNPS, which I could write a whole other post about. (Actually, I’ll just write it now. This lesson has lots of patterns, you can cut them up into strips and give different linear and quadratic patterns to different kids. Give them to different groups and then have them walk around and check out the patterns that the other kids worked on). My classes on this schedule are an hour and a half long, and the VNPS seemed like it would be too long for that, so I have been doing Desmos activities in the remaining time. As the class comes to an end I’ll have kids work on using Desmos to make models of data that is important to them.

Today we used a different shell center problem and it just kept on giving. I showed the kids this prompt and asked them to think about how many would be int 30cm x 30cm and the 40cm x 40 cm and an equation.

The kids ended up doing a lot of thinking, including two students who weren’t here for the first cycle. Two of the three groups got to an equation after 45 minutes, but one group defined the 20cm case as n=1, while the other made an equation where n=20. This was led to a great conversation that we have been having about equivalence, but also about this thread of what I guess I would call “Mathematician’s License,” (like “poetic license”) One of the groups was trying to convince themselves that they had done it wrong, and I had to stop them and say “You made an equation the describes this situation, and that group did as well, and they aren’t the same. That’s ok. In fact, that’s what mathematicians do!”

All the groups seemed only 80 percent clear on the problems, so I made an extension question. I asked the kids about the 20cm x 30cm rectangle and they were all able to think about an equation, and no one’s equations were the same. The two groups from above actually tried solving it using the other groups value for n! It was great to see ideas spreading around the classroom. All the kids were supposed to sit down to work on the Desmos activity, but those two groups kept lingering around their boards. One group had a functional equation and they kept working on the ways to ‘simplify’ it. The other group was struggling a little with their equation, because they wanted to figure out how to write it so that it could apply to rectangles of any size!!!! I was shocked that a kid would even ask that. I told him that we would probably need some multivariable equation to try and figure that out and he was like “are we going to do that this cycle.” What!?!!? I had to restrain myself from not nerding out because we needed to get to work on the Desmos activity. I’ll say this is the first time I’ve ever had a student linger around and do more math, let alone ask me to do more. I think it shows that the kids have built up a lot of confidence and ownership in the first 4 days of the class.

Clog: Why won’t the kids take notes???

My kids are awful note takers. It’s not just me, this is what they are telling me. Each Friday I ask kids to do a 6-question weekly reflection with questions like “This week I took useful notes.” For that item, students all consistently report the lowest scores over the first 4 weeks of the class. It’s clearly the biggest takeaway from doing all of these weekly reflections, so I should probably address it.

Notes were an important takeaway from what I learned when I began looking into the thinking classroom. In the past I didn’t do notes, but I had really well laid out tasks which included everything I want students to take notes on. These tasks would be organized in such away that they could review the important things whenever they studied. The act of deciding what things are important seems like an important academic skill, and by not expecting them to do this meant I was setting them up for failure in higher ed. The meaningful notes that Peter Liljedahl described echoed this:

…teachers can highlight particular parts of the work that is on the boards, but it is important that the students select themselves, and synthesize and reorganize notes on their own.

Unless of course they don’t. I’m not sure why the students aren’t reporting that they are taking notes, but I can assume that my teaching has something to do with it. I usually I rush through the notes at the end of the class, perhaps because I don’t yet stop early to give them to time to write things down. I could write a whole post around my issues with pacing and the thinking classroom (tl;dr version: “how is class over already!!!”), but maybe it would help to give kids some more guidance around the note taking process. Perhaps the reasons they are saying they struggle taking useful notes isn’t because they don’t have time, but that they aren’t used to doing it. I have been giving them some structure so far which you can see in this google doc. On the first class I gave them the just the first page, a note sheet with a few blank lines and said “Write a letter to your future dumber self about what we learned today.” I quickly pivoted to something with more structure. They got a two-page document with a number of important things that the we would cover over the whole course. It had lots of places for kids to put in things that were relevant, and they could do so over the course of the class. What I found was that kids treated it like a worksheet, looking to show me one that was totally filled out (one kid even went and googled some of the new stuff), while others filled out nothing while planning to sort of wait until later when they would “know what to write.” The last page on this is what I made for today.

Download (PDF, 23KB)

Today I decided to make it a point for kids to take notes on an important equation, the vertex form of the quadratic equation, since they will need for the project. I made a note sheet and I had the kids do it after we worked through a bunch of different quadratic equations and graphs on whiteboards. The activity they worked on encouraged them to make connections between tables and equations and we stopped with 15 minutes to allow time for note-taking. Then I handed out the note sheet above and basically told kids “We’re going to take notes now, these are going to be important later, and you can use what you see on the boards to write down the important parts”. This was definitely the best notes they have taken so far, even though some kids kept their paper blank and others wrote things they will not be able to refer to later.

