Understanding Others #Election2016

This morning as students were walking in, I glanced at my Facebook feed.

Many of my students are Trump supporters. The most vocal among them are definitely Trump supporters. A number of them were happy. Not all, of course – some were upset, many were surprised, most were just tired.

My Facebook friends are a thorough mix – Clinton supporters, Trump supporters, people who deeply dislike both candidates. (I appreciate the mix – it’s important to me that I’m not in an echo chamber and hear many points of view.) The Trump supporters were pretty quiet this morning. My feed was a mix of “I’m glad that God is sovereign,” and “I’m deeply sad and frightened and how could we have elected this bigoted person?”

The disconnect between what I was reading and what I was hearing was a bit surreal.

In first period, there were a couple of instances of graffiti on the property of the one vocal Clinton supporter among my students. (Probably not the only Clinton supporter; just the only vocal one.) One student, who has repeatedly said he’s just glad he’s not 18 yet and can’t vote, pointed out that the losers were being more gracious than the winners.

I spent most of the day telling my students how other people feel. Yes, you’re happy because your candidate won – and that’s not bad. You can be happy. But you need to understand that a lot of people are very scared right now. You need to understand that, whether or not you think it’s fair, your candidate’s campaign is associated with xenophobia. You need to remember that, and understand how your glee comes across to people who are afraid for their safety. You need to be gracious in victory and raise the level of political discourse. Fine, you can’t change the nation – start with yourself.

I also spent a lot of time telling people to take off their “Make America Great Again” hats. You can be happy that your candidate won – but you still have to follow the dress code. No hats! I probably came across as trying to crush their joy; actually, I’m just a stickler for the rules.

At least one student left today with a greater understanding of how other people are feeling. Probably two. That’s a worthwhile day. And even if none of them had, I spent the day thinking about where other people are coming from and how other people are feeling, and that’s worth doing.



When Admin Listens

Over the last few years, there’s been a recurring discipline issue come up at school. It’s been recurring because, while the rule is clearly outlined, the enforcement mechanism has not been. Last week, enough was enough, and the administration figured out a workable enforcement mechanism.

Before calling the whole school together and telling them what was going to happen, though, they called the student leadership together and asked them what they thought. It went something like this.

Principal: “Hey, we value your input. [A] has been a recurring problem. We want to do [X] and [Y] to fix it. Here’s how that would work. What do you think?”

Various students: “[Y] is a great idea, but [X] doesn’t feel fair.”

Principal: “Hmm, ok. The logic behind [X] was this.”

Students: “We don’t think that’ll work because of these reasons.”

Principal: “Ok. I’m going to keep [X] as an option if the situation doesn’t improve, but for now we’ll just go ahead with [Y]. Any objections to that?”

Students: “No, we’re cool. But while we’re at it, can we talk about this other issue? We have some ideas on how to improve it.”

Principal: “Yeah, we’ve been thinking about that. We’re thinking of doing this.”

Students: “That’d be cool, but we have some other ideas, too!”

Principal: “Those are cool ideas. We’ll think about them, and let’s talk about them more later.”

Our students have often felt that they don’t have a voice and that their suggestions are not listened to. It was very, very refreshing to see administration actively seek out the input of the student body’s chosen leaders and then – this is the important part – change their plans based on student input. Color me impressed.

L’Hospital’s Rule

I was out the day we went over L’Hopital’s rule in Calc II, and my sub covered it. (Yay for subs who can teach Calc II!)

When I came back, my student asked me, “So, why does L’Hospital’s Rule work?” So we proved it – at least the 0/0 case, which was all I had in my notes.

“Ok, so why does the infinity/infinity case work?” (I love that she asks these questions!)

“Hmm…” I answered as I stared at it. “Maybe because…uhm….hmmm. I’m not sure. Can I think about that and get back to you?”

I had to look it up, but today I got back and proved it. And she still wanted to know!

Next time, hopefully, I’ll be there, and we’ll prove both that day. But I should add these to my notes.

Student Calc II Questions

For the past three years, I’ve gotten to teach an Independent Study in Calculus II. (Yes, that’s right, you should be jealous.)

We normally offer AP Calculus AB, but that’s our highest normal math. Every once in a while, though, we have a junior in Calculus AB and we have to figure out what to offer them their senior year. A few years ago, we had a student like that, and their family asked me to do an independent study with them. And thus, Calc II was born. We cover Calc BC without the AB topics (So…volume by shells, arc length, surface area, a little bit of extra diffeq like logistic and linear equations, integration methods, vectors and parametric equations, and series. Lots of series.) and then have a month or so to cover whatever we find interesting.

