I learned a lot of tough lessons in my first year teaching Calculus. Around March I started doing myself some favors and found ways to roll a bunch of topics backwards into Pre-Cal. That bet paid off and we're easily a month ahead in Calculus this year.

I also made a note to address another huge Calculus topic in Pre-Cal: the relationship between position and velocity. For whatever reason, kids see this stuff in physics but never see as much more than a formula they're supposed to pull of a sheet. They ought to subtitle the AB curriculum Physics Makes Sense Now with all their emphasis on position, velocity, and acceleration.

We have this stretch early on where we talk about function behavior. It's pretty typical, using words like increasing, decreasing, constant, and undefined to describe things and the domain for which that's valid. It goes hand in hand with Piecewise Functions.

This year we did all that and then added some context.

Graphs increase and decrease sure, but what if that graph represents something physical? What could induce those changes in behavior? That is, the slope of the direction change is the velocity at which the change happens. While introducing this I drew something similar to this graph and had a kid act it out, setting a reference point in the middle of the room and having him/her walk back and forth. We even had a discussion about whether the steepness of the direction change matters. The surprising thing for most of them was the connection between constant position and zero velocity. Often they only remember slope as a positive or negative idea, not so much the zero aspect. Nothing crazy, just a small placeholder for the ones I hope to see next year.

The nice immediate pay off is within a day or so a student of mine was working on a physics worksheet covering this exact same concept, only adding a velocity calculation step.

AuthorJonathan Claydon
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You may have heard of this before. There's a fun origin story. It was a popular presentation.

Like any idea I have, the second year takes it to higher places. Varsity Math is now an institution. I'm not saying the Wall Street Journal stole my idea, but the coincidence is funny.

A year ago I was making everything up as I went along. Now that we know what we're doing, I had a plan in place from Day 1. It was a little necessary too, as my current Calculus crew is VERY aware of all the shenanigans from last year and will not be denied.

Changes and Upgrades

First, I have invited Statistics to play along. Varsity Math is now a blanket term for anyone in an AP math class. The last thing I want is for stats enrollment to suffer over some t-shirts. Second, I'm running the thing like a legit organization: receipts, tracking charts, deposits, the whole thing. The scale (89 students) is too large to wing it. On the second day of school the kids had to report back what all Varsity Math meant.

LOTS of questions about what a $6 speech sounds like. Mostly after itemizing the merchandise it was much easier to charge $40 than $34. Also, it doesn't actually cost $10 to play laser tag, I'm cutting them a deal and the "speech fee" is there to make up the difference.

The t-shirts are from a local outfit. The stickers are Sticker Mule. The patches are from Patch Warehouse.

I spent a month collecting a LOT of money. Yesterday was merchandise distribution day:

The patches are the best. They are really well done and were really affordable ($1.77 each). There were several backings to choose from, and I went with an adhesive to allow for more mounting options. Allegedly they'll stick to a letter jacket but sewing them might be the safe thing.

Community, Stupid

All of this started as a way to combat apathy in our AP students. We were having high attrition rates. By giving ourselves an identity, we've made AP math a desirable destination. I have several kids willing to put the work in because it's such a good atmosphere. And even though I don't teach stats, I still know a lot of those kids (including 4 veterans who were 11th graders with me in Calculus last year), and they are pumped to be involved.

We aren't done here. Coming soon, you will hear all about how we're taking Varsity Math to future generations through some collaboration with our feeder middle schools.

And one last tease: have I thought about how some of you can get your own Varsity Math gear? Of course I have. Stay tuned...

AuthorJonathan Claydon

Previously I examined results from my first A/B/Not Yet Calculus Assessment.

Now we've had a second one. It covered two new topics and the optional Limits retake I included because the class average was so low. Here are the numbers:

The retake had the intended effect. Students who opted in generally improved their rating. I had a few who performed the same (whether that was a B or NY previously). I learned a couple things from this. First, I will keep including optional retakes from time to time, but I'm not going to make it a guarantee. I worry about student dependence on those. It's been an issue with SBG experiments in AP classes at my school. Thus, the Asymptote category up there I'm going to leave it up to students to improve that on their own time. In the event I do I put an optional, in-class retake on something, I'm going to have students request it in advance. I didn't count, but the number of students who attempted the Limits section wasn't worth making all the copies. Now I think I'll keep them on smaller, separate slips and only make copies for those that request them.

Due to some weirdness in our upcoming schedule, I'm going to address the Asymptote issue through a little daily "test" like I do with parent functions and unit circle values.

I make solutions available, so I am limiting the feedback I give. I need to structure what happens when they get a test back a little better, but I think I'm getting them to buy in to using the solutions as a resource. I'm also getting better at being harsh when making the decision between a B and a NY.

