A popular question on the official AP forums is "what in the world do you do after the test?" and there are a variety of answers. Some of the projects are intense, others not so much. Those of ending school deep in June over a month after this thing have my sympathies. My kids desperately wanted to make a movie, but there was no way we had the time. I also had just finished the batch for this year and was not in the mood for more.

Lots of stuff worked against me after the AP test. For one, they had other tests to take, so random handfuls were out depending on the day. Then, college placement exam testing cropped up taking more random handfuls away. In the two weeks since the exam I've had them all together twice. It's better now, but they're out of here in 6 schools days.

Random Activities List

Financials - discussed doing your taxes (primarily that high tax refunds aren't some kind of magic bonus) and the basic of credit cards/borrowing money.

Engineering - support tennis balls with coffee straws, the ball had to be 12" off the ground and you couldn't tape your creation to the table for added stability

Field Day - just take them outside and let them hang out

Exit Interviews - a few questions just to see what they thought about the class, and to help me make some improvements for next year. I never learn a ton for these, but it's more about one last little relationship building item before they leave forever.

Sidewalk Chalk - why not? A lot of them did it when they were in Pre Cal. I generated some regions between curves and had them pick sets at random. They had to sketch the graph and compute the area of the region. With calculators and desmos the work part took about 15 minutes if you focused the whole time (hard for a senior in May). Later in the week they'd reproduce their findings on the sidewalk. Two regions per kid, about 4 blocks per kid to show the work properly and everything.

The only shame here is that the second group finished a little after noon. At 2:50 a storm rolled in and the whole installation vanished before anyone really noticed we did it.


Not a bad set of things. I will add to this list next year because I'll see them a little more and I know how to plan around the random absences a little better.

Goodbye Varsity Math. It's been real.

AuthorJonathan Claydon

It's the day of the Calculus AP Test. It's surreal to be here after being a bit overwhelmed in July. Last time I went on about things that went poorly. Since then I realized there's a lot more to add to that list, but it's probably counter productive to list them all. The revelation, is how to move on.

In the midst of AP review, it became clear that I didn't hit a fundamental concept hard enough. And that is how many different ways and contexts you can discuss this relationship. Props to Glenn for pointing out the bonkers desmos graph.

That was the theme all year long. Kids couldn't believe how much this subject is really about vocabulary and context and not a lot of raw skill. Raw skill is kind of the difference between a 4 and a 5, but by more or less ignoring the hardcore algebra, I have several capable of a 3 or 4.

The importance of that relationship pops up in questions like this one.

A completely symbolic question. Very little algebra. It's all words and notation.

So that gets me thinking. Would it be smart to spend the first semester on concepts alone? Something I haven't liked is "holding back" on concepts simply because it's not February or whatever. Is it necessary to shield students from integrals until you've exhausted derivatives? Couldn't you introduce the concept and save the mechanics for later? It seems like I could do myself a lot of favors by covering Calculus conceptually first and coming back with algebra and calculators at the end. A lot of the material I covered with integrals felt like it came up too late to really implant itself. Combine the goal of early and often AP material exposure, and dragging the course through its natural progression really limits when you can start using that stuff.

The second thing getting in my way is assessment. It needs to change. Regular assessment seemed only to serve the needs of having grade entries in the gradebook. I don't know that kids learned a lot from them. I could do some sort of weekly thing in the fall, but in the second semester it was really getting in my way. This curriculum is so spiraled I find it hard to isolate into nice, testable units. Well, nice, testable units that tell me something anyway.

Homework felt kind of useless too. I couldn't find a reason for assigning it other than, it's an AP class, so....yeah. I'm lost on this one. The whole completely optional thing is going to devolve into a waste of time because they'll stop doing it. Dropping the hammer on due dates and flinging 0s changes their grade from a measure of knowledge to a measure of punishment. But I have this nagging urge that they should be doing something when I'm not around? Weekly concept question or something? Again, blah.

And look, this is and is not all about the AP Exam. I've never taught a course with a 3rd party indicator of "success." I avoided tricks and shortcuts like crazy. I dislike a lot of the same things about overtesting as you do. But, honestly, the AP Calculus Exam is pretty good. Sure you can game it with tutors and everything, but kids without access to that stuff have a fighting chance if they get a chance to see how simple the material can be (and yes I know AP Exams suffer the same poverty/racial bias as others). I really wish the Calculus I was exposed to was more in the spirit of the conceptual rather than an overload of capital letter formulas. I get it way more than I did while taking it and I don't want my students waiting that long.

