In May I had the pleasure of being invited to participate in Cohort 2 of the Desmos Fellowship. We would be getting the VIP tour of Desmos headquarters and get the opportunity spending the weekend learning about new features and brainstorming ideas with teachers from all over the country. As is the nature of the awesome teachers who use Desmos, for me it served as a TMC17 preview. So many familiar faces!

The in face part of the fellowship wrapped Sunday and here's what the great folks at Desmos had in store for us:

Friday

A nice meet and greet at headquarters to give us a chance to get to know one another. I was on the end of the arrivals, missing the initial introductions. I admit I must not have scanned the Cohort 2 names well enough because it was such a surprise to see so many familiar faces. It was also a pleasure to meet so many of the Desmos staff face to face. Excellent people all, and they have wonderful taste in fancy water. Just, you know, don't ask too many questions about the TI-Emulation Layer...

At the conclusion, most of the pack wandered out to dinner having received a quick briefing about the weekend ahead.

Saturday

We spent the morning getting insight into the design process from Michael, Jenny, and Shelley. The primary focus of the weekend was Activity Builder and what we might want to do with it. The folks at Desmos were also looking for our feedback on what works and doesn't work about the current state of Activity Builder and the Teacher Dashboard. These folks know their audience and think really carefully about what works best for people in the classroom.

We worked through some Desmos designed activities and discussed the principles at play. Does an activity present a challenge? Does it build on student vocabulary? Does it create an immediate need for the math concept at hand? Does it minimize a student's ability to guess and check their way to completion?

These are some really big questions I've asked myself and were part of my reservations in waiting so long to deploy it.

We were given some unstructured work time to develop concepts for fresh Activity Builders, working in groups arranged by content area. Working with the handful of Calculus folks was tricky, it's a real no man's land of application for this stuff so far. Sam and Sarah had a great conversation about motivating the product rule with an area model. Myself, Josh, and Sean tossed around ideas about area under curves and solids of rotation. Both of these topics offered some technical challenges that required us to spend some time talking about the math before we ever created the first slide.

The rest of the day I volunteered to help Jenny user test some new ideas for Teacher Dashboard. I successfully managed to request a feature that was sitting right under my nose, if I had just bothered to stop for a second and click.

We concluded with an introduction of Computation Layer, a more advanced method to tie slides within a Activity Builder. It's not quite ready for primetime and something that's not quite on my radar. One day. I adopt things slowly.

There were some short breakouts in the afternoon, I listened to Dave and Julie discuss their uses of Desmos when it comes to assessment. This is something I plan to do more during the upcoming school year. Julie made us take her Desmos-based midterm.

Sunday

The morning focus was on helping spread the word about Desmos in professional development. They get tons of requests for training from schools but don't have the staff to fulfill the requests. Being a part of the cohort gives you an opportunity to become a Certified Presenter. If duly motivated, you can prep a demo reel for scrutiny by Team Desmos and if they like what you got, you can get the official blessing and be deployed (and paid) where needed. Another opportunity I might consider for the future, but not right now.

To give us an idea of what they were looking for, Dan walked us through the Charge! activity. We had a discussion about what the go to tools would be for this task and how technology helps and hinders the solution.

We were given more free time to conclude our thoughts from the previous day. Lots of furious work on all sorts of interesting things. I mocked up a dynamic rectangle generator for Sam and Sarah:

I then spent my time hacking through concepts in sequences and series, eventually playing around with Taylor Series generation in Desmos.

We ended the day wandering around the room seeing what everyone had made. So much creativity and talent on display. Some people in the cohort have already developed some real chops with Computation Layer, and some really bonkers things are possible (yellow shading!).

Conclusion

Whenever I attend professional development, I keep my goals simple: have one good conversation about teaching and learn one new thing (and take pictures of random Lambo's that unfortunately don't belong to Eli). I had no idea you could display dynamic values on a graph (the "Area=" thing in my rectangle demo). Sam and Sarah's discussion of the area model proof of product rule (and the two page storyboard) really taught me something I thought I already knew. Dave and I talked Active Calculus, Scott and I talked Pre-Cal spaghetti, Elizabeth shared interesting info about SFUSD, Mary got real fancy with thrown footballs, Stephanie recommitted herself to blogging (we'll be watching, Stephanie...), and on and on...

Thanks to Desmos for being such active participants in the math teaching community and being excellent hosts! It was all over way too soon.

