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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These days I haul everything up to school a few days before the official return to work. It's way easier to focus without a lot of people around or meetings to attend.

Staff development was a little strange this year. I found very little to worry about. In fact, I think I spent more time tightening how Varsity Math is going to run than focusing on how the first week is going to go. Probably because 65 of my 71 Calculus students had me before. It's like we just took a break. That could be good or bad.

Anyway, the eternal pet project. The Room. Just some tiny tweaks to make things more efficient.

Starting with the yellow chair and continuing clockwise you've got purple, blue, green, yellow, red, with white right by the door. It all comfortably seats 36. Everyone has a tv now. Purple and blue used to share. Now I can spread them a part a bit and walk between them for once. I scoot the podium closer to the middle of the room. Previously I had started drifting into the corner and it was a little too far away. Notebooks are now on shelves so I have a bigger aisle at the extreme left of the room. My spot in the room doesn't exist anymore. In 2009 it was like 20% of the room. The large bit of green paper is for Calculus work. Pre-Cal stuff gets to go outside.

We're just about at final form here unless something urgent like classes of 40 start to become a reality.

AuthorJonathan Claydon

As average class size ticks up (31 last year, 33.8 this year), more and more space needs to be sacrificed for student comfort. For several years teacher space has started to disappear. It was pretty irrelevant last year, even smaller now.

Next, some other public areas need to disappear. Last year I had a supply table.

The thinking was for the sake of cleanliness I'd keep all the mess making stuff at the front. Kids could come grab it as necessary. It worked fine, although with the usual "send someone to get supplies" delays. I need this table for other things, so added features to buckets on each of my six tables.

The thought is I can install a "the bucket should look like this" procedure at the end of each class period. I haven't had problems with bucket maintenance, but I'd like it if my little scissor cups weren't destroyed throughout the year. It'd be nice to pick up 45-60 seconds here and there now that there's no need for supply runs. Why not put markers in here? Have you seen what kids can do to markers?

AuthorJonathan Claydon
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They throw the word "survival" around a lot at new teachers. People in all parts of the business talk about how little prep pre-service people get. You can student teach and observe all you want, it's just so different when the kids belong to you.

Well, you've jumped that hurdle. You're no longer the rookie. Likely some wide-eyed new teacher is going to look to you for advice now. Unless no one in your department left and you're still the new kid. It happens.

Hopefully some time was spent in reflection, whether during the summer or in the heat of the moment as some well-crafted lesson blew up in your face. Everyone's been there.

What's so great about year two?

Let me tell two stories. In 2006 I was thrown on a construction project that was finishing. Some months before I started working, a steel mast was moved to solve a problem. Two years later it caused another problem which became my problem despite never seeing the thing get installed or know any of the motivation behind the move. In 2007 I was negotiating a generator rental. They had some problems with terms. I consented to changes but nothing was executed by anyone with real power. Job goes by, generator bills paid on time (which is all anyone cares about), and everyone's happy. In 2009 I get a call at like 8pm because my negotiation fake out was causing someone else problems, said generator company using a random e-mail I sent as their source of argument. It all went away (like I said, nothing was ever signed, I'm not stupid).

Point is, things rarely come back to haunt you in education. The lesson you're going to deliver better this year? The kids never have to know it sucked the first time. The student you were happy to say goodbye to? Unlikely to cause a problem for you ever again. Those final exams you kept? You can throw them away! School year's end and you move on. You get a reset button.

That's what I love about August. Summer's over, sure. But all the excitement is still there. Flipping through the newly minted class list, figuring out where the heck they're all supposed to sit, rethinking your bulletin board, and even seeing what new and exciting things might be on the duty list.

Enjoy the freshness. Don't underestimate its importance.

AuthorJonathan Claydon

I'm going to be picky for a second. Pop open any Calculus book and you'll find a table of integrals:

Stewart 7th Edition Single Variable Calculus

Stewart 7th Edition Single Variable Calculus

For whatever reason, the natural base is always called out as unique and special. If you look at the equivalent derivative table you'll see it gets a call out from a generic exponential. But why do this? The natural base e is just a number, albeit irrational. If you integrate a base e exponential using the generic rule, you get e^x / ln e which reduces to e^x.

Calling it out as something special with a different rule loses site of base e being one of many possible bases for exponential functions. That somehow e isn't just a number. The same hang up exists with π whether you've noticed it or not. And it furthers the love of special cases: specific steps must be remembered for almost everything, when really you've missed an opportunity to show algebra in action.

