Post AP test, I try to give the older ones some access to the kind of adult information they all hear whispers about but never learn until it's too late.

For the last few days we've spent some time on financial literacy. Specifically, building a spreadsheet that would make it easy to compare the real costs of owning a home, with some generous assumptions built in.

Using the (apparently secret) mortgage formula I dug up a few years ago, we built a tool. Each kid made a version of this. The input variables are the sale price and the appraisal value (sourced from databases local to the area). We plugged in some assumptions about property tax calculation and insurance. The point is to have them think about a house as more than the base line mortgage payment. And to see how ungodly high interest can pile up on a 15 or 30 year loan. Also, property tax? Say what?

This spreadsheet has other modules in it, but this first one served our purposes. It can also be extended to part two which involves buying a car and then ballparking what kind of monthly income it would take to afford the car and the house.


They were given a link to the following instructions. The price range is mid-tier for this part of the city. Another assumption in the scenario is that we're about 15 years in the future and have acquired the cash to make a 20% down payment on something.

Note the mandatory fidget spinner.

Over in the corner I set up the bank. I had them make a few blind choices to acquire a random set of loan terms. Then they chose between a 15 year and 30 year option.

I had fun with it. They were required to begin the dialog with "Excuse me Mr. Generous Banker, may I have a loan please?" The bank was only open for 40 minutes (we had about 80). I'd get up and go on break at random, even in the middle of a transaction. Kids would play along and complain when there was a line. "There's always a line!" One regret is not having a bowl of lollipops.

I had a couple kids walk out and then yell that they didn't like the terms of their loan. I directed them to the complaint department.

Super fun task. A more complicated version might subdivide the loans based on the amount they're trying to borrow. I think that's how part 2 with car loans will go. Terms dependent on what kind of cash they're trying to drop. Kids are doing some dynamite stuff with their collection of materials. The hilarious part was listening to others watch someone get their loan terms at the bank and react with "ooh, nice one! or, oooh you got the bad one!" without any real idea what they were talking about. Listening to them chit chat about their interest rate was hilarious. "You know this is what adults do, right? This is what we talk about?" "Ew, gross."

Gross, indeed.

AuthorJonathan Claydon

I set a goal of overcoming the biggest problem our students have faced with Calculus, the language demands. Many of my students have found the calculation demands to be reasonable, but stumble on the words. That has been the feedback from three rounds of AP exams so far. This year those complaints still registered, but not has high as before. Upon examination of the 2017 questions, I think we're making big gains in accessibility. This is a reflection on what I think I achieved with my instruction.

When I say accessible I mean a) the topic was addressed in class b) kids had thorough practice and c) kids had the pieces to apply a skill on their own. In no way do I attempt to feed them infinite scenarios and create long long lists of steps. The goal is a focus on big ideas to allow them to be comfortable and adapt what they know to different situations. Also when I say accessible there is no guarantee kids actually converted that into correctness. There are too many variables with a students preparation to really know.

Based on number of question parts present (1a and 1b counted separately. etc), in my opinion I think this is how accessibility broke down:

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I was very happy with the level of familiarity my students should have had this year. I made some strides in improving the way we covered information to improve our struggles with the language barriers. Post exam conversations bore that out. Yes, it was difficult, but the majority said they recognized a lot.

Just as a reminder that accessibility doesn't mean correctness, my non-1 rate for 2015 was 8% and 10% for 2016. For all the gains in accessibility the non-1 rate this year could be, like, 20% max or something, or worse. The road is long, but we're moving.

AuthorJonathan Claydon

Today's the AP Test. What's changed in the last year? Here are three areas of improvement worth celebrating.


There are 35 taking the exam this year, down from 50 a year ago. Though about 65% of the population is in a good state of preparedness. This is based on my observations through how they spent their class time and what comes up when they attended after school sessions. The kinds of questions I'm getting are more focused and we have had some excellent discussions. Last year that number was like, 20% or less. A big factor is some adjustment I made on my end. I tweaked my benchmarking process and rearranged what happened after Spring Break to give my exam takers about 10 days to just sift through stuff and work. Last year it was about 3 days. I demanded more of the kids. These 35 responded to that challenge.

