Summer Camp In Great Detail

Summer Camp has concluded. It exceeded expectations. In the end I had 40 campers who learned a lot of stuff and played a lot of games. And for a brief second we were almost derailed by a tropical storm, but a Tuesday night right turn sent it elsewhere. Let me take an opportunity to break down the lessons in greater detail and give you a glimpse of the economics of running this thing.

Economics

What's it cost to run this thing? I charge a \$20 fee (there were 4 no-shows), got a donation to cover food expenses, and my principal is able to compensate me (we have a policy where certain extra duties can earn you \$25/hr assuming that duty is approved as extra).

Overall I wound up behind by like \$30. Primarily due to some drones that broke between Session 1 and 2. Fees get deposited into an activity account I control and expenses can be deducted from there. It's the same account that covers operating Varsity Math as a whole. Anyone who has been the business long enough knows most of this gain will roll back into classroom supplies at some point.

Attendees

Some general information on who attends:

The kids attending got some basics during the school year. The spreadsheet lesson expands on that with a study of conditionals (if statements and conditional formats), specifying ranges, using built-in formulas, sorting, and how to lock on specific cells. After some brief explanation, kids spend 25 minutes figuring some things out with a dummy data sheet (~50 entries of names, ages, locations, and preferences). Functions used: COUNT, AVERAGE, MEDIAN, MIN, MAX, COUNTIF, IF, SUMIF, SUM, and RANDBETWEEN.

Drones

A discussion of the physics behind drones, and examples of what various amounts of money get you (from \$25 to \$1200). The main takeaways are that all quad copters operate on the same control scheme, operate with localized 3D coordinate systems, and more money gets you a greater set of self-preservation features. Kids spend 15-20 minutes flying a drone from a set of 6.

Once the batteries die we go back in the classroom and I give them an opportunity to fly a Mavic Pro if they're feeling brave. Fun fact, they all find it easier to fly than the smaller ones. The extra money buys you a lot nicer flight platform.

Let's Buy a House and Car

A short version of the lesson Calculus students got at the end of last year. We build a spreadsheet that calculates monthly payments for a house and car based on loan terms and amount borrowed. It then adds the payments together and outputs the theoretical yearly income to afford that stuff. Students pair up and role play as if they were making the purchasing decision together. One student finds a house (max \$300,000), the other finds a car (max \$35,000). Once they agree they come visit the bank and ask for a loan (randomized on index cards handed out by me). They make use of the local real estate database and property tax database to get a real sense of what it's like to own a home. Then for fun we see what it'd be like to manage a house that costs a few million. "I don't want to grow up" is the common sentiment at the end of this one. Primary goal of this lesson is to debunk the myth that renting is for suckers (given our location in a big city, most of our students rent).

Statistics

A quick intro lesson involving variance and standard deviation. We start with giant bags of peanut M&Ms. Kids get a partner, bag of M&Ms, and open a shared spreadsheet to input the counts of the colors in their bag and the total candies in their bag. We have a discussion on what seems "normal" for a particular color and which bags are outliers.

I walk them through calculating the variances and standard deviation of the bag totals, then have them analyze the individual colors. We talk about what we can infer from the standard deviation, with the caveat that we'd need a bigger sample to apply this logic to all M&Ms.

Then I have them collect wingspans and heights in centimeters.

They perform the same analysis. We talk about who represents the average person in the room and whether the bigger sample size makes this more statistically significant.

Engineering

I started my career in construction, managing budgets, writing contracts, and dealing with the million little problems that result when trying to put a building together. I hung onto the drawings from one of the projects I worked on. I pick one little area and pass out most of the drawings associated with that section (wall layout, electrical, fire protection, etc).

They spend some time with a partner deciding which drawing is which (they aren't labeled). I let them wander in the wilderness for a bit and then provide some vocabulary to help. Once we're in a agreement we talk about some of the finer details on each drawing and I show them the larger drawing that these were sourced from.

After some Q&A of what it's like to be 23 with a staff and 4 and in charge of \$7 million, they get an engineering task of their own. It's your standard pasta structure that supports a tennis ball, but pasta costs money (\$1 for round spaghetti, \$2 for flat linguine) and so does tape (\$2/ft for painter's tape, \$5/ft for duct tape, \$10/ft for electrical tape). Assuming the structure succeeds at the task, we discuss the various amounts groups were able to spend and accomplish the task.