So it wasn’t a complete fix to our problem with note taking, but I’m not taking it personally. It is a new routine, and it is one that contradicts a lot of norms that in the school altogether, as well as messages that the kids are being sent about school and learning. Our school is about experiential learning, so students who choose to come here probably aren’t kids who instinctively look to document things with the future mind. Kids also have some pretty damaging thoughts about how learning and knowledge happen. Ronny, who spent the whole time with a blank paper in front of him, “I already know this, so I don’t need to take notes…the right answer will just come to me later.” What a difficult set of beliefs to set for oneself. Leonardo DaVinci, Martin Luther King, Abaraham Lincoln and all these other genius needed volumes of papers to write their thinking down, but somehow when you get done learning you can skip the notes? We talked some more and he has a lot of reason to believe what he does. He is basically saying that the Regents is the only place where it is important to use what you’ve learned, and in his 11 years of experience, he was able to be successful. This way of thinking doesn’t set up Ronny for success in the future and places an impossible burden on him for when he gets older. If you struggle in college, wouldn’t it be nice to say “my notes are bad” instead of having to say “I guess my brain stopped working”? Seems like some kids don’t think of my class a chance to practice using the effort to become smarter, but as a chance to reinforce the smartness that they already have.

Clog: Bringing along the stragglers

The Thinking Classroom experiment may be a success. The white board contact paper is starting to gather dust in the corners, the kids trust the fancy randomizer, and there are consistently good days. I’m all ready to write a post about successes or a sort of “growth” post about my what I’ve learned the most (spoiler alert: it’s about managing flow). It’s just, well…there are these two kids who I’m worried about.

On Wednesday we started on an open middle problem and two of the four pairing had a student sitting down, facing away from the board, and looking at their phone. Paul likes to mind his own business, and isn’t too interested in talking with me or any student. Denisha has flirted with pursuing a GED, with support from her parents, but decided to give this year one last shot, but so far hasn’t earned any credits in any class that didn’t her performing music.  They both didn’t hear the full explanation about the class during registration, so maybe this isn’t what they expected. I am aware with both having behavior issues in previous math classes which have escalated to administrative interventions. While both of their attendance is around 50%, it surprised me that neither have had an even moderately successful day working with their groups.

On Wednesday, Paul was struggling in a grouping that made me question throwing out the randomizer. He was paired with a student who has had excellent attendance, and is pretty bright, but isn’t really a big “includer.” This student has a tendency to stare off into space, deep in thought, before emerging with an answer that he can’t seem to communicate without writing it on the board. Paul had been paired with this student before and didn’t seem to be contributing anything, even though I asked. It seemed then that Paul wasn’t being vocal then, but his body language showed he wasn’t even participating. I had to try even harder to get the marker into Paul’s hand, but he was said he “don’t learn like this.” He seemed sad that he wasn’t able to pull the answers out of the air like his groupmate and wanted me to sit next to him and tell him what to do.

The randomizer also placed Denisha in a pairing that wasn’t ideal. Her partner was probably the third least talkative kid in the class so I knew I would spend a lot of time over there getting the conversation going. The two were both quiet, Denisha seemed detached. Denisha’s partner seemed quiet because they weren’t clear about the next step in the problem, while Denisha seemed like she was trying to hide and not be seen. If I visited, she would look up and confidently assert that she knew what they were doing, but wouldn’t be able to answer any questions about the actual problem. After some questioning it seemed like she wasn’t aware of what the problem was or what her partner was doing to figure it out. When I wasn’t nearby she would zone off or get sucked back in to her phone as if she was waiting for us to go over the assignment.

Both of these students seem to struggle asserting themselves in math and are also uncomfortable with collaborating around a task. The tasks that I am giving out seem like they are pretty “low-floor,” but Paul and Denisha are not accessing or engaging with them in up until Wednesday. They don’t seem to feel safe in this environment. One of my big goals in this experiment is to create a culture where students spend more of their time feeling safe, but it seems like these two students are spending most of their time avoiding feeling “dumb.” It’s tempting to want to blame the victim here. To imagine the kids could have been more successful if they attended regularly, or to assume that these kids would “get it” if they “just got on board.” I think I should do more to meet their needs (and am open for ideas here). I’ve tried using more manipulatives and am going to work more on having students interact socially before they start working on math, but it’s hard to see if it is working or not.

