COVID19 – A Day in the Life

This is a Day in the Life of post in the 6th week of our Corona Virus School break. I wrote a previous Day in the Life post six years ago and it can be found here. Here is the #mtbos call for similar posts, also from a long time ago. The idea for this post is to record what it’s like to be a teacher in the middle of this craziness, specifically a teacher with young kids at home.

Background: I am a math / computer science teacher at a suburban high school in upstate NY, I’m married to a elementary school librarian, and we have three kids: Ca, a second grader, S, a kindergartner, and Ce a two year old. We acknowledge that we are quite privileged, we have a very comfortable home, both have jobs that are flexible, and our kids are fantastic and mostly compliant.

Wake up 6:30, boys (Ca and S) up at 7, Ce up at 7:15. This is later than before the craziness, shifted about an hour back. All three kids downstairs, put away clean dishes, make coffee. My wife sleeps in, she’s naturally a night owl, and I’m a morning person. Boys start off playing nicely together, Ce needed to “help” me. Then boys start rough housing, but I’m making breakfast and Ce is playing nicely, so a quick talk and they relax just enough so I can finish making breakfast.

Kids are eating (with much loudness, but eating none-the-less). I start by writing down the school schedule for boys on separate whiteboards by checking their separate clever.com, google classroom, and google doc schedules for the day. Full schedule for both, probably between 2 to 3 hours of schoolwork each.

Respond to one email from my student before interrupted again.

My wife comes downstairs with Ce (I sent her upstairs to “help” my wife get ready) and we go over the schedule for the day, what meetings, when? workout?

We get kids started on schoolwork, I’m sitting next to Ca who’s doing reflex math (practice of his math addition and subtraction facts), S on other side doing math review sheet, but needs to be read every set of instructions for every problem. 

Write DM to Michael Pershan egging him on to do this challenge, get interrupted by all three kids a total of five times for the first DM, three times for the second DM.

Wife with Ce eating breakfast (finally, this is the third attempt). I have a 9:45 meeting starting up, so leaving the three kids with my wife. I go upstairs to quiet(er) spot and have a PLC meeting for 45 min. Not too much new information.

After meeting, try to answer another email, but I hear a commotion downstairs, so I go down to help wrangle kids. Wife has meeting currently going on, Ce is in room but playing happily, S is working on raz kids (online reading platform with “quizzes” at the end), but when I check on him was actually done and was just looking at himself in the selfie camera, and Ca is independently reading on couch. They have more stuff to do on their list, and I tag off kids with my wife and she goes upstairs to continue with her meeting, get Ca started on three digit + and – and give two piles of coins to count up. I made up some story about how I earned this much money and he earned that much, so how much more money did I earn? If we go in together can we get that awesome LEGO set? I’m skipping the assigned lesson and doing my own to combine two of his lessons, three digit addition and subtraction, and working with money. Teaching my own kids math is a great part for me about this break. Love it. Get S started on his A-Z scavenger hunt (needs to write down items from the house that start with the letters A to Z). Ce wants to be read to, threatening a full meltdown, so I start reading to her and Ca is calling from kitchen that he’s done, and throws out some sum, but not sure if it’s correct. I ask him to put change in jar and bring whiteboard to me…

(12 min later)

… he does.

Subtraction is good, its actually a 4 digit minus a 3 digit and has borrowed from the first 1 to the second one, 1182 – 561 or something. Get to talk about how the “11” represents either 11 hundreds, or 1 thousand and 1 hundred. Show him way to think about it without borrowing from the 1 in the thousands place to the 1 in the hundreds place (hence getting an 11 again). We move on to the addition, can we afford that LEGO set? He adds correctly in his head, and I ask how he knew it, and he explains nicely. I’m impressed. 

Clearly boys need to go outside and burn off energy. This is yet another spot where we’re privileged and lucky. We have a nice chunk of land and the weather is nice. This would all be so much harder in November / December. Ca wants to use his rollerblades (for the second time ever, got them last fall) so I run out to garage to get some safety equipment. 

