- I had a light teaching load day. And I was giving a test in one of my classes. And I got a lot of logistic work done.
- I got a super nice email from someone this morning (saying they heard that my NCTM Orlando talk that I gave with Bowman was great) and that put me in a good mood.
- I had three conversations with three of my advisees about their midsemester grades and they all went well. And a short convo with another advisee was nice because they opened up a bit. And one of my other advisees showed me this ridiculous video of a squirrel.
- I got a lot of planning done.
- Lunch was delicious. They had mashed potatoes, so I took two helpings.
- I had my “mentor meeting” with the new faculty member I’m “mentoring” and we walked to a local cafe and had tea and shared a strawberries and cream dessert and had a nice conversation.
- A student who said he was going to email me to set up a time to meet actually did, and that made me happy because I wanted to see follow through.
- My calculus class went really well today. I was so sick and tired of all the algebra we had been doing, and I had been feeling like I was in the doldrums, and today we mixed things up with a short 15 minute activity that I think helped me finally feel like we were almost out of the algebra thicket.
- We had a birthday in calculus so we got to sing the birthday song to a student (and she got to wear a birthday hat… sadly it broke…)
- I met with a student after school, and we had a lovely meandering conversation about calculus and other stuff, but what I loved is that she mentioned some stuff we had learned last year “for fun” and she talked about how that blew her mind (e.g. Graham’s number). It was a meeting that could have taken 15 minutes but because I was just having fun, and so was she, we ended up chatting for 45 minutes.
- Before leaving school, I ran into three students, one who I’m teaching now, and two who I taught last year. And we had a short but fun conversation, and they were talking about stuff we did last year and it just made me feel good.
- My friend and colleague Maria told me that she was working with a student on precalculus, but they really GOT geometric series because the stuff I had created was really “sticky” and he really understood it.
- My friend Maria got me thinking about random numbers and H and T coin flips and for 10 minutes, I had fun going down a small mathematical rabbit hole.
- My friend Alice and I were emailing about how we never see each other anymore, and I told her I stopped by her office today and she wasn’t there, and then later I came to my desk and she had stopped by and I wasn’t there.
- I got home before 6pm. Which, if you know me, is rare.

# Author Archives: samjshah

# Fried… Brain dump.

Today I had the most crazy day. We have a 7 day cycle, and “Day 1” is my hell day. I see all of my classes, including “the long block” (and other commitments during most of my free times). But the reason today was even more insane is that it was *parent visiting day*. In theory, it’s such a nice idea. But of course, it is not something I love, having people in my classroom that I don’t know, and who are possibly (probably) making first-impression judgments of me. So in practice, it’s scary.

In all of my classes, I’ve formed new groups. So today I was going to do a 25 minute group building exercise I designed. So in my classes, we’d devote about half the class to kids talking about how to build the best group they can for each other, and half the class to kids doing math. That was the plan. In theory. In practice, the group building exercise blossomed into 40 minutes, and we only had 5-10 minutes of time for class. So parents didn’t even get to see their kids thinking about math, really. And that bummed me out.

Also, since the activity was new, I didn’t quite know how it would go. And now that I’ve done it, I still don’t know. Which is weird. Normally I have a sense of things. I heard some really awesome conversations, and in some classes, kids were opening up. I do think some kids thought it was “another reflection exercise a teacher wants us to go through,” but I think others found it genuinely useful. I will say that in my first class, one parent asked me if there’s a book I could recommend that informed how I think about groupwork (which made me happy) and in my second class, another two parents told me they work with adults who can’t work well in groups and they are going to steal some of what I did in their work. And I did ask a student in my first period class (who I saw later in the day) what he thought about the activity, and he was pretty positive about it. So that made me feel pretty good about things. I think that in my next two classes, things weren’t as smooth, so that’s why I’m feeling unsure.

Wait, this is the one good thing blog, not the “I’ve had a crazy day and I can’t think of anything good because I’m frazzled” blog. So now that I’ve done my brain dump:

- I got to reconnect with a colleague in the history department who I rarely see, and we had a nice 20 minute conversation after school about our time at my school. It was fun!
- I am going to see the school play tonight, and I have a bunch of students and an advisee in it. So I’m excited about that.
- Before going to see the school play, I am going to dinner with a friend! Like a real dinner, not like we get food and bring it back to school and work together, like we normally do.
- A student left my precalculus class saying he was going to be thinking about this problem that we were working on all weekend.

