What an interesting six weeks it’s been. Through an unexpected series of events, I have found that my attention needs to be focused on stuff happening locally at school. Turns out if you’re in a place long enough, you wind up with a lot of things to do. A comparison:

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Once upon a time I used to teach a single prep and coached soccer, that was it. These days I have 3 preps, random administrative/paperwork tasks, co-sponsor our National Honor Society, sponsor our math competition team, coach volleyball, and in recent weeks have had to sub in for soccer. In the last six weeks, not only did TMC fall apart, but our head principal announced his departure at the end of the school year, and our head boys soccer coach took an administrative job effective immediately. Though he continues with team duties through the end of the season, there was a stray athletic period that I got tapped to cover and plan. It’s also that time of year where new students are invited to join National Honor Society, there’s an awards dinner to plan, and our math competition is in a couple weeks. Oh, and AP exams are soon too.

The students need me and I’ve cut out things unrelated to those activities, which includes a decrease in writing. In fact, some major changes on that front as well.

For example:

Writing that took just a couple minutes, it conveys the point succinctly and got 2300 impressions. A blog post on the same idea would’ve taken 30 minutes or so to write and maybe generated 100 views. Blogs as an effective way to spread ideas feels pretty dead.

In fact, it’s more grim when I dive into history.

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That’s 5 years worth of data. Teachers are seemingly interested in archives, nice and prepackaged things. That 19.89% from Specific Posts is 3 specific posts. Two are from 2012, the other from 2015. You have to scroll a long time to find anything from the last two years.

I’ve always said it’s never about the numbers, it’s about pleasing your main audience, yourself. Well, my main audience doesn’t really need this format anymore either. I know my moves and I know my philosophy. There have only been tiny iterations in the last couple years, and all of them very specific to my teaching situation. I also find I’m repeating myself in a number of posts, as I know people are not intimately aware of things I’ve written in the past.

Starting in June, I’m reconstructing this site. I’m going to make my general philosophies and classroom management ideas easier to find and better present my archives. The blog as it was will remain in tact and none of those links will go dead. But with seven and a half years worth of ideas, I need some organization. So many things I’ve written about are out of date with my current thinking.

Thank you for your patronage. There is still value in this resource and I want to do a better job of making it easier to navigate while allowing me to focus on the local stuff that matters.

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AuthorJonathan Claydon
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Every so often I stop and realize that I have been at this for a decade. I have never been actively working on such a particular idea for so long. I think it’s safe to say the crisis of career I faced a long time ago has been settled. This is what I’m supposed to do. In recognition of this “holy crap 10 years” and the fact that I like making charts, I present a series of charts about things I’ve been doing for the past decade.

For this one, let’s broach a taboo subject, teacher pay. Before I dig in, let me state that I am satisfied with how I am paid. My district makes significant efforts to keep staff pay a priority despite funding shortfalls from the state (we have a redistribution system in place in Texas, that might change this year, our district currently pays in significantly more than we get back, leaving us to pinch pennies). We’re in an urban area and there are lots of districts to choose from as employee, and they know staff pay matters. Education is still government work though, so there’s only so much you can do. The rent’s still going to rise.

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Although public school teacher pay is a matter of public record in Texas (go poke around any school district HR page and you can find the salary schedules pretty easily), I have obscured the y-axis here. This is meant to be a general discussion of pay over the course of 10 years. More or less, I’ve been sitting at US Median pay (as issued by the Census Bureau) pretty much always. Only in recent years have I surpassed inflation. I’m 8% over an inflation adjusted 2010 salary. In 2010, health insurance cost 1% of income, rent 20%. In 2019, health insurance is now 10% of income, rent 24%. Despite the salary gains, most of it is now getting lost to overhead. I don’t even have kids or a spouse and health insurance costs hurt. The best part is despite having full coverage, a major medical emergency could bankrupt me easy. To say the recent tax table adjustments did me any good is laughable (I blew 3 years worth of my “tax break” on a car repair right after they came into effect). It’s probably accurate to say that every teacher knows exactly how far their money can go.

Another fact, I have always had supplemental duties. You stick around a school long enough and you’re highly likely to wind up doing something extra. In the spring of 2018, despite taking a year off from coaching, there wasn’t a single pay period where I wasn’t paid out for an extra duty (drive a bus for $50, keep score at a game for $30). In 2019, I make extra money by teaching math (high needs stipend), coaching volleyball, driving a bus for various athletic teams, keeping score at soccer games, sponsoring National Honor Society, and sponsoring our Mathematics Competition. Currently 16% of my salary comes from extra duties. I very much enjoy my extra duties, but they do require extra time.

If you’re a teacher reading this you know this is reality. If you aren’t in education and wonder why teachers work multiple jobs, well this is why. For a variety of reasons, wages stay pretty flat while everything else gets more expensive. If your situation has gotten so dire that you’ve had to take to the streets to get people to pay attention, more power to you. Teachers in a lot of places aren’t asking for much, covering the rent should not be an outrageous demand.