Games

Students don't get enough exposure to games. I spent the last year finding a variety of things to teach them. Some of them became huge fan favorites. Coup was by far the surprise hit. Once introduced they'd often get a game going as we waited for everyone to show up in the morning.

• Spit on (or Screw) Your Neighbor - a quick card game my relatives taught me
• Coup - an advanced rock/paper/scissors kind of situations where bluffing plays a big role
• Trivia Murder Party - part of the Jackbox Party Pack (sold on consoles, I used a Nintendo Switch), 8 players and an audience compete in a trivia game with a twist, it has a fantastic final round mechanic
• Z-Ward - a parsely game from Memento Mori, an RPG-lite experience modeled off text adventures from the 80s where kids take turns giving one command at a time
• Flappy Space Program - get as many little birdies orbiting your planet as possible
• Wits and Wagers - if Estimation 180 were made into a board game
• 5 x 5 - the excellent quick strategy game from Sara VanDerWerf
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Big Moments: Push

A series of seven posts on major turning points in my teaching career. A study of where I was, where I am, and where I'm headed.

ALL POSTS IN THIS SERIES

It is really easy to declare a lesson or unit "feature complete." The base mathematics that we teach hasn't evolved much at all. Methods and initiatives come and go, but at a certain point it's easy to decide that there really isn't a better way to teach someone about a triangle.

I admit that I grow attached to the way I approach things, but every school year I push myself to actively think about how I'm going to do things and how I will push students to do things that we never did before. As Dylan Kane put it in his TMC 16 keynote, find 10% of your practice to improve. Many years of finding the 10% have dramatically changed what I expect of myself and my students when it comes to output.

Where It Was

I started teaching academic Algebra II. As mentioned in my discussion of curriculum, I followed the book because it was available and that's what my team was doing. If you needed practice problems or homework or something, there were these workbooks you'd flip through and make 100 copies of worksheet 6B, or worksheet 6C if you felt like giving them a challenge. These things were always the same, maybe 15 problems, most of them rote level knowledge problems with a random word problem at the end. Nothing very dense, and they had a tendency to communicate to students that math was full of special cases. With only 12 problems, usually 3-4 of them existed only to present gotcha situations.

I started keeping a binder of the worksheets I'd copy alongside the tests and quizzes that were given. After all, it'd be the easiest way to pull them for copying a year later.

Eventually I added a wrinkle and would take the idea of a worksheet and have students present the work as a poster. Sometimes I'd generate the problems they were working.

It was about this time I realized that I needed to trash the binder. Keeping that binder locked me into a way of thinking about what student practice should look like. I needed the freedom to adapt to a new set of circumstances, and force myself to offer a greater challenge that even worksheet 6C could provide.

The assignment side of this was previously discussed. Moving to SBG pushed me to be better about what I taught and how I taught it. Writing my own curriculum that supported SBG pushed me to learn my content better and think about how to integrate it into more coherent narrative. The third component is raising the expectations of what a student should have to do in my classroom.

Where It Is

In 2014 I made a concerted effort to improve the type of classwork my students would do. There was still a need to practice mechanics and we still do plenty of that. What I focus on when I talk about pushing is more extensive, project-type classwork. These are assignments that combine many days of students learning and have them meet a number of specifications to demonstrate learning. Often they have to put together several mechanics and offer an explanation of their thinking or how they fulfilled the specifications of the assignment.

For example, what's better? An arbitrary 25 problem set of vectors where you calculate the magnitude and direction of each, or a scenario where a student designs 40+ vectors, does all the same calculation, and then explains scaling operations? And oh, all neatly contained in an adorable picture of a pig?

Students get a better feel for how realistic it is to run into a special case. Many students making these drawings used perfectly vertical and horizontal lines. Their calculator throws a fit when they try to determine the angle. Why might that be happening? What aspect of a perfectly vertical or horizontal line might be the cause? It takes the talking points you'd normally just tell them and turns into something they'll ask you about. In the course of making these drawings, students do just about everything I'd want them to do with two dimensional vectors. None of this happens if I don't push myself to make the assignment better, to evolve the assignment from a single task everyone completes to a rough spec sheet everyone has to meet.