The full list of stuff they were given since late March:

  • 8 topic, 50 question Free Response Collection
  • 50 multiple choice questions from various practice exams
  • reference sheet
  • study recommendations
  • varied fundamentals (limits, polynomial sketching, trig values, etc)
  • 6 released FRQ, 2 calculator, 4 non-calculator, to let them simulate a full set
  • access to the 2014 practice exam from the secure teacher portal

The goal is to demonstrate how to prepare for something over a long period of time. Cramming the week before won't aid their long term retention in anyway. Though I can't control it, they were forbidden from doing math yesterday. Their preparation materials were given out slowly over a period of six weeks. We spent two of those weeks finishing the curriculum while they started work on their own time.


Huge gains in conceptual understanding this year. Primary inspiration drawn from this question:

It's not enough to know the mechanics of calculus with defined functions. You need to be able to apply it in the abstract. We did extensive work throughout the year applying principals using functions defined only in theory. Kids found it strangely simple. I think more of them understand "f prime" as a thing that can be manipulated in a number of ways now.


I also realized last year that curve sketching and function sketching in general is a huge a weakness. I made efforts to improve it in Pre-Cal to help me out for 2017-18. For this group of Calculus students, we took time to review the concepts of polynomial sketching and how it can help us analyze the behavior of a function (specifically spotting things like false critical points). As part of our review weeks, I made a point to mention how a picture can help a situation. Take this question:

A couple years ago I did a horrible job preparing students for something like this. Particle motion is a topic my students feel very confident about, provided they have a picture. The questions are almost trivial with the use of a calculator. But here it's easy to feel screwed. Unless you realize drawing that cosine function jump starts this problem in a huge way. Students also had hang ups with pi-terms as coefficients. We spent some time with it and now it's not a big deal.

There are similar situations where a polynomial is given. Breaking it into binomials and making a sketch gets where you want to go quickly. No tedious quadratic formula required.

Further Steps

Several students had weak connections between the behavior of a derivative and the impact on the original function. For example, about three weeks ago I got a lot of blank stares about identifying where an object changes direction, or what positive values of the derivative mean. We were successful in clearing up this confusion, but it was a little strange it had to happen in the first place. Other than that, the majority of concerns lie with differential equations. This was expected, given how late it was introduced and the limited time we spent with it (about a week).

There's probably about 10% of the curriculum we didn't address. But I feel good about my students' understanding of the 90% we did cover. In analyzing a practice exam, this group ideally could pick up 10 more questions over last year.

A huge thing I noticed a couple years ago was class time being diverted to in class assessment. I have a gradebook obligation to the kids, but continuing to be creative in this area will help us get more time back. In year 1 I gave 14 in class tests, year 2 had 12, and year 3 only had 8. At the moment I'm not sure what, if any, formal paper tests my Calc kids next year will have.

AuthorJonathan Claydon

Have you been teaching for a long time? Do you feel like there were certain points where something changed? When some aspect of the profession just starting clicking in a way it hadn't before? This summer I'm going to spend some time ruminating on big moments in my career so far. Where else could we go? What might be a solved problem? How could this help someone new to the profession?

Topics of Discussion:

Assessment - what are you trying to learn about your students?
Curriculum - what story are you trying to tell during the year?
Teaching People - what gains can you make when you pay attention to who you're teaching?
Technology - what happens when you focus on simple workflows?
Production - what tools make your materials the best they can be?
Push - what can iteration do for your students?
Family - what if you treat a class period like a community?

Collector's Edition:

Music - what if you grit your teeth and learn to love trashy pop songs?

It's fascinating how your attitudes about teaching can change, and I hope this reflection reveals some opportunities about what could be next.

AuthorJonathan Claydon

Every year I'm amazed at just how much there is to do at the end of the year. It's already time for the second year of Summer Camp. I mused last winter that offering an enrichment program to my existing students might be a hit, and they proved the theory correct. Despite the wandering topics, the kids had a great time. I had a great time. It was a great time.

After the first day last year I knew I was doing it again. 


Like last year, I want the students to dictate the agenda. If they want to wander down a rabbit hole, we will explore all there is to see. I'll lay out a few base objectives and go from there. I want to simplify the focus a bit and just have a few bullet points to hit.

  • financial literacy
  • spreadsheet/programming literacy
  • space
  • drones
  • games

A new component will be a game of the day. There are a billion non-phone non-video games out there, and the only one my kids seem to know is UNO. I think we can do better here. Last year's live action parser proved to be quite popular.


