General Ideas for the Classroom

My First Day, 2018 Edition

I had my first day with kids this past Thursday. We had only 30 minutes with each of our classes, so I went back and forth about what I wanted to do. Some years, I like to get them in their groups and we start right away. I have a compelling question or *something* that starts the first unit, and we charge ahead. When I do this, I’m thinking “I want kids to see what we do every day in class. We do math. We work together. We don’t waste time.” [1] Kids seem to enjoy that. They are usually revved up and excited to start, even though we’re all a little sad that summer is over. (Okay, very sad.) But there’s energy in the air.

This year I decided to do something different. A colleague of mine did this for a class we both co-taught years ago, and I really thought it would be a great way to start this year.

Part I: The Initial Card Sort that Sorted My Kids Into Their First Groups

I said hello for literally only one or two minutes, and then I shared the activity we were going to do for 15-20 minutes. We were going to do a puzzle-y card sort to figure out who was grouped with whom. But in order for the class to be successful, they all needed to work together. I projected a sample card. I said anyone is allowed to use a calculator. But some of the cards might require some laptop assistance. So they had a little laptop symbol on it.

card1.pngSo in this case, for example, I knew almost none of my kids would know what binary numbers are, but using google they could find a converter online that would say this was actually “170.”

Each card had a kid’s name written on back. So each kid got “their” card. And their goal was to find others who were in their group because their cards formed a logical group. Here’s a sample group to show you what the cards looked like and how they link:

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See if you can tell what the link is among these four cards…

I’ll give you a second.

I will reveal the answer in the next line, so don’t keep reading until you are sure you want to know.

Okay, the link is the number “ten.” So 10! is the number of seconds in six weeks. When the kids type those equations into desmos, they will see the number 10 show up. Neon is the 10th atomic element. And “X” is 10 in roman numerals.

You can see why kids are going to need each other and the class is going to have to work together. Because until someone recognizes that “ten” is a category, these all seem very unconnected. But as soon as you know someone’s card represents “ten,” then things like the neon symbol or the “x” make sense.

I’m kinda proud of these, so I’ll show you another:

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The theme? “Pi.” The first one is circumference over diameter, the second is a recipe for pie crust, the third is an approximation for pi, and the fourth is a world record holder for reciting the digits of pi.

(If you want to download my cards, here you go: Group Card Sort! And the explanations are Group Card Sort Explanations.)

I only had allotted 15-20 minutes for this. I had no idea if this would go quickly or take forever. In all four classes I did this in, I was able to get them to finish in 20 minutes but only through some careful prodding/help. If I were a bit more hands off, I could see this easily taking 40 minutes and it being time well spent. But alas, I didn’t. Here’s how I intervened:

  1. After 7 minutes, I stopped everyone. I asked who knew what they had. A few people did.
  2. Throughout the time, I gave a “few” hints where I could, but mainly I was acting as facilitator to help others help each other. So for the pie crust recipe one, I had the person go around asking if anyone was a baker (or I would shout out to the room if anyone liked to bake, and had them come to us).
  3. When someone wasn’t doing anything, I had them go help others. They might have been confused about their card, but they could help others (and get help from others).
  4. Sometimes when a kid “got it” but still had some uncertainty, I would put them out of their frustration and tell them they got it. If I didn’t have time pressure, I wouldn’t have done this, but it didn’t ruin the activity or anything.
  5. After 15 minutes, with my proddings and connecting, kids were doing pretty well. So I stopped everyone and had people who knew what their card represented be quiet. There were always three or four people who were stuck. So I had them share their card or write their puzzle on the board and see if anyone could figure it out in the remaining few minutes. (We wrote the different “solved” categories on the board, so sometimes they could figure out their card by seeing what it might be.) They gathered, talked, and some classes barely finished in time and others didn’t. I didn’t focus on that. For the ones that didn’t get them all in 20 minutes, I quickly went through the explanation of the remaining few cards.

