Some updates on two initiatives: providing resources and shutting up.

First, partly for accountability purposes, I'm doing all the Calculus homework and providing solutions via shared Dropbox folder. I passed out a link which lets me track usage.

Homework is assigned Monday and due Friday. The giant spikes are Thursday nights. I'm fine with that. Due Friday means due Friday. Other AP classes are a tad more demanding because of reading, so this gives them a chance to find time when necessary. I have 50 students, and I'd say 2/3 of them said they use this resource regularly. The assignments aren't super long.

Second, helping less. They were struggling with related rates, I think that's like the law in Calculus or something. Here are some easy things, overthink them to death. Sigh. Anyway. They needed some more practice, I had a scheduled absence coming up. I pass out the problem set and say you have to do 5 out of 8, solutions are posted. I'm not going to much use to you (because I'll be absent but I'm not going to tell you). The gigantic spike on the right there is them accessing the solutions while I was away. Perfect.

PreCal is also getting the helping less treatment, which I'll save for a later date.

AuthorJonathan Claydon

Some weeks ago I was in a meeting. For the opening talking point we were asked to discuss our passion. Other than meaningful assessment, my passion revolves around the war on boredom. My students should be doing something as much as possible. As time goes on, that's become my students should be doing something genuinely interesting as much as possible (tricking them into learning as they like to say). I want to be the math teacher I (more or less) never had.

I had some nice teachers. But were they great? A brief recollection of my math classes (I attended 6 schools from K-12):

Elementary School (K-5)

I remember stressing about counting money in kindergarten. In first grade we did jumping jacks prior to our state testing. In third grade we learned times tables and long division. In third grade we played a game where a student would stand up, they would proceed to stand behind a class mate. If you were standing and got the fact right, you continued to the next class mate. If you were beaten, you traded. One kid (my academic "rival") blasted through most of the class, spitting out multiplication facts in an instant. I was excited when our teacher let us talk about big numbers, like millions. In fifth grade I stressed about fractions. We took a quiz on mixed numbers. I got a significant number of them wrong. This upset me. I (seriously) requested we review them all. The teacher snapped "I will NOT do all of them" and went over none of them. I still remember the stare. She retired only recently.

MIddle School (6-8)

Sixth grade was the best. This guy asked the most interesting questions. I was fascinated by prime numbers, Roman numerals, and the very adult multiplication and division notation we learned. We looked at the Game of Life. Kids were divided into ability groups. There were different tests depending on what you could handle. I was so happy to be in the coveted C group. He'd pull us aside, give us Fawn Nguyen like things to tackle. We changed groups often, we had to come up with a name and a logo. There was an in-class economy, using tiny black and white bills. You earned a salary, he had a long list of things you could spend money on. He was super organized. He expected the same. I was not. It caught up to me a couple times during the year. We did a travel project at the end of the year. It was part of a national contest of some sort? You made up a road trip and had to calculate all the expenses and show the work.

Seventh grade was pre-Algebra. I was excited to play with equations and letters. The teacher would call a bunch of people up to the chalk board. You'd have an assigned problem and had to solve it for the class. I was that guy who would try to do it as fast as possible to impress ever--no one. She'd have grades ready, you could elect to have it shouted out loud or go up to the desk. I always went up to the desk.

Eighth grade was whatever. I'm told the teacher did a "many angry phone calls from many parents" kind of job. I don't know. A girl who sat near me raised her hand and said "I'm confused" a lot. She's a lawyer now. I would get bored and flip ahead in the book.

High School

This was kind of forgettable. Geometry was interesting, the teacher didn't enjoy jokes. Constructions were exciting. Proofs were whatever. I took Algebra 2 from a guy who said "what" like 1000 times per class. He'd answer way too many questions during tests. There'd be a line 15 people deep during a test. I moved to Texas, was put in a Function/Trig/Stats class. Felt really bad at math. Couldn't figure out transformations.

I took Pre Cal as a semester block. Teacher would go over two sections, then we start our homework. She'd then sit at her desk. Every day. I figured out mathematical induction, I was proud. Modular division and binary/hex numbers were neat.

