Carl's Teaching Blog

A place to talk about teaching and learning

Category: Clog (Page 1 of 7)

Clog: A Couple Stories from presentation week.

Story 1: learning through presenting

The first presentation of the day was a student presenting a math project about Misleading Graphs. This student clearly had no fear about this process. Earlier in the year he got on stage for the mental health panel and had also signed up to have 4 panels in one day. His confidence was as high as his substance as he was able to describe multiple types of misleading graphs and the news sources that keep making them. Even on the best presentations we have to keep asking questions that push the student. It is pretty rare when a student demonstrates total mastery over the math, the context, and the strategies the used. In this case, he didn’t really understand all the features he used on google sheets, and one graph that he made stepped over the line of being ‘misleading’ to just being incorrect. Presentations are great places to talk about wrong answers because you can really walk through the student about why it would be wrong, and correct any misconceptions on the spot.  Sometimes even the teachers have misconceptions. That’s a great thing about presentations is that there is space to really root out any misconceptions.

Story 2: a kid comes in and says “my teacher is in the hospital, so they sent me to you to approve my independent project.” Independent projects have become a thing of the past thanks to me and the rest of the team. We’ve asked that projects that to be presented to only come class projects to avoid getting things that aren’t on a high school level. However, someone gave him a green light but couldn’t finally approve the work that the student did, so I had to step in and help him finish. The paper was titled “Old Testatement.” I was worried.

His paper was actually super interesting! He asked two questions. Could Adam and Eve have populated the Earth in the 6000 years since being cast out of the garden of Eden, and could the the earth have been covered by flood of Noah’s ark (which we learned was originally told in the Epic of Gilgamesh) have actually covered the Earth? It was brilliant! He made an exponential model to describe the growth of human population from Adam and Eve’s 44 kids, and used the volume formula to find out that the earth would have required 3 times the amount currently in the oceans to be as high as it was described in the book.

The ingenuity and the curiosity on display wasn’t the best part. He actually became a different math learner during his presentation. He was vocal about how much he hated math class, and this disdain was what led his teacher to go along with this independent project idea.  He presented with three other kids, and offered to go first because  he felt his project was the “least worthy.” But when he finished the kids sitting next to him said he did such a good job that they didn’t know how to follow it. We also commented on how well he answered questions and explored his original problem. He left the room with his back straight and his head held high.

It was a great example of independent thinking and what is possible when kids are pursuing their own questions. Now the policy around independent projects seems like it should be reconsidered. Or, we should have more opportunities for kids to do modelling tasks where they pursue questions as opposed to doing it just because. Having a ‘mythbusters’ class where the kids try to model some historical story or other event could be really interesting. Kids could also try and compete with each other and come up with the best model possible.

Clog: Oh, This Is Much Better

After a morning flash of insight, I spent way too much time on this Linear Regression Desmos Activity. It seemed like too cool of an idea to not do, although I’m sure it could be better. be For 4 weeks I’ve followed the IM 8th grade unit on data associations with my Algebra class, but I didn’t really have a cool way to talk about what linear regression is, or have a way to teach the kids how to use the regression features in Desmos. In retrospect, I could have sailed into the #MTBoS and found what other people are doing around regression, but I sort of burned my boats when I started making this thing. I trudged on in making this thing until 8 minutes before class, when I realized I needed make copies, and get upstairs. In all the work on the activity and the copies I didn’t get a chance to get the laptop key. We couldn’t use computers!

So I was up in the front of class, trying to keep my kids engaged while Jayla went to find the teacher who last had the laptop key (he was in the bathroom). “Alright guys, let’s review what we’ve been doing the last few days.” Doing a little mini-lesson at the board seemed like a good way to kill time. “How many people know what kind association this might be?” I said to the class while gesturing towards a hastily drawn scatterplot. Students looked back at me with silence and agony. It was clear they were not engaged, maybe because they knew the computers were coming. Their body language screamed that they were not invested in doing any part of this whole lecture thing. Then I thought to myself, “Teaching like this SUCKS.”

Over the past cycle I have been working on teaching with IM. Those materials have a lot more interaction, and realy prioritize the student voice. Kids were getting used to debating about which terms should be used, and agreeing on what is the right answer. There was a smooth flow to those classes while this little mini-lesson felt spreading the last of the natural peanut butter jar. The previous cycle I worked with a co-teacher who really pushed me to have more interactive lessons, with videos for the lectures, so I really haven’t done any kind of lecturing in a while. It really blows.

It set an awful tone for the Desmos Activity, which required a little bit of me in the driver seat since the activity was unclear in some parts. After the Desmos I had the last few lessons from the IM unit. The kids did a card sort, and used the card sort to learn about frequency tables and made some stacked bar charts. Everything felt kind of normal again.

Well kinda… I still need to fix that Desmos Activity, let me know if you have any feedback!

