At TMC14 the entertaining Steve Leinwand gave a talk about some of the trappings of math teaching. One section of the talk dealt with asking the simple question "about how much?" with a expression containing some oddball square roots.

At random around 11pm one night, that point resurfaced. A weakness I've noticed for a while is that students lack an understanding for the value of things like sqrt(2) or how you could use what you know to approximate sqrt(27). Or the value of 3/2 or how to estimate 1/3 of something. I had a conversation with another student once about the final price for a car, and they had no idea about how to approximate tax/title/license on top. After explaining it, they ask the poignant question "why does no one mention this in school?"

This year I think I'll do something about it. It's like a really focused version of Estimation 180 without all the pictures. I'm thinking I pose four situations a day and have a discussion about how these could be approximated to build their "oddball" number sense.

I probably wouldn't type them all in advance, this was an exploration exercise. Probably after a few months I could compile them here for those of you that would like a home version.

This could be fun. If you too have noticed a deficiency in number sense, don't complain about it or blame calculators, try to do something.

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AuthorJonathan Claydon

My classroom is my eternal playground. Some highlights of this year's version.

The teacher space is tiny. There are 36 kids in here at certain points of the day, and they need the space more than I do. My first year my teacher desk was 1000% bigger than this. A class of 25 was also mind blowingly huge at the time. The device cabinet has moved over here and the landing zone for kid things like pencil sharpeners and tissues.

There's seating for six at every group now. I developed some emergency plans in case that's not enough. The back of the room is a lot more efficient. One of those TVs used to float out in the middle of the room which was a pain to walk around. I'm hoping it's not too cramped in the little rows between the tables.

I had notebook in two spots last year because there used to be some other things on this table. Whatever junk it was is gone so all the books should fit over here without an issue.

I organized the supply table a little more. The glue sticks are in a container for dishwasher pods. Every table has some scissors is former pineapple containers. The bonus was all the pineapple I got to eat to acquire these containers. No more staplers, they all got broken. RIP all the staplers.

I am extraordinarily pumped for this school year.

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AuthorJonathan Claydon

Prior to the start of school, I stumbled on this sign (not on my campus):

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Further up there is a diagram showing exactly how the cabinet is supposed to appear. Now, look, this isn't intended to call this person out and tell them they're doing it wrong or anything like that. And I'll be the first to tell you that I'm not strict about much. Chances are there were a series of incidents that lead to this sign and intervention was necessary. I have a serious face too. But, how you react to this sign could be an interesting indicator of your classroom culture.

To me, a sign like this is an immediate sign of mistrust. You, dear child, are GOING to screw up and I WILL catch you.

I have a lot of devices in my room. Being the control lover that I am, I too appreciate a nicely organized cabinet. When I ask for them back, I get them back. The kids make a stack on a table. We use them often enough they know how this works. Then I stick them back in the cabinet. No boxed threats required.

Students are not by nature against you. You can make a lot of progress if you recognize that they can be trusted individuals with something to offer.

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AuthorJonathan Claydon
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As my iPad set grew, charging them started to become a problem. We have a cart to store them in that has a few power strips and some dedicated USB chargers. There are only so many outlets to go around, so I couldn't use all the stock chargers. I had a set of 10 and had to do charging in shifts. It made the cabinet a mess. The dedicated USB chargers are underpowered for their task (10W, 0.5A shared among 4 ports, a full size iPad draws 12W on its own), and when the cart is loaded up, they can't sustain enough juice for an iPad (a string of ding-ding-ding noises as the iPad gains and loses power).

Enter this bad boy.

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These are 5-port, 40W, 8A chargers by Anker. They cost $25 each and I bought 5. These have the juice necessary to power a ton of devices and let me get rid of the mountain of power chargers cluttering up the cabinet.

