The Calculus exam is in two days. My ambitious plan played out well on my end. There was plenty of time to work through review. I have now told the kids to stop studying. Cramming on May 3rd isn't going to make a miracle happen. Plus there are other tests they should probably worry about.

How did review go? Kids showed up, my after school schedule was slightly derailed by some freak flooding, but adjustments were made. I didn't quite get them all in as much as I wanted, but the dedicated ones were there. The biggest take away is that none of my 51 test takers seem lost. I bring up a topic and they can fairly quickly recall the strategies and concepts associated with it. Whether that translates into performance in an exam setting, who knows. We scanned some released material together, nothing really shocked them. They saw plenty of things they knew how to do or recognized. I thought I had done a good job preparing kids last year, but I realize that it just wasn't enough. We are in such a better position.

I won't be proven write or wrong for months, but sitting here today my gut feeling says 55% of them pass, about 25% will do so handily. The 2 crowd could prove me wrong, we'll see. Not three years ago such realistic chances were just a bunch of wishful thinking.

Only like 9 weeks to wait this out...ugh.

AuthorJonathan Claydon

You know those (somewhat) interesting problems about water troughs you slugged through in high school Calculus?

Well, unlike the similar triangles of a whale tale, this problem might actually be of real use. Behold:

It takes about 8ish hours of driving rain to fill this thing. Something I've witnessed twice in less than a year (maybe you've heard of us?). Surprisingly it doesn't overflow the bank (though it will spill into a road upstream). How many parachutes did this civil engineer pack? How many sources feed this thing? What keeps it from overflowing? Is there a bigger outlet upstream? What kind of flow rates are possible? How long after the rain stops would it drain? And biggest of all, just how much water is that?

AuthorJonathan Claydon not taking the AP Exam?

This may or may not be an issue for you, but it's something I find it just as important as preparing the kids who are taking the exam. (And regardless of hearsay and tradition, making the exams mandatory as a part of the course is not something the College Board is ok with)

Last year I had two classes of Calculus. In one, 17/30 were taking the exam. In the other it was only 8/20. I was not happy with my choices for kids who weren't taking the exam. Our review started about this time of year and the plan was to work through free response questions that were grouped by category. Problem was, throughout the year the kids had spent some time with AP style benchmarks and knew exactly how well or not well they could handle the material. I had several data points validating why my non-testers were non-testers in the first place. Having them work through the same free response load as if they were on an even footing was just so inefficient.

This year, the kids were given even better AP style benchmarks which help render an official opinion about their chances. The scant 17 (out of 68, yay progress!) non-testers had many data points indicating that they didn't grasp the content well.

So what are my options? What are my responsibilities? I could sit on my high horse about it, make them work through the 100-item review set I made (50 MC, 50 FRQ parts), watch them not succeed with it and say "I told you so." Or, give them an opportunity to rehash the material and see if they can pick up a few things, or demonstrate what they do know. While not necessarily able to dissect the subtleties of a free response questions, they get the whole integral/derivative thing.

I developed a set of exercises for them to complete, one for each day of our review period. Plus a couple of mini-projects. All of it due in a couple weeks. It covered material I felt like they could complete independently within their understanding of the course. On the day of the AP Exam they take their own version which serves as part of their final exam (students in AP courses not taking the exam aren't allowed exemptions).

I'm not saying I let them off the hook here and threw them a free A. The benchmarks and their course grades properly reflect their struggles, but when they walk out of here, I want them to feel like they got something out of it. At a minimum if someone ever asks them about Calculus they could give an elevator pitch.

Non-Testers Exercises (TeX files and PDF)

AuthorJonathan Claydon
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It's about time for the AP Exam. The students are registered and it's time to see if I can be a bit more organized this time. Bonus! We covered everything I wanted to in respectable detail, rather than the horrible rush job I pulled last year. Main features:

  • skill reviews through warm ups and some explicit class work
  • focus on free response questions through my own, home grown Ultimate™ Free Response Questions (8 questions with 7 to 10 parts each covering most possibilities)
  • no class time dedicated to a practice exam, too time consuming
  • after school sessions to provide smaller, more focused groups (I have two classes size 32 and 36, it's hard to address all their needs)

I did the after school bit last year and it was pretty useful. We spent a lot of time with released material and the kids made a lot of progress in the three weeks I did it. This year I have more kids and that required a bit more organization.