It’s a little bit different every year. The class is really just one – or last year, two – students, and these are students who have already been with me for two years. At that point, I know the student and can tailor the class to their interests and needs. Like a lot of proofs? Sure, we’ll prove everything? Dislike proofs, but need a lot of practice? Ok, more hand-waving, fewer proofs, more time practicing. This year, my student is asking really, really good questions: “Wait, what would happen if…?” kind of questions, questions that I’ve never really thought about too deeply. My answer is often, “I don’t know, but let’s find it. If we try this,… .” If nothing else, she’ll learn that math is about exploring and finding answers for yourself. I’d like to make sure I come back and explore some of these questions more intentionally next time around, so I’m going to make more of a point of blogging about them.

  • When we covered the shell method, we derived the formula for the volume of a sphere. When we did surface area, we derived the formula for the surface area of a sphere. We compared them. We noticed their connection. We talked about why that would be true. She wondered if there are other shapes where that was true. We explored – cylinders yes, circles yes (but circumference and area), squares no, rectangular prisms no, triangular prisms no. Why is this true? We were stumped.
  • When we started integrals that use trig substitutions, we set up a triangle to do a sine substitution. She asked what would happen if we set it up the other way. We tried it out (use a cosine substitution) and saw what happened. (Works just as well!)

Her questions and her obvious desire to understand and explore also make me be more careful with my explanations – ok, yes, we did a clever algebra thing with this integral; what did I see that made me do the clever algebra thing? I should take it a step further – what’s an integral that would also need this clever algebra thing?

In Praise of Algebra II Teachers

We started angles today – yay! I love trig, and the beginning of it is purty.

We’ve had four different Algebra II teachers in four different years, so I’m never entirely sure what students will know walking into my class. They all cover the same material, but every teacher has their stronger topics and their weaker topics.

Last year’s teacher was thorough. These kids have seen things. She also worked with a curriculum development specialist to overhaul the curriculum and get it into really good shape. At the end of last year, she asked me what I’d like her to cover with an extra couple of days. I mentioned the unit circle, handed her all my lesson plans and card sorts and games, and let her do her thing.

Apparently, she did an awesome job. The students know about radians! And are halfway comfortable with them! And voluntarily produced the words “unit circle!” I’m excited.

We even had time at the end of class today to do a card sort activity (that someone in the mtbos posted, but I can’t remember who…sorry!) where the kids had a sheet of angles, and a bunch of cards with radian measures and degree measures, and they had to match them. They did great. Also, I was proud of them for going at it with basically no directions except “Pick up a blue, yellow, and orange pack from my desk and match them. The blue sheet should be vertical.”

So, to last year’s Algebra II teacher: thank you. You rock. You served your students very well, and I am blessed to get to enjoy the fruit of your labor. Bless you.

Why a @Desmos Activity?

This post is really more a process of me thinking something through than anything else. However, if I missed something, I’d like to hear about it, so I’m going ahead and publishing this.

It’s summer, so I’m revising my courses. I’ve been looking at a lot of resources, and this morning was devoted to Desmos Activities.

I’ve used Desmos activities in the past. I’ve made some Desmos activities. There are things for which they are excellent. Having students write the equations of graphs, for instance – it’s a lot easier to hand them a Desmos activity than print out or project a bunch of graphs. It reduces the work involved in checking their work and lets them spend more time on thinking. Those are good goals, and Desmos helps me achieve them.

I’ve got a list of Desmos activities that I want to incorporate into my class this year. I’m especially impressed with activities on how to graph. Polygraph and Marbleslides both encourage good thinking and they’re fun. That’s a rare combination, and it’s important. Really well done.

As I looked through the calculus activities this morning, I noticed a few worth incorporating. The Daylight Hours is a really nice extension that covers some worthwhile calculus while making a nice connection to the physical world. The Rate of Change of the Exponential Function could be good.

But with many activities, I found myself thinking, “Why would I use this instead of what I’ve been doing?” Take the Functions Defined by Integrals activity. (You can see it here.) I could have every student pull up their laptop and work through the activity, and it would be fine. It’s a good activity. Or I could do what I normally do: throw a graph onto the board, ask students to find the area between x = 2 and a bunch of other x values, then talk about how what we really have here is a function. That would be fine, too.

The activity has students talking to their neighbors and responding to other ideas. But I can do that at the board by giving them a question and two minutes to talk to their neighbors before calling them back for a class discussion.

The activity uses different colors to emphasize the difference between positive and negative area. I can do that on the board.

The activity has students estimate. I can do that at the board.

The activity has some good questions that I hadn’t thought of. I could ask them at the board.

The activity has students figure out the notation on their own. I could have them do that on paper silently, then compare with a neighbor, then talk as a class.

