## Carl's Teaching Blog

#### Category: Clog (Page 3 of 8)

My class ends. I erase the board, tuck the unused worksheets on top of the folders and head out into the hallway when I see Benjamin. He has not been to class once, so there is no way I can’t go call him out on it. “You know, the reason I’m trying new material is because you signed up for the class.” Benjamin was in my class last cycle, and when he signed up I told him I initial told him he couldn’t take it because I had already taken this course. Then I caved. Both because he’s awesome to have in class, and because I like coming up with new stuff. “Why not just repeat the class from 2 cycles ago…” Benjamin replied “it’d be easier for the both of us.” What Ben is saying there is that today’s class was a struggle. You know it’s bad when even the kid who hasn’t even been there for two weeks can see how bad it is.

So I had an idea for a lesson. This lesson would fit right in with the unit where we finish talking about average median mode and start talking about standard deviation. In the past I have kids just do a huge mega table to understand the calculation side of it. What I don’t do is get the students to understand why such a calculation is important in the first place. So today I decided to make the new lesson. I thought that this lesson could involve the data that the kids generated in Friday’s circle, some practice with calculating the average, and the idea of “reliability.”

What I had them do was look at some bar graphs of the data from the last class. They could look at the bar graph and think about why the graphs show different ‘spreads.’ These bar graphs could then be used to calculate the average by looking at the values. They can then take that average and look at it in the context of the rest of the values on the graph and be able to make a statement about which graphs show the most clustering around the mean. I figured students would come up with their own ideas of which ones are clustering around, and then say stuff like “Graph A has the smallest range, so the numbers might be close to the mean” or “Graph D has most of the responses as one value, so that one is really close to the mean.” This would all lead to a magical debate, after which the class would realize that we need an approach to look at these data sets in order to figure this out. Then I would say “Well that’s why we have the standard deviation!!!” The kids would cheer, and high five each other, then I would get into the powerpoint.

#### So what went wrong?

Maybe, I think the ideas could have been easily discerned from more cherry picked data. Just because I wanted to use data that the class generated doesn’t mean that the data will lead the kids to make the mathematical conjectures that fit my lesson objectives. The idea of using a bar graph to discern the average was a totally new concept. I thought it would be review but it ended up bogging down the conversation with questions of which average was right. Also, the question on the task wasn’t really relevant. I asked kids to say which numbers seemed the most “reliable,” e.g. If we were to draw a value from the set, can we say that the value should be close to the mean with some reliability? That was too abstract. I am using real data, I should lean on the context more. Maybe something like “If the mean was chosen to represent how everyone in this set thought, and everyone took these numbers really seriously, which set would have the most angry people in it?”

Does the class have the right culture? I don’t know, we do the circles, we have been doing partner work, we have also been doing boring worksheets and attendance has been sporadic. If I want to take kids on some kind of conceptual journey, I am going to need to structure the class so that this kind of journey is normal. Today whenever there was a space for conversation it was met with crickets and disdain. A little like the kids are saying “Dude, can you stop talking and just tell us the answer already!” This was especially the case with kids who weren’t there for most of the cycle.

Am I even teaching the right thing? Mean absolute deviation makes a lot more sense. Having kids do all this standard deviation business for a standalone 8 week statistics module may harm them if they only see it as a series of calculations.

What do I do now?
After talking with the push-in teacher for the class, it is clear I need to get more concrete. I’ll probably roll out the powerpoint, or skip standard deviation altogether and opt for the MAD. Lastly, I might curl up into a ball with a pint of cupcake frosting and hope that tomorrow I’ll wake up with the fortitude to teach my way out of this situation. (I’ll also probably think of some awesome come back for Benjamin too, and imagine my self saying whatever it is and picture him having a response like “Wow Carl, that one sentence has left me both smarter, and humbled. I want to be a better man.”)