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AuthorJonathan Claydon
Tagsdesmos

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

I have found I like to obsess on the minor details of teachers: just how you make all the stuff it turns out you have to make. I rarely see anyone talk about it, but it's a more important part of the job that you'd think. What are you going to use to make your assignments? tests? graphs?

What about decorating the classroom? Pre-made posters are great, but what if you want to do your own? Let's say you manage to turn math class into a brand, how do you generate the merchandise?

The tools I have found to get the grunt work done have had just as much impact on my teaching as ideas behind lesson design.

Where It Was

Pretty simple. I was issued a laptop by the school district, it had Office and MathType, so I used Office and MathType. You get serviceable results:

What's wrong with this? Nothing really. But you spend enough time making stuff in Office and MathType and you learn the frustrations. Equations won't align, tabbing out problems is fiddly, images won't wrap properly, low-res graphs that don't scale nicely. And WordArt, while very extensible, suffers from the same fiddly nature. I wasn't happy, so I went looking for better methods.

Where It Is

Anyone who has taken a college math/engineering/science class probably knows LaTeX, whether you recognize it or not. The default font typically gives away LaTeX generated documents. Through observations in Twitter land I noticed that there were a few people using it for high school classrooms. Finally fed up enough with Word, I ordered a LaTeX book and set to the work in the summer of 2011. A year later I wrote a lengthy post about some fiddling I had done to make LaTeX comply with my needs. Most of the tricks I discovered then are applicable to how I use it today.

It solved my main problems with Word immediately. If you want 1 inch of blank space under a problem, you will get your 1 inch of space. You want a dotted line separating two sections, you got it. It offers a precision I was looking for with beautiful results. It make sound weird to say I care that my math problems look pretty, but I want my math problems to look pretty. LaTeX was designed to make math look as pretty as possible. It also makes my assignments distinct. Though tedious I find it important to generate my own assignments, it's the best way to give students work that's relevant to exactly what we've been doing. I have never liked being dependent on the disembodied "they" that students think are responsible for the origin of all problems.

I also wanted killer, crisp figures to go with the nice math markup.

I knew enough about print to know the differences between screen resolution (72dpi) and print resolution (300dpi). If you've ever scaled up an image and wonder why it looks horribly blurry you have fallen victim to this difference, 3 inches is not always 3 inches. The best way to always win this battle is correctly sized images from a vector image program. I happened to learn Adobe Illustrator. If you need a 3 inch by 3 inch image, you'll get it and it'll reproduce flawlessly on paper.

Of equal importance was giving students the opportunity to make nice looking products. The best classroom investment by far has been a high capacity laser printer.

Big printers like this do cost a bit of money, but at the scale I operate it's pretty cheap. A set of toner lasts two school years. With all my students hitting it from their Chromebooks, we probably cranked out 3000 pages of stuff last year.

Where It Is Going

Improving the tools behind my assignments helped me improve all other aspects of my classroom. Adobe Illustrator is a powerful print tool, I could now generate any poster I wanted. It is the central piece in managing all my Varsity Math merchandise.

Each iteration is a vector image and duplicating assets from year to year is simple. I get super sharp results every time. Wrapping my head around Illustrator had some start up costs, but it has enabled some really great products. I am by no means a great digital artist, but these tools have given me the ability to craft and develop my own personal brand, whether it's a t-shirt or a worksheet. The quality of my products is important to me.

Takeaway

Being deliberate in your workflow choices is an important part of the process. Find a way of production that works for you. Find tools that makes products that represent you well. You may never have a student say anything about it, but students do notice consistency. I noticed when my teachers put effort into their products. A quality worksheet didn't make many any more inclined to the do the work, but it was a subtle way of communicating they cared. Even when working in industry my bosses could tell who put thought into their products and who didn't. It mattered how you represented yourself on paper.

Take the time to think about how you produce. Find a tool that's outside your comfort zone. Teach yourself something new, you never know what the lasting impact could be.

Posted
AuthorJonathan Claydon

A year ago I laid out a vision for my first five years of Calculus. We're now over halfway, how are we doing? Pushing the program forward is still a very slow process, but there are appreciable gains happening.

Data Dive

For those of you unfamiliar, for many years our program did not register on the AP radar at all. Kids would take the exam but nothing would happen. By the end of my first five years, I wanted to make the passing rate appreciable and predictable.