The sessions aren't mandatory, but I strongly suggested they would be a good idea. I gave nine dates and I said they should show up to a minimum of three, but maybe no more than that, because I'll probably be repeating myself.

The ultimate free response questions were quite the labor of organizing and pouring over released questions. I can't post them because they are heavily inspired by College Board material and would probably get me in trouble.

What I CAN share, are inspired by a couple of my trademark dumb tweets.

The titles were too good to NOT use.

The source PDF file for interested parties.

Still holding my breath here. Our progress through the free response will slowly allow me to exhale.

AuthorJonathan Claydon

Previously: Sidewalk Chalk Adventures, Return of Sidewalk Chalk, Sidewalk Chalk Three, Sidewalk Chalk, the Fourth One

Fifth year. Big year.

Stats: 3 teachers, 12 classes, 250+ kids, 800+ sticks of chalk, 2000+ feet of sidewalk

My favorite spring time activity celebrates its fifth year. I almost got Calculus involved to make this stretch even further, but the timing didn't work out. One year we'll get enough kids involved to cover the entire 4000 ft perimeter.

On to the photos:

Best day.

AuthorJonathan Claydon

You could also file this under community, stupid.

Early on, the goal was learning how to teach. Over the course of the last school year I realized it's time to start paying attention to who I teach.

It starts slowly. A kid tells you their favorite video game. They tell you about the GameBoy they owned when they were younger. You talk about the one you owned at the same time when you weren't as young. A class who laughs at how quaint and ancient the 90s were. One tells you about a hobby they think is embarrassing. Another is going to be the first in the family to graduate high school. The first admitted to college. The first to graduate college. Next they want to know what college is like. Can I actually do it? It sounds so hard. My sister tried to go to college and had to drop out. Mister, by the way, how do you get a driver's license?

A kid tells you how many siblings they have. You find out what their parents do for a living. Another mentions their parents divorce. A parent is deceased. A parent went to jail. They've been in jail. Adopted. Abandoned. Undocumented. Almost pregnant. Pregnant. Gay. Self-harming. Abused. Hospitalized.

Hundreds of them. All of them sharing very personal things with you. All of them assigning some minor or major role in their life to you. Some are just students who had a good time. Others needing you to fill in as a father figure. Most well-adjusted, happy teenagers. Many with major life events that changed them markedly. Many more with common struggles but completely different outcomes. Seniors from years ago who not only graduated college but claim you as their inspiration. One delivers office passes in April. In June you're at the funeral.

This is supposed to be a job? It's just work?

This human aspect is just so hard to convey to the people I know in other work environments. The scale is just so different. My previous job involved juggling the needs of like, 5 people. Now it's 300.

Effectively transferring math content to these kids is an amazing part of my day. Kids constantly impress me with their cleverness and eagerness to figure out what's going on. My number goal is to make our time together their favorite part of the day. In the varied classes I've taught, it was incredibly rare to find a kid who lacked a desire to learn something from me, math or otherwise.

I will always love teaching them math. But what has improved that the most is learning more about my students as people. Summer Camp is only marginally about the content. It's about furthering the relationships.  It is very hard some days to deal with the hard truth they drop in these conversations. At the same time a kid tells you how much they appreciate your advice, or the letter of recommendation, or the extra time for a project and it makes your week. It puts pressure on me to do right by them. To be prepared. To have something worthwhile to share and respect their time. I will gladly invest the time planning and grading if it means continuing to have a positive experience together.

AuthorJonathan Claydon
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The thought occurred to me over winter break, what would be my ideal teacher-student environment? My current situation is quite good, but what if a lot of (curriculum based) restrictions were removed?