Today’s class was another time trying something new for this cycle: Academic Circles.
Circles come out of our school’s effort to utilize Restorative Justice(RJ) practices across the school. Restorative Justice practices in schools serves is an answer to the very real problem of the school-to-prison pipeline which is rooted in traditional school discipline systems. Because traditional school discipline is punitive, and because New York has a strong police presence in our schools, students who are often in trouble get directed out of the school community with suspensions and expulsions, and often into the juvenile justice system. These students, who need to learn self-discipline skills are denied the chance to learn it and instead learn that the school doesn’t want them as part of their community. At a Restorative Justice school, students are pushed to remain in the community and correct the negative effects of whatever bad behavior occurred. One of the things that typically happen is that students go to a restorative circle. In the circle there is a structured conversation with the people affected by their action and seek to repair the harm they have done to the school, thus restoring the school community to it’s previous state. To help make the circle process a respected part of the school culture, this year we’ve been encouraged by include the slightly different “academic” circles in our classes. I have seen circles in people’s advisory classes, humanities classes, and even science classes, but not in math. Well….not yet!

A typical academic circle consists of students sitting in a circle, with nothing in their hands, and a talking piece that is passed around to designate who can talk. Sometimes there can be questions that students draw out of a bucket and use as a prompt. In the circle you want to build community among students, and you want them to know that their voice matters. (There are probably better definitions of the circle out there, and I will try to post links if I can find some).

What I am trying

For math this posed a difficult test. In a class where there is a lot of calculation, and easily discernable right answers, it might kill conversation, and community, to have conversations about one problem, that it would be hard for everyone to provide interesting contributions. Given how real math phobia is, I decided to not have any calculation going on in the circle at first. There is also the need to produce multiple representations in math that are just as important as words. It might be useful to have kids be able to draw a quick graph or look at what everyone else is thinking and discern trends and patterns.

So far I have decided to focus on error and estimating. Each Friday for the first two classes of the cycle I had the students sit in a circle in class. The students each have a mini whiteboard and marker with which they can draw their answers. In later classes we can use these to draw graphs or express creativity, but for now they will be used to answer the questions. The questions for the circle were tricky, if I want everyone to feel successful. Instead of making prompts, I’ve asked the students to create the questions as we go around. For today’s class asked students to think about a question that can be answered on a scale of 1-10. One kids question was be “How do you like today’s music on a scale of 1-10.” Students will also make a prediction to what they think people will say. As they answer this, I am jotting down the answers on a board that is in the chair next to me on the circle as a little dot plot. This allows me the chance to jump in and point out when the data looks interesting “What makes this dot plot stand out form all the others?”

The kids seem to enjoy it, and the improvement in community is noticeable compared to last cycle. It gives them a chance to speak their mind (which is a bit much for some people), and it is a break from the regular. I also have the chart paper saved, so I have an interesting pool of data that I can use for a yet-to-be-designed lesson or activity. The yet-to-be-designed activity will be around the question “Based on the data how good are we at guessing what people will say?” and will lead into a discussion of inferential statistics. Another idea I want to do is collect a bunch of statistics around a topic and ask kids to pick a stance on the topic, and pick a different statistics that supports or challenges that stance. It is rough trying to involve everyone in the circle, with the bottleneck being my writing down the numbers. Perhaps, I could tap the numbers into my phone or some kind of laptop so I could write faster, and the kids can figure out the results form reading people’s boards. If you have done anything with Academic Circles, or RJ, please let me know in the comments.

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.

#### 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.

Yesterday’s blog helped me prepare for this class, as it ended up being 90% Work Time. The Work time was necessary because we are beginning working on our survey project. The students are working on this assignment, which asks that they work through a number of tasks independently. Structuring the time to work on these kinds of projects is a struggle, as almost all students have holes in their learning. Today also needed to be a better class than Monday. The class looked like the waiting room at the DMV as everyone was killing time until it was my turn to see them. There definitely needs to be new ways to help kids become more independent.

Starting with Questions

Today’s class I began with some questions that I wanted students to respond to on a small sheet of paper.

1. Have you read the initial prompt of the assignment?
1. Did you complete all of the previous work listed on the front?
2. Did you complete the plan for the questions you will analyze on the back?
2. Did you go online to get our spreadsheet data and set up your own copy?
3. Have you made a data table? (The first item in the toolbox)

These questions took 2 minutes for students to read and start to answer. While they were on the board I went to each kid and looked at where they were at and confirmed what their next step should be. I made it around the room in about 5 minutes! The whole thing took about the time it would take for kids’ computers to turn on, but it made the class get focused very quickly on what steps they need to take.

The questions line up with each day of the project, which now provides structure for upcoming Work Time. Perhaps the rest of the days can have a big question for each day of the project, so kids can know how they are doing.