Calculus was full of new and interesting notation. There was a related rates problem about a pool that was way easier than it looked. We spent a long time as a class working through it. The valedictorian was in there, he made me feel inadequate. I figured out f, f prime, and f double prime curve relations though. He didn't. The teacher was very friendly and cared and made an attempt to learn something about you. She let me draw things on the whiteboard whenever I wanted.

Ok, that was great...

...but what's the take away from all that?

I expect my experience is typical. One alleged disaster. A lot of mediocrity. One teacher who inadvertently convinced a 5th grader that it was unacceptable to not know something. Nice teachers who may not have done a ton of interesting teaching. But among that group, who had a passion for the job? When asked, what would those teachers say?

Then there's 6th grade. That was 20 years ago. I remember so much about it. It was fascinating. He was fascinating. Math was the best. I want that. My students deserve that. Math is more than problems 1-29 odd. Just because an experience is typical does not mean it's ok. I want to be better.

AuthorJonathan Claydon
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Stumbled on this the other day.

Holt Geometry

Two observations:

The abstract use of "geometry software" with no hint about what it might be, where I could obtain it, or how to set up what's being shown.

The dull task that could be replicated with paper in 30 seconds.

Do the people that write these things ever attempt to teach? Ever attempted these half-wit "labs" they come up with?

AuthorJonathan Claydon
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I had a scheduled absence, and a need for Calculus students to occupy themselves for 90 minutes. Amid their normal Throwback Thursday routine, I had them create some art.

Take some colored paper, and demonstrate the four major derivative rules: power, product, quotient, and chain. A generic example, specific example, and written explanation were required.

Pretty pleased with the results. General consensus is that AP = lecture format. Boo to that. Sadly, something so simple presented at your average Calculus workshop might be a little too mind blowing.

AuthorJonathan Claydon

A niche use case, but a neat feature. If you need to demonstrate something from an iPad, iPhone, or iPod, running the app AirServer on your teaching computer is the way to go. It acts like an AppleTV without the need for a physical AppleTV or switching projector inputs or any of that mess.

There's irony here somewhere

There's irony here somewhere

But, your school wireless network may not support it, or like me, AirServer misbehaves from time to time and you need a back up.

On the off chance you teach from a Mac, and on the off chance you recently updated to the latest OS X, you have a built-in option now.

Step 1

Plug your device into the computer using a USB cable.

Step 2

Open QuickTime Player and select "New Movie Recording"

Screen Shot 2014-10-25 at 12.06.27 PM.png

Previously, this was a way to record using any built-in cameras or USB cameras attached to your computer. Now, it supports iOS devices as external "cameras," designed for recording the screen of the device, but also handy as a document camera if you open the camera app.

Handy for recording a workflow for your students (it will grab audio from your computer microphone). Handy for a wired document camera solution without the need to fiddle with your projector.

You could also connect a random student iPad and show off something if that's your thing. And yes, the window will change its aspect ratio if you rotate your device to landscape.

Requires the device to be running iOS 8, and the Mac to be running OS X 10.10 Yosemite.

AuthorJonathan Claydon

Recently, I discussed attempts to stop explaining so much. Experiments with assessments are showing success. Skills are great, but I want to see who is thinking. Part of the reason I don't mind letting students (even PreAP, the horror!) use their notebooks on assessments is that a well done thinking question can't be anticipated. Through the course of working with the skills, the student either developed a strong working idea of the concept and therefore can answer just about anything, or they didn't.

Last week, variations of this question were posed:

Sure, you can slap that into y= and see. But it'll be obvious that's what you did when your explanation comes up short. Also, I never approached rationals that way. How do you interpret that ratio? What secrets will it give away?

There were three versions of this question. In two of them, the ratio straight up didn't work. The asymptote or discontinuity would show in the wrong place. This one though, will produce asymptotes at x = -7 and x = 3 as shown. 90% of students agreed and said, yes, this could be the correct graph because they factored the given ratio and saw the right looking numbers. Full credit was awarded. A small handful though...

While not explicitly being tested, we discussed a few days earlier how you get a general idea of a ratio's behavior by doing some testing on either side of the asymptote. Choose a test point on either side, and see if it would produce a positive or negative number. While not super accurate, it'll get you close.