A passing rate exists, but is far from appreciable. A couple kids are starting to break through. The HUGE news here is the gains in the mid ground. There finally appears to be some evidence that my kids are able to clear the biggest hurdle, registering on the scale. The 1 designation is officially "no recommendation." All of these 2s are officially "possibly qualified" which was previously unthinkable to have so many show up here. The frustrating part, if you know anything about AP scales, is that means 50% of my exam takers were within a couple questions of passing.

Let's qualify this performance a bit. Not all of my students take the exam. The share of non-takers in these results:

Once we hit a point where passing is the expectation and not a surprise, I will be a bit more demanding about taking it. At the moment my priorities with exam takers are making sure they demonstrated some proficiency that could indicate success. Cost is also a factor for my students. I'm not comfortable forcing an exam fee out of a student who really doesn't need it.

Where are the gains coming from? I made significant investments in reinventing the curriculum. Most notably, students learn the major concepts early and spiral back on them through the year. It allows us to cover the depth of material more efficiently. I made a point of emphasis to focus on abstract matters more (derivatives where f(x) and g(x) are defined symbolically, for example). After the release of the FRQ I thought it'd come from this section. For the first time, all six questions were within the scope of what we covered well. Turns out, multiple choice finally had its day:

Our FRQ average remains the same (below 10/54, global average is about 20/54). Multiple Choice was a huge surprise, the average increased 8 pts. year over year (20/54) and is trending towards striking distance of the global (29/54). When dissected by question category, my students were pinging right at average on certain topics. While the top quarters are still pretty sparsely populated, raising the floor is the first indicator that bigger gains are on the way. On FRQ we are slowly squeezing out all the bottom tier performance.

What is the health of the overall program? Solid. Kids remain enthusiastic about enrolling in AP Calculus. The significant rise in the middle of our results will hopefully convince more that doing well on a scary AP exam is within their grasp.

Next year we will also be able to offer smaller class environments to our Calculus groups. This could help raise the number of eventual exam takers as well.

Interpretation

The existence of a "middle class" of scores was very encouraging. The hurdle to getting a registered score of any sort is the hardest part of the exam for our kids. Once you have a 2, climbing the ladder only requires a few additional questions. I have clearly misunderstood how I approach FRQs. Last year I increased student exposure to these kinds of questions. The feedback at the end of the year indicated that they wanted more. I also have not been strong on enforcing answer standards. It's probably a safe assumption that some amount of credit was left on the table due to notation and statement errors. The large number of responses landing in the middle quartiles of the FRQ show that students are doing really well on a couple questions, and really poorly on the rest. They are not consistently strong in enough topics.

Next Steps

I haven't finalized my curriculum for next year yet, but most of my notes involved circling things and writing MORE next to it. The essentials were there, kids seem to be lacking the reps. Exam preparation went well last year, many students answered the call of what it takes to get ready for something like this. Attitudes are definitely overall positive and all the kids give the class two thumbs up, and soon I feel like that success can be demonstrated on paper. If anything, BC is performing ahead of predictions. I thought I'd have 5 students for the inaugural section and wound up with 15.

And yes, the AP Exam is just an exam. It is not the most important aspect of our program (that's arguably laser tag night), but as an instructor it's nice to have an independent way of validating your ideas. My approach to Calculus is very non-traditional, to not only register on these metrics but show steadied improvement is a huge boost for my credibility.

If you find yourself in the midst of building an AP program, it is a long road, pace yourself.

Posted
AuthorJonathan Claydon

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

I model a lot of what I do on the teachers that came before me, the ones that stood out in the course of my schooling. I mused on my various math teachers a couple years ago and tried to think about what made the good ones stand out. It has been a focus of the way I manage my classroom to bring a family atmosphere to the room, to make students look forward to walking in the door, and taking advantage of all the increased productivity that provides.

Where It Was

You can't really start with explicit goals about classroom culture, especially when you're new. You spend so much of your time the first couple of years wrapping your head around the teaching aspects that some classroom management is a second priority, if not lower. At the end of the school year you'd just like to be able to say that students generally do things you ask and seem to know a bit more than they did before.

I did notice that it is possible to not enjoy teaching a particular class. I've had groups where consistently there wasn't much noise unless I was the one talking. Students rarely spoke with one another and the minutes just dragged. If it felt boring for me to teach, what must it be like on the other side?

To improve student communication, I started playing around with desk arrangements. This was motivated by a desire to improve how students worked together and a need to accommodate growing class sizes.