I either hate scripted curriculum or just really enjoy wrapping my head around subjects, because I'm ready to break Calculus apart and the year isn't even over.

AuthorJonathan Claydon
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My classroom is not the biggest, so to give the students the room they need, I downsized my corner significantly.

This is what little space I keep for myself. But it works out well with how I run my room. My kids do a lot of working on their own, but I don't do that thing where they work and I sit away isolated in a "don't talk to me" kind of way. In fact, this little desk encourages me to wander the room.

A few years in I realized I don't do a lot of work at school. The only time I ever sit down for long periods of time is if I'm giving tests all day. There's room enough to grade if I so choose. I have a stack of plastic trays for graded papers on that big white computer cart. I usually have errands to do during my one break period. Should I ever need some space, I just sit at the student tables.

And no, that computer isn't used for instruction. I have another one for that. That's part of the reason this succeeds, there are no cables running over here.

Other than needing a chair with armrests, this idea worked out. It kind of had to.

AuthorJonathan Claydon

A while ago I shared some thoughts about my iPad workflow (singular). Maybe you read it? A non-descript tall man did and then it got retweeted to the moon and back.

I didn't touch on the logistics much. It is not a 1:1 environment. The classes that used these the most had 36, 35, and 34 kids in them. Sharing was required.

Here are the ingredients of the tasks:

  • iPad/iPhone sitting on the same wireless network as my teaching computer
  • Desmos
  • Pages
  • Brother HL-3170CDW
  • handyPrint ($5), makes USB connected printers visible to iOS devices

Printing wasn't always involved, but in the case where the kids were designing something, the idea was the print it out and add some details. Any sort of like on high mandated Chromebook thing would need to answer the printing question for me. Desmos is exponentially better than spending time graphing things by hand. The Pages portion isn't totally necessary, but if you want to be efficient with toner and paper, Pages lets you place multiple photos on a page. Printing from the iOS Photos app gets you just one.

The sharing thing went better than I had hoped. For graph matching tasks like the one in this photo, usually two per kid was fine and I wouldn't pass out all the devices. Some kids elected to use their phone, which is totally cool with me. Sharing in this context offered a chance for more discussion. I've done this in academic and it lead to a lot of one kid just waiting for the other to figure it out. My PreAP group seems to be more eager and less likely to let that happen.

In instances where a printout was required, I would pass out all 25 and there was less sharing, but it still happened. Students working together were allowed to design whatever it was together and share output, so long as they printed two copies and annotated whatever additional information was required. Each kid had to hand in something. Often they'd sit there and share the device but create enough unique work so that they were NOT the same, which was cool.

I never felt constrained by having fewer devices than students. And I'm having a hard time convincing myself it's time to purchase more. I had several pairs who preferred sharing to working on their own. I dare say this is almost the perfect ratio. As always, I will continue to see if there's something better, but this was hard to beat.

AuthorJonathan Claydon

I'm concluding my first year teaching Caculus AB. The exam is two weeks from today.

It was a bit weird start to finish, there is a lot I want to fix.

The Bad

Teaching a course for the first time is overwhelming. Teaching something so trenched in tradition as an AP course even more so. In July I attended a week long orientation for new AP teachers and it was decidedly old school. Lots of fiddly TI-84 knowledge, handouts, and homework. And it's tough to argue with this approach. The leader of our workshop is incredibly well respected in the AP community and demonstrates results year after year.

Throughout the year I felt like I lectured way too much. But at the same time there is just so much fiddly stuff in this curriculum that it felt difficult not doing so. I also screwed up a lot or found myself overlooking details that became important later. For example, I had a big misfire with Riemann sums that I didn't notice until like, last week.

I had very little in the way of creative presentation. I had a couple of interesting ideas in the fall, but there was just nothing in the spring really. My current Calculus resources aren't much more than the assessments I gave. I felt rushed every day of the second semester and wrapped up the content over a week later than I wanted to. Our hybrid block bell schedule was a hinderance most of the time, but that's changing next year.

Assessment could have been better. Calculus is so much more conceptual than I thought and after January I felt like their grades in the course were completely irrelevant. I assigned homework 15 times. I have no clue if it was much use. I found the textbook of no use to the students other than for homework problems.