I'm liking the set up so far. The next big step is the transition to a majority of AP material as our assessment base.

AuthorJonathan Claydon

All sorts of annoying little details have to be immediately recalled in Calculus. There you are trying to find an equation of a tangent line and BAM, not knowing the value of sin(pi) stops you cold. Or you're comparing which differential equation model grows faster and suddenly you have no idea if e^x grows faster than x^2.

Enter an old idea, stolen from any number of teachers in your past and here, explicitly from a workshop I attended a year ago. Every so often I'll package up annoying little information like that into a "test" to start the day. I'll have instructions to number 1-15 or something and I'll ask them a host of trig values, sin(pi), -cos(pi), etc. Or I'll show them some pictures of functions and ask for the associated vocabulary word. Or mix the two. It's no different than spelling tests or multiplication tests, minus the "minute math" panic attack part.

The teacher in question would collect these and grade them. She asks 10 questions, every day, on a variety of old and new things, often repeating questions. Simple little knowledge that needs to be in the front of your brain by May. She wasn't really interested in the grades, just being able to perceive that her students were getting better.

Here's the 40-graph Parent Function set I use:

I have them know sin/cos (and limited tan) values for 0, pi/6, pi/4, pi/3, pi/2, pi, 3pi/2, and 2pi. In the future this exercise will probably include other simple things like fundamental trig derivatives/integrals, and possibly some first and second derivative type stuff.

It's been 4 weeks and a simple thing like this already has me feeling better about our progress.

AuthorJonathan Claydon
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If a teacher tells a student they never make a mistake, I would be highly skeptical of this person. I make goofy, annoying errors ALL the time. I also admit it. Case in point. I had students evaluate a series of points through a piecewise function. I made a typo. Because, typo.

I didn't catch it until some kid in the second testing class asked about it. The Desmos graph I built while writing the test was correct, I transcribed it wrong. There's three versions of the test, so I had to go hunting around the room to find who had the problem. One class took it completely unaware of the problem. Or, they adapted, like this kid. The way I wrote it they are correct in stating that h(-8) through h(-4) would be undefined in this case. Full credit for you. A few assumed it was a mistake and worked it as though it were written as intended.

It was especially goofy when they had to graph the h(x) they were given in the next section. Again, my bad.

Annoying, but manageable. Maybe I'll remember to fix this between now and a year from now when I test this subject again. There was a typo on the Calculus test I gave the same day. Sometimes I can't win. I managed to catch that one before I handed it out at least.

AuthorJonathan Claydon
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It's hard to convey what my room is like on a daily basis. During various TMCs, I'll start telling stories and people will get bug-eyed with a "you aren't serious..." face.

Last year I dealt with a line up at the door problem by marking part of the floor as lava.

Where do you go from there? Shark. Duh.

This year's Calc crew wasn't surprised. Reactions varying from "oooh, shark!" to a monotone "of course." Pre Cal just thinks I'm weird. After doing the Glenn high five thing on their way out, I've convinced a few of them to simultaneously jump the shark AND land the high five in one motion.

"Mister you're a child." You don't say.

AuthorJonathan Claydon

In Calculus I struck out with an intention of using the bold A/B/Not Yet assessment strategy. Given the broad strokes used to grade AP Exams, it seemed like a good fit. And unlike the SBG system I use in Pre Cal, I don't necessarily have to be weighed down by mandatory second attempts. That can be time consuming. One of the problems I had last year in Calculus was burning class days on assessments for the sake of filling a gradebook when there were probably more important things to do.

I gave the first one a couple days ago. The test had three sections. Class 1 and Class 2 are equal in size (36 vs 35). Here's the test if you're interested. I enter A as 95%, B as 85%, and Not Yet as either 50% or 0% depending on effort.

Chunking content gives me detailed information much like SBG. But I'm not forced to include it next time. Part of A/B/Not Yet is to offer opportunities for retakes. At the beginning of the year I vaguely mentioned that retakes would be "a part of the process" with the intent of figuring that idea out later.

I think I know how it'll go now. If the class as a whole does poorly, that's a sign that I should address some things and offer it a second time. Here, I should address some things about Limits and give everyone another shot on Test 2. The other stuff seemed to take pretty well, so a retake on those will be up to the student to do on their own time.

What else should be done differently? Well, I want to foster more student discussion about what they were asked. I said on the first day that a bunch of C students does me no good. First task upon handing these back will be pulling up the solutions (posted to a class website) and discussing what happened. I think most of the issues that happened in the Limits section will get cleared up just by talking with a peer for 5 minutes.

Like SBG, the act of putting a rating will make the student focus on the rating. It's unavoidable. Though I'm hoping the discussions and the retake triggers will encourage them to sort out weaknesses, i.e. care about learning, so we have a stronger group for the more difficult second semester.