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For a long time I have tried to make a mental note of the real math I do all the time and find ways to package it into lessons for random points in the school year. Again and again I find that other than managing finances, I am constantly needing to plan events, or buy stuff at classroom scale. Like you, I’ve bought classroom quantities of supplies before, whether its notecards or glue or snacks. Each year we have a laser tag party for our AP math kids, an event for 70 people that requires a decent amount of food. Turns out juggling unit prices and headcounts is just as important as talking about polynomials, if not more.

Finally, this desire came to a head earlier in the week when I was extremely tired, hungry, and not in the mood for planning a 90 minute College Algebra lesson. We’d just finished up some topics and taken an assessment so I figured, you know what, let’s take a little break.

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Yesterday and today, students were required to plan a party for 50 people. They could work alone or with a partner. They had to plan two scenarios: sourcing all the supplies from a grocery store, and sourcing the food from a restaurant or other vendor. In both cases they had $500 to play with, which makes for a pretty decent party.

I wrote up this outline about an hour before the kids came in:

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Viewable Copy You Can Duplicate

These are all seniors and have surely attended and planned many family events where alcohol was part of the preparation, so yes, there’s an item in there where they could consider beer costs. Let’s not ignore that kids are already in the real world, shall we?

Once we went over the directions, it was just…magic. Flipping through grocery ads, planning menus, discussing appropriate quantities, it was awesome. There was a very quiet buzz as they went through everything. I have a couple kids who are always hesitant to start work and they jumped on this. They spent their 90 minutes period figuring out their plan and doing research, and they spent their 50 minute period today wrapping it all up and submitting.

One kid did tell me straight up I couldn’t come to their party. 😭

The best problems can be brilliant in their simplicity. I could see throwing this at the AP kids after the test and getting an equally amazing result.

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Every so often I stop and realize that I have been at this for a decade. I have never been actively working on such a particular idea for so long. I think it’s safe to say the crisis of career I faced a long time ago has been settled. This is what I’m supposed to do. In recognition of this “holy crap 10 years” and the fact that I like making charts, I present a series of charts about things I’ve been doing for the past decade.

A simple one this week, answering the question “how many students have I taught?” It seems simple but it has a complicated answer. Every semester we submit grade sheets to the registrar, and every year I print a second copy for myself, just because it seemed like a good idea. I keep them in a binder that I never look at.

Twenty semesters produces quite a stack of paper, and I had the ambitious goal of trying to count everyone in there. Problem was, I have taught a number of students multiple times (in some cases progressing with them through Alg 2, Pre-Cal, and Calculus). I’ve had all kinds of kids for athletics, some of whom I was simultaneously teaching in a math class, but most of the time not.

After a lot of scanning and parsing ID numbers, here’s the results:

The real number is higher than 1124 and probably closer to 1300 or 1500. This is a count of students who had a seat in my class. This doesn’t include kids I coached but never had to grade, kids I coached in middle school and never taught/coached in high school, and kids I know through other roles, such as National Honor Society.

Despite all those qualifications, that is A LOT of students and part of what makes this job so hard to relate to people not in the field. Teachers deal with SO MANY people on a daily basis. People that you are very involved with, every day, only to have complete turn over a year later. The 2+ enrollments don’t tell the real story either. Many kids showed up 4 or 5 times (coached in 9th, taught in 10th, 11th, 12th). To be so responsible for a student’s high school math experience is really staggering, and a reminder that the work matters.

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AuthorJonathan Claydon

Another function relationship project, this time from BC Calculus. Prior to the break we were working with functions defined as the integral of another, and how you could figure out absolute minimums and maximums of a given function. There was a lot of interest in this topic from the AP test last year. A number of items designed to show fluency in function relationships didn’t go well for students at large. The issues involved being very particular with your evidence and how you use notation. At TMC 18 while you were playing games at game night, me and Dave Cesa were sitting in the corner talking about this. We know how to party.

Now, we went through these ideas at the very end of the semester, so to simplify things, we made an assumption that our function would have an initial condition of f(0) = 0 and that all accumulations would happen left to right. First thing for the new semester is revisiting that idea and being a little more flexible.

Here were the student instructions:

Students used Desmos to graph their function and compute integrals at any milestone point, local minimums or maximums of F(x). Students calculated the area of their discrete pieces and kept running totals along the x-axis. In tending to precision, they collected their data into a table of x and F(x) and used a series of integrals to show their computations.

While I’ve covered this topic in years past, I have not been as particular as I need to be when it comes to notation. A real struggle in FRQ for my students is showing their knowledge of notation. Often they will cut corners by not including it, or it will be written incorrectly (integrals without dx, for example).

Like their AB counterparts, students didn’t shy away from tricky situations, including points that would register as “fakes” that they could ignore when rectifying their totals. Desmos allowed us to construct polynomials easily and get a feel for using integral notation with named functions. In parallel, when computing integrals with Desmos I will have students replicate the process on their TI-89 to verify they are proficient with both.

AB Calc will repeat the project in the coming weeks and all of this is a good sign for better efforts with precision and argument structure.