The surface objective is to explore some random stuff in the summer. The secondary objective is to focus on relationship building. All of these kids are enrolling in AP Math next fall. Unlike last year, about half of the campers will be new to me. This a unique opportunity to work with them prior to letting them experience the full insanity of Varsity Math.

The fascinating thing is just how many kids are super excited to do something in the summer. Most of my participants jump at the chance because their summers are fairly unremarkable or their parents want them to be up to something productive. I handed out 60 permission slips for about 50 spots. Two days after handing out the forms both sessions are half full. I expect camp will sell out before the deadline. It's awesome.

AuthorJonathan Claydon

A few years ago I hit upon this project for polar equations of conics. Objects orbiting stars can be modeled more or less as polar ellipses, with their host star as the focus point. With a little Wikipedia finagling, you can recreate our solar system.

It's pretty cool, and with new Desmos labeling abilities, it's easier to distinguish what's what. However, the project had a case of the samsies. Every kid or set of kids was making the same thing. There was a lack of creativity. I don't know why it took me so long, but this year I changed it up. I wrote up an explanatory document and let them design a solar system of their own.

We got some very nice and orderly systems, and some whose planets wouldn't survive very long before ramming each other to pieces. I encouraged creativity with the themes.

This one took a little longer than I thought (about 2 hours or so), but I find it important to relax a bit on time requirements if kids are putting in a lot of effort, and that was definitely the case here. Lots of good discussions about how to vary their objects, what various eccentricities would do, and how to manipulate orbits just so.

AuthorJonathan Claydon

It's a little baffling that this is our sixth adventure out on the sidewalk.

The complete archive:
Sidewalk Chalk Adventures
Return of Sidewalk Chalk
Sidewalk Chalk Three
Sidewalk Chalk, The Fourth One
Sidewalk Chalk Five


I'm a fan of big, obvious evidence that my classes have something to say. Sidewalk Chalk Day is one of the oldest ways we make that happen.

This year, about 250 students in Pre-Calculus and Calculus took to perimeter of our school and decorated the campus. For Pre-Cal, students were tasked with designing two types of polar equations. They graph the functions and write the equation responsible. Calculus has played along too, but never on the same day. Their task was to generate a slope field, region between curves, or f/f'/f'' family and immortalize it in chalk. Students use Desmos, print out their creation and bring to life like it's elementary school all over again.

Fly High

For the latest installment I brought along some new helpers:

It's always hard to capture the scope of this project as it has grown over the years. We cover about half a mile of sidewalk over the course of 5 hours and consume a small mountain of chalk. These spectacular views brought to you by my robot friends:

It's a great way to spend a spring day. Enjoy this fly-by:

AuthorJonathan Claydon

Fun milestone a couple weeks ago:

Sounds crazy right? Lots of people would have you believe the future of computers in the classroom is those dystopian pictures of kids in cubicles with headphones on. Turns out you have other choices. So what were we doing during this magical week?


We were wrapping up area between curves and various volume expressions. I figured it was a great opportunity to let them play with integral notation on Desmos. Super duper handy for expressions of volume/area with respect to the y-axis. TI-84s can't touch this.

Later in the week I gave them a pre-loaded set of regions with a request for a particular integral expression (area between curve, solid built with square cross-sections, etc) and had them enter their results into an activity builder.

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Student's ability to play with function notation here is awesome. Being able to collect math input through Desmos was a neat experiment.


What haven't we done on computers in Pre-Cal this year?

To start, we finished a study of three-dimensional vectors with an opportunity to make some 3D objects in Tinkercad.

With our study of vectors and polar coordinates, I offered students a glimpse at what spreadsheets can do faster than people. Namely, kick out a bunch of polar points and convert them to x-coordinates and y-coordinates.

Some students needed helpers:

Then, super quickly, and with several "ooooooooohh"s, we dropped the x/y table into Desmos for an initial look at the graphs of polar equations.

We refined the ideas present here through the use of an exploration activity made with Activity Builder.


In each situation the computers came out because they can perform the task better and faster than pencil and paper. In the case of Pre-Cal, they extended math to a place they didn't know it could exist before through spreadsheet formulas. Calculus got a chance to speed through volume because of the ability to see a region, talk through the logic of how to define an integral around it, and then see that integral computed in the same window. That took us a million button presses and a stack of copies previously, with no option for functions defined in terms of y.

A+++ would teach again.