I'm at the very beginning of making a successful math program. The Calculus kids I have this year are amazing, and some of that is because we've spent a year together already. I have a group of 11th graders in Pre-Cal this year primed to take their place, and in theory out-achieve them. How can I serve their needs? What would they want out of school if some restrictions went away?

Enter summer camp.

It starts with a hunch that a lot of my 11th grade students are like me, they enjoy learning for the sake of learning on some level. What would they like to learn? What are some things they've always wondered about but never had access to? It relies on a second hunch that they like learning things with me. It wouldn't matter what we were talking about as long as I were in charge.

I posed the question, would you be willing to come up to school for a few mornings in the summer and learn whatever, if I taught it?

Short answer: camp got approved and I have a healthy list of attendees. Now what happens?

Soon, I'll need to get real, legit commitments. I gave the kids two possibilities (the week of June 13 or the week of June 20) and had them bounce the dates off their parents. Some had to work, some are going out of town, but a lot were available and willing to learn stuff in the summer. Imagine!

What are we going to learn? I have some ideas but I want this to be driven by student interest as well. Programming is at the top of their lists, and some wouldn't mind discussions about space travel, astronomy, robotics, or even mundane things like how to their taxes or something.

The camp needs a name. I already have an established brand. Rolling a summer camp into the Varsity Math universe of nonsense was an easy move even if this isn't explicitly a math camp. T-shirts and stickers are likely. We're also probably going to charge about $20 just to give the kids a sense of investment (make it free and they'd probably bail when June came).

AuthorJonathan Claydon

I just finished mapping out the remainder of Calculus for the semester. Two weeks from today we'll be done with all the new stuff. And not the I mentioned it once very quickly right before the exam so it totally counts as covered kind of done.

Guiding the way was a very important document. I don't plan with a textbook, I like to work off something that makes sense to me, that I wrote. First seen here, by some miracle, I've checked off everything I set out to do.

There was some juggling at the end, assuming you can understand my notes. A nicer version will be coming when school ends and I've had some more time to think. Turns out my milestones were a little optimistic. I was lagging behind until about February when I realized that the semester was far less dense material wise. Also, the kids have been catching on well.

Really you have to back up a step and look at the document I wrote first. I spent time analyzing 8 years of free response questions to get a feel for themes and penned a guide for myself. The curriculum plan was meant to group topics by what the free response genres require.

More on these in a minute.

Now What?

Alright, so new stuff wraps early April, but the exam is another four weeks after that. What's the plan there?

Most important, I want a plan that makes sense for the group that isn't going to take the exam. Through some data I've been collecting, I have 10 or so kids in each class that need another tour through the material. Throwing exam prep at them isn't going to help anyone. I realized last year that even if a student isn't going to take the exam, letting them leave with a bunch of holes isn't useful either.

Kids opting for the exam are going to work through a long set of free response questions I wrote based off the outline above. The most popular thing on your average Calculus blog is someone going through and categorizing all the released CollegeBoard material. It's....not the most helpful. Some of them stretch back way too long (should I concern myself with the topic covered by 1982 #3b? Probably not). And even ignoring that, plucking individual questions items don't work because they don't stand well on their own.

The best choice in my opinion was new stuff. Instead of 4 parts like the released material, mine have 7 or 8. I don't want my kids to focus on memorizing 2009 #3, I want them to understand the scope of volume expressions or problems that reference a data set.


It'd be worthwhile if everyone had another run through the skills. I will probably title them assignments just like that, you watch.

The Obvious Exclusion

Again, if you compare my plan to the discussion you see on other random Calculus boards, I'm missing something obvious here. I'm not spending time on a full run through of the exam. WHAT? I tried it last year. The value was minimal. Takes too much class time. Material density is low also. Though I will provide one last run at multiple choice topics by handing out something derived from the practice exams I have access to.

Things I will eventually share: the derivative, integral, and calculator skills review.

Things I can't share: my original free response collection, the multiple choice prep sets, it's too derivative of the CollegeBoard material I have which has super strict "don't put this on the internet" rules.