AuthorJonathan Claydon
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At the beginning of the year, there's that old line about "don't smile until January." That particular strategy probably won't work out for you. But, it is an important time to decide what's important with each prep you have.

For a variety of reasons, I haven't given homework really ever. Even when I switched to PreAP preps last year I didn't see the need. I have certain goals for Pre-Calculus in mind and homework didn't seem necessary to meeting that goal.

This year marks the start of what I want to become a successful program. The 71 Calculus students I have are 93% returning faces.

You might think I created a problem. It's a big group who just a spent a year without math homework. Surely I've killed their work ethic and dug myself into a ditch. The old "how are you preparing them for college" argument.

A flaw in that argument is that expectations have to be built over decades. To make a student properly understand the demands of college, they must be held to the demands of college starting in 4th grade. I think that's silly. If you communicate expectations and communicate WHY you have those expectations your students will adapt.

Whatever your class, the first couple weeks is where you can mold whatever expectations you want, regardless of what a previous course/instructor required of them.

My kids didn't have homework last year. This year they (barely) do. I communicated that. I design the assignment to be short and purposeful to show I respect their time. In Pre-Cal they used their notebooks on all their tests. In Calculus they can't. I communicated that and explained why.

Students of any age will play along if they believe what you're selling.

AuthorJonathan Claydon

Something I stare at from time to time.

I've always taught five classes. Who knew my little room could hold so many people during the day. I remember distinctly one of these years getting upset that I had a bunch of classes creeping near 30. It's funny now.

I find these numbers interesting. It correlates well with an uptick in my school's population.

Desmos tells me that in my 34th year I will have 505 students. You think I can move into the auditorium?

AuthorJonathan Claydon

That time of year. Everyone on your timeline slowly trickled their way back to work. I just wrapped week one. I'd say it's unique among all my week ones thus far.


I did a few local PD sessions on notebooks and SBG like I do. Last year I helped a local middle school adopt some of these things unilaterally. Their experiment is helping convince other middle schools in our district to start experimenting with their practices. Insane progress.

I don't talk much about my online teaching exploits locally unless prompted. I lay pretty low. Of course, then I became a PAEMST finalist.

The official seven days of PD were pretty straightforward. I prepped the room way before my report date. Experience is so invaluable. I think the last thing I worried about was the school part. I spent most of my time tweaking how I'm going to manage Varsity Math things this year.


Speaking of the finalist thing, I found out a few days before Day 1 that I'd been put on the agenda for the superintendent's first day of school trip around the district. Totally cool. A little freaky given that it's you know, the first day. But he came by, said hi, the kids were great about it.

The real star of the show this week has been the kids. If you ever get the chance, find a way to teach a group and have the majority come back the next year. Calculus is 99% kids I know or taught last year. We were at cruising speed immediately. A very loud cruising speed.

It contrasts heavily with Pre Cal, a lot of kids I recognize but never taught. So we're in that super polite, quiet stage. I gave them some classwork and it was silent. It's unsettling. By the end of the week that started to pick up once they figured out I want them talking to each other about things a lot. A little Estimation 180 did the trick too. And no matter how many times I said they don't really need to take stuff home, I'd see this:

All them were taking their books home! Insane. Curious how long that keeps up.

Long Game

Over the summer, you might have seen this little gem:

Every year I work on helping less. Well, secretly helping more, but making kids take more charge. That started last year with a link to a dropbox folder with homework solutions. I expanded it to a class website (using my new purchase) that has that and more. Test dates and stuff are published there. I'm not going to call them out. I'm going to post test solutions too. Their first homework assignment was to tell me the grading policies and how much all the Varsity Math stuff was going to cost.

Missing in Action

There are some traditional things missing from how I do the first week of school. I don't have a syllabus. I don't explain sbg. I don't go on about what different assignments are worth. I don't go on about what I expect on a regular basis. I don't say the word discipline once or talk about write ups or anything. I tell them to get a notebook and how to request a restroom pass. Done. Then we play 99.

Wait, what? No syllabus? But but but....I can hear you say. In my opinion, a high school kid is not going to read the long list of things you're excited to cover this year. And unless you've set things up to where you reference the syllabus on a regular basis, it's wasted paper. A giant college class you see twice a week. Sure, give a syllabus. A group of kids you see every day? Nah.

How do tests work? Explain it when you give one. How do I track my grades? Explain it when it's time to start tracking. How do I get a pencil? Wait for someone to ask. How should I put stuff in my notebook? Wait until you have something to put in there.

My procedures have always been more effective when the moment comes. If there's something that needs to be explained, I explain on the day that's relevant. No sooner.

In summary, great first week. Feels like October. Legs didn't hurt. Voice got its stamina back pretty quick. Only mildly exhausted. Pumped.

AuthorJonathan Claydon
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