Assignments like this don't exist in a binder from 2009.

Where It Is Going

These open-ended approaches have been working wonderfully in Pre-Cal and the last year I taught Algebra II. Calculus has been a greater challenge, but progress exists. While not Calculus specific, I had a lot of success (post AP test) giving kids a couple days to create Desmos art, again with very limited requirements (use 30-ish equations, make something neat):

The creativity on display was something else. Everyone had something unique to contribute to this assignment using the same set of limited requirements. All of them felt the task was accessible and that it was theirs.

Takeaway

There are big and small ways to push yourself. At a macro scale, you can try to never teach the same lesson twice. Limit what you reference from the year before. Approach the topic with a fresh point of view and a see if that helps improve your understanding over time. Or start small. Take one lesson that has never gone well or one that your team complains about and throw it out. Almost every subject team has some topic they don't like, but real push comes when you decide to do something about. Delete the folder from that unit off your server. Throw out the binder that has the copies of this assignment. Find a new way to do it. Put more work on the student. Find ways for them to put their personality in what they're learning. Start with that one lesson, see if that doesn't have you second guessing others.

If you want students to engage, give them a reason to engage, give them a skin in the game. But don't take your foot off the gas. If you've always wanted to students to do more writing, make them do more writing. If you've always wanted to hear them explain a concept, make them do it. Kids are way more eager to learn than we often give them credit. Don't be afraid to push.

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Back to Camp

We finished one day of Summer Camp and I instantly remembered why I love it. There's a great energy in the room and it's pretty relaxing to have an ocean of time available to accomplish what you want. I have 45 eager campers this year (up from 30 last year) spread out over two weeks. I extended the time as well, allocating 3 hours a day. When I sat down to plan I was worried there wouldn't be enough to do but I very quickly found there was too much to do. The eternal guiding principal: kids need time. Stuff got cut.

To organize myself a little better, I carved out some themes. Every day features a competition, a long learning component, a moment to get up and play/build, and a game to close us out. Then to really make sure it would fit, I wrote a schedule.

The kids get to see this as they're just as curious about what they're going to be doing. Last year's group got input into what we did. This year I decided I had enough in the back catalog to cover our bases. Most of these activities were hits from last year, or build on ideas I used during the school year. For example, Let's Buy a House is a shortened version of what Calculus students did. The engineering task is a longer version of something we did in camp last year. I offer a variety of building materials and tapes for sale, and the kids have a budget. They design and build something that completes a task with a cost of materials. I have more elaborate plans for this project, enough to make it a separate piece. As the kids attending camp are incoming AP students, I gave statistics an entire day. And bought like 10 lbs of candy to make it happen.

Hopefully each kid can walk away with one thing they can make use of later. I don't care if it's a spreadsheet command, engineering idea, or a new card game they can play with their family. You know, other than make another generation obsessed with Baby Shark. So much fun.

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Big Moments: Curriculum

A series of seven posts on major turning points in my teaching career. A study of where I was, where I am, and where I'm headed.

ALL POSTS IN THIS SERIES

Curriculum has fast become my favorite focus in recent years. It started with an observation as I taught Algebra II, that the way I did things was inefficient, uninteresting, and lacked depth. Students were doing surface level material and never getting very far in a particular topic. There was a lack of cohesion in the school year. It felt that we were just studying things at random, hopping around on a whim. I want curriculum that's interesting to teach and that spends 9 months telling a story with identifiable payoffs.

This is different from a discussion of individual lessons. I'm talking about big picture. How do you create the tool that drives the school year?

Where It Was

I followed the textbook, roughly in order. My first year I spent a lot of time relearning the material, just trying to make sure I didn't make any major mistakes the next day. Even then I still screwed up, a natural process when teaching something for the first time. I wasn't worried about what message I was trying to send over 9 months, I was just worried about making in through to the next Friday. As I was transitioning into standards based grading, I noticed that the curriculum just wasn't satisfying. Planning this way is also just terrible. I have sat in on one two many conversations that go "well, we have 2 days for 1.1, and 1 day for 1.2, but we HAVE to finish 1.3 by Tuesday..." Ugh. Just, ugh. What generally happens 9 months later when you plan like this usually includes the phrase "...we just ran out of time." This shows a lack of vision. In August, you should have some idea of where you want to be in May, with a working knowledge of how to get there.

