Carl's Teaching Blog

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What would you do with a million dollars?

On June 1, 2017

I like the idea of a sneaky project, that creeps up on kids. For example, I’ve started a unit project by asking my unsuspecting students the following question on the board:

What would you do with a million dollars?

The project, linked here, leads students to learn about budgeting for an economics class I taught. Students reply to this with the typical fantasies.

I’ll buy a new car, and some new Jordans, and a new house!

But by adding a few caveats, we’re able to grab all of these kids wildest dreams and smash them against the rocks of reality. The main caveat is that students have to survive for 20 years off the million dollars, and they have to pay taxes. They first have to choose whether to receive the money all at once, or over 20 years. Kids immediately go to calculating the tax bracket and realizing that receiving all the money at once means you pay much more in tax compared to having the money split up over 20 years. At this point I tell students to opt for regular payments (although I imagine an interesting side story might be to take the money upfront and try to invest it in a stock market simulator to see if they can earn back the original amount).

From this point in, students have to figure out how to live on 50,000 a year. This is pretty close to the US national Median income, so it should line up with what they’ll make as soon at they enter the work force.

So then I ask them to think through what they would do with that 50,000 yearly amount, and make them budget how much they would spend on all of the following things:

Clothing
Household Products
Furniture
Utilities (heat, electircity…)
Inside Entertainment (Cable/netflix/music/videogames)
Phone
Gas
Health insurance
Life Insurance
Outside Entertainment
Anything else…

Once they come up with these numbers, I have them put it all in a spreadsheet that gives them little suggestions of websites to use to estimate all of these amounts. The final thing I have them do is write a little paper describing what they did with the money.

If I had more time I would have them actually learn the mortgage formula ahead of looking for houses on Trulia, and use the mortgage formula to estimate a range of houses they want to look for. My kids used the estimators on Trulia and Zillow, which assume a down payment, and also don’t let the kids use their brains, so I would like to not depend on those.

Clog: The circles keep going

By Carl Oliver

On May 19, 2017

In Uncategorized

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: A Post-Mortem

By Carl Oliver

On May 8, 2017

In Clog

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.

Instead the class sucked

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?

Is it a bad task?

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.”)

Clog: Trying to get on board with Academic Circles and Restorative Justice

By Carl Oliver

On May 5, 2017

In Clog, Improving Teaching

Today’s class was another time trying something new for this cycle: Academic Circles.
What is an Academic Circle
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.

Clog: Suddenly a math argument breaks out

By Carl Oliver

On April 28, 2017

In Uncategorized

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.