The big nagging issue is that AP Exam hanging over our heads. My school has no success in recent history. And I dislike teaching to a test as my main goal.

The Good

There are some things to celebrate. Low AP scores were one challenge, quitting was another. Varsity Math was a huge success. My Pre-Cal students are capital J Jealous. We have t-shirts, stickers, and 90 minutes of laser tag in the school cafeteria to prove it.

Speaking of Pre Cal, taking on PreAP Pre Cal offered dividends. Calculus numbers are higher for next year, and I know 95% of the kids on the list.

The idea of Throwback Thursday worked well. I kept that up (sometimes accidentally) all year long. A lot of the Calculus curriculum is putting new vocabulary to old math.

On the assessment front, increasing their exposure to College Board material seems like it's working. I gave a series of practice exams at the end of each grading period. Prior to Spring Break, they had a big one that helped me determine who could succeed on the real exam. The 25 of 50 who cleared that hurdle stand a fighting chance.

While I find teaching to the test a negative, I don't find the AP Exam to be a bad test. It is very concerned with concepts and vocabulary. I think there is a lot I can do differently to get the conceptual ideas across without overtly invoking the test as much. A lot of the high volume algebra that most instructors try to scare kids with really isn't present here. In fact, as a strategy that seems bad, it is way too easy to overthink what's required of you with this material, and overloading students with mountains of algebra and trig identities just makes them paranoid.

The Action

Discovering that focus on concepts got me thinking. Did I do enough to get them fluent in the concepts? During after school review sessions many students told me that they had no problem with the math, but couldn't get a handle on the vocabulary. The math really feels secondary in our preparations. The kids are kind of funny about it, they get mad that intimidating questions on differential equations boil down to Algebra 1 ideas.

But where do I go from here? I want to change a lot. I don't think my assessment strategy works in the second semester. I don't think we talked concepts enough. I did way too much talking. Stuff just took forever.

I intend for Calculus: Varsity Math Strikes Back to be an entirely different animal.

AuthorJonathan Claydon
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I've been at this a while, but you, dear up and coming teacher, should know that your career can take some turns. One direction is burn out and sadness. The other direction might lead you here:

I'm not sure if it's a direction you knew was possible. Is this the success of good relationship building? No idea. I hope so? There was lots of good work on this paper, and this student is a super hard worker. I really didn't know what to say. I did eat the cheeto, not that it affected anything. I can't be bought that easily.

How do you communicate the idea of building a classroom where a student feels safe taping a cheeto to their test knowing that you won't have a problem with it?

AuthorJonathan Claydon
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Now that the polar coordinate system is behind us, it's time for the end game material in Pre-Cal. That means sequences, summations, and limits. Over the years I have been spending less and less time with the sequences and summations portion. Primarily because I want to use it as a foundation for Calculus, discussing the problem of arbitrary area. A secondary goal is using the idea of a summation for some financial literacy.

In the short time I spent with sequences and summations, here is the random order of events:

  • Discussed sequences as an idea, everyone remembers them from some time in the past, no big deal. I wrote a series of random sequences on the board (linear, quadratic, etc) and had them generate terms. Then they added them together. No sigma notation yet.
  • Then I did a magic trick. Well, a Nowak trick. Students create a random linear pattern, generate the first 20 terms and add them together. Have someone verify your sum. They did this on little half index cards and I collected them and quickly called out sums like some sort of genius. This drove a few kids crazy trying to come up with theories.
  • Next we go Dan Meyer with some penny pyramids:
  • This group of kids weren't too intimidated by this. Many of them figured out the pattern to the number of stacks and were able to get the correct answers manually. Several thought the answer might be possible through the magic trick I demonstrated before.
  • At this point I show them sigma notation and how to use it on the calculator. They compute a few for practice.
  • Then it's Fawn's turn and I mix in some Visual Patterns. I picked pattern 2, 18, and 19. Two of those are simple, 19 is a fun kind of frustrating.
  • Next step is converging and diverging series. I pick two sequences: 4*(0.74)^n and 4*(1.02)^n and have them compute the sum of each for 10, 50, 100, 500, and 1000 terms. This is some good calculator practice and gets them to observe a few things. Why does the answer start repeating for the first one? Are these giant numbers I'm getting for the second one right? I give them some hints about the things possible in calculus when I mention that there is a simplification for computing the sum of an infinite diverging series. "We're going to learn that!?"
  • Then a summary assignment. Generate some terms, generate some terms and sum them manually, compute sums on the calculator, and identify convergence and divergence.