It was really fun for me to watch, and I saw kids really getting into the puzzle-aspect of things. The first time a kid figures out their card and finds someone else with the same thing, it’s just a wonderful feeling. It honestly feels impossible to kids at the beginning. They literally start looking for anyone with the exact same card as them, or if they have a picture they’re looking for other people with pictures. But as soon as they realize it’s more challenging and more interesting, I get to see how they react and what they do. Do they sort of back down? Do they go help others? Do they hope someone comes to them? My big goal was having kids realize they can’t do this alone and most cards won’t tell you what they are so you need to hear about others and help others.

Oh! One big thing. I realized in the first class that kids were just kinda sitting with their cards. So I made a rule that until the card sort was over and everyone in the class figured out their cards, no one was allowed to sit down — not even when using their laptops. This actually got kids up and moving. It was a small thing, but I know it was super helpful to making this a success.

I wish we had time for kids to say hi to their first group and do a little group norm setting, but alas with only 10 minutes left, I had to transition.

Part II: New Years

So I totally saw Howie Hua’s first day post and was in love. It was positively inspired. Often times, people post awesome things they do in their classrooms that are awesome but just not me. When I read this, I felt: “OMG THIS IS ME!” He celebrated new years with his classes. Here’s one of his students’ videos/tweets:

And it really got me thinking. The first day IS my new years. My life doesn’t go in January-December cycles. It goes in September-August cycles! And it was the perfect time for kids to make a new years resolution. They had 90 seconds of thinking to come up with something.

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Then after 90 seconds, I threw up this screen, obliquely referencing the Maurader’s Map from Harry Potter (but opposite-ish) and I had them recite this pledge:

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Then I gave each kid a baggie that I prepared. In it was a super fancy piece of origami paper, a mardi-gras necklace that someone had a zillion of and was throwing them away, and a noisemaker I bought from amazon. It mabye took me 45 minutes to put these all together. But totally worth it. For some reason, I believe that being given your own personal goody bag is way more exciting than having someone pass out necklaces, noise makers, and origami paper individually.

I then handed out party hats too (but those had to be returned to me). I actually always keep a stack of party hats in my office, and when it’s a kids birthday, I give them a hat, candy, and we sing a short birthday song. As I said, this idea of Howie’s fit me!!! Anyway, kids had to write their name and their resolution on the origami paper which I collected. (Later that day, I put them together in a ziploc bag and hung them visibly in the room so this doesn’t become a thing we did but wouldn’t return to. I was thinking I’d give them back to kids after the end of the first semester so they can see how they’re doing on their resolution. But I might have another brilliant idea. Who knows!) As soon as the bags were out, the noise makers were making noise. And that was a lovely cacophony of BWWWAAAPP and BAAAAAAAA noises. (That was also why I had kids pledge to do no evil with what they were given… *grin*)

In any case, I was standing at the front of the room when they worked on writing their resolutions. When they were done, they had to bring up the resolution to me and wait at the front of the room with me (with the necklace, hat, and noisemaker). After 2-3 minutes everyone was up. And then… we took a class picture, all decked out, blowing on the noisemakers and just being amazing. And oh yeah, we also took a class boomerang (which is an app that lets you take a 2 second video and plays it over and over).

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The boomerang was my favorite part because kids were jumping up and ducking down and doing fun things. And I kind of am obsessed with boomerangs. So there’s that.

I think I’m going to get these photos printed and framed, and hang them up in the classroom. I don’t know what to do about kids who were missing  (there were a few) or who transfer in after some schedule change, but maybe I’ll list them missing on a caption instead of some awkward photoshop job?

Our first day together. (I did post the boomerang video and our class photograph on the google classroom site in case any kid wanted it.) [2]

And then it was the end of our first 30 minutes together. I was really happy with how it went. I like the feeling that I left each class starting the year with good vibes. Thanks go to my chemistry teacher colleague and friend for the card sort idea which I made into something my style (with my kind of clues!), and to Howie Hua for helping me make a memorable moment to start the year.

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[1] We do a lot of the logistics things in the following week. They read the course expectations at home and fill out a “get to know you” google form which also asks them questions that require the expectations to finish. And then each day or day, I talk about one or two things I want to be explicit about (like how to write me an email, or that’s it’s okay to go to the bathroom and they don’t need to ask, but they do have to discretely let me know they’re leaving if I don’t see them, or that they need to bring a waterbottle to class because they can’t leave to get a drink).