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AuthorJonathan Claydon

A huge problem in AB Calc has been an understanding of a function, its first derivative, and second derivative in a lot of contexts. Students have be able to infer the behavior of a function from the graph of f’, a table of f’, or just the equation of f’. Being able to construct all three elements when given one is a path to fluency.

Prior to break, students in AB Calculus had to create a polynomial that represented a first derivative. Based on that graph, they had to identify minimums, maximums, and points of inflection for the original function f. In addition, they highlighted the differences in concavity and when f could be expected to be increasing or decreasing. They translated their findings into tables of f’ and f’’ that validated their findings, gave justifications for their findings, and sketched f based on the derivative they created.

We were working on this fluency in class through a variety of prompts. Sometimes we started with a table, other times a picture, and others the equation. Here students created an equation and built out the whole process on their own. The results are a lot more polished than the version I tried last year.

Here’s the full write up students were given:

Most impressive to me is that students didn’t shy away from tricky to analyze functions. A lot of students created derivatives that would generate “fake” maximums, minimums, or points of inflection (where f’ or f’’ has a value of 0 but doesn’t complete the required sign change) and it can be tricky to do sketches based off that. But every student who attempted one was on the right track with their thinking. A few hit a common curve sketching snag of drawing an original function with the right features, but everything was upside down.

Collectively though, this group is doing a great job with the ideas.

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AuthorJonathan Claydon

Every so often I stop and realize that I have been at this for a decade. I have never been actively working on such a particular idea for so long. I think it’s safe to say the crisis of career I faced a long time ago has been settled. This is what I’m supposed to do. In recognition of this “holy crap 10 years” and the fact that I like making charts, I present a series of charts about things I’ve been doing for the past decade.

In 2011 I started writing about my teaching adventures. At the same time I started using a twitter account to promote those writings and follow people in education. The early goal was to write something I would enjoy and take in what other people were sharing. Fun fact, in early 2013 that first twitter account got banned because the service I used to push blog posts to twitter got flagged. Simultaneously, one of my posts had garnered enough attention to get invited to Global Math Department. I had filed an appeal with twitter but there was no indication they were going to do anything about it. I needed a twitter handle to stick into the GMD slides, and lo, the one I use today was born. Eventually my account was reinstated but by then it was damage done. RIP original twitter account.

Though I have been writing continuously since 2011, I did a platform migration from Squarespace v5 to Squarespace v6 in late 2012 or so. You wouldn’t have noticed, because barely any one read this back then (people at TMC 13 did, which made it hard not to scream OMG YOU READ WHAT I WRITE the whole time). I did another major migration (that you wouldn’t have noticed aside from a switch from red to blue) to make the Varsity Math store possible. Either way, my currently available view counts only go back to January 2014.

For today’s chart, I thought it’d be interesting to compare tweet impressions to pageviews. Twitter analytics were only available starting in Sept 2014, and their scale is reduced by a factor of 10. Otherwise the web page view data is hard to see on the same chart. No y-axis values because this is just about trends. I don’t know that a web page view is the same thing as a twitter impression, but if you compare the raw numbers, 4 years of web views is 8.5% of my twitter impressions in the same time period.

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I tweet a lot during TMC, and I tweet A LOT on the last day of TMC. Stats aren’t available, but on a lark at the end of TMC 14 I did some dumb predictions about where TMC 15 would be (having no clue). Enough people liked it I did it again. And now it’s a thing. For fun on the last day of TMC 18 I enabled every twitter notification on my phone just to watch the insanity (I do the tweet storm from a computer). I have amassed a bit of an audience and that’s cool. The goal of my twitter feed is to be very school focused in a very un-serious way. My feed makes a little more sense when you meet me in person. I tweet a lot of gold when I’m grading. Kids are hilarious.

As others have noticed, blogs seem to be less important to teaching, not that mine ever got any huge runway. In fact, the biggest traction I get is from stuff that’s wound up on Pinterest. But yes, I have an audience. And yes, I am very thankful for you. If you’ve ever left a comment or sent me an email, I appreciate them and make a point to try to reply to them all. Other than some spikes here and there, getting traction with a teacher blog is tough. Things just don’t stay in the spotlight very long at all, and it seems like a lot of people have run out of time for reading them. Tweets are easier to parse, but you still have to tweet a lot for people to pay attention (in general a tweet will be “seen” by 10% of your followers if you’re lucky, about 5% will click links). Google Reader dying in 2013 hasn’t helped.

I post less than I used to, but I have less to figure out than I used to. In 2013, 14, and 15 I wrote over 70 entries each year. Now it’s around 50. I was deep in the weeds trying to figure stuff out some years ago, primarily working on improving the quality of student products and exploring technology integration. Those two problems were HUGE and have been kind of solved. I still have things to work on, but I haven’t needed to rely on writing as much to do them.

This site still has a purpose, and it will continue. I still treat myself as the main audience and there are still things I want to see on here. It has been a boon for documenting ideas throughout the school year to discuss at end of year appraisals. And 2018 was a good year for the site. Audience numbers were up and its role as a vehicle for Varsity Math was huge. I have an infrastructure in place to make regular merchandise offerings a reality. I eagerly await the TMC 19 shenanigans.

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AuthorJonathan Claydon