The week to week stuff just stopped cutting it for me.

At the same time, I also realized that students do NOT care what chapter you're in, or what the section number is, or any of that textbook organization type stuff. They are, however, slightly more interested when you talk in topic names.

The use of SBG and topic names had an effect on the way I discussed curriculum. I stopped caring about chapter numbers and section numbers and instead focused on the material itself. It wasn't Chapter 5, Section 2 anymore, it was Motivating the Quadratic Formula. That was an important step I think. When you view a course as a collection of topics, you're more inclined to organize them into something that makes better sense to the student.

Algebra II, a course I will always defend, offers a great case study. Is it necessary to deal with the start up cost of solving equations 5 disparate times through the school year? Could you cover all the mechanics up front?

Where It Is

It was those Algebra II questions that lead me to a very intense project, my Pivot Algebra Two idea from 2013. Rather than think about the course as a list of functions where you work on the same skills weeks apart, what if you focused on the skills and iterated through their applications for various function types?

This skeleton lead me to rewrite the entirety of Algebra II around the major skills I wanted students to develop. I wanted the basic operations we learned in August to help us with more challenging situations in May. Along the way we could take a minute to summarize what we had applied to a subset of functions.

The end result was the most fun I've had teaching. We went really deep into topics that were unthinkable before. We had time for awesome projects. It was a great group of kids. All of it driven by a cohesive narrative. The project paid great dividends down the road.

My initial run at Calculus was challenging. I spent the following summer grinding away at the curriculum, looking for inefficiencies. I was searching for my narrative. After a lot of work I found it: the integral and the derivative need each other, let's explore the many contexts of their relationship. The result was a road map that gives students a basic idea of the course in about 5 weeks.

No saving things until later because they "weren't ready" or something. The more a student knows about a course up front, the more you can with the material later, the more you can communicate the story of Pre-Cal, or Geometry, or whatever.

Where It Is Going

Thinking about the story I want to tell with a course has been a huge breakthrough. Textbooks are of little concern to me. I use them as reference to get an idea of a course's topics and building a model document from there. For example, next year I will be teaching Calculus BC for the first time. I will consult a textbook but the actual rhythm of the course will find its way into some document like the one I use for AB. There's a possibility I'll be doing College Algebra as well, meaning a return to the idea I started in Algebra II. As an instructor, manipulating curriculum in this way has made me incredibly familiar with a course. I could write pages and pages about a logical progression of Pre-Cal from memory. I've been thinking about the interconnection of its topics for years.

Every year I find it easier and easier to fine tune a curriculum. Delete some wasted days here, find a new connection here, and carve out room to go deeper.

One of these days I'll figure out a way to take these personal notes and develop them into real guides for people who want to do the same thing. It's been several years, but that was the concluding step for my Algebra II project.

Takeaway

Many of you are probably in the same position. I know lots of teachers who have little regard for the order preferred by a textbook publisher.

When you sit down this summer to think about your courses, consider the story you want to tell. What connections do you want to establish? How can you spiral back to information as much as possible? How do you want August to influence May?

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Activity Building

A couple years ago at TMC15 I got a sneak peek at Desmos Activity Builder. At the time it was fairly limited but there was a lot of promise. At the time of its introduction I wasn't sure I could make use of it and that proved true. I didn't have access to enough devices and the iPads I did have were aging quickly and becoming a pain to manage. I attempted one of the first Marbleslide activities in early 2016 and the hardware just croaked.

Fast forward a bit and now I have access to a fleet of Chromebooks. The number of students who can bring a device from home has increased dramatically. iPad hardware in particularly has accelerated so rapidly in recent years that the struggle I saw before is gone.

I experimented with a few use cases this year, just to see what there was to see.

Match Me

Started simple. I took an activity I had done previously where students had various graphs on paper and had to recreate the pictures in Desmos. It looked like this:

Not bad, worked pretty well for a couple years. With Activity Builder I could work through the same idea but get students to add more detail and learn a bit more about the functions of the calculator.