[2] I just realized this photo could be fun to have up on the screen on parent night, when parents/caretakers come in two weeks to hear me talk about our class.

 

 

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Start Of Year Edition: Even More Things I Want To Highlight From Twitter

A few months ago, I had “liked” so many tweets but I wanted to archive them somewhere so I wouldn’t forget them. So I wrote a post. I don’t have too much time, but I want to do that again. [Update: Okay, I might have spent a few hours compiling this. But I’m so glad I did.]

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A lot of people use four 4s as a way to get kids thinking. I liked this idea of having a sheet and kids using post it notes to fill in the missing ones. It’s compact. I might use the small post-its, and have kids use a different color post-it if they have a different solution than the one posted. It might be good to keep in a public hallway for everyone to work on, or maaaybe in my classroom (if a group finishes something way before everyone else but I don’t want them moving on yet). But four 4s is all over the web, so I might need to change it to 5s or 6s. :)

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Ummm. Oh, okay, @mathequalslove had a tweet which showed she already thought about how to create a first day activity around this, along with amazing facilitation notes. Yay!

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@abel_jennifer tweeted out saying she was going to be bringing math kids on a (multi-day?!) field trip to NYC and wanted to know what mathy things kids could do here. Many people responded, and so she compiled the responses in a google doc. I never take my kids on field trips. I should. (Maybe as a reward for completing the four 4s challenge?!)

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@stevenstrogatz linked to Harvey Mudd’s math department goals. It’s beautiful and shows they worked collaboratively to generate a shared vision. Our department has done this too, though we need to refer back to it and see where our strengths and weaknesses are so we can move forward.

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@mrdardy shared his geometry curriculum with someone looking to explore new ideas for their class. He shared the book he wrote with them [which I highly recommend checking out!]! And in that folder, he has an awesome short paper he writes called “How to Succeed in Geometry.” However it is soooo not specific to geometry. It’s amahzing and most of what he writes is true for my kids also. I should look at this when revising my course syllabus this year!

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@zimmerdiamonds posted a nice open-middle problem that I think I could use this year with my new Algebra II class.

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@Caitlyn_Gironda gave a presentation on making AP calculus more engaging, and she shared her slides, but also a set of folders filled with great activities! Because she’s aweeeesome. I need to look through these before teaching my (non-AP) calculus class this year!

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I love this question. The activity is here. I could see it being used for a first day challenge. I wish there were like 10 of these, instead of just one, with different “levels.” That probably exists somewhere. Ooooh, or maybe after kids do this, they create their own to challenge other kids. This could be a groupwork task, where at first they solve this together… but then the work together to create something complicated that stymies other groups! <3

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I always forget where I can find desmos activities made by other teachers. It’s the desmos bank. The link is here: https://sites.google.com/site/desmosbank/

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@mathycathy posted how she had some students’ desmos projects printed on canvas to hang up in her room. It shows her kids how much pride she has in their work! But more importantly to me, she shared her project, which is kids making a pet house in desmos. The activity builder for it is thoughtful and kids learn about lines just by playing with them! I think I could modify this to add in other kinds of graphs (parabolas, square roots, etc.) for Algebra II.

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@cljreagan posted a problem she used in her precalculus class on the first day.

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I wonder if I could do this for my standard Algebra 2 kids, actually?! Start with them working with whatever approaches they could come up with, individually. Then after a minute of individual thinking, they share their thoughts with their group. Then the group works together. Then finally, graphing! And a discussion about why the graph might look crazy in the places that it does!

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A terrific teacher: is, says, does, does not.

I think I might want to do this for a terrific student also. The teacher I look up to most in my building does something like this as a way to build class norms. This wouldn’t involve the refining and consensus building that she asks for, but I might use it anyway. I could transcribe them into a draft teacher poster, and then talk about ones that might be problematic for me (based on either who I am, what I can do, or things I philosophically disagree with) and be transparent about those things. And then I can have kids look and see if there are anything on the draft student poster and see if there are similar things they want to discuss/refine/change. Then I can create a final version to hang up.

