I've stumbled upon a lot of random things in the midst of camp, and this is a good one.

If you're of a certain vintage, you probably played a text adventure or two. You remember, the "use lamp" and "exit north" variety as you try not to die. Well these folks Memento Mori make a variety of "text adventures" that can be played out loud with a group of people. The maps/situations are small enough to fit on a single sheet of paper and you can run through the game (with plenty of error) in about 40 minutes.

Best part? There are a ton of scenarios and the PDFs cost a whopping $1.99.

It's a fun introduction to some old school computer programming, as your players have to speak in simple commands such as "go north," "save game" and "examine backpack." As the moderator it's great to stymie them with a "I don't understand that."

In camp this week I have 8 pairs of 2. Each pair gets to say one command then the next pair goes. Watch as the group hopelessly wanders in and out of the same place as the other side of the room screams in frustration!

If you'd like to hear a few adults wander around the jungle aimlessly, listen to The Incomparable Game Show #33.

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AuthorJonathan Claydon

Session 1 of my camp ended a couple days ago. Within seconds of the first day ending I knew we were doing it again next year. Such a great week.

The Good

There's always that small amount of dread when you plan a big event that attendance will disappoint. But no, everyone showed and were eager to see what I had prepared for them (no pressure).

I was equally nervous about how much I had planned, and maybe it was the time off, but I forgot that it's actually pretty easy to fill class time, students take (and need) a lot more time with things that you anticipate.

Opener? Solid.

Quadcopters? A little quirkier than I expected. I only had a couple kids really into them, drones in the $40-50 range are tricky to control well. But, we had a good physics discussion about them.

Space? Great discussions here. I had to cut out a lot of my planned material. We focused on a few things. Main idea: space is hard. I had research some of the launch systems that have been used, the new ones under development, and we watched a bunch of videos. We briefly discussed the Curiosity and New Horizons missions with a few spoilers for the The Martian thrown in there. There was just too much here.

Engineering? We had a great discussion about my previous career and we scaled it down a bit with some spaghetti constructions. Materials had a cost associated with them ($1 for thin spaghetti, $2 for thicker stuff, tape was $5/ft), then we compared output and cost of materials. I had some research planned here but had to cut it.

Financial Literacy? Probably the most successful part. We played with Sheets for two days. We played with some basic formulas/functions and I gave them a task designed by my sister (an Excel genius) to work through.

Computer Science? Playing with Snap! was minimal, unfortunately. A longer camp would be required to do it justice. The Sheets stuff was a good, immediately practical substitute.

The Great

The kids had a blast. Many of them wished it was longer, and quite honestly, I wish it was too. Such a great time with these inaugural campers. We had a lengthy discussion about how to give the non-attendees #summerjealousy when they return for Calculus in August.

Next year will be huge (and probably backed by a grant).

Extra exciting? There's another session, it starts Monday, OMG!

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Varsity Math Summer Camp is here, finally. By the end I hope to have an interesting answer to the question "what happens when you have no official curriculum?" In addition, I get to see what's it like to teach small groups for the first time in a while. Around 35 kids/class has become the norm. Long ago when I was less adept I maxed out at 20. What could I do with small numbers now? Session 1 has 20 kids, Session 2 not but 16. My room is going to feel massive.

Goals

Big Ideas: Space Travel, Computer Science
Small Projects: Quadcopter mechanics, engineering scenarios, financial literacy

I have 2.5 hours for four days with each crew. In my planning, the first thing on my list bolded and underlined was "OMG you better not lecture for 45 minutes on any of this." A lot of what we're studying the students have limited prior knowledge, so it would be easy to sit there and wax on about the nature of the Apollo launch system or whatever, but it'd be far more productive to let them find out how it worked on their own.

Second, I like the results when students are given multiple passes on a topic. Each 2.5 hour session is broken into small pieces to facilitate one talking point. Rather than spend a marathon on space, we'll do a little space over the course of the camp.

Opener

I thought we'd have a little fun at the beginning of each day. I subdivided the room into 4 groups. Each team competing for a varying number of Starbursts. Through happenstance, I found out about the Remote Associates Test, a old instrument for measuring creative thinking. Given three words, what's a fourth word that ties them all together?

In addition to that, a BrainQuest pack of 7th grade trivia. Should be fun with a group that just finished 11th grade.

Quadcopters

You can find a billion of these of Amazon. I bought four of a model that was highly rated and not super expensive. Handy bonus, the radio is 4-channel allowed all four to operate simultaneously. The batteries last 5-7 minutes, but extras are easy to come by.