Students could more in the matching realm, in this case finding a sin and cos function that matched the black line. Eventually they could create projects that included center lines, amplitude markers, etc.

Pretty good. Being able to build more complex prompts let more students know more fiddly details about the calculator. I liked that a lot.

Assessment

I used Google Forms quite a bit this year, and realized (well ok, Dan nudged me) that Activity Builder can be used to gather the same kind of information, though one screen at a time. Bonus, it understand math notation natively. I experimented on Calculus and used sketching screens for part of their final exam.

Sketching with the sub-par Chromebook trackpads isn't the best, but that can be remedied with some cheap wired mice. Pretty cool to see 89 sketches on top of each other.

I also used it for a two-fold assessment. Students were given access to a saved calculator with a bunch of regions on it, they had to determine expressions for the area or volume of that region, and then enter it in a separate Activity Builder.

Also cool. I really appreciate the detail that has gone into the teacher dashboard screen. Though there is room for improvement. Examining student responses screen by screen wound up being a little tedious here. Though I'm not sure a spreadsheet generated by a Google Form would've been any more efficient.

Going Further

I really liked what I learned using Activity Builder this year. Though Dylan Kane and others dropped some quality thought bombs on the subject. There can be a lot of silence while students work through these. Instant gratification may not lead to the most genuine student guesses. A subset of students may just hammer away at parameters until it works. I tried to counter the idea by requiring explanations after students had a chance to experiment. I think it helped a bit. Though Dylan's Conics activity is really something. You get no idea what your submission looks like until hitting a button.

There's a lot to think about here. The challenge of drawing a circle around a subset of dots is just brilliant. I need to bring more of this to the way I design activities.

Conclusion

Really excited to see how this evolves over the next year. There has been a lot of effort put into the feature and it's impressive how far it has come since I first saw it. Desmos curated activities are top notch. I think Activity of the Year should go to Jennifer Vadnais and her mini-golf game:

I know the intended audience is a younger crowd, but I had plenty of juniors and seniors cursing this thing. Bravo.

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Big Moments: Assessment

A series of seven posts on major turning points in my teaching career. A study of where I was, where I am, and where I'm headed.

ALL POSTS IN THIS SERIES

Assessment is a topic I focus a lot of energy on every year. Regardless of the number of times I have taught a course, the assessments are fresh each year. I write 20 Pre-Cal assessments a year, for example. The premise behind all this creation is I want to reflect my most current feelings on the course. I don't want assessments I wrote five years ago to affect the way I teach curriculum in the present day.

Where It Was

My assessments were standard fare. I taught Algebra II on-level with a team of teachers. Being a first year know nothing, I made use of the tests written by the team. There was no policy that you had to use the team tests, but they were available and I had no idea what I was doing. It was the best choice. They had about 25 items and were usually two pages. Grading these was a pain. Should I award partial credit? What's worth -1 versus -2? Should this item count for 4 pts or 5 pts?

In my second semester I began writing my own ~25 item assessments. I had more experienced double check them. I wasn't sure what was too easy or too difficult. They had no issues with what I produced which was a nice validation. The pain was still there. And what the heck do I do with students who clearly didn't understand what was going on? I have to write a completely new 25 item assessment?

Then I started noticing stuff. Kids weren't interested in any of my comments. They looked at the number at the top and that was that. Often I found graded papers in the trash. Regardless of class performance, once the assessment was handed back, we never spoke of it again. The number of points per item felt arbitrary. Partial credit felt arbitrary. It would feel like classes did ok on page 1 but would bomb page 2. Kids had no way of knowing if they did well on any particular topic.

I came to realize that these big units are missing something. But no one seemed to have a better alternative.

Where It Is

In the spring of 2011 I implemented a method of Standards Based Grading. My particular jumping off point was Dan's mini-thesis on the subject. It made a lot of sense. Why do you have to assess in such giant chunks? Why do you have to assign arbitrary point values to items? Why are you going through all this effort to provide feedback if kids are just going to throw it away? I couldn't find satisfactory answers to these questions. The risk was worth it. Worst case I'd go back to the established normal.

There are dozens of SBG methods out there. It is not a rigid system. A major talking point I had to reiterate when sharing the idea with others. Lots of people new to the idea want a checklist of rules to follow. The moment that sets you free is when you realize it's about making an assessment that helps you as an instructor, chapter numbers be damned.