All of this builds towards approximating area under curves using left, right, midpoint and trapezoidal sums. Students who went through last year's version remembered it well now that I have some of them for Calculus.

Most Pre-Cal curriculum I see sticks this stuff in between vectors and polar coordinates and I find that a little awkward. Putting it right before whatever Calculus material I intend to cover has worked better for me.

AuthorJonathan Claydon

I don't write much about Calculus because frankly I'm not sure I know what I'm doing. I need another summer to reflect. The primary goal last summer was to find an assessment strategy that worked. What I came up with has been doing ok. Given the ultimate goal of the class, demonstrate 50% proficiency on a very context/vocabulary heavy exam, it has become less useful as we wind down. In fact, the last on these SBG-ish assessments will be given in April, about a month before the 2015 AP Exam. After that we're out of new material. Plus, at this point I kind of know what I have.

How? Mixed in with their standard assessment have been mock AP Exams. A theory about our historic awfulness on the exam has to do with exposure to AP like questions. After digging through tons of them, the AB test requires far less gritty math skill than you'd think. In December students took about half a test and could work on it together. A few weeks ago was their big trial by fire, half an AP test (30 multiple choice, 3 free response based on released College Board material) done independently.

Results are not spectacular, but I'm feeling ok:

As it's about time to hand in your AP registrations, I gave an official opinion to each student based on their performance. I had to be mean and tell a lot of ambitious kids no. Two kids with 3s were two points shy of a 4 which was stupendous. Now, I have no authority to prohibit them from taking the exam, but they should know if they're going to wind up wasting their time. Or this has all been a long con on their part and they'll do great, who knows.

That healthy chunk of 2s gives me something to work with. Many of them were not far from a 3. I advised most of these kids to register. Another subset I left it up to them, some of them were in that group of 1s.

You can look at that and think, well those scores do suck. And they kinda do. With six weeks to go I feel like everyone is capable of jumping a level. All of them (that weren't just utterly lost) said it really came down to vocabulary, the math was not difficult.

I'm trying to change expectations for students in this class, and we might just slowly be getting somewhere.

AuthorJonathan Claydon

There's not much to explain that hasn't been said already:

Sidewalk Chalk Adventures
Return of Sidewalk Chalk
Sidewalk Chalk Three

A few tweaks this year. Previously the equations were scripted. I handed out a list and kids made the picture and then drew it outside. This year they designed their own: one limaçon and one rose curve with appropriate equation or table. I showed them how to do all sorts of odd things with rose curves. The scope expanded as well, enrolling my co-worker and her troupe. In total it was about 230 students who produced two graphs each. No joke, all of that put together covers about 2000 linear feet. Powered by Desmos. Because, duh.

Selected images:

There were a lot of pokéballs. Tons of these were fantastic. The size of this installation is ridiculous. Unlike previous years, it's not scheduled to rain right away so this will stay put for a while.

Three years ago I had a stupid idea walking to my car. You never know, man.

AuthorJonathan Claydon

Second semester can be rough. It is a busy time of year for me being "on" for 12 hours most days, and 16 hours on others. By Feburary I'm a little spent. And that's when I'm not trying to teach something for the first time. This February I was a little hashtag overworked, for real. I've always found student opinion to be valuable feedback. I figured prior to Spring Break it was time to take the temperature of the room. I asked my Pre Cal kids if there's anything in particular they liked, whether they found the class difficult, if it's different than prior classes and whether or not they get attention. The pile was large:

Call it fishing for complements, but these are some nice validation after a 10 week grind. It's also a chance to see what the quiet kids have to say. I am always curious about what quiet kids have to say about the hot mess noisy environments I've been known to cultivate.

Here's a selection (click for bigger):

Try it next time you're feeling a little down or if you're worried that something may not be working as intended. I don't spend a lot of time with these, I scan them kind of quickly. I'm looking for a couple of indicators: the student feels comfortable and supported. If most of them tell me that, things are going ok no matter how strung out I may feel.

AuthorJonathan Claydon