Jimmy Neutron

Today in my Advanced Precalculus class, I formally gave kids a name for something we had been doing — working parametrically. And I showed kids on Desmos how to graph parametrically (right now they only were working on circles with different radii and centers, and changing how long it took to go around the circle). So literally going into this, all I did was show kids how to graph a circle on Desmos parametrically.

After that, I gave them 10 minutes to play around. I presented them with some options/challenges:

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The stuff they were creating, when given no instructions and just time to fiddle around, was awesome. So many cool moments! So many times kids were showing off their graphs to others! There was one student who realized they could create ovals at an angle, and so they decided to create the Jimmy Neutron logo. And just a short while ago, I get this in my email:

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Yay! Huzzah for deciding to give time to play, and huzzah for kids making cool math images for fun!

Toothpicks

In Adv. Precalculus in our previous class, I had kids work on Dan Meyer’s Toothpick 3-act. I do this every year before our unit on sequences and series. They totally got into it. I didn’t need to be there. They solved that problem brute force.

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So I gave them the extension: You have 40,197 toothpicks.

I told kids to spend 25 minutes working on the problem. They could stop then, or continue if they had time and were obsessed. They had to figure out how many rows the final figure had.

I collected the work kids did. A few actually got the right answer! It was awesome! One kid told me he really enjoyed working on it. A couple other kids half raised their hands when I asked if anyone got obsessed with it. I’ll take it!

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I took that same class to see the math-art show that I helped curate at my school. I wanted the gallery to be a space where kids enjoyed math. The last two classes I took were fun – but today, these kids totally got into it. They were psyched to go, they looked through everything, they were serious about the discussion prompts I showed, and we had some very insightful observations. Seeing the kids interact with the art in this way made me gloriously happy.

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Similarly, the Lower School math specialist showed me a cool pattern that the kindergartners were making with tiles we ordered for the show.

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At lunch today it was “thanksgiving” – which mean mashed potatoes, stuffing, cranberry sauce, tofurky… MY FAVORITE THINGS!

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It’s funny… I had a lot more other good moments today. But the day still felt long and exhausting. So I’m glad I took a few moments to recount some of these moments.

An Impossible Triangle

This is my one good thing for Tuesday, because I forgot to write one, I didn’t get home until after 9pm, and I couldn’t think of anything good from the day. But I just remembered one.

I was doing “sign out duty” (where I sit in the front hall and have kids sign out if they are leaving the building). One of my current precalculus students (who I also taught two years ago in geometry) came up to me SO excited. He was — in front of three of his friends — telling me about a math problem that his brother was working on. That he got interested in figuring out. And that he couldn’t solve. But he was obsessed with solving it.

The problem was from his brother’s geometry problem sets. (I wrote the problem sets the following year so my current precalculus student never got to do the problem. I had seen this problem before, but I cribbed the version from the Park School of Baltimore’s problem solving materials.)

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In geometry, when we went over this problem in class, I showed them this youtube video first:

 

In any case, my one good thing is my student who got obsessed with his brother’s math problem. And that he got obsessed enough to tell me. And ask for a hint because he wanted to solve it. And when I told him he might want to cut the figures out of paper, he told me he already did that! Which shows me how obsessed he was with this problem. And yeah, I know, why shouldn’t he be — because if there wasn’t an explanation, all of math is a lie!

I gave him another hint, and he went on his way.

High School Musical

In multivariable calculus, we had our second book club. But it was the first one led by students. The leaders were amazing and the discussion was rocking. Lots of good questions, lots of good thinking. Kids were drawing connections between our reading (of Abbott’s Flatland) and things they had been reading/watching for other classes (documentaries, Crime and Punishment). One kid even mentioned “Attend to your Configuration” was like:


which made me chuckle.

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In Advanced Precalculus, kids saw Pascal’s Triangle for the first time, and they were SO IMPRESSED with all the things hidden within it. So many cool observations/insights!!!

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I had my standard Precalculus kids work on a combinatorics problem. And I thought many students would solve the problem in one way — and use pattern recognition but without a full understanding of why. Instead, I saw so much perseverance in what kids did. And almost all of them solved it a different way (involving combinations) after getting frustrated with listing everything out. The realized that listing was not efficient, and needed to have a better way to approach things. So they switched. I loved that.