Pre-Cal currently uses a two-attempt system. Work a topic once, get a score, work it about a week later, demonstrate you got better or still have it on lock down. What constitutes a section is entirely up to me. If a topic is particularly dense, I'll divide it among multiple sections. If we make advancements from week to week the second attempt will probably demand more of the student. It lets the semester flow smoothly. What topics were relevant this week? What could use more work? What might I delay? Regular, targeted assessment lets me keep pace with the flow of any given school year. I don't stress out if we aren't exactly aligned with previous years. If I want to flex the order of some unit, I can write new assessments to match.

Assessments are short and sweet. Always one page, never more than 5 separately assessed sections. Students can use their notebooks to help them work. From time to timeI let students work together. When first deploying SBG, the sections were pretty rote exercises. After spending a few years in the freedom that short and sweet assessment brings you, Pre-Cal is less about rote exercise and more about putting together pieces to reason through a situation.

As designed, students were to use methods of solving quadratics to determine that the two intersection points where the solutions to one of the three equation systems. This student realized it could be reasoned through with knowledge of transformations.

Here students were given a suggested value for angle p. As designed students could check a cosine ratio against a trig table to see if 59Âº was a reasonable expectation. This student not only checked cosine, but wanted to see what sine and tangent had to say. All three ratios helped the student reason 59Âº was close but not quite. Other students use the assumption of p to find a value for the second interior angle and check that as well.

Assessment to me is less and less about seeing if students can follow a script I write in my head. I want to see what they can do with the topics we talk about. Often and on purpose the questions they are given on an assessment are combinations of things they do in class, or require that they design something on the fly. I give no review sheets. Classwork is the review.

Here I provided some requirements and students had to produce something that met the idea, and then describe specifically how their modifications met the goals.

Where It Is Going

Calculus presents a bigger challenge in this department. It is a simple course but there are a lot of moving pictures. You spent a few months talking about tiny pieces of the course until all at once around the end of January, students can see the whole picture. Providing more time for students to discuss material has become more important than having them work through paper tests.

I have tried a variety of SBG methods in Calculus and none of them seem to stick. Calculus has become my biggest assessment playground. At the conclusion of our unit on area between curves and volume, I turned to Desmos Activity Builder. This and Google Forms are both very interesting options for assessment. A Pre-Cal student who complained mightily about having to labor with a pencil to answer all my writing questions mused about whether Calculus would have more opportunities for typing this kind of stuff. That student might be on to something.

My wide-eyed group of BC students are the assessment playground for next year. Will they even take a paper test? Will I grade them in any sort of normal manner? We shall see.

Takeaway

What do you want from assessment as an instructor? What do you want students to take away from assessment? How are you using your opportunities to assess to let students demonstrate and explain what's been going on? I don't think chapter tests written by a textbook answer these questions sufficiently.

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Transition

This school year was something else. I thought I knew my capacity before, but this shot beyond that idea and more. When the school year closes next week I'll have logged 205 days on duty. August 1 I dove head first into coaching volleyball, followed by a few weeks off and a four month soccer season, just in time to start staying after school to facilitate AP Exam tutorials, organize the end of year laser tag party, and juggle some stuff for the senior picnic. All the while I was pushing new initiatives in Calculus and Pre-Calculus. And if you've never coached a sport before, it's typically an extra 30 hours a week when you're in season on top of the normal classroom expectations.

Some months ago I wrote about my vision for the Calculus program. Not mentioned in that post because it was under my hat is an understanding that I need to transition out of my athletics role to make the plan of reality. Our administration granted my request to make this my last season. As of June 2 I'm out of the athletics game.

It started at random. I was not hired to coach. I received an e-mail in October of my first year teaching asking if I'd be interested in helping out. The school had recently added a third soccer team for 9th graders and needed someone to run it full time. Previously one coach had to juggle two teams and that wasn't feasible. Admitting I knew nothing about soccer, the head coach was willing to work with me. Eight years later I have to say I'm not sure I'd be as good at teaching if it hadn't been for all the things I learned working in athletics.