Clog: No one’s ever going to win!

Today was the first day of my new class. We’re calling it The Lottery. The “we” for this cycle is me and my co-teacher, who is awesome. We’ve talked a lot about the class and it is challenging me and my regular routine, and it’s leading to great results so far. My typical probability class is serving as the frame for this class, and we are modifying it. Heavily. It’ll probably be a whole different experience by the time we get finished. We’re calling it the lottery to tap into some of the kids natural curiosity about something around them, as opposed to my previous class which centered around a make-believe carnival.

Today we began class with another number talk, and then we did four corners about the lottery.

Dice, Playing Cards, Cuisenaire rods, and all the random stuff we brought in so kids could make their games.

Next we decided we came up with this thing called “Games of Chance”. We wanted kids to work hands-on with a task that put them in the driver’s seat. This task asked them to work in small groups to make up games that other kids could play. They made up the rules of the game, the price to play the game, as well as the prize that winners could take home. To help make the tangible game we gather a pile of useful things (Dice, cubes, playing cards, etc).

The kids came up with an array of interesting games. One was flip over one of twelve cards, another involved rolling a dice, and then drawing a card from a deck of cards over and over until you got the amount on the dice. At the end of co-teacher’s 15 minute timer, groups paired up and played each others games. Students were deeply engaged in the activity, as I orbited around the edge of the room.

We had enough time for 3 different games to be exchanged before we stopped  and got into a circle to talk about the games that everyone played. Hopefully we wanted to see if students were having the kinds of headaches that the mathematics in my class could serve as the aspirin. My favorite comment was from a student who seemed visibly frustrated. “We made a game that was basically impossible,” said the student, annoyed by the game that their group settled on, “It’s so hard, no one’s ever going to win!!!” This sounds exactly like the kind of thinking that people should be embarking upon for a class called “The Lottery,” don’t you think?

Clog: First Day VNPS Anxiety

Today was the first day I got to teach a class this year! I’ve been coming in to school daily since mid-August 15th, so there was quite a bit of anticipation for actual teaching. The class that I’m teaching is called Problem Solving. This class was largely developed out of the Crossing the River with Dogs book by another teacher but has been, and continues to be, heavily adapted. The first section that I plan to teach in this 8 week course is Draw a diagram. Specifically, the Farmer Ben problem. It’s where you have to count up the number of cows and ducks that Farmer Ben could have if he had 22 animals which have 56 pairs of legs.

Before we got into a problem, we started in a circle. My plan is to do a circle kind of sporadically through the class, in order to build community and support my school’s restorative justice initiative. Once we sat in the circle I asked kids to think of a problem they solved and then choose one of three questions out of a hat:

  • What helped you understand the problem?
  • What was the process you took to solve it?
  • What were other ways it could have been solved?
  • How did other people help you solve it?

In retrospect, I probably should have started with something fun like “what are you watching on Netflix.” Instead we heard everyone listing all of the problems in their life on the first day of class. A few people harped on their personal flaws, or biggest mistakes, or some other horrible things that happened to them, and how they worked their way out of it. It wasn’t a mood lifter, probably going to have to tweak that for next time.

Next we counted off into groups of 3 and started doing VNPS using the Farmer Ben Problem. I wanted kids to think and to be a little uncomfortable, and that definitely happened. There were a few things that left me wondering whether I was setting kids up for failure.

One of Peter Liljedahl’s shifts for creating a thinking classroom was about reading the problem out loud instead of putting it up in words. Hopefully it will underscore the importance of paying attention and listening. Immediately after I finished reading it people asked me to read it again. After reading it the second time one student asked me to read it again and he had a look on his face like I just asked him to walk across fire. “I read it once, that’s why you need to pay attention,” I said, ushering him towards his white board, “you have to ask your group mates.” A few minutes later it was clear that he was standing on the side of his group mates while the other two members of groups were barrelling towards a solution. I checked in with the group and those two students knew just what they were doing, but that first student was silent and making a face that said “I have no idea what’s going on.”

Meanwhile, another student was making a face that said “I suffer from anxiety. Working independently on math problems was my sanctuary. Now my heart can’t stop beating, and I just want to go do the problem on my own.” This left me a little stumped. The student and I spoke after class, but I struggled to help this student connect the group work we are doing, to any real world that she has imagined. If anyone has any ideas of how to tweak the VNPS for these two students, let me know in the comments.

My first ever implementation of VNPS went very well for the majority of my class. Kids were talking and thinking together with a familiarity and comfort usually reserved for weeks into the cycle.  Some groups didn’t want to stop working after the time ran out. It is definitely something I am going to have to keep doing and keep tweaking. Next time I do it, I might use a 3-act of some kind that could have us do Act 1 in the circle, and Act 2 on the whiteboards.

Clog: A Post-Mortem

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.”)

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