Get him all dressed, skates don’t fit, but he’s out and skating. My wife comes down and can help out with Ce. I get my rollerblades and skate around too. S very jealous, but Ca takes skates off 10 min later because his feet hurt, so now S is skating around in those skates, and Ca is happy too. Meanwhile, my wife and Ce are upstairs going through clothes for Ce. Ce comes outside and is somehow occupying herself. My wife comes outside, and I run inside to make lunch. Call them inside to eat lunch, put on a Binging with Babish video for them to watch while eating lunch, it’s about homemade ice cream sandwiches. This is another great thing about this break, we love to cook anyway, but there are so many great resources online to support them learning how to cook too. We then set the kids up for their respective quiet times, each in different rooms. My wife gets a workout in and I start writing this post. At 1:30, I have scheduled office hours, so I login but nobody shows up. Office hours started off quite a bit busier at the beginning of this weirdness, but has been very lightly attended lately. I have plans to see their lovely faces more often, so I’m not that worried just yet. Good news, it’s relatively quiet, so can get some school work done. I go to a currently running desmos activity for PreCalc and continue leaving feedback to activity.  (while during quiet time, I hear dropping of … something from Ce room, doesn’t seem dire, so ignore). Two minutes later she’s called me into to fetch a book or something.

Leave more feedback in the desmos activity (love this feature).

Wife gets back from workout, immediately starts work on her stuff after she checks in with S to make sure he’s not actually napping, and I check in on Ce and Ca to make sure they aren’t actually napping. Ca and S have dropped their naps a while ago, and Ce would nap at her child care place, but has dropped it on most days. We encourage them not to nap (unless they seem super tired) because if they do nap, then they’re up and awake until after 9, and we just need some time to ourselves!

Check deltamath for PreCalc and Alg2. For the PreCalc weekly assignment, about 1/3 have started and completed, 2/3 haven’t started yet (it’s Thursday afternoon, they have until Sunday night)

For alg2, 10% completed, 20% started, 70% haven’t started yet. I’m sensing trouble here.

Write tweet to Zach (founder of deltamath) wondering if it were possible to see how long people have spent on an assignment because it’d be interesting to get an idea about how long they’re spending on the assignment because it’d be nice to know and I’m curious.

Check classroom for other alg2 assignment, it’s a google doc set of questions on some fantastic Stats videos, Against All Odds. 2/28 turned in, check those two assignments, they’re ok. The technology is failing us here because it requires graph paper to make a useful box plot, especially if you want to compare two box plots, but google drawings does not make any of that powerful or easy. 0/28 turned in from other section. Not time to panic yet, but it’s not a good sign that so few alg2 students have started the either of the two assignments that I’ve assigned this week.

Ok, move on to another class, Computer Science Discoveries. Only 5 of 15 have started assignment, write a reminder post on classroom to hopefully get some more stuff in motion.

Ok, move on to the last class, App Design. They’re working on a big app of their own design, will have several weeks to work on their app, so they fill in a journal to buy prednisone online UK keep me in the loop for their progress. Journal entries are very spare this week, uh oh, write reminder comments for all but one student. It doesn’t mean that work isn’t getting done, but I have no insight to that, I can’t see what their actually working on, I have to only rely on this document. Make mental note to check on this tomorrow.

Start planning for next week for all four preps. I normally have three preps, but took a fourth prep this year. Yikes, that was a bad bet, four preps have made life significantly more difficult over this weirdness, my two computer programming classes are singletons, so nobody to bounce ideas off of.

Precalc H – overarching plan, design deltamath work, (interrupt by Ce), design book talk on chapter 1 of a book that we’re reading together, Infinite Powers, (interrupt by Ce who wants out of quiet time, so I lie and tell her 3 min, but will hopefully be more like 15).

Brainstorm for how to keep (get?) kids engaged in all my classes… coming up a bit blank, but there’s a wonderful tweet by Avery Pickford that’ll help.

Meanwhile gather yet another fun idea, this time from Bowman Dickson:

Ok, it’s 3:30 and quiet time is done. Here’s the sum total of the work that I’ve gotten done today:

  • 1.5 hours of meetings time today (and only half that with actual people)
  • 1.5 hours of giving feedback, checking up, writing emails
  • 1.5 hours planning for future

BUT, much of this time is interrupted by the kids, or might get interrupted by the kids. I relish having a set amount of time to get work done, but I can’t do the same kind of work if I might get interrupted. (2 min after this sentence is written, a series of yells and “owws” put me back in action)

Another thing that makes this all difficult is that one of us is on duty with kids at all times. We also are doing the best we can with this all, so it’s pretty much one parent with all the kids from 8-3 or so, so the other one can work. Quiet time is the only chance that both of us doesn’t have to be involved with kids, but even then, many many days there are interruptions from one of the children every 10 min over the two hours of quiet time.