Coaching is an interesting game. I'm an outsider to the profession. I never intended to coach, never played sports at a high level, and have no aspirations to run a program or be an athletic administrator. But the people who have a passion for it are really incredible to watch. All the effort I put into math instruction they put into making kids comfortable to push themselves in other ways, to represent their school and community in a positive manner. Coaches are also often the biggest advocates for their students in the classroom. So many kids have come through our program who push themselves in school because they know their coaches set high standards for them.

Coaching taught me so much about the operation of a school district. Facilities management, the role of an athletic department, and how much the real soul of a school is guided by the men and women serving children through sport. Varsity Math doesn't happen if I hadn't been involved in athletics. The skills required to navigate account management, acquisitions, and logistics were all learned through watching my head coach navigate the process year in and year out to make sure we had the necessary supplies.

Coaching taught me so much about a diverse population of students. I met so many kids I wouldn't have otherwise through coaching. Many of them boys with weak male role models in their life who turn to their coaches for guidance. Getting a glimpse at coaching girls was eye opening. It's fundamentally the same job but young women have very different needs. Some of the students we will graduate tomorrow have been under my care in athletics since they were in 7th grade. It's a rare opportunity to watch students grow up like that. I am really going to miss those kids.

There are bad coaches. I have known several. But I urge you, if you are a classroom teacher who knows little about your athletic programs or have never bothered to strike up a conversation with a coach on campus, or you aren't even sure how to get to the gym, give it a try. You might be floored by the kind of work these people do for your students.

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Post AP test, I try to give the older ones some access to the kind of adult information they all hear whispers about but never learn until it's too late.

For the last few days we've spent some time on financial literacy. Specifically, building a spreadsheet that would make it easy to compare the real costs of owning a home, with some generous assumptions built in.

Using the (apparently secret) mortgage formula I dug up a few years ago, we built a tool. Each kid made a version of this. The input variables are the sale price and the appraisal value (sourced from databases local to the area). We plugged in some assumptions about property tax calculation and insurance. The point is to have them think about a house as more than the base line mortgage payment. And to see how ungodly high interest can pile up on a 15 or 30 year loan. Also, property tax? Say what?

This spreadsheet has other modules in it, but this first one served our purposes. It can also be extended to part two which involves buying a car and then ballparking what kind of monthly income it would take to afford the car and the house.

They were given a link to the following instructions. The price range is mid-tier for this part of the city. Another assumption in the scenario is that we're about 15 years in the future and have acquired the cash to make a 20% down payment on something.

Note the mandatory fidget spinner.

Over in the corner I set up the bank. I had them make a few blind choices to acquire a random set of loan terms. Then they chose between a 15 year and 30 year option.

I had fun with it. They were required to begin the dialog with "Excuse me Mr. Generous Banker, may I have a loan please?" The bank was only open for 40 minutes (we had about 80). I'd get up and go on break at random, even in the middle of a transaction. Kids would play along and complain when there was a line. "There's always a line!" One regret is not having a bowl of lollipops.

I had a couple kids walk out and then yell that they didn't like the terms of their loan. I directed them to the complaint department.

Super fun task. A more complicated version might subdivide the loans based on the amount they're trying to borrow. I think that's how part 2 with car loans will go. Terms dependent on what kind of cash they're trying to drop. Kids are doing some dynamite stuff with their collection of materials. The hilarious part was listening to others watch someone get their loan terms at the bank and react with "ooh, nice one! or, oooh you got the bad one!" without any real idea what they were talking about. Listening to them chit chat about their interest rate was hilarious. "You know this is what adults do, right? This is what we talk about?" "Ew, gross."

Gross, indeed.

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Three Year Report

I set a goal of overcoming the biggest problem our students have faced with Calculus, the language demands. Many of my students have found the calculation demands to be reasonable, but stumble on the words. That has been the feedback from three rounds of AP exams so far. This year those complaints still registered, but not has high as before. Upon examination of the 2017 questions, I think we're making big gains in accessibility. This is a reflection on what I think I achieved with my instruction.

When I say accessible I mean a) the topic was addressed in class b) kids had thorough practice and c) kids had the pieces to apply a skill on their own. In no way do I attempt to feed them infinite scenarios and create long long lists of steps. The goal is a focus on big ideas to allow them to be comfortable and adapt what they know to different situations. Also when I say accessible there is no guarantee kids actually converted that into correctness. There are too many variables with a students preparation to really know.