After some sharpie labeling and cable snaking, here they are installed:

The body is coated in rubber, so mounting them to the side with a velcro patch didn't really work out, but this is ok. When outputting full power they get very warm (VERY warm), so they need some air to breathe. I plugged in 20 devices and heard none of the ding-ding-ding problems from the underpowered chargers. Plus, look at all these adapters I don't have to use:

As a bonus, I used the fifth one to solve a nagging problem I had last year. With the prevalence of cell phones (I can hear you now OMG CELLPHONES HATE HATE HATE, but calm down a bit), my outlets would get commandeered whether I granted permission or not. Often it was at the expense of the pencil sharpener or some other critical thing.

Sitting on the top of the cart is my solution, a phone charging station. Charge it here, stop touching my outlets. 

The reduction of cabinet clutter is fantastic. There were three power strips in that thing, all plugged into each other (super safe guys). Now it's only one.

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AuthorJonathan Claydon
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This was detailed over a year ago, but a lot changes. A refreshed look at how you can make a whole fleet of iPad devices communicate together and offer students a universal experience.

Before starting, updating the software to the latest version of iOS wouldn't hurt. Everything but an original iPad can run iOS 7.1.2 (current) and will be able to run iOS 8. When iOS 8 arrives in the fall, I won't update my devices until it's time for regular maintenance over winter break.

App Store

You may have done this already when setting up the device. It asks for an Apple ID at the start. If you're inheriting devices or weren't the one who took it out of the box, you'll want to sign in your account here. Use an e-mail address separate from any personal Apple ID you use. Every device you sign in with the account will able to access the same batch of purchases.

Disabling automatic downloads will prevent student devices from grabbing copies of things you may not be ready to deploy yet. Enabling Auto Updates will apply updates as they become available, preventing you from manually applying them on every device.

Acquire purchases by launching the App Store from the home screen and finding the "Purchased" button on the bottom right.

iCloud

You shouldn't have to do anything extra. By signing in to the App Store with your Apple ID, it should appear here as well. It's also possible this was entered at set up. Again, if you're inheriting a device or did not set it up initially, you'll want to check here. Notice most of the features are disabled. The Safari features let each device share a common pool of bookmarks, it also enables one device to see what tabs are open on others. To enable the kind of fun photo discussions I've done in class, you'll want the photo feature enabled. This allows devices to contribute to a common photo pool. Photos actively in the shared pool appear by going to Photos > Albums > My Photo Stream.

Google Drive

You'll first need the Google Drive app from the App Store. I use Google Drive to accomplish another type of classwork sharing. Every device is signed in to an account I made specifically for this purpose. If your school e-mail is tied to a large scale Google Apps for Education deployment like mine is, you won't want to use that. In theory you can ask students to sign in to their own Google Accounts here if they have them, but this is less fiddly.

Restrictions

Students will distract themselves no matter what, but a few options in the restrictions screen will prevent them from doing any real damage (like deleting an app). When you first tap Enable Restrictions you'll be ask to set a passcode. This is different from a passcode to unlock the device. After restrictions are enabled, you will need this passcode to make changes.

I disable a lot of features. All of the iTunes and App Store related ones will remove the icon from the home screen. If you enabled Auto Updates as mentioned previously, they will run with the App Store hidden. If you choose not to do Auto Updates, you'll need to come back to the restrictions screen and flip the switch any time you want to check for updates. Without the icon present, you'll never know they exist.

Towards the bottom of the Restrictions screen are options for Twitter, Facebook, and Accounts. In each case you'll want to disable the ability to make changes. Since you can't delete the Mail app or Messages app, you'll want them to be nonfunctional if a student attempts to open them. When properly set, Mail and Messages will display the error above. Hitting OK drops back to the Home Screen.

Goals

No need for computer based syncing, no need for backups, and no need for any crazy apps. My devices are designed to be clones of one another that allow any work created to be offloaded quickly.

More importantly, with iCloud and Google Drive, students get a chance to talk about what others are creating. iPads shouldn't be expensive workbooks.