The next set of things is actually pretty normal for what happens on a usual day. Kids go outside and play, I get a workout in (my wife and I have been good about supporting each other with finding workout time, and I think that’s a big reason that we’re doing ok), we make food, kids eat food (sort of), bath time, reading, and everyone is quiet at 8pm. That’s a big block of time, 4-8pm, but there is really no space to do anything other than just doing life (and no time for anything related to school).

After 8? BURNED OUT. We’ve been watching different TV shows, some old, some new, some trashy, some quality. It’s our first time to talk to each other without a child interrupting all day. We love it. It’s something to look forward to every day.

I’m writing this all as sort of a stream of conscience journal entry so I can remember what it was like trying to “teach” in this weird time with little kids at home. I don’t even have it bad either. I know teachers with little kids at home but only one parent. I know teachers at home whose spouse has lost their job. I know (lots) of teachers who live in a city with small kids, and finding good outdoor spaces is very tough. Not to mention families who have actually GOTTEN SICK. Yikes. My grass is super green right now.

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COVID19 – Meetings with Students

Once again, here’s a lightly edited twitter thread about my experiences teaching in the COVID19 craziness. This is the fifth week that we’ve been away from students.

This week I asked the students to attend a small group (<=5) 10 min meeting with me to talk about our past and our future for the class. Since we’re asynchronous, this is the first time that I’ve “required” them to go to a google meet. I assigned no other work this week. There were three days of google meets scheduled, this took up pretty much all the time that I can put forth for school work during the day (with the other meetings and such also scheduled). You can check Zoom App Altarnatives here.

Of my ~100 students, ~70 showed up to the pre-scheduled meeting. At the end of the day I sent out an email to the students who missed and if they responded back then I gave them another time to meet up. This stretched the meetings out to a fourth day. That covered ~20 students who were successful on the second try. At the end of the week I sent out emails to the last ~10 students, parents, (and special ed Ts) who didn’t respond to my emails and didn’t get any of the info that we talked about in the meet. Will call home next week if there is still no word.

It was great talking to the students, some of them for the first time since March 13th, even if it was quick. I write all this to talk about how much effort this relatively small payoff is costing me. I didn’t assign any work this week, I didn’t run any office hours.

I heard about their lives, how they’re working extra hours because they can make some extra $ and help their family. How they’re babysitting for their siblings. How they’re babysitting for health care provider’s kids from the neighborhood. How they actually miss school. How they’ve shifted their awake times back several hours (median amount is probably ~4 hours). How they are getting wildly different amounts of info from their other teachers, order prednisone for dogs online some had heard about the new grading policies from all their teachers, some none. I had several other meetings for school this week, I have a whole bunch of prep that I’ve done for next week (still not done), and I have some grading to do, as well as set the Q3 grade.

This was worth the time and effort. I write all this as confirmation about this teaching job being WAY harder now. This tweet absolutely nails it:

AND (!!!!) I teach mostly juniors and seniors at a relatively well off suburban school. I can’t imagine what it’s like at other districts.

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COVID19 Update

Hello forgotten blog. I’ll go back to forgetting about you, but I wrote a lot of text into your flashier cousin, Twitter, and here it is copied, pasted, and lightly edited.

I’ve been asking the students to fill out weekly feedback forms. What is going on? Do you need anything? What is working? What can we do better? etc.
Here’s the form sent out a couple of days ago.

Takeaways:

  1. The kids are mostly stressed or bored. Many specifically mention being stressed AND bored. Not many are loving it (mostly a duh, but it’s interesting to see that there are some who love it.) Some are anxious and are worried about the health of their family.
  2. They self report having a LOT of work. I don’t know if the teachers at our school (including myself) are having trouble portioning out the appropriate amount of work, but this kind of agreement is substantial. (5 is tons of work, 1 is very little)
  1. The students who are responding* don’t need much from me. They have pretty much everything they need. *But they aren’t all responding. So a lot of effort needs to be put forth by me to make sure those who aren’t responding are doing ok. This is not a trivial amt of work. 
    I’d say a good 1/4 of my time spent on school each week is spent manually tracking down Ss, and why they haven’t been connecting, and how I can help. Sometimes their internet is out for a week. Sometimes they were grounded and had no access to internet (not kidding). 
    Sometimes I’ll email with questions: how are you doing? are you stuck? can I help?
    and get nothing back, but then a couple of hours later I notice that work is getting handed after a week of silence. (????) I’m having a hard time with this whole game.
  2. For the most part what we’re doing in class (asynchronous week long lesson plans, with brief lesson videos, and 2 or 3 assignments given out on Monday and due the next Sunday, and then office hours available every day) is working for them (once again, for those who responded). 
    They like the weekly assignments, easier to keep track of and portion out. They like the office hours (although they are barely using them). They like that we haven’t had synchronous lessons. 
  3. What are other teachers doing that they’d like me to do more of? A couple of the Ss said that they’d want one synchro lesson per week, and although this is a small %, I think I’m with them. 
    That’s about it. This is such a new environment for everyone, that I can’t fault them for not thinking meta enough to know what is working and what isn’t. Seriously. How would they know if something is working besides whether or not they like it?
  4. I love this last question. I get nothing from about half, but the other half is fantastic. I hear about what they’re watching on TV. About new pets. About exercise routines that they’ve picked up. About being nervous about their parent in health care who is now working with covid patients. About being sad about not seeing their friends. About being sad that prom isn’t gonna happen. About how they’ve been practicing their driving and are getting good. About being proud having just finished a long english paper. About wanting me to tell their other teachers to “chill dude”, they have tons of work. About how their family is driving them nuts, but also they’re enjoying their family for the most part. About what they’re cooking. About how they just need a break (despite our spring break being taken away). About how they actually miss school and can’t believe they just typed that. …

    It’s a wonderful field. And since I didn’t make it anonymous like I do most feedback forms, I’ve written a dozen follow up emails checking up based on things that they’ve written in the form. My biggest frustration is getting a small slice of them to engage. They are busy, but I want my slice of their attention. It’s that whole adage, I get 80% of the payoff from 20% of the energy. But to get that last 20% of the payoff, it’s 80% of my energy. I’m left with a zillion Qs that normally drive my classroom but feel much more unanswered with all this change. Are they learning math? Are they enjoying math? How can I improve? Are they learning from and helping others (this one is a certainty – not anywhere near as much)? 
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PAEMST!

This is an update to my previous PAEMST post.

In the middle of October I took a trip with my wife to DC and participated in the PAEMST (Presidential Awards for Excellence in Math and Science Teaching) awards conference for three days. It was a great trip, the 7-12 awardees from 2017 and the K-6 awardees from 2018 were combined into one conference, so with one math and one science from each year and the fifty states plus US territories and the USDoD schools, there were about 210 fantastic teachers involved. Way too much to write up in a blog post, but it was an amazing experience.

The four NY PAEMST awardees. From L to R: your humble narrator (7-12 math), Elizabeth Guzzetta (7-12 science), Marianne Strayton (K-6 math), and Anneliese Bopp (K-6 science).
7-12 Awardees
K-6 and 7-12 awardees
Of course, I couldn’t help but do some math on some really pretty hyperbolas from the lights in the Washington Hilton.

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Mathematic Mistake – Car Talk Puzzler

RAY: Everyone, almost everyone remembers the Pythagorean Theorem. A squared, plus B squared, equals C squared. And there are numbers like three, four and five; five, 12, 13 which satisfy that little equation.
Many hundreds of years ago a French mathematician by the name of Fermat said, this only works for squares. There is no A cubed plus B cubed, which equals C cubed. There is no A to the fourth plus B to the fourth that equals C to the fourth. Etc.
As luck would have it, a young mathematician issues a statement that he has three numbers which prove Fermat’s theorem is incorrect. He calls a press conference. Now, he doesn’t want to divulge everything right away. He wants to dramatize, build a little bit, does he not?
So he gives them all three numbers. But he doesn’t tell the power.
A equals 91.
B equals 56.
C equals 121.
So, it just so happens that at this little impromptu press conference, there are all these science reporters from all the po-dunky little newspapers that are around this town. And one of the guys, one of the reporters has his 10-year-old kid with him, because this happens to be a holiday. He’s off from school. And the kid very sheepishly stands up and raises his hand, and he said, I hate to disagree with you, sir, but you’re wrong. The question is, how did he know?

https://www.cartalk.com/puzzler/mathematic-mistake
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Classroom Top Four – #4 Interests and Interesting Things

Previous entries: #1 Course Evaluations#2 Whiteboards and Furniture, and #3 Teacher Technology Use.