AuthorJonathan Claydon

Maybe this isn't a big problem for you, oh Calculus teacher, but it's a yearly issue for me. What do you do about kids not taking the AP Exam? No one would fault you having them work through the remainder of the curriculum, because not taking the exam isn't an indicator the kid is woefully lost. However, the way I do things, if I advise a kid not to take the exam, or they've chosen not to, there's a lot of evidence behind that decision. It is very likely they need (and have needed) some help for a while.

Last year I didn't have a lot of these students. Coming up a with a list of practice assignments for them to complete was easy, and fielding their questions wasn't a big burden. They did their thing and, hopefully, they got to leave Calculus with at least some fundamental knowledge about the course.

This year the challenge is bigger, I have a significantly larger number of non-testers. My filtering process got stricter (on purpose), so it was a natural result.

To improve these students' ability to be self-sufficient, I generated assignments for them as before. However, I added a little treat. For years and years and years kids have been asking me to make a database of recordings. I struggled with workflows, file sizes, and practicality, ultimately deciding each time it wasn't worth it.

Enter iPad Pro.

I've had Wacom devices for years, and still use a Cintiq daily in my classroom, where working with a full computer makes sense. Here, I have a more focused purpose: short (<5 min) explanations for kids who already heard this once, with material relevant to a specific assignment. Enough to help them answer their own questions so I can focus on other tasks during class time. Generating things like has been tedious with those devices. Having a self-contained slab I can write on works better.

The workflow is dead simple. Attach iPad to a Mac, open QuickTime player, start a New Movie Recording, and select the iPad as the camera:

An external mic is optional, the internal microphone will probably do the job. Export the files as 720p movies, and plop them in Dropbox.

Their titles mirror that of the relevant review assignment. A non-tester grabs a computer, opens the shared folder link, and works at their own pace.

Some MAJOR clarifications about why I don't consider this in the same category as super buzzword-y "Personalized Learning":

  • This is a limited run engagement, kids are using this for 2 weeks while I address other issues with exam takers
  • They got live, in person exploration/explanations from me once before, these videos are not intended for first time learning, the kids using these have some working knowledge of the concepts in play
  • This is intended for use during class, I'm not explicitly requiring they do any of this at home
  • The videos were produced quickly (record video, export, done) with a laser focus objective: offer clarification through worked example if necessary
  • This is an opportunity for kids who have been behind the curve to feel some accomplishment and back track

I'm not replacing myself with videos any time soon. I stand by my belief that having kids work through an exhaustive database of tutorials, machine graded tasks, PDF worksheets, and whatnot is nowhere near a valid replacement for talking face to face, having in person discussions with peers, etc.

If you have access to sufficient devices and are considering some kind of tutorial database, use it sparingly. Find a specific use case and keep it simple.

AuthorJonathan Claydon

As a general rule, I don't like to let activities linger in a particular state. There are always subtle tweaks to make or the tough decision to cut something loose and try again. The advent of Chromebooks in my classroom has opened up a lot of opportunities we just didn't have before. Realized recently when it was time to talk about three dimensional vectors.

Historically, I turn the room into a giant coordinate system, we discuss how to orient ourselves in 3D space and I've had them build stuff out of straws. It was interesting at the time, though time consuming. Due to the nature of building things out of straws and electrical tape, the creations didn't last very long either.

Enter Tinkercad. I'd like to thank Autodesk for a monumental shift in the way they approach access to their software. Fifteen years ago, AutoCAD or the various things a college student might need were prohibitively expensive. It all came down to knowing the right person in the dorm who had license keys of a shifty nature. Since about 2010, they've done a total about face, making tons of great stuff available for free or cheap for students, teachers, or anyone who isn't a corporation. Tinkercad is a browser-based 3D modeling app that lets you mock up whatever you like. There are pre-built simple solids, and you can browse a whole library of community built objects and drop them into your design.

Rather than mess around with a bunch of straws and tape, I set my Pre-Cal kids loose on Tinkercad and gave them about 50 minutes to make something. The site's export options are intended for 3D printers, so we stuck with screenshots from a few different angles. We got some really awesome stuff.

Chromebook trackpads aren't the greatest, so this was a tad challenging for some. I do have touchscreen models, and kids with those were very happy with themselves. Wired mice can be had rather cheap in bulk, so that might be an idea for next year.

AuthorJonathan Claydon