Where It Is

I'll skip all the variations, but after a few years I settled on something that worked reliably. Tables that sat six people, each area with its own screen. It can hold 36 kids really comfortably, you'd be surprised.

The goal is to reduce the size of the room. Yes there might 30+ kids in here, but any given student gets to spend their time focusing on five others. These arrangements start out random and eventually students get input about who they're with. By the end of the year it can be hard to tear them apart from their tables.

Not every group becomes the best of friends, but nearly all of them become productive working units throughout the school year. When a student has questions, I'll catch them whispering to their neighbor about it first. When it's time for classwork, the questions are flying across the table. When it's time for a project, you really see them come together like a family, even if they aren't working with explicit partners. I have a soft spot for kids flinging "please" and "thank you" as they share supplies, jamming out to whatever pop music I have playing.

I encourage their bonding in a number of ways. Central to that is friendly competition through a little chart I operate on the board.

It's a game with no rules that has a million rules. Some groups get REALLY into this competition, others are a little less concerned. In all cases it's a small way of encouraging kids to work together for a common goal, even if that common goal is a bunch of made up points. A couple of times I've overheard Pre-Cal students strategize how they're going to beat the system in Calculus.

This desire for group identity comes from my 6th grade math teacher, who assigned us teams throughout the school year, complete with jobs and an in-class economy (you were paid a regular salary and could buy stuff from a store). While its tough to remember how well some of these groups worked, we were 11 after all, the concept was fun. That idea is one of many reasons I loved his math class. Throughout the year many students embrace classmates that ordinarily they'd probably never talk to.

As students work I make a point to visit each group, however briefly. Each takes up its own identity, each has its own little jokes, and I think it is important to allow them a private audience with me. They use these audiences as opportunities to ask questions, get feedback, or just talk about something random. I feel this face time is the most important and something that stuck with me in school. There were teachers who were personable and would take a minute to talk with kids informally, and there were others who were all business all the time, the ones you couldn't be sure knew your name. I felt the ones who demonstrated that there could be time for informal chats were the ones who got the most production out of their rooms. It's not about making them like me, but making them like their learning environment. It brings out the risk taker in them. Kids aren't afraid to be wrong around me.

Where It Is Going

The six-person dinner table style has been the most efficient use of my class space for years now. While there are classroom management challenges that come with arranging kids this way, the benefits have been more than worth it. The grouping encourages me to be efficient with my time at the podium and to give students as much time as possible to get to work. Student conversations are lively and friendly. I field a lot of questions, but a lot fewer than I would if they were sitting in rows. Kids in rows tend to look for you first. Kids situated around their own dinner table and more likely to spend several minutes dealing with issues themselves, either eliminating the need for me or saving me as a last resort. It also MUCH easier to field repeated questions when you can talk to a small cluster at once.

Next year I am keeping this methodology but with some more flexible furniture. I'll fill in some details later, but now I have some purpose built tables on wheels that allow for more dynamic arrangements. I will have smaller classes (some as low as 15)  next year that will allow us to go from multiple dinner tables to one giant family gathering.

Kids are more willing to take risks when they are comfortable. Giving them a small little family to work with has improved the comfort level for so many of them. It's easy to feel lost in giant classes. Reducing the number of people you have to focus on and arranging everyone such that it's simple to strike up a conversation gets even the quietist kids talking.

Takeaway

Math class doesn't need to be an individual experience. Giving students the opportunity for "math with friends" has paid tremendous dividends for me over the years. Some groups have taken the family concept to some amazing extremes. I have had instances of groups refusing to be separated, buying each other Secret Santa presents, and throwing their own private end of the year parties. And in some cases these were kids who didn't know each other well or at all at the beginning of the year. In fact, they were assigned that table at random and got 4 or 5 best friends out of the deal.

This method of grouping may not be feasible with your arrangement, but find a way to improve student to student communication. Encourage it as part of your normal procedures. You need to be a regular presence, but you don't always have to be the star of the show. Students, even the difficult ones, are interested in learning something new in math class. Raising the comfort level is an excellent way to foster that urge.

Posted
AuthorJonathan Claydon

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

The way I have integrated technology into my practice has to be one of the most radical changes. Rapid progress in the industry and the way my school allocates funds to technology has caused me to reevaluate the tools I use with students on a yearly basis. There is a lot of stuff out there to try, and a lot of wild directions you can head down. Not all of it is an efficient use of your time. The greatest discovery I have made when it comes to classroom technology is to find a simple workflow or two and design projects that use it and use it well. A dozen discrete apps is not the answer, a dozen discrete applications within the same frame of operation produces far better results.