On Friday I had a pretty successful day with Paul. First I explained my new grading system for the class in very clear terms. I then re-explained the whole philosophy of the class again to connect their grade to the class. Then we had the weekly quiz, which Paul would was unprepared for. Paul, and another student instead worked on quizzes from earlier weeks that they missed. Then I had those students work on a problem maximizing the area of a rectangle given a  perimeter together using manipulatives. Paul was much more confident in working with this new partner, and was more vocal when I asked them to explain why they thought a square isn’t a rectangle. We ended with a conversation of what he needs to do to earn credit. I think it was a big step forward for Paul. Denisha wasn’t there, but maybe I have an approach that I can try with her. Not changing the expectations, but being as clear as possible about them, providing more ways to access the problem, and keeping to work to build confidence.

CLOG: Good Day Today! …And My Somewhat Excessive Randomizer

Yesterday I posted about how I began my Thinking Classroom experiment. The experiment actually started in the 2nd week of november, so at this point I’m actually 3 weeks in to it. Today I actually had the best class that I’ve had so far. It wasn’t a perfect class, but it was good enough to make me forget some of those rough days that happened along the way. There is a lot to write about, and I may not get around to it, but I will start with a digression to talk about my randomizer.

The Randomizer

Before my first class I made a randomizer that basically assigned seats to random numbers, and assigned those randomized seats to students. It was basically one that Joel Bezaire described. My school has really unpredictable attendance, however, and also has kids show up late. I needed a randomizer that wouldn’t assume that we would have the whole roster there and be smart enough to take any number of kids each day. Based on the kids in class the sheet should figure out how many pairs are needed, and then assign the random seats. This thing does all that automatically whenever a new kid is inputted into this google form that I have kids fill out (and I can also decide how many kids I want to have in each group).

It works like this. Kids fill out a google form with their names and click sign-in. This also helps me keep track of attendance and lateness. Then as the names come in, the spreadsheet puts today’s group on the right. It also automatically adds more groups as needed, and some blank seats in group “N” in case we need to form a new group. Check it out in the video below.

Bonus: If you use google slides, you can paste the two columns from the spreadsheet into your google slides, then select that you want to “link to the spreadsheet” so it will automatically fetch the new results. This way you can automatically pull up the random seatings by clicking “Update” in the slides and avoid having to even open up the spreadsheet.

This is what my random groupings table looks like in google slides. You can click the ‘update’ button at the top and the table will pull in any new kids that weren’t added before

If you want to try this out without doing the spreadsheet wrangling, I made a version that should be pretty easy to plug your classes into. All you basically need to do is:

  1. Make your own sign-in sheet with 3 questions: Name, Period, and “Sign-In” or “Sign-Out”. It should look like this one: Randomizer Sign-In Sheet.
  2. When you’ve made your sheet, click on the responses tab and click on the green square that allows you to view a spreadsheet. Make a new spreadsheet and call it whatever your heart desires.
  3. Go to the Randomizer Spreadsheet (Here you can see the results of the sign-in sheet, as they come in from the form above, and you can see the results come in.
  4. Go to the “Randomizer” tab of the spreadsheet above, and click on little menu on the right, then select the option “Copy to” and choose the sheet that you made in step 2.
  5. It should almost be working, There is this one cell on the randomizer that is highlighted in orange that will have an error message. Click inside it, and confirm that it says “=arrayformula(‘Form Responses 1’!A:E)”. [Note: you shouldn’t have to alter anything, you should just have to double click and then press enter.]

So that’s my randomizer, let me know if you think it is useful. I can go more in depth about how it works but I want to say a little bit about why I think the class was better.

Today’s Firsts

Today’s class was a highlighted by a few small firsts. It was the first time that I tried to do a mid-work-time consolidate. This was an idea that I talked to someone about at NCTM Seattle and it was a move that would make a lot of sense. I wanted the kids to work on two sets of visual patterns one linear, and one quadratic, so I wanted to stop after the linear one and make sure everyone felt confident thinking about how we go about describing linear patterns before moving on. Once students got through with the linear set I could consolidate what we’ve all done as a class before moving on to the quadratic set of patterns. I was just about to do this mid lesson consolidation when I decided to roll out another first.

Almost all of the groups were at a linear equation for the first set of visual patterns except for one. This pairing was a girl who had only been in the class once before and another kid with better attendance whose work usually gets presented first and is kind of shy. Both students could use the confidence boost of figuring it out. They explained the equation in words, but somehow got stuck when it came time to write it on the dry erase contact paper that was attached to the storage closet in the back of class. While they were going back and forth about what to say I just sort of drifted away. My attention turned towards the front of the class where the two other groups were sitting idly with their linear equations locked and loaded. They would need to do something while we waited for the big consolidation, so I asked them to do a different problem as they waited, which was a first. For one group, a visual pattern that I had on the board got them immediately engaged. The other group was asked to look around the room at a problem they hadn’t done but others had. (In retrospect, I should have just given that second group the visual pattern as well because I think that group wasn’t as engaged in the consolidation later). In a few minutes we were able to do the halfway consolidation, with all groups feeling confident that they can handle any visual pattern I can throw at them.