The activity has students collect data about what the area is. This decreases the calculation burden and frees them up to do more thinking…but this topic falls at a time of the year where I want my kids to get some more practice with calculating areas. (Whether or not you agree with that as a good instructional goal is fine; I don’t even know if I agree. It’ll be on the AP exam, so we’re practicing it.) So while in general that’s a good goal, I’m not sure it’s a goal that I want to pursue.

The activity also draws in the graph of the function defined by in an integral, which is nice. That stands out to me as one of the nicest moments of the activity, actually. But…I could do that at the board. I could even have the kids use the data we’ve collected to sketch what they think the graph of the function will look like, which raises the cognitive level of the task. Although now that Desmos has a sketch feature, they could incorporate that into their activity.

The activity lets me see what every student has written in response. That’s nice, and something that’s hard to do in a classroom. That’s probably the biggest advantage of doing an activity – I can see everyone’s response instead of whatever percentage my teacher ears catch. But…I only have about 12 students in my class. I can hear most of what they say, and I can tell from their body language when I need to wander over and be closer to them.

The downside is that I’ll have students write “I don’t know” and move on. Yes, I can see the “I don’t knows” on the dashboard, but if my eyes are on my screen, then they aren’t on my students. That means I’ll miss the facial cues and body language that tells me how they feel about this.

The other downside is that it’s digital. My students spend a lot of time staring at screens. I don’t want to add to that time unless it accomplishes something I can’t easily do another way. Also, my students often lack the discipline to stay on the screen I want them to. As soon as I ask them to open up Desmos, I know that Twitter, Instagram, the physics textbook, or email will also be opened. So the Desmos activity really has to be special to make it worth those distractions.

There’s a lot of buzz around Desmos. And don’t get me wrong, I really like Desmos. We use it probably once a week in my precal class because it is so. much. better. than a TI-84. I am not in any way trying to bash Desmos.

But I’m not yet sold on the activities. I definitely like that they’re available. I have and will use them in class. There are other times where I’ll look at them and modify my non-digital lesson, like this one caused me to do. Seeing the thinking that the Desmos activities try to provoke, especially the ones written by the Desmos Teaching Faculty, challenges and improves my teaching. I love that there’s a library of things I can look at. Even if I don’t use them as is, they’re still useful.

Why am I writing all this? To criticize Desmos? No! Emphatically no! Like I said at the beginning, I want to do more Desmos activities this year! I’m writing this as a reminder to myself.

I’ve noticed a tendency in my thinking to want to scrap what I’ve spent the last few years building and replace it almost exclusively with tons of Desmos Activities and 3-Acts and Underground Mathematics questions and those sorts of things.

All these things are tools. Desmos is a tool. A useful tool, a powerful tool, a helpful tool. Maybe it’s a nail gun. There are times where a nail gun really is the best tool for the job. But sometimes screws work just as well as nails, and I can use the drill I’m comfortable with – with some improved techniques by watching the nail gun – instead of switching.

So, while I’m revising my curriculum this year, I need to remember not to go overboard. Some of my lessons need to go. Some of them need to be tweaked. And some of them are good as is.

Unless, of course, there’s some major upside to this activity that I’m missing. That’s entirely possible, and if I missed something, I’d really like to know. Desmos guys? Will you let me know what I missed?

Small Bites

How do you eat an elephant?

One bite at a time.

Throughout the year, I tweak my curriculum a bit – move a day here or there because of calendar changes, add or rework or remove problems. This means I’m rewriting the keys as the year goes on.

But I do a lot of other things during the school year, also, so this job is never done as fully as it deserves. I don’t get to sit down and rework whole units, add Desmos activities, or the like. I’ve seen some really creative ideas over the last few years, and I can drip in a few of them, but not flood them in like I want to. Now, I think what I have is good. I just think it could be better.

So, one of my goals this summer is to rework everything and really get it hammered into shape. Incorporate Desmos, reverse the question, raise the ceiling, lower the floor, notice and wonder more. For my entire curriculum. And have the keys written. And do all the other things on my summer list, like STEM improvement and have coffee with friends and get some sleep and sew a lot. Oh, and figure out what I’m doing for Computer Science next year, because I’m teaching Computer Science next year, too.

And, of course, that means that I’m looking for resources. Reading new blogs, digging through Desmos teacher activities, looking at 3-Acts, hopping around Underground Mathematics and NRich.

What the online mathematical community has created is amazing. There are a million resources that are just. so. good. Guys, you rock. I don’t have to create new things; I’m looking to modify and adapt and incorporate your awesome things into what I’ve already created. But it’s also a little overwhelming. I feel like I’ve sat down in front of an elephant.

So, one bite at a time. Triage: Precal first (because it’s more students and needs more work), then Calculus. Rewrite assignments and lesson plans, then tests. Work on the units that need the most help first. Save the keys for later. Curriculum map last.

And if I don’t finish the whole thing…well, there’s always Christmas break.