# Best. Email. Ever.

So what feels like eons ago (September 14th), we were talking about higher dimensions in my Advanced Precalculus class. Why? Who knows. Wait, I know. Maybe. Yes, we were working on an introductory problem which dealt with a cube, and we were extending our results into higher dimensions. By patterns. Yes. Okay.

Some kids were into thinking about this… And so I posted this on our google classroom stream:

I didn’t get a reply from any kid. That’s pretty much the usual when I post things like this. So I’ve learned not to hold my breath. But I like to post things (a) to let kids know I love it when they dig math, and (b) to provide a window of opportunity in case someone wants to bite.

So yeah. I didn’t get a reply from any kid. UNTIL TODAY. WHICH IS NOVEMBER 1ST. A kid emailed me saying she got 4 other kids interested in reading this book and having a book club on it. I am so beyond thrilled I can’t even express it! You see, I had “book clubs” in my multivariable calculus class for the last two years and we read this book both years. And my school has phased out multivariable calculus (for a better course! proof and structure!). So that means no more book clubs for me, and I miss that.

I still am wary about this becoming a thing. But I hope there is follow through, and I get to read *Flatland* with kids this year!!!

# A challenge problem, New groups, Bells

I had a headache most of Sunday, so I didn’t get much done. But I did get to school early on Monday and met up with a student who was working on a challenge problem I posed. He shared his thinking with me, and I shared what made sense and what didn’t about his thinking. I’m just excited that he was working on this *for fun*.

Also, in one of my calculus classes, I revealed the students’ new groups (they’ve been with the same people since the start of the year… so about six weeks). It was nice to hear so many students say how much they were sad to be leaving their first groups because they loved working with them. (They weren’t bemoaning their new groups, though…) The fact that they would be *sad* about leaving their groups meant that the group was actually a meaningful collaboration for them.

I gave a visual pattern to one of my precalculus classes, after having introduced “the hotel bells.”

And as students saw different ways to come up with the number of squares in the *n*th figure, they started realizing how rich this problem was. And they started seeing things they hadn’t seen before. And bells started ringing. And that tintinnabulation made me so happy.

# Slope!

I had a meeting with an advisee who I saw a couple weeks ago. They made a goal to speak up more in English class, so I asked how they were going to achieve that… *I’ll… just try harder? *So I suggested they keep a tally of how many times they spoke in class. At our meeting, I inquired about that goal and they pulled out the sheet where they had two weeks of tallies recorded by day. AMAZING. This kid is awesome. I also had a second great conversation with a different advisee, who mentioned how much they enjoy our homeroom. I AGREE!!!

After school, a number of my students were participating in this music-dance-art piece that one of our art faculty designed. It’s a bit complicated to describe, but it was the highlight of my day. From 5-5:45pm, I was transported. So many thoughts went through my head, and by the end, I had taken out my phone to write out a few of them. One of them was of this artist, who I hadn’t thought about in forever.

Today in calculus, one of my kids said something wrong, and I was like “that was a great wrong thing to say and I’m so glad you said it!” It was such a great thing to know I had that teacher move. And I truly believed it.

I also did this “do now” in calculus to illustrate a point. We’re now drawing a bunch of tangent lines and estimating the slopes of those lines by picking two points and estimating the slope between those points. In years past, I’ve had students just choose two random points that were often pretty close together, so they’d get terrible slope estimates. This year I asked this:

Then I asked this. Very different, because you are introducing some error into your slope calculations because you’re eyeballing coordinates!

… and before having kids share their slopes, I took a poll:

Kids did this anonymously, and all but two students thought the *green* points would give a better estimate for the slope. It totally makes sense to me why they’d say that. We’ve said that when we find the Average Rate of Change between two points super close together, it’s an amazing estimation for the Instantaneous Rate of Change. And the green points are closer than the blue points.

So then we share our data:

I had kids just make observations. And of course the big observation is there is a huge variation in the green point slopes, and not much variation in the blue point slopes. Kids were surprised because they expected the opposite.

Then I revealed the true answer, and we talked about their misconception.

I thought this was a *great* moment today, mainly because I was happy the 7 minutes we spent on this was super effective, and I think they’ll remember it more than me simply saying “pick two points far apart when calculating slope!”