This one is short and sweet. And it totally depends on you. Share your nerdy math things with the students. Please. Students at any level should see how you enjoy the subject that you teach, and how you’re interested in math other than the math that you’re required by your school to teach. I can’t know what you are interested in, but I share a ton of math art with my students. Often it’s things that I’ve created, but that isn’t required. I share some of the best math art things that I find on twitter. A fair amount of my classes have a “oh and here’s something that my nerdy math twitter people were talking about…” moment.

Oh and if you have a twitter account and it’s shareable to your students (no inappropriate things for students), consider talking about it. I don’t have lot of current students who follow my twitter account, but I do have a fair amount of former students who follow me on twitter and while a hundred days go by without any contact, it’s an amazing feeling when they share something that they learned in college and thought about something that we did in class that was related.

Everyone is a fanatic about something. Share that with the students. Many of them are still growing into what they want to nerd out about and you can be part of that.

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Classroom Top Four – #3 Teacher Technology Use

Ok, here we are after a full year between Classroom Top Four #2 and #3. Wow. Good news is that I have more refined opinions on this specific topic, partly because I changed schools and the friction of the change has made me more thoughtful about what I’d want in an ideal classroom.

Previous entries: #1 Course Evaluations and #2 Whiteboards and Furniture

This post is about the teacher use of technology in the classroom. Student use of tech is a different challenge. 

My favorite setup:

  • A projector. Large, clear, bright display on some flat surface on a wall. Large, clear, and bright is so important. Yet so hard to achieve in a school (seemingly). Oh and it needs a remote with a “freeze” button.
  • An Apple TV connected directly to the digital projector. No network necessary (not using the streaming media features at all). HDMI only please, no VGA conversion.  Sounds like a small nerdy request, but it’s important.
  • An iPad with an Apple Pencil. This tablet easily mirrors to an Apple TV that in the same room (neither need internet access for this, technology magic makes it happen, but I’d want internet on the iPad).
  • Notability app. Super powerful and easy to use software for making hand written notes, marking up images, and exporting pdfs to google drive.

Notes:

  • The full Apple setup totally isn’t required, but I think it’s the best current setup. I’ve been happy with an android tablet (that came with a real stylus), some random box to mirror it to the projector, and some app that did a similar task to notability. At each step there were some more hiccups, the mirroring connection was more buggy, the writing app was a bit more janky, and the export to google drive took 8 clicks instead of 3. I’m no expert though, there certainly may be improvements in all these areas.
  • Writing with a real stylus on a tablet is super important. You need to be able to put your palm down on the tablet and have the tablet just read the stylus’s input. When it’s done right, it’s almost as natural as writing on a sheet of paper, but it has so many more benefits compared to paper. Also this is super important for:
  • You need to have the students write on the tablet without thinking. It shouldn’t be a learning curve. You freeze the projector, give a student the tablet and stylus and say “solve this problem for me please” while everyone else in class is working on the same (or similar) problem.
  • No Interactive White Board. Sorry Smartboard/Activboard etc. I don’t block half the room with my projected tablet. I can walk around the room and be present where classroom management requires me to be. I can give the tablet to a student so that they can (somewhat anonymously) share their work.
  • Take pictures of student work and project them. Mark them up and discuss. No need for names, just “here’s some wonderful work that I captured from your class.” You know the kinds of kids that will be all “yo, that’s my work!” and the kids who’d rather be not called out. This gives them that option, and its soooo easy to do this in notability. Plus button, take picture, insert, crop and resize all takes < 20 seconds.
  • Export your notes at the end of every class to a shared google drive folder and make sure the link to the google drive is in somewhere they can find it (best place for me? the about section of their google classroom). Done. Why not? Yes it doesn’t totally capture the class, but nothing ever does, and it’s a great solution for students who miss class, who’d rather not write and just pay attention, etc.
  • Put Monument Valley on the tablet and give it to students who finish a test early and are just mindlessly scrolling instagram or snapchat.
  • Use the Desmos app, or some other app and take screenshots of things that you’d like to mark up in the software.

What am I missing?