Based on number of question parts present (1a and 1b counted separately. etc), in my opinion I think this is how accessibility broke down:

I was very happy with the level of familiarity my students should have had this year. I made some strides in improving the way we covered information to improve our struggles with the language barriers. Post exam conversations bore that out. Yes, it was difficult, but the majority said they recognized a lot.

Just as a reminder that accessibility doesn't mean correctness, my non-1 rate for 2015 was 8% and 10% for 2016. For all the gains in accessibility the non-1 rate this year could be, like, 20% max or something, or worse. The road is long, but we're moving.

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Calculus Victories

Today's the AP Test. What's changed in the last year? Here are three areas of improvement worth celebrating.

Preparation

There are 35 taking the exam this year, down from 50 a year ago. Though about 65% of the population is in a good state of preparedness. This is based on my observations through how they spent their class time and what comes up when they attended after school sessions. The kinds of questions I'm getting are more focused and we have had some excellent discussions. Last year that number was like, 20% or less. A big factor is some adjustment I made on my end. I tweaked my benchmarking process and rearranged what happened after Spring Break to give my exam takers about 10 days to just sift through stuff and work. Last year it was about 3 days. I demanded more of the kids. These 35 responded to that challenge.

The full list of stuff they were given since late March:

• 8 topic, 50 question Free Response Collection
• 50 multiple choice questions from various practice exams
• reference sheet
• study recommendations
• varied fundamentals (limits, polynomial sketching, trig values, etc)
• 6 released FRQ, 2 calculator, 4 non-calculator, to let them simulate a full set
• access to the 2014 practice exam from the secure teacher portal

The goal is to demonstrate how to prepare for something over a long period of time. Cramming the week before won't aid their long term retention in anyway. Though I can't control it, they were forbidden from doing math yesterday. Their preparation materials were given out slowly over a period of six weeks. We spent two of those weeks finishing the curriculum while they started work on their own time.

Conceptual

Huge gains in conceptual understanding this year. Primary inspiration drawn from this question:

It's not enough to know the mechanics of calculus with defined functions. You need to be able to apply it in the abstract. We did extensive work throughout the year applying principals using functions defined only in theory. Kids found it strangely simple. I think more of them understand "f prime" as a thing that can be manipulated in a number of ways now.

Pictures

I also realized last year that curve sketching and function sketching in general is a huge a weakness. I made efforts to improve it in Pre-Cal to help me out for 2017-18. For this group of Calculus students, we took time to review the concepts of polynomial sketching and how it can help us analyze the behavior of a function (specifically spotting things like false critical points). As part of our review weeks, I made a point to mention how a picture can help a situation. Take this question:

A couple years ago I did a horrible job preparing students for something like this. Particle motion is a topic my students feel very confident about, provided they have a picture. The questions are almost trivial with the use of a calculator. But here it's easy to feel screwed. Unless you realize drawing that cosine function jump starts this problem in a huge way. Students also had hang ups with pi-terms as coefficients. We spent some time with it and now it's not a big deal.

There are similar situations where a polynomial is given. Breaking it into binomials and making a sketch gets where you want to go quickly. No tedious quadratic formula required.

Further Steps

Several students had weak connections between the behavior of a derivative and the impact on the original function. For example, about three weeks ago I got a lot of blank stares about identifying where an object changes direction, or what positive values of the derivative mean. We were successful in clearing up this confusion, but it was a little strange it had to happen in the first place. Other than that, the majority of concerns lie with differential equations. This was expected, given how late it was introduced and the limited time we spent with it (about a week).

There's probably about 10% of the curriculum we didn't address. But I feel good about my students' understanding of the 90% we did cover. In analyzing a practice exam, this group ideally could pick up 10 more questions over last year.

A huge thing I noticed a couple years ago was class time being diverted to in class assessment. I have a gradebook obligation to the kids, but continuing to be creative in this area will help us get more time back. In year 1 I gave 14 in class tests, year 2 had 12, and year 3 only had 8. At the moment I'm not sure what, if any, formal paper tests my Calc kids next year will have.

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