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AuthorJonathan Claydon
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During a Calculus workshop I attended, the primary purpose was to run everyone through the curriculum in four days, discussing common student pit falls along the way. It gave me a very new perspective on the class and made it seem so much simpler than it felt 12 years ago. Then I went a reworked the free response questions 18 year old me faced and it was stupid simple.

But, throughout it was assumed that we all knew how to structure the class. Quizzes, tests, and piles of homework done on notebook paper. How anyone decided that was the "standard" way of conducting a class was beyond me. And something I've always wondered, is that the working assumption when studying education in college? I wasn't an education major, but it seems like all the ones I meet just KNOW that you give quizzes, tests, and a pile of homework done on notebook paper. And points. You must be VERY fiddly about points.

Here are my goals for Calculus:

  • homework will be involved, a bit
  • frequent assessment is necessary
  • exposure to the AP format is necessary
  • conceptual understanding is HUGE
  • similar to Algebra II, some foundational skills must persist all year

How I'm going to attempt to implement those goals:

Homework

It's got to happen, really just for some persistent exposure. I have no intent on burying them in it, and will try to make sure the assignments are short and have purpose. Initially I was thinking one notebook for notes and another for homework, but forget it, let's just put it all in one place and if they need new ones in the spring, they need new ones in the spring.

Assessments

Calculus is such a small set of skills when you sit down and look at it. Isolating them into a good SBG list is a little difficult. Plus, with an AP crowd, I don't want them to become dependent on reassessment, a common issue with high level students and SBG. The prevailing idea is to keep assessments frequent: every 7 - 10 calendar days. However, there will be two skills section and one conceptual section, each assessed holistically (probably each section rated between 0 - 5). No fiddly points. I don't think letting them use notebooks on the assessment will help my cause. These are the kids who are really going to have to learn to stand on their own in the face of mediocre college instruction.

Skills can be reassessed whenever. Conceptual not so much. There won't be any built-in replacement, just a series of skills marks accumulated during the grading period (they can be altered by coming after school and trying again). I think I know what this looks like when recorded in a notebook, but I'll wait to see it in person before I share.

The big twist will be a six weeks exam. Something that's existed in our Calculus classes for a couple years. Though I want it to reflect AP format a little better from an appearance and time point of view. In 40 minutes, it's roughly 9 multiple choice questions and a free response question, graded according to AP standards.

Reasoning

The major diversion from my traditional SBG skill system is to allow myself options. Maybe I want to throw in some product rule and quotient rule months after we covered it? Maybe I want to throw in some trig equations? Through the generic heading of "skills" I establish the ability to dig through the whole back catalog. Learning derivative rules in October is great but they need to stick around until April. Everything in the curriculum has to matter.

Our Calculus trainer implemented this through daily pop quizzes. Anything is on the table for these. I don't agree with that method, but the idea has merit.

Confidence is really the enemy here. For whatever reason, our Calculus students buckle under the pressure. I'm hoping frequent exposure to the AP format and forcing them to commit certain things to the deep layers of their memory will help them feel good walking into that exam.

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AuthorJonathan Claydon
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It's been a year. Time to recap the best math professional development game in town. In summary, I had a fantastic time.

Exactly. To the recap!

Sessions

Algebra Two

Earlier in the year in the speaker proposal phase, there were requests to hear about my kooky Algebra II idea from last summer, now that real kids had helped me troubleshoot it. I submitted it as an independent session, but it worked better to integrate it in the general purpose Algebra II session. And so, I became partnered with Glenn. It became pretty evident that he and I had similar experiences hating the traditional Algebra II approach. Our theories matched up nicely. The plan was to discuss the universal concepts, what that means for curriculum structure, and some ideas for creating interesting and science based modeling lessons.

I thought we were going to have some room for discussion, the original draft called for a "help me with this topic.." and a "My Favorites" type deal. But it became apparent that most of the people in the group had never taught Algebra II before and were hungry for resources.