It blew me away that these students saw something generally correct but still weren't satisfied. The behavior on either side needed to match too. While the top picture was inaccurate (-6 placed on the wrong side of -7), the student was suspicious, and I love it. The kid in the bottom picture nailed it exactly. I agree with the behavior for THIS asymptote, but hey man, this is the right number and all, but it's still no good. Disagree.

I mean, just wow.

Here's the bigger picture idea. It didn't occur to me to try this line of thinking with rationals until my 5th year teaching Pre-Cal (6th year overall, 4th year of listening to smart people on Twitter). When you say you want kids to really know the material, are you sure you've got a complete handle on it yourself?

AuthorJonathan Claydon
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Standards based grading has been a huge success for me. It's helping my students have conversations about success and becoming determined about showing improvement. Most of them have stopped talking about That Number. The number that I dislike. The one all the top kids in your class obsess over. 100. Ideally, it should all be about growth and feedback, but tradition dictates we give kids a number. They live and die by that number. See also: college, where sub-par teaching methods and the pursuit of 4.0 poisons just about everything.

AP culture feeds the beast. That GPA bonus is enticing. Surely extra credit must be offered. I NEED to have an A. If you can just give me two points mister, it's just two points!

I dislike it intensely. It takes a fantastic opportunity, exposure to high level curriculum, and turns it into a war for 100. How do you teach a group of Calculus kids, kids who have fought for 100 forever at this point, to forget about the stupid number and focus on learning for the sake of learning?

A few years ago I helped adapt my typical SBG approach to Calculus. Subdivide the class into topics, test each topic twice, honor the best score, and offer full replacement after school. Throw a six weeks exam in there to keep a little accountability. It didn't work. Sure, kids demonstrated improvement. But many blew off the initial attempt. TONS of them showed up after school to try and replace everything. All in pursuit of monkeys, er, 100.

This year? Reset button.

The Strategy

The first failure is trying to take Calculus and force it into nice little topics. After a two year experiment, it was pretty clear Calculus doesn't like being treated that way. It's a Big Ideas kind of class. It's primarily conceptual. Everything matters. You can't forget about September.

The second failure is removing too much accountability from the assessments. That after school thing was a crutch. Special rules had to be written.

The third failure was a disconnect between the assessment material and the design of the AP Exam. AP scores were terrible. Blowing off assessments probably didn't help. Seeing the format of the exam too late probably didn't help either.

What do we do?

Giant tests out of 100 are out of the question. Assessment needs to remain short and frequent. Reassessment should be available, but limited. Concepts matter. More accountability needs to exist. I should have the freedom to put anything and everything on them.

The Method

After a lot of discussion with a fellow Calculus teacher who wanted to do the same thing, we arrive at our current method. These are given once a week-ish.

It's a hybrid sort of thing. Each section is evaluated in a big picture sort of way. No nitpicking -1 or -2 junk, just feedback and an overall evaluation. The front page is skills. The top is for the deep catalog stuff. The bottom is fresh. The back is all conceptual. Written answers, thought questions, justifying answers and all that. Each is a separate entry in the gradebook. Kids still go right to the number, but it's not That Number. Only skills are eligible for a retry. Concepts are important. Six weeks exams are now mini-AP tests.

The Hook

Students should keep track. Students should get a pat on the back for success. There should be a goal unrelated to 100.

Since each test is a unique set of semi-permanent scores, the tracking is a little different. Each test is recorded on a line with the results from the three categories. If the total is 16+, you get a shiny, Calculus-only silver star.

It's the dumbest thing in the world. But an 18 year old will commit crimes for a sticker. And now that's how they talk. Did I get a star? I starred this one! I'm all ABOUT those stars! NOOOOOO 15, I HAD IT!!!!!!

Take a step back for a second. There are 20 points total. A 16 represents 80% (a comfortable 5 on the AP test, the reason it was chosen). A 15 is 75%. Think about that kid with the 15. What happens if they got a paper back with a 75? I probably can't do this. This is as hard as everyone said. Now I'm behind in math too.

When would a student with a 75 be ENCOURAGED by that result? Be willing to stop by after school to make sure that darn it they get a sticker next time? In the fight for 100, 75 is pretty unacceptable. And yet, my students have no problem with it, because the dreaded 100 has been abstracted away.

