Another one about in the books (well, in like a week). It's was a Yea and Nay kind of experience.

Yea

A unique class of kids I coached when they were in 8th grade were supposed to have one last soccer season together as seniors.

Nay

One of them developed an unfortunate illness and had his season cut short, was a bummer (though rallying) moment for the program.

Yea

My 9th graders won district (my first such feat in over 5 years). And they only lost once (11-1-3)!

Nay

The last week of the season was canceled due to rain and we never got to celebrate properly.

Yea

Met a lot of interesting people on the PAEMST state finalist PR tour. Kids that participated in my submission process were super pumped.

Nay

Some weird local ironies as part of the experience. And the national competition is still behind. I might know an answer by 2017? At least when Kanye runs for president in 2020, right?

Yea

Calculus became a successful program much earlier than I anticipated. Numbers are up, and the kids lack the AP fear that used to be a hallmark. Varsity Math is so very much a thing now. Year Two exceeded my expectations. Will we see that in the scores? I'm optimistic. New and exciting development: I have one ambitious BC student next year.

Nay

Seniors are still seniors sometimes. Some unfortunate classroom management hiccups dampened the mood a bit.

Yea

Ending on a high note, though I do exert a lot of effort outside the school day, it is no longer draining, treading water, "what in the world am I doing?" kind of work. The sweet spot.

Onward to Summer Camp.

Posted
AuthorJonathan Claydon

I missed most of the fireworks, but apparently Algebra 2 was on a lot of minds the other day.

I'm going to +1, or Like, or Heart or whatever this statement. The course designated Algebra 2 manufactured by your average textbook is the worst thing in the world. It could be really interesting, but it's foundations are fake. The problem is, everyone is scared to tell the kids it's all fake.

The Texas Standards defining Algebra 2 are five pages (Algebra 1 is five, Geometry and Pre-Cal are six for comparison), and use the phrase "real-world" three times and the word "life" three times. It's really just a list of a random assortment of things. No suggestions on just how you might want to wrap what you're trying to sell. Naturally, your textbook/teacher just fakes it. "Oh, well it's important to know the real and imaginary roots of a 4th degree polynomial because......" or "Logarithms are excellent models for...."

Just stop it.

When I taught Algebra 2 traditionally I got exactly what I deserved, kids remembered 30% of a random list of things and saw very few connections between them. The topics sat in their silos as we kept checking the boxes on the list. And I sat in meetings wondering when the kids would ever get it.

There's a tangent argument about that view and the design of college math placement exams, but maybe another time.

Ok, Algebra 2 sucks. Thanks for sharing, you say.

I'm not sure how I can raise my hand more enthusiastically or force my pro Alg 2 thoughts into the timeline (I spent like, all of 2013-14 talking about it). I embarked on a really crazy experiment a few years ago and the results were eye opening. The work remains unfinished, but it was an important foundation. If you cut the bullshit, there are some interesting things in this course. But locally, I couldn't get anyone to listen to me. Because the textbooks didn't agree with me. And following a textbook is easier.

But I wouldn't change my approach. My students responded because I was honest about what I was trying to teach them. I stated a specific goal. We're going to do a lot of impractical things here. I'm not going to lie to you about their uses. It was going to be a math class for the sake of learning math. This is going to be an experience in Math Language, not Literature. And we're skipping all the big time nonsense (shout out to complex conjugates and 4th degree polynomial solutions!). Algebraic manipulation, while not particularly real world, can be interesting to a seemingly uninterested population. It's not an insane proposition.

At the end of the year, when we spent a LOT of time talking math sentence structure and grammar, I opened up our discussions. I showed them modeling and authentic scenarios. We had the kind of big idea conversations you want in a math course.

Most of their course work was fake work in a fake world. It was variable and coefficient manipulation. Over and over. It was verifying algebra with graphs. Over and over. But I can tell you this intrepid group was with me the whole way. Disinterested is not a word I would use to describe them at all. They enjoyed being good at Algebra because I wasn't trying to fake the purpose of Algebra (nor did I overload them, a lot of material was cut).

Conclusion

In my opinion, the goal of Algebra 2 is to expand a student's vocabulary (insert "toolbox" or other cute ed-metaphor here) of mathematical functions. It's a lot of fake stuff that regular people (and even me outside of teaching contexts) never use. Much of the content needs to go. The entire focus of what the content is needs to change (widely applicable processes vs function family checklist). But more students could be taught to appreciate the underlying ideas, as long as we're stuck with it.

I don't know, I'm at a loss at what else to say. The amalgamation that is Algebra 2 can be saved, it can be done in interesting ways, real live (not just the math weirdo) random kids can be taught to appreciate the beauty of what's going on. You just have to be honest.