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Mathematician Once Removed

This post is part of the Virtual Conference on Mathematical Flavors, and is part of a group thinking about different cultures within mathematics, and how those relate to teaching. Our group draws its initial inspiration from writing by mathematicians that describe different camps and cultures — from problem solvers and theorists, musicians and artists, explorers, alchemists and wrestlers, to “makers of patterns.” Are each of these cultures represented in the math curriculum? Do different teachers emphasize different aspects of mathematics? Are all of these ways of thinking about math useful when thinking about teaching, or are some of them harmful? These are the sorts of questions our group is asking.

Anna Blinstein and Michael Pershan asked us to respond to a prompt so we could have a set of posts for this Virtual Conference. The essay was “The Two Cultures of Mathematics,” by mathematician W. T. Gowers. Gowers breaks down pure mathematicians into essentially two categories based on their beliefs:

  1. The point of solving problems is to understand mathematics better.
  2. The point of understanding mathematics is to become better able to solve problems.

Caveat: I didn’t read the essay in much depth, and I’m sure that I’m purposely misinterpreting his conclusions. That’s ok with me, but don’t go rioting outside Gowers’ door because of this silly blog post.

I find it interesting for Gowers to define the culture of math and hence the culture of mathematicians with the *solving problems* lens. While it’s not an inclusive definition of what a mathematician, I’m ok with that, it’s a good place to start. But am I a mathematician by this definition? I don’t solve novel math problems, I’ve only ever solved problems that someone else has already solved (with exception of something personal, like how long can I make this $20 last at the horse track). Nor do I build theory or structure to help others solve novel problems. I teach teenagers how to use centuries and sometimes millenia old math to solve problems that have already been solved.

At best I’m a mathematician once removed, I teach those who might go on to solve novel problems on their own (although, as far as I know, none of the roughly thousand students that I’ve taught have done so). I don’t think that I’m one of the shoulders that these students are standing on if they become mathematicians, but I am lending a hand for them to boost up to a slightly higher position.

And I’m ok with this definition of a mathematician, it doesn’t bother me much one way or the other. I play with math. I make things with math. I teach math. But I’m certainly not solving new problems or creating structure to solve those problems.

Why am I ok with this? Because when I solve a problem that I’ve never solved before, it’s still new to me. It doesn’t take too much of the enjoyment away from me to know can I buy prednisone over the counter in USA that millions of people have already solved this problem. Likewise, I don’t find it less enjoyable to hike a mountain that someone has already conquered: it’s still a new view for me to take in, a challenge for my body to take on, etc.

I also find a lot of value in solving a problem that someone else has already solved because then I can compare approaches to the solution. When I see a really cool math idea scroll across twitter, I often see if I can replicate that math with some sort of computer program. I’m not doing anything new to humanity, but it’s new to me, and that’s what’s important! Similarly, when we as math teachers can get kids genuinely interested in some variety of math (even if it’s not on the curriculum), we are making a difference. If it’s new to those kids, then that’s all that matters.

 

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Learn to Code through Math #learntocodethroughmath

The #learntocodethroughmath project is something that I created sort of by accident. I see the audience for this project as someone who is somewhat comfortable with using Desmos to create math-artsy stuff with lists, functions, and parametric functions and is interested in learning how to code using Processing. So yea, pretty narrow. But hopefully fruitful and inspiring!

Here’s the original tweet that started things off:

Click on that tweet to see the three tweets in that thread. I’ll add more to that thread as time goes on.

Here is another set of tweets that ignited the project.

(To avoid twitter dying and killing my content, I’ll post the images from those tweets here too)

Tweet 1:

Tweet 2:

Tweet 3:

Tweet 4:

Tweet 5:



Tweet 6:

Tweet 7:

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The Rough-Draft Move

I’m baaaaaaack. My last post on this blog was six months ago, and that’s a shame. I’m shifting my “writing bucks” from the photo180 blog over to this blog. Some posts will feel a little photo180-y, but most will be more “fully featured”. 

Removing friction from the learning cycle in a classroom is super important. Whiteboards, group work and overall positive classroom culture geared towards taking risks and helping each other out can go a long way. Dan Meyer recently blogged about the classroom move of rough-draft talk. Although it was a small change to my normal classroom routine, it paid off quite well. I asked the students to make a rough-draft of a trig graph that we were working on. This was still early days with trig graphing, but after a four minute rough draft session, the students were ready to talk about the graph. Every graph in the room had things to build off of, and every set of students had a productive conversation about what to draw. They were all coming from somewhere positive. This is a classroom routine that I think will stick with me.

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