That's all I want. If you are motivated by getting As, ok. But I want you in tutorials because you're eager to learn, not because you're going to beg for some extra credit. And in class where the real evaluation isn't until May? Your number out of 100 is the least important number there is.

AuthorJonathan Claydon
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Open ended activities have never been my strong suit. In the past it devolves into answering a million questions and a clear sense that the students aren't doing the heavy lifting. Many things blew up in my face in the my first couple years because of this. I moved to pseudo open-ended tasks. Students weren't following a recipe of steps, but they weren't wholly responsible for creating the work at hand.

With a slightly different population, it turns out my students can be easily bored with that approach. Very slowly, I've forced myself to get them to invest more effort into their work, and I have stopped explaining every little scenario.

A couple recent examples.

Composite Functions

The last little while we were discussing adding, subtracting, and multiplying functions together. Previously, I treated it as a wholly mechanical lesson. I wanted more context this year. We discussed perimeter, area, and volume as parallels to the various operations we study. On the relevant assessment, I defined length(x) and width(x) and asked for this:

We never did these as class work, but we had discussed their relevance to composite functions. Reading the answers to this gave me a really good idea of who gets function combination on a conceptual level. I've noticed that my little group of nerds is really good at rote mechanical work, making differentiators like this important. The mind blowing part is that no one gave me that "what do I do?" look that I've seen before. Win.

Rational Functions

Division of functions is an excellent segue to rationals. I had a progression last year that was ok, but clunky. After various discussions about holes, asymptotes, and how to identify each, I gave them a closing task. Design some. If they really get how an asymptote or hole is created, they can design a ratio that meets whatever specs I give.

Kids had questions, and tons of other kids were eager to share the answers. I didn't do much other than stick an errant iPad back on the wifi so they could print. Watching it work made it very apparent how and when direct instruction fails. For many students it was obvious that they were absorbing all of this passively and nothing "clicked" until it was time to make something. Assuming direct instruction is working for your students is foolish.


There is still work to do. But I'm so happy to discover this early, so many other things I have planned can become that much more interesting as a result. I always tell people to challenge their students, that you'll be surprised what they can do, and something forget to do it myself. It's paying dividends in Calculus as well, where you really don't have the time to explain every minor scenario.

Neither of these activities involve "real world" problems, which may bother you. But reality is in the eye of the student. If a student can create a host of things that validate their understanding of how an asymptote is created and defend their method, is that not real? Has that math become something more than words in a textbook?

AuthorJonathan Claydon

I think a lot about room design. Nowadays, everyone in my room sits in a 6-kid pod like this:

The groups at the front of the room are a tad different, but you get the idea. This design facilitates what I want most, kids talking. To optimize it, I need to have a handle on who sits with who. Developing group chemistry is half of what makes the table system successful. In previous years, the kids are in a random arrangement for six weeks. I observe who works well with who, who seems to be displaced from their friends, and adjust it. At the semester, I give them options: choose a person or choose a table. I take their suggestions and make a third chart that lasts the rest of the year. This also gives them an anonymous way of communicating big time conflicts, if they exist.

In Calculus, I want these students exposed to more of their class. When I took Calculus, there were 12 of us. I sat in the same seat the entire year. Yes, I knew the names of everyone. But it would be tough to tell you when I got to interact with them. My groups are in a similar situation. The overwhelming majority have had classes together for years and years. They all know who is who. But could they learn more than that?

Enter moving buddies. You, dear Calculus student, get to choose a permanent partner. They will travel with you on your adventures through the room, meeting and working with exciting new people. I had them write down partner choices on an index card, a few had no preference, and I had to settle a couple disputes.

Each rotation lasts two weeks. This will continue for the rest of the semester. We'll do it again next semester, but some fiddling may be required if someone drops. Without getting too crazy with combinations, I did a bunch of random sorts and then made some edits until every pair of buddies visited at least 3 unique locations. I tried to make sure a set of 4 didn't travel together either. If you track a kids' movement, they'll sit with over half the class in the cycle.

I expect any payoff will take a long time to develop. But it beats sitting still.

AuthorJonathan Claydon