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I got to hang out briefly with my friend Lisa S. after school. She and I work late together, and so we did some of that working, and grabbed a super quick dinner together.

 

 

Terrible Day, Turned Around

I had a terrible day today. I couldn’t fall asleep yesterday so I was up until past 2am tossing and turning. So I was exhausted. And one of my classes fell flat and I realized how little an impact I was having on their learning. And even though I was trying to be productive, I got very little done. But… a friend brought me leftover cake she had. And so that totally was going to be my one good thing.

But then I got something in the mail at school, around 5pm:

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Now I know that every freshperson at UChicago gets to nominate someone, and then based on the form letter and unengraved clear thingie they sent, this probably goes out to every single teacher that was nominated. (So yes, I know it’s not in the same category as an award that puts me on stage next to the president of a university at graduation.) It’s not even really an award. It’s probably more marketing than anything else.

But to me, what it tells me is that I had a student last year who said something nice about me. And after a day when I felt like I’m not doing a good job, when I’m just exhausted with my late nights working, when I don’t feel like my kids know yet how much on their side I am… and I’m wondering if I will ever get them to that point… this felt good. Because even if I am not there yet, I can get there.

A Grid of Triangles

I ended today by having one of my classes see the math-art gallery. And then when the clock struck 3:20pm, school was over. A former student (who I taught Geometry to last year, who is now studying Algebra II) came up to see me in the gallery. Why? He had a problem he invented.

He drew a meticulous grid of squares with triangles in them, that look liked this:

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His question that he wants to solve? How many triangles are in this?

Why I love this? He came up with the question on his own (possibly while doodling). And he wants to solve it! That’s the type of playful curiosity that I love!

So him coming up with the question (and sharing it with me) is my one good thing. If he follows through on solving it… now if that happens, that will be another day’s one good thing.

Killer Class

In Advanced Precalculus, my kids were working on something I call “The Arrow.” It’s new this year — something my co-teacher and I dreamed up to make combinatorics make sense. It’s incredible. My co-teacher told me today “I’ve had so many amazing insightful conversations around combinatorics this year, I feel like I have had more than I deserve in my teaching career.” (Or something like that.) I agreed, saying it was an “embarrassment of riches.” The kids — on their own — have come up with a formula for combinations and permutations (they don’t know it yet… we haven’t given names to them yet). And in doing so, they actually derived the binomial expansion. No Pascal’s Triangle. (That comes later, as a consequence of everything that we’re doing.) They spent 30-40 minutes persevering and had so many gaspable moments.

They had insights about tree diagrams, connected them to “tile problems” (the structure we dreamed up), kept on asking why instead of moving forward just to move forward. It was the most beautiful noise. I wish I had a videotape of this class — so I could show it to future classes so they could see what my ideal class looks like.

It was the best.

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In my 90 minute Precalculus class today, I took my kids to the math-art gallery that I helped curate. I was nervous about it. This is my tiny, quiet class. But because I had a great structure to facilitate the visit (given to me by my partner-in-crime Brendan), the visit went well. They kids for the most part found pieces they were fascinated by. And I heard some interesting conversations.

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I bought a game (we didn’t playtest this at allrecently, but hadn’t opened it. It’s a 1-5 minute game. I broke it out in our math office, and we played a few times. I love that my office has quirky teachers that enjoy being quirky. After this, we played a game where everyone got a slip of paper, and we had to write our names and a counting number on it. Then we gathered the papers, and the person with the lowest unique number wins. (So if the papers had 1, 1, 2, 3, 7 on them, the person who wrote 2 wins! And if the papers had 2, 3, 4, 4, 8 on them, the person who wrote the 2 wins!) I don’t know why but we totally geeked out about this too. (As a side note, I had a multivariable calculus student do an interesting final project on this problem a few years ago… and how it relates to the Nash Equilibrium… she’s now at MIT!)

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We had a firedrill and it was beautiful weather outside. So although my class was interrupted, it was worth it for the moment of zen. Especially since today I taught all of my classes — and one of them was the 90 minute block. On a Friday before a long weekend.

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I have a teacher friend who had a medical issue this summer, and so things have been hard for her this year physically. I hadn’t seen much of her, except in passing in the halls. But I happily got a text from her asking if I was free for dinner — so I went to meet up with her in Park Slope and get some delish thai food. It was great catching up with her!