AuthorJonathan Claydon

Career wise, it's been a bit of a strange year. Some odd ups and downs I wasn't expecting. At the same time, I've never felt more comfortable on the job. The day to day is going well, improvising continues to be a skill I can rely on, and I continue to refine little details that get my kids thinking about concepts in better ways than they have before. We may do fewer exercises than the kids down the street, but darn it I think mine understand better (I hope).

At several points during the year I've had students wonder out loud why everything just feels so challenging to them on their own when I make it appear effortless (ignoring the daily typo ritual that is Calculus) and simple. It's been a consistent message for the last several years of teaching. What I do that's so special when it comes to explaining? I have no idea, and that's a tad scary.

Anyway, my retort comes down to reps. On the grand time scale of life, they just haven't put in the sufficient reps yet, haven't had that turn the corner moment. I ask them "what's something you feel like you're really good at?" Often it's a sport or some skill (instrument, drawing, Call of Duty, whatever). And my follow up is "at a certain point, didn't you just realize I'm really comfortable with this?" with an appropriate amount of head nods. Really I'm just repeating an argument here from December. Look, I'm even going to break out a similar graphic:

In true business exec fashion, the y-axis represents comfort levels but lacks a scale. I spend my day teaching, which I know how to do pretty well now, but I split time between subjects with which I have very different comfort levels. The cracks are more visible despite all the thousand of teaching hours (see previous reference about lots of typos).

Guiding students towards that turn the corner moment is one important aspect of the job, but taking myself on that path is equally necessary. I feel like kids trust you more when you can tell them what it's like on the other side. While the typos and errors and goofs are a tad frustrating for the Calculus kids (though a great example of how real math is done), they still trust me because they spent a year in Pre-Cal with me, a subject I can recite forwards and backwards. Why do I like Pre-Cal so much this year? I've sung that song so many times. I developed a lot of big beats. I know I can do ambitious projects at scale. Calculus just doesn't have all the catchy verses yet.

But how do you push? More specifically, the question is how do I push? Coasting is such a tempting thing to do on the other side of the turn, and I can feel it in Pre-Cal. Especially during the time crunch of soccer season.

Finding Important Moments™ through the year is how I push. They are landmarks that keep me interested and that always needs attention. This year I took two fundamental Important Moments™: Vector Crafts and 3D Objects and rebooted them entirely. The content of the class is getting rebooted this summer.

Refinements are always possible. When I first embarked in education, an old college professor asked if I considered what it'd be like teaching the same thing for ten years. Despite the day to day mechanics of the job being quite predictable, I can say that despite my comfort, the content continues to provide a challenge.

Examining how content flows is of great interest to me, and something I hope to wrap into a cogent presentation at TMC16 this year.

AuthorJonathan Claydon

Missed an opportunity here. An unfortunate side effect this time of year. Some days I just have to coast. And with something like Pre-Cal that I've been doing for a while, it can be easy to overlook an obvious improvement.

It's polar equation time around here and it's one of my favorite things to teach. The graphs are just so bizarre to kids and yet the mechanics behind playing with polar systems are simple enough that we can explore lots of things. For example, this rose curve:

Among the last things I do with rose curves is have them write out some explanations of the properties: equation, petal count, petal separation angle, and x-axis offset (for sine functions).

Where I mess up is just launching right into an explanation of how to determine petal separation (360/no. of petals) and the offset (90/b where b is second parameter of r = a sin b theta). I do discuss that random 90 by showing them r = cos theta and r = sin theta and that 90 degrees is their "natural" offset. But the method could include some discovery. Busting out protractors, measuring this stuff, and collecting theories would've been significantly more interesting. Primarily, because while describing that set of 6, several kids offered alternate methods to the 90/b thing. Including several thoughts like "oh, it looks like it's always half the petal separation" or "can't I count how many gaps there are between 0 and 180, multiply it by the separation, subtract that number from 180 and the remainder has to be the offset?"

Great ideas! How many others kid noticed the same thing? How many didn't bother because I straight up told them?

Lessons learned for next year.

AuthorJonathan Claydon