All the groups had their confidence tested when they were faced with a non-linear visual pattern, and they were all able to use a recursive strategy and explicit strategy to find further patterns. It was actually pretty impressive seeing the group from the back of class with the most intuitive strategy to figure out what the equation was.

It was a pretty good day, I am not sure how I am going to get the kids who weren’t here (about 1/3 of the class) up to speed on what they missed. Any ideas?

 

CLOG: Thinking Classroom Intro and First Class

Today I am about to get started on my Thinking Classroom experiment. I’m probably more nervous than I should be, so writing this will help. This post is to both organize my thoughts, and serve as a nice opening to a series of posts that I’ll write as this experiment unfolds. Today I am going to talk about what I’m going to try, but first I’ll recap how exactly this experiment came to be in the first place.

How this came to be

I was at the NCTM Regional in Kansas City, heading to an early morning shift at the #MTBOS booth, when the security guard informed me that the vendor area was closed. Naturally, I checked twitter, and saw a few tweets coming from a Peter Liljedahl session, so I headed over there to catch a little bit of the end. I proceeded to have my mind blown. Turns out the Thinking Classroom had dozens of great ideas behind it, and not just by the VNPS stuff:

 

Having a classroom built around thinking was my plan for years! 3 years ago, I stopped calling my classes algebra and started calling them Mathematical Thinking, to signal that this is going to be a different experience. Liljedahl’s research laid out a 10 point plan for making the class into the experience that I hoped to create, with research and charts to back it all up. The biggest headline of the 10 point plan was the Vertical Non-Permanent Surfaces, which I had piloted last year. The session gave me some ideas about notes, assessment, and how the teacher provides more problems for the students as the class progresses.

After the talk, I headed back to the booth and talked with Joel Bezaire who had also done some Thinking Classroom stuff in his school. He made it seem really realistic. He told me about Dry Erase Contact Paper, the kinds of problems he uses, the spreadsheet that randomizes kids, and some of the blog posts he used. He also helped me think of ways to make it work at my school, which is not traditional and I don’t have as much time with my kids who all have really different abilities. In another stroke of luck, Peter Liljedahl was doing a session around the corner at the infinity bar after I finished talking to Joel. He was super nice and answered my questions until well over his allotted time. I also was able to download a lot Dylan Kane’s Blog Posts about the thinking classroom before my plane home took to read on the flight home. The fact that all these stars aligned made it clear that the universe wanted me to try the thinking classroom this cycle.

Fast forward to this morning. Things seem pretty much set. First off I have students! 11 students signed up for my class for this cycle, and a few more will trickle in which is good. This means getting kids into groups won’t be too hard, and I can save some of the whiteboard paper I would have used for a class of 30. As each kid signed up I showed them this video from Alex Overwijk, and explained some big ideas. “We’re going to do group work, and we’re not doing a whole bunch of worksheets. Instead, we’re going to maximize how much time you spend in class thinking…” Once class actually starts, I’ll need to reiterate the main ethos of what the class is, while also getting them immediately working. In the past I usually started class with a speech about me, my syllabus and how great our time together will be, but this is always boring and dry. Instead I’m going to explain a little bit about what we are doing, use the randomizer, and then get into some visual patterns and some function notation.

_______________________________

Update: I taught the first class and it was pretty interesting. The class was small in number with 4 kids of 11 kids (there was really bad weather last night, so it’s possible that people couldn’t make it in). The small class size could have been a good thing since it lowered the chances for a wide scale revolt. I made this randomizer that is basically the one Joel Bezaire described, with some modifications for my small class size, unpredictable attendance. The scary thing that comes along with small class size is the lack of different kinds of thinking. What if the small groups only come up with a couple of answers? Today the class all went through the visual patterns and came up with a few different ways to solve it. In the future, it will be hard to ensure that all of the different kinds of thinking that need to be elicited will actually show up. Maybe I’ll have to write up imaginary group work and post it somewhere else in the room as a “shadow group.”

The math wasn’t that substantial today, but we did plow through it. All the kids say they liked it and thought it was a fun. I am not clear on how we will introduce precise mathematical vocabulary and notation. Function notation will be the first thing we’ll see how it goes. Maybe I can just roll it out!

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