On Day 3 we were fortunate to have Eli from Desmos drop in. While Glenn was discussing his super clever modeling activities I was asked what kind of modeling I've done. The only thing I've done is Penny Circle, so we talked about that. And in 10 minutes I found myself instructing a group of people through Penny Circle in front of the guy who helped build the thing and let me beta test it a year ago. Mind. Blown.

iPads and Notebooks

I lead two afternoon sessions. I walked a few people through Inequality Explorations and Photo Sharing. Attendance was low, but we had a good time. It was a murderer's row during that time slot, so I don't blame people for skipping, especially if they aren't in an iPad environment.

Friday was the notebook session. It was well attended. It you're curious, I used this year's notebook write up as the framework for the session.

Keynotes

Man, these were killer. Steve Leinwand was fantastic. I was ready to start the school year 30 seconds after this talk was over. Dan Meyer discussed some nitty gritty details about who contributes to the math teacher twitter discussion. It flirted with being a little inside baseball but it touched on an issue I noticed last week in an AP Calculus workshop: there is clearly an "us" and "them." And we should probably call each other? Eli gave us the Desmos State of the Union and briefly toured the new interface for us and gave hints about things that will be ready for the school year. We were able to play with their latest lesson, Central Park, a few days before it went public.

Others

Because I lead a morning group and had two presentations of my own, I didn't attend much else. I contributed a tiny bit to Justin Aion and his discussion of 180 blogging. I enjoyed listening to the discussions that popped up during Nix the Tricks. On Saturday Hedge let us play with all sorts of fun toys, and my group delved into the finer properties of a marshmallow gun. Then we went to the planetarium (yes, the school had a planetarium) and I passed out in the dark.

Conclusion

You could call this conference Meet Your Heroes. But the rockstar vibe is incorrect. It's more like, here's every great post you read this year, on display live and in person. Last year at TMC13 was a lot of fan girling by me and generally being exhausted from the great energy. This year I had the explicit goal of having conversations with a checklist of people. All of them happened and all of them were amazing. It was humbling to meet a lot of people who knew who the heck I was, and it was cool to meet all of you! Please, e-mail/tweet me if there's anything I can help you with.

It's easy to feel intimidated at this thing. Everyone is so crazy smart and cares so much about their work. The Saturday night EXPLOSION of conversation in the lobby made that clear. I had many moments where I was just impressed. Then you watch them eat a cheeseburger, and you're like "hey, I eat cheeseburgers." Then you calm down.

TMC is about bringing together people where there is a base line assumption: I like teaching, I have scoured the internet to be better at teaching, and I want to share how excited I am about teaching with other people. Think about this when Colleague X starts whining about children any day now.

Until we meet again in Los Angeles. I can't promise I am not going to FREAK OUT when Mr. Stadel walks in. Just saying.

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AuthorJonathan Claydon
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All summer it's been looming. Last week it was finally time to do something about it. I attended a training for new/newish AP teachers. And now, a collection of ideas that have resulted.

AP Community

  • Our instructor for the week knew what she was doing. A teacher of Calculus AB and BC for many years, and with a history of establishing successful AP programs from nothing. A task similar to what I have.
  • The most beneficial aspect was the fact that our instructor has been an exam reader for a number of years and gave all sorts of insight on just how brief an appropriate mathematical justification can be, and how the AP exam is way easier than it looks.
  • The AP Calculus community in Texas is full of all sorts of resources. The mathematics chair at the University of Houston started an effort to better support the AP communities in the state by starting Houston Area Calculus Teachers. It's a dual effort to support the needs of high school teachers and show college professors that yes, they are partly to blame for 50% failure rates.
  • The AP Calculus community in Texas is full of rock stars in its own right. It shows you how impossible it is to find every quality teacher out there. You would think the likes of TMC and the MTBoS movement would bring everyone out, but I would imagine that for every person attending TMC, there are 50 quality teachers who have never heard of it or any of the people who go.
  • AP curriculum is mired in the traditional. While covering the entire Calculus AB curriculum in four days, our instructor offered hints of good strategies. She was not a "here are the rules, memorize them" type person. Lots of leading to have the students develop theories on their own. Simultaneously, there were a lot of over-copied handouts and discussions about nitpicking students on points and being stingy with re-assessment. We did two less traditional activities (some f and f prime matching, 3D solid construction) that BLEW EVERYONE AWAY as I sat there thinking "math class can be like this all the time you know."