AuthorJonathan Claydon
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Activity Builder is here! People in the Desmos morning session of TMC15 were hacking away on it before the big reveal. I watched people hack around with the possibilities and participated in a few of their activities. My problem was I'm not sure what, if anything, it does for me.

At the moment we do a lot of recreate the picture.

With Activity Builder, it wouldn't be hard to recreate this exact thing. With the added benefit of progress tracking and the magic of class overlay.

My big reservation: permanence. This is part of the reason I've never gotten into whiteboarding, the associated work never gets saved. Students could dutifully complete my match the graph activity but wouldn't take anything home with them at the end of the day.

How do we solve the permanence problem? Have them jot down their answers? In my mind it's the followup activity that matters. Whether you were doing it with a TI-84 or a custom Desmos activity, there should be a follow up where students keep some token. I realized that the hard way and found the real retention happened when we busted out the hard copies.

There is some potential here, but I would caution intrepid activity builders about the need for permanence. Digital collection of stuff is great, but lack of reference material can be a problem later. In some distant future where I'm in a real 1:1 environment (devices belong to students), archiving what we do through this new tool would be a must.

AuthorJonathan Claydon

Last year Calculus featured a lot of guessing. And despite my haphazard first time through the material, there is a tiny heartbeat. How exactly are we going to get some real results? Basically, redo everything.


First, I thought about what went well during AP review. I outlined 7 broad units: Prep, Position/Velocity/Acceleration (curve sketching), Particle Motion, Rate Models, Data Tables, Volume, and Differential Equations.

Prior to TMC I took a list of AB standards (sent to me by Elizabeth Warner) and hacked them up to fit broadly into my units.

Then I spitballed with Lisa Henry and Dan Anderson at TMC on Thursday night. Lisa helped me realize a way to better integrate AP material into the curriculum. Dan helped me with homework issues. Then we spitballed some more on Saturday afternoon in a larger group as a flex session.

Now I really had to hammer out some details. I nitpicked the standards again and wrote a curriculum.

It starts out pretty ambitious, so I expect some thing to slip. But I'm ahead of the game at the start of the year and I don't plan on regular testing during the second semester.

Speaking of...


The idea I had last year was great, but we're moving on. Short and sweet weekly-ish skill checks based on the A/B/Not Yet system from Sarah Hagan. This will have two parts. Students will take the skill check for 30 minutes and I'll collect them and rate them. When returned, I'll have them look at posted solutions and they have to comment on their work. I'll probably file the act of commenting away as a daily grade or something. Probably no tracking chart at the front this time around. Not sure if I'll add my own comments. As discussed frequently, if you score something, all kids care about is the score. Might be something they'll have to ask for after school? Hmm.

How about conceptual? I'll mix it in there somewhere. Same A/B/Not Yet, but I'll just title it Concept Check.

Primarily that will get handled with AP material. We're doing a lot more of that (exclusively during second semester). After pouring over the standards, I hacked away at practice exams and figured out roughly when I teach the topic associated with a question.

Multiple choice stuff was the disaster last year, more exposure (and more vocabulary focus from the start) can't make it any worse. I'll group these into appropriate sets and hand them out near the end of each grading period.

Last year I exposed them to free response material, but missed an important part. I'd give them a question, they'd try to figure out what was going on, and I'd go over the solution. They'd nod. Then we never touched it again. No chance to demonstrate any learning from the feedback. Now when we tackle free response stuff, we'll do several rounds. And I scanned free response questions from 2009 to 2015 and figured out the Ultimate™ version of a topic. So rather than cherry pick released stuff and hope for the best, I'll write some really long questions that cover the seven things you can ask about volume, for example. Revisiting old topics will be a feature of Throwback Thursday I'm sure.

Questions for Later

What if we have a skill check and a big chunk of them are Not Yet?

Can I really avoid skill checks the entire second semester?

Will I be able to keep up the pace I've set?

How aggressive will they be about retakes? Should I limit attempts? Only Not Yet redos allowed?

It's the Community, Stupid

If you're skeptical about the whole math teachers on the internet thing, let me offer this as an example. All of this is influenced on collaboration with and the work of nine people, from every part of the country.