For roughly 30 minutes for 3 days, I will hand each group a radio, copter, and manual. They figure out how to fly it, why the propellers are oriented the way they are (two spin clockwise, two counterclockwise), what "six-axis" motion means, and how the copter might be changing its orientation in any axis. Then we race them. And I show them the big one.

Space!

This batch of students was in 7th grade when the Shuttle retired. They don't know much about it, or the litany of vehicles that get things into space, or even where we've been in space.

For two days, the students will do some research on the methods NASA and others have used to fling things into space. Plus we'll throw in some Flappy Space Program. Day 1, the variety of launch platforms used since the 60s. What were the payloads? Which ones had manned missions? Who are the new players? Can anyone find the sweet video of the SpaceX auto landing? Day 2, we get more specific and discuss the missions that went to Mars. Which ones failed? Which ones are currently ongoing? How did they get the vehicles to the surface? How insane is that Curiosity landing rig anyway?h

Each group will have a chunk of research to do and then they'll present to rest of their group. Initially I wanted to make some display pieces, but this is summer and anything we put in the halls will eventually be destroyed in the back to school cleaning. Though maybe we do something here.

Lastly, we spend some time on the STS specifically and a look at the technical problems that lead to its retirement.

I might modify this section a bit for Session 2, perhaps with a focus on the International Space Station, for the sake of variety.

Engineering

A brief paper airplane contest, then a spaghetti construction project. Teams will be given an objective. Supplies will have costs associated with them. Structures of different heights will have different profit payouts. It's like Hotel Snap but with pasta.

Financial Literacy

Over two days we'll run through the basics of a spreadsheet, learning how to manipulate cells with formulas, sorting things, etc. In the end we'll look at how to build a budget, how recurring expenses affect a budget, and how you can determine the amount of money you make each day.

Second, we'll do a overview the housing market. Why are they so expensive? Am I really a sucker for renting?

Computer Science

The big one. We explore the Snap programming language. Everyone is a novice with programming, so there's going to be a lot of start up exercises. Eventually I hope to get them to the point where they can develop a maze. Or at a minimum draw some geometrically styled art.

Conclusion

I really want to value students time here. The kind of learning you do of your own free will should be engaging, interesting, and active. Bringing kids to school in the summer just to do all the talking would be a waste of this opportunity. I'm hoping this experience trickles its way into the regular school experience. The quadcopters already have me thinking about new ways to introduce 3D Vectors. What else could benefit?

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Time to shift modes. Summer is a chance to digest all the issues from a school year and reconnect with people that enjoy this work as much as I do. Bonus, the Varsity Math franchise is expanding!

Varsity Math Summer Camp
June 13 - 16, June 20 - 23

A random idea that provides an opportunity to build on what makes Varsity Math so successful, the relationships. Having so many (61 of 68, 89.7%) for two years was an excellent experience, and I'm seeking to build on that even further. I have 36 campers who plunked down $20 to spend four mornings of their summer with me. It'll be my first real 1:1 situation as I checked out a Chromebook set so that we could work on programming, financial literacy, space travel, and some engineering topics. I don't have all the details planned, but each morning is 2.5 hours and I want to give them time to research and discuss things as much as possible. Oh, and did I mention we're going to fly a bunch of quadcopters around?

CAMT, San Antonio, TX
June 29 - July 1

It's the big Texas Math Teacher conference. I'm not going explicitly for the conference, I was invited to be recognized as part of the ongoing PAEMST PR Tour. They're having me wave to the crowd on Thursday morning. If you're attending, I know the tallest people on twitter will be wandering around.

Twitter Math Camp, Minneapolis, MN
July 16 - 19

The big one. Really the main thing I look forward to in the summer. I'll be presenting a session on the 17th about chopping curriculum up into more logical pieces, sharing experiences from Calculus and Algebra II. There's no snow in July, right?

Projects

I have two main ideas to look at, teaching wise.

Mainly, Pre Cal is in need of a reckoning. I've taught it for six years now and it needs an update. Teaching Calculus for a couple years has given me a lot of insight into what needs to change at the level below. I need to improve my ability to get kids thinking more abstractly about certain topics.

Second, in another small step for Varsity Math, I have a BC student next year. If you go to Calculus trainings this is usually how any big time AB/BC program is built, one experimental student at a time. This student showed stunning aptitude in my AB course, has a desire to pursue engineering, and is a great candidate for giving me a chance to see what BC is all about. In my long term goals for the program, having a full class of BC is one of my targets. The kid is really looking forward to it, and so am I.

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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.

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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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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 Funnelβ„’. 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 naΓ―ve. 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 Funnelβ„’, 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?

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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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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?

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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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