Structuring

  • Running a Calculus class is going to have to be different than my recent approaches.
  • The scope of the curriculum is really narrow when you think about it, and after scanning it many times it seems like it's organized well.
  • Homework is going to be necessary, but not "1 hour a night" necessary.
  • Students are going to use two notebooks I think, one for notes/practice/activities, and the second for official assignments.
  • An AP modeled exam is going to happen every six weeks. It seemed pretty clear that free response questions are where you really learn what a student knows.
  • Desmos and TI are going to have daily showdowns. TI skills are necessary for the minimal calculator sections of the exam, but Desmos will be there to make them modern mathematicians. Graph manipulation skills should be universal, regardless of interface.
  • My SBG system needs to be altered significantly. Calculus doesn't seem to like being constrained into an easy to manage topic list (and the material only lasts until March). Given the nature of the AP Exam, I want flexibility to hold students accountable for material at any point in the year. Conceptual thinking is such a major focus too, and that needs to be assessed in a way that works well. I think I know what this looks like, but I haven't finished the prototype yet.

An exciting future is in store. Expect this course to be featured prominently here this year.

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AuthorJonathan Claydon

Not long ago I mentioned how beneficial a 180 Blog can be professionally. Personally, it has the side effect of giving you tons of action shots from your classroom throughout the year. Every so often you'll hear someone mention that student work outside on the wall doesn't tell the whole story.

This year I combed through my photo collection to make a fun poster.

I picked out 80 of the best pictures (and secret selfies the kids thought I wouldn't find) from the collection and assembled them on this 24" x 36" sheet. It took an hour or two of fiddling in Illustrator. Printing it cost about $40. You could do a cheaper version by running off the 4 x 6 prints and taping them down (about $20), but that would take up a lot more space. These photos are 2 x 3.

It looks amazing in person.

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AuthorJonathan Claydon

Summertime means maintenance time and a chance to refresh the iPad fleet based on what worked last year and the types of tasks that have been worthwhile.

Let's run through how our finalists were selected.

1. Google Drive

Used for getting material off the device and viewable on a computer. Each iPad is logged in to a generic Google account I've made for this purpose. Works well.

2. Google Docs

Drive no longer has the docs and sheets components included. Google chose to make them separate apps. When you sign into Drive with an account, these two apps will use that same information, no need to login twice. Though I don't use them much, our students save all their English/Social Studies writing to Drive, so letting them sign in on my devices is a quick way for them to print an essay or whatever.

3. Google Sheets

Replacing Numbers. Though I've yet to find a good use for a spreadsheet that can't just be done with a pencil.

4. Adobe Ideas

Solid sketching app. Now that Desmos supports image overlays I don't need the layering capability of SketchBook Express. Ideas can export to Drive whereas Sketchbook could not. Having them both on the device was confusing.

5. Pages

Useful here and there. Some projects were accented well by students typing and printing headings from Pages. It's also a good way to put multiple images on a sheet to save paper when printing. If you print an image directly from Photos, it will use a full page no matter the physical size.

6. TI-Inspire CAS $29.99

Only here because I picked it up for $5 a number of years ago and the calculator function replicates a TI-89 rather well. We'll see if it sticks around for version four.

7. PCalc $9.99

A scientific calculator with a long development history. Started life as a Mac app and spawned an excellent iOS version. Early returns indicate large class sizes, so I may not have enough TI-84s to go around. This and TI-Inspire can help fill in the gaps.

Not a lot of flash. Simple apps that support simple workflows. No electronic flash cards here.

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AuthorJonathan Claydon
TagsiPad