The emphasis of this discussion is on student devices. I have a number of technology bits that help me do my job, but many are unique to my situation and would be hard to apply at scale.

Where It Was

In 2009 we had little to offer students. I had an interactive whiteboard and some student response devices. In 2010 I made a concerted effort to make use of those things as best I could. They aren't bad at getting an idea of what everyone is thinking. Though in practice they had their inefficiencies. Waiting for everyone to submit took time, reliable communication with the devices wasn't guaranteed, and they reinforce an instructor centered model. Kids sit there and work something for a second in their rows and silently interact with me. I kept them around for a few years after before abandoning the whiteboard software. Here they are still kicking (though not in use) in 2012:

In 2012 we got our first deployment of iPads. I tried almost everything you could think of with iPads from 2012 through 2016. In the early days I was trying desperately to avoid the app that was going to put us all out of a job:

I knew that wasn't the future I wanted. We really did try everything. Kids took pictures and drew stuff on top of them. Kids worked problems in interactive PDFs I distributed to them. I tried all sorts of random apps to see if there was anything worthwhile. Eventually I realized I wanted my technology to answer a question. Why is this better than pencil and paper? What better products can this produce?

A year or two into my use of iPads I found the first piece that would answer this question. Technology can improve the speed and quality of our graphs:

We slowly gravitated to more graph-oriented tasks. In 2013 when I taught Algebra II it was the hallmark of the course. We could graph anything and everything quickly and efficiently with our in class devices. I got the iPads working with a printer so we could present our findings.

The iPads shined in this role. We didn't use them every day or even every week. But when it was time to make something nice, it was a workflow they could do well. More importantly, it was a workflow that got out the way. We spent very little time wrestling with technology headaches and most of our time doing something with the technology.

Where It Is

In 2016 I transitioned away from iPads to Chromebooks. In the years since the first iPad deployment my school district adopted Google accounts for all the students and the Google Docs platform had improved tremendously from my first frustrating efforts with it years ago. iPads also had a number of hurdles associated with them, most notably the regular maintenance.

As my stable of iPads grew and grew, the tedium of keeping them on the latest release with appropriately managed permissions just became too tedious. Chromebooks offloaded a lot of that responsibility and were built around the idea of multiple users.

Now when it's time to use technology things look like this:

The main workflow ideas remain. The computers give us the ability to make nice finished products. The computers are the best graphing tools we have available. Let's use them to make the best graphing products we can. At the same time, the computers have allowed a number of other opportunities.

I distribute instructions via Google Docs now, allowing me to be thorough with my expectations. The keyboard makes it easier to have students work through Desmos Activity Builder response questions. And a big feature this year was learning some rudimentary spreadsheet commands to generate information we could graph in Desmos. These computers were a regular feature of class. The workflows were so simple and known that every student understood the expectations when it was time to get a project done. We weren't wrestling with technical hurdles and I wasn't constantly trying to bend some hot new app to my needs. Simple worked and it worked well.

Where It Is Going

Access to computers presents some new opportunities. They have offered new use cases that weren't possible when working with iPads. Maintenance issues are a thing of the past and their batteries last forever. All the same it's the workflow that has shined.

As I continue, the focus is to keep technology use simple. What does it replace well and what does it let us that we couldn't before?

One area I might tackle next is assessment. I experimented a bit with these ideas. Collection and review of student work continues to be a problem. It can be difficult to scan and comment on student work in a meaningful well when collected. Math input on a computer is still nowhere near where it needs to be to replace the cost and efficiency of paper. Discussions are still best done in person than on a message board. One day that may not be true, we shall see.

Takeaway

If you are struggling with how to implement technology, start simple. Find one use case (in my case it was graphing) that you can work on. Come up with a simple procedure (make graph, screenshot, print) that you can implement a few times over the course of a school year. Expand your operation slowly and don't be overwhelmed with the latest new thing. Simple workflows will long outlast any fad app.

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AuthorJonathan Claydon

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:

Spreadsheets

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
Posted
AuthorJonathan Claydon

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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AuthorJonathan Claydon

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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AuthorJonathan Claydon

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?

Posted
AuthorJonathan Claydon

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.

Posted
AuthorJonathan Claydon