# Today…

Today, a student told me about an independent study project she was doing that involved photography.

Today, a student had a leftover donut from her work with ninth graders, and she gave it to me.

Today, in one of my classes, a group figured something out and created a new handshake that involved all three group members putting their hands up into a vertical plane, having their fingertips touch (so they were forming 120 degree angles with each other), and then they curled their fingers together and stuck their thumbs up. They were celebrating figuring something out. I loved watching that.

Today, in one of my classes, students were briefly investigating Pascal’s triangle and they were excited about their findings.

Today, our cafeteria had polenta for lunch and I got two helpings of it and thank goodness for that because it was divine.

Today, in one of my classes, a student saw me write and asked why that wasn’t undefined. Which made me realize that I had never talked about 0!=1. Shame! But we were in a rush, so I mentioned two reasons (a conceptual and a pattern-based reason), and then offhandedly mentioned that in the same way mathematicians defined 0! to be 1 to “extend the idea of factorial” they had also found a way to understand (-4)! and (1/2)! Kids seemed hungry to know more, so I told them they could think about investigating this as one of their math explorations.

Today, a student stopped by the math office quite late to ask a question about something from our last test. And we had a nice conversation about math but also a few other things like soccer. It made me happy.

Today, one of my colleagues complimented how we started calculus this year (introducing the idea of the derivative and the idea of the integral secretly), mentioning he couldn’t imagine starting the course in any other way now. (He’s teaching the course with me for the first time this year.) I was so happy because I really like the stuff I created for the start of the year.

Today, well yesterday actually, that same colleague had done some groupwork conversations in his classes and mentioned that they went really well. And that inspired me to start thinking of doing the same in my classes. Which I’m simultaneously excited and nervous about.

Today, a colleague told me that one of my students was so proud of herself for her grade on the last test… and that she’s gained more confidence in herself. I was giddy because this was a kid who was supremely nervous at the start of the year.

UPDATE!: I forgot to mention, so I’ll write it now… Yesterday, a student I taught last year in the lunchroom stopped me because he saw a video he knew I would love and wanted to show it to me. (It was how to cut a bagel mathematically…) I love that he thought of me and took the time to show it to me!!!

# Hell Day

Every seven school days I have a hell day. That means I teach all my classes (including the long block), I have advising meetings, I have a team meeting during lunch, and after school I proctor study hall until 5pm. Basically, I barely have time to breathe… and today our “community time” was taken up by a guest speaker. So I literally only had 65 minutes free from the start of school until 5pm. And of course, I stayed at school until 8:30pm to prep for classes tomorrow and do other stuff on my plate.

What’s even worse is that since I was gone for three days last week, I have been playing “catch up” in my classes. Which has been extraordinarily boring and I’m doing way more speaking than I like. I feel like the worst teacher.

So I’m going to dig deep and find something good to write about today.

- In one of my precalculus classes, a student told me they had been thinking about a challenge problem I had posed, and has a possible inroad to a solution. I don’t know the answer to the problem. I didn’t really want to think about it too deeply because I didn’t want to do too much “leading.” So I’m intrigued to know what this student figured out. They said the problem led to three different “cases” which each had to be worked through… muy interesante.
- In my other precalculus class, a student told me (before class started) that they got “nerdsniped” by the problem and then after working on it and not solving it, they went to bed… but then as they were falling asleep their brain was whirring and they thought they had a path to a solution, so they got out of bed and worked on it and found a flaw in their thinking. Obviously I loved this so much.
- In calculus, kids seem to be pretty decent using their calculators and desmos to approximate the instantaneous rate of change at a point by finding the average rate of change between two points that are very very very close to each other. I remember this being challenging when I taught this years ago, and it was challenging this year too, but I *think* they’ve got it.
- In one of my precalculus classes, I have a student who has some gaps because they were at a school with a very different curriculum last year. And they felt bad that they were holding their partner back. I was just so happy to hear their partner say so warmly how talking through these ideas was helpful to reinforce their own understanding. It was so empathetic and lovely.
- We had a guest speaker today, an alum (from before my time), who works for the Department of Homeland Security. She works on human trafficking, and she gave a pretty awesome talk about how she got to where she was in life (in a meandering fashion) and some of the work she does.

And that’s literally it. I can’t think of anything else that was good from today! ACK! I need to be on the lookout for good things more, and I need to remember them.