AuthorJonathan Claydon
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I've heard lots of opinions on the unit circle. Some treat it as an object to be memorized and others something that can only be derived. And then a group who hates the whole thing and wonders why it's included.

Here's what I use traditionally:

The problem of the coordinate system is I think you lose the connection to the triangles embedded in the circle. It's not readily apparent that those xy pairs represent something other than a dot. But I've seen versions of the circle with embedded triangles and their a cluttered mess. Last year I was better about referring to them as (adjacent, opposite) rather than xy but forgot to reinforce it when doing inverses.

I played around and got here:

I really don't know if it's less confusing. The triangles are there, but do you get a sense for appropriate quadrant orientation?

Ideally I don't want a student to try and memorize the thing. Every time we get here I talk about how the first quadrant establishes all the patterns. But they still just think they have to memorize. Would four sets of triangles be better? Or a set of three axes with the base 30, base 45, and base 60 triangles in each set? Does giving it a special name like Unit Circle automatically tell a student this has no connections to other things I know about trig? Should I not name it? Banish the "1" and just label the hypotenuse as "r" ?

I am going to incorporate the decimal equivalents. I don't care who you think you are, students have very little grasp for the value of root(3) / 2.

AuthorJonathan Claydon
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It has ended. It was excellent. It had kittens.

A recap of some of the events.


Headed to the airport at 5am after little to no sleep. All in an attempt to make it to a taping of the Price is Right. We showed up with 5 minutes to spare to what we thought would be a quick day. It's a 40 minute off the cuff show, how long could it take to film? Seven lines and five hours later, I sat in the studio audience. Then there was two hours of clapping and screaming.

Finally made it to the hotel for the meet and greet at 9pm.


Day 1 excitement! I presented a lot last year. I wanted to take a break this year. But I had a My Favorite I couldn't pass up. I gave a short speech about Varsity Math. And a Cheeto.

I was in the Desmos morning session. Lots of Pre-Cal and Calculus people in there. Glenn Waddell, Bob Lochel, Jedidiah Butler, and Michael Fenton offered four mini groups to focus on the wide range of subjects represented in the room. Lots of play time. Fenton helped me make my solar system prettier. Picked up on some stats functions that I didn't know were built in.

In the afternoon I attended a talk about Formative Assessment with Peg Cagle and how she managed rooms of 40. Helped me with some ideas I have about assessment in Calculus. Then a fun round table lead by Sadie Estrella. Thirty minutes of people telling great stories.


In true TMC fashion, I got a look at secret Desmos features that will appear in about a week. Just in time for a presentation I'm supposed to give about the subject next month. I asked Eli my annual set of two questions.

In the afternoon I sat in on a number sense session from my man Stadel and Graham Fletcher. It was an interesting experiment using Estimation 180 in which some people are shown a task that helps with a new estimate and others aren't. We also spent about 10 minutes trying to decide what number was halfway between 10 and 1000.

In the evening the California locals threw a BBQ in a park nearby. The food was delicious. John Stevens brought an adorable set of helpers.


The energy begins to drain. More play time in the Desmos morning session. At this point it was a lot of hopping around the room looking at what people were working on. Had some fun Pre Cal discussions.

As promised one year ago, I rode in the Estimation Mobile and we got cheeseburgers. I think we invented two estimation tasks and a 3ACTS waiting for In N Out.

Fawn Nguyen gave a keynote. Nobody cared. (Everybody cared).

And finally, I spent an hour spitballing ideas about AP Calculus with some people. I have lots of work to do there before school starts.


TMC13 was full of wonder and being a fangirl. TMC14 was a chance to start sharing and being recognized as a contributor to the community. TMC15 was the friendly one. No more fangirl, these were friends with a common goal to be great at their job. There were all sorts of comfortable moments from the Price is Right saga, the meeting room Wednesday night, to the dozens of casual conversations I was able to have with people who are pixels in my timeline the other 360 days of the year. It is a precious 5 days and I think I succeeded in completing my checklist even it's just 5 minutes to say, no, I don't look like a cartoon robot.

Thanks to those of you that indulged my questions and thanks to those of you who said hi and recognized me and my work. I finally got a nice headshot, so I'll be easier to spot. I started documenting stuff for my own benefit but as the audience has slowly creeped up to a pretty big number, it is crazy to know that some of you benefit from it.

Until we meet again in Minneapolis.

(The song was amazing).


AuthorJonathan Claydon
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