To the broader argument of Algebra 2 being some sort of necessary force to getting kids into college? That's junk. And I agree with Dan on the misguided power we've given the course. This is a problem that starts at the top. College Algebra and Math Placement Exams are fake products and students who are successful in them have fake knowledge. Until you admit that's the problem, you're going to keep staring blankly at the wall wondering why 19 year olds who just want study political science hate rational expressions.

I'd love to know if I've missed something in this whole kerfuffle.

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AuthorJonathan Claydon
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The AP Exam is in the books. The kids and I have had a good talk about the process, and the free response questions have been released.

I think I summarized it best on Twitter:

I have learned a LOT about teaching Calculus in the last year and my kids did a dynamite job. Optimistically, my passing rate is going to a) exist and b) be significant. Now for a more thorough breakdown with an approximation of how many points my kids were capable of getting on each.

Question 1: Data Table Analysis

A prominent feature of the exam and one my kids found easy. It is an incredibly straight forward data table question and as one girl described it "I was dancing in my seat." Part c and d required some justifications and I'm not totally sure what kind of reasoning would've earned credit.

7-9 points

Question 2: Particle Motion

Also straightforward, and super bonus for it being a calculator question. While part c and d asked some simple questions (find the position at a point, find the total distance traveled), the setup may have caused some of my kids to goof. The problem gave an end condition, not an initial one, requiring a reverse integral in there somewhere I'm pretty sure. And while all of mine should've triggered on "total distance" as a phrase for integral, I'm not sure they would've set it up right. The given function changes direction.

4-6 points

Question 3: Function Behavior of a Piecewise Graph

Straightforward again, and many kids calling it the "easy" one. Part c asks about justifying the location of an absolute minimum and maximum. Lucky for the kids, the local min/max shown just so happen to be the absolute min/max. Whether or not more than a couple could justify it is another story.

7-9 points

Question 4: Differential Equations

Praise Calculus Davidson on this one. All your low hanging fruit here: sketching a slope field, finding the equation of a tangent line, and finding a particular solution. The dy/dx given is a little goofy to integrate, but not impossible. Lots of cheers when I drew the slope field, though a bit of a mood killer when I said this sort of thing might be worth 1 pt max. To which I got "yay! I got at least 1 point!"

7-9 points

Question 5: Volume/Related Rates

AKA The Funnel™. There were complaints about this one far and wide. No traditional volume question this year, instead the concept of rotational volume was wrapped in a related rates context. A couple made a go at things they recognized, such as a request for average value in part a, but for the most part this question was a wash. In my planning, the time/reward scale for related rates just wasn't there this year.

0-2 points

Question 6: Differentiation/Integration of Abstract Functions

A very interesting question that exposed some flaws in my curriculum. I invested a lot of time in discussing integrals and derivatives in very abstract ways. Questions like, what does an integral represent if you know nothing about f(x)? What I failed to do was extend that idea further. Here students were asked to apply the chain rule, quotient rule, and integration to functions labeled f(x) and g(x). Select values of f(x), g(x), and their derivatives were given in a table. In a tear to my eye moment, I had two students admit they caught on to it and applied the rules correctly. Most saw it as an easy question but went about it wrong.

0-3 points

Conclusion

The goal was to give them a fighting chance. From what I saw here, they all had a fighting chance. My approximations add up to 25 points on the low end and 38 points on the high end. Assuming I successfully did something about the dreadful multiple choice situation, that gives me some actual optimism (A 3 generally requires about 40 points). I was optimistic last year, but I was naïve. When I applied a critical eye to the 2015 questions like I did here, the absolute MAX the 2015 group could've gotten was 20 points. There was just no way to really succeed with a low FRQ score like that.

Other than The Funnel™, the kids felt adequately prepared for the free response. One even said "we were over prepared. We needed more multiple choice practice." To that, I was happy, but rolled my eyes a tad (through the year they ONLY had 161 items to practice with....). Others admitted defeat, but that was to be expected. They recognized it was due to limited preparation on their part.

All in all, great news. 2015 averaged 12 pts on the MC and 9.3 pts on the FRQ, a mid-range 1. I could easily see the 2016 group move the average composite score from a 1 to a 2. That is some serious progress.

Did I mention all of this happened with no textbook, minimal homework, and laser tag?

Posted
AuthorJonathan Claydon

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.

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

http://www.mathalino.com/reviewer/differential-calculus/04-05-water-flowing-triangular-trough

http://www.mathalino.com/reviewer/differential-calculus/04-05-water-flowing-triangular-trough

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?

Posted
AuthorJonathan Claydon

...kids 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)

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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.

Posted
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.

Posted
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.

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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).

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AuthorJonathan Claydon