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This idea. It reminds me of something I used to do called “Path to Glory” (which I heard about so long ago and I don’t remember from whom…) where I asked kids to fill out a 10 question True / False test … but they weren’t given the questions. They just had to fill out the answers.

Then they all stood up. And then I read the questions and kids decided whether it was true or false, and then those who got it wrong sat down. And we’d continue on the PATH TO GLORY (the last person standing).

I always incorporate this on the last day of my calculus classes, and the T/F questions are questions about the kids in the class or me. It’s cute, and I think special to me. Because it shows my kids I know them and listen to them, and it’s a community closing activity. (It could be a community building activity too.)

 

 

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@eulersnephew posted a google doc with a ton of amazing quotations about mathematics that he’s been compiling. The tweet thread then led to this wikiquote page with quotations about mathematics. And he linked to a google drive folder that @MrCoreyMath shared with lots of posters of mathematicians and what they work(ed) on (modern and old time-y). He also has a poster with a lot of questions students can/should be asking themselves when they solve a problem or are working on a problem.

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@joelbezaire posted a great challenge. He gives his kids this chart, and asks them what the relationship is between the four variables. Then when kids think they know, they go up an add a line (which then gives more data for kids who might not see it). He created these exercises (called Variable Analysis) and they are here (along with more about how he facilitates it).  pic15.png

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The post of his activity is here. I watched a documentary of the MIT Mystery Hunt, and there was an awesome communication activity in it. Watch this video (11:19-13:50). I think it would be hilarious to watch kids do this.

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This quotation:
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And this quotation:

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@allison_krasnow shared this site with great collaborative activities for students. *Swoon.* *I’m in love.* To whet your appetite, here’s a screenshot of what awaits you:

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Which of course reminds me of Play With Your Math by Joey Kelly and CiCi Yu (twitter for site: @playwyourmath), which I will also screenshot to whet your appetite:

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Sara Van Der Werf does an amazing “name tent” thing at the start of the year (I’ve done it and enjoy it!). But I always struggle in the moment to come up with good questions. @averypickford shares questions he uses for student interviews which could make good name tent questions. The questions he’s going to use this year are:
“What was the last movie you saw or book you read that you really enjoyed or had a lasting impact? If I gave you enough 💰 to live comfortably w/out going to school or working, what is 1 thing you’d do with your time? What is something you’re particularly good at? What do you think is important for me to know in order for you to be successful in this class?”

@algebrainiac1 shares her questions in a blogpost.

@JennSWhite tweeted that she does:
Day 1: If you could be any creature real/fictitious what would you be & why?
Day 2: What is the sure-fire way to lift your mood/spirit?
Day 3: If you could have dinner with any person alive/dead who would you pick & why? What would you eat?
Day 4: What superpower would you want?

@Riehlt says: “”If you had three wishes, what would they be?” I got this from a school phycologist and used it for many years. It really gives insight to what they value and has revealed all sort of things; hardships, illnesses, deaths, body image, family conflicts. A few rich, fame, etc.

@EmilySilman asked kids to finish this “If math were an animal, it would be _____ because _____” or “If math were a food, it would be _____ because ______.”

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Just because cool!

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@JennSWhite posted this picture from the second day of her classroom. A group activity:
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When people asked for more information, she shared the puzzles and the solutions! It was inspired by @nomad_penguin’s post here. And links to Mark Chubb’s post which talks about things to consider if doing activities like this in your classroom.

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@a_schindy posted some posters she hangs up in her classroom about the behaviors/traits of a mathematician (from Tracy Zager’s Becoming the Math Teacher You Wish You’d Had). And, importantly, how she had a conversation about what was on the posters, which she blogged about here.

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@BearStMichael shares his classroom norms and his thinking about how to introduce them/start the year. This is a must read. Full stop.

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Edutopia tweeted a sweet way to end a particularly harrowing or energetic class or challenging discussion. It’s a video, so you have to go here to see it. It’s called “the three As”  (appreciations, apologies, aha!s). The purpose is the reflect on the day and the dynamics. Kids stand in a circle and just say an appreciation, an apology, or an aha moment!

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@Lisa99Bailey posted these pencils she made for her kids. Here’s the original tweet so you can see what she wrote on them bigger. Other people, in the replies, also added “Be Original” and “Be Inclusive.” I think I’d want to do this randomly on a day that had nothing special so it was truly unexpected.

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And @MrsDi, in the replies, had a great idea to spread the love: “Super cool! How about on the next batch you have the kids each write an inspiring message and put all those pencils in a classroom-share location? Or… trade with the classroom next door?”

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@davidwees posted this

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and shared the isometric drawing tool that NCTM has for creating stuff like this!

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@bowmanimal tweeted out a great blogpost he wrote about changing how we think about assessments. It is fantastic. An excerpt:

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Years ago, maybe at PCMI, I also heard of a great quiz idea. Partner kids up to take a quiz. And they have to do it silently, and write notes to each other to help them communicate. They’ve made all their thinking visible for you, and they have each other to rely on. I can’t believe I’ve never done this.

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A number of  years ago, I did a random act of kindness day. We didn’t do content, but we wrote thank you cards to people in the building. I haven’t done that recently, because other teachers have taken to doing that in other forms, and it felt like it wouldn’t be special if I did it. But if I end up doing something like that again, @allison_krasnow shared @MsCummins12’s blogpost about reading How Full Is Your Bucket with her kids. I really liked the idea. I think if I did a random act of kindness day, I might read the kid with books, have a discussion, and then have kids plan random acts of kindness that aren’t thank you cards. What are ways we can be kind that takes a different form? And then their homework will be to actually execute those acts of kindness.

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@HankReuling posted this great puzzle (a sangaku!). It took me a page of work to solve. But then I saw someone replied with three lines of work. But that didn’t take away from the sense of accomplishment I had! Have fun playing with it!

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@DavidButlerUofA posted a display / game he does with kids called “Numbers and Letters.” I had seen the British show Countdown on youtube on which this is based. I love this as a display, and there is a random element to it which is eggggselent!  It might be fun to get a moveable whiteboard to the front entrance where we have this up, and encourage caretakers and kids alike to engage (and the younger kids can take a short in-school field trip to work on this together as a class). Maybe have a jar of starbursts for anyone who contributes an answer?

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Sara Van Der Werf @saravdwerf compiled all her week 1 activities here. I’ve done some of them and am a fan.

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Look at these. I’m in love. From @solvemymaths (post, post, post, post).

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@rwhite_teacher1 created “extension cards” for kids when they have finished early. The google drive folder is here. I don’t quite know how I’d use them in class, but I like the sentiments. It might be more for me to remind me about ways I can ask kids to extend their work.

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This is one of my favorite @benorlin comics. I want to show it in class early on.

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A public WoDB bulletin board space!

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And, in case you were wondering, there are actual fancy posters you can buy too! My department head just ordered them for us!!!

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@rundquist wrote “Don’t just ask what they learned, ask what they unlearned.” It’s a great exit ticket question.

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I’m teaching Algebra II this year and I remember how this vocabulary in particular used to be tough for kids. The only change I might make in this is not have the equation equal 0. Kids like to set everything to 0, and that’s crazy. I don’t want to reinforce that.

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@davidwees posted a neat set of pictures to think about exponentiation and logarithms, using the Connecting Representations instructional routine I learned in my TMC17 morning session. To see the images/tweet, go here.

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@glennwaddelnvhs posted a google doc compiling all the great exit ticket questions that people have come up with!

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@TracyZager tweeted a 2-page PDF of great questions to help kids utilize their own intuition when problem solving. A random snip of that PDF:

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@mpershan tweeted about using Anna Weltman’s Loop-de-Loops! in class. I’ve always wanted to do that! It’s a great exercise in generating mathematical questions. His class came up with these:

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And AMAAAAAZINGLY, Lusto created a beautiful interactive webpage for this.

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Fin.

Desmos Pre-Conference 2018 Recap

This is a quick blogpost that I’m using to recap just some of the information from the Desmos Preconference before TMC18. I was dealing with some other stuff when I returned from TMC, and then I had to take a short few-day jaunt to see my parents/aunt/uncle. Now I’m finally home and starting to do things like write college recommendations and think about my new class for next year (Algebra II). But I’m afraid if I don’t take the time to reflect on some of what I took away from the conference, I will not end up using it. But at the same time, I feel like it’s so much stuff that to do it comprehensively, it will take too long and that’s keeping me from starting. So here’s my pledge: I’m just going to do what I can, and not worry about being incomplete, and then I’m going to #pushsend.

Tonight, I’m going to #pushsend on the desmos preconference day.

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I went to one session, led by Heather Kohn, David Sabol, and Mary Bourassa. These three desmos fellows shared how they use Desmos in the classrooms. Here are a few gems:

  • Heather often creates handouts to accompany activities. For example, for Will it hit the hoop? she has a spreadsheet for kids to fill in (e.g. “Predict, Screens 5-11” “Analyze, Screens 12-19” and “Verify, Screens 20-26”). 
  • I shy away from doing cardsorts (or even short activities) on desmos because I tend to have some groups finish way earlier than others. But this would happen even for paper cardsorts! So here are some tips. First, just so all groups start at the same time, you can pause the activity on the first screen (which you can have be an introductory screen). When everyone is ready and logged in, you can then unpause the activity which allows everyone to start at the same time. More importantly, you should create a slide after the cardsort/activity which links to another activity or has some extra practice for those kids to work on. And for extra fun, you can have this slide be a “marbleslides challenge.” But one tip is to use the teacher dashboard to pace the activity to the slide before the challenge, so that you can make sure kids aren’t rushing. (You can check in with the first group done and ask them a few questions to make sure they’re getting things.)
  • You can do a Which One Does Belong on Desmos (example: go to https://student.desmos.com and enter 5CK W7N). Have kids vote on which one doesn’t belong. You can then display how they voted! If no one picks one, after they finish and you discuss, you can have them go back and everyone has to pick the one that wasn’t picked… and then explain why that last one might also “not belong.”
  • David was worried about how kids will access desmos activity knowledge later. There’s a lot of digital work and verbal work in class, but then things aren’t archived. So here’s a great example of how David deals with this. He used Andrew Stadel’s “Math Mistakes with Exponent Rules.” On day 1, he used the first day PDF to have kids work the problems in class. Then on day 2, he screen grabbed the second day PDF and made a desmos cardsort (sorting them into true/false) and used the dashboard to showcase wrong answers and have class discussions. Also, after the cardsort, he had a screen that said: “Make a FALSE statement that a classmate may think is actually TRUE.” Then that night he created — using what kids wrote for their false statements — a paper copy with all these FALSE statements (sometimes there’s a true statement that a person wrote!) where kids had to identify the errors!
  •  A great question in a desmos activity is to show a lot of work/visualizations/etc. and write: “What would you tell this student to reinforce what they know and correct their errors?” If the student work has some nice thinking and some subtle not-so-good thinking, this often will lead to solid class discussions.
  • Mary uses Desmos occasionally for assessments. There were only a few questions, but they involved deeper thinking (e.g. given a graph of part of a parabola, can you come up with the equation for the parabola?). The presenter asked her kids to do all their written work on paper handed out for the test. Yes, students could revise their work/answers based on what they saw on Desmos, but that had to be reflected in words/notes/changes on the written paper. So a student guessing-and-checking on desmos with no supporting work will not garner credit. (For students who finish early, put a screen with marbleslides challenge.) One big note: make sure that at the end of the test, every kid goes to a blank last screen, and then PAUSE the activity. That way kids can’t come back and rework problems or show other students particular questions on the assessment.
  • Rachel K. (attending the session) said that she often had kids project their laptops up to the airplay and lead the class through something they found/built/figured-out on the Desmos calculator, or will have one kid lead a desmos activity on the big screen.
  • I often worry about how to lead effective discussions on activities that kids are doing. For pre-existing Desmos built activities, there are “teacher tips” that help teachers figure out what to focus on and how to facilitate conversations. But more importantly, whether Desmos built or random-person built, every activity has a teacher PDF guide (Click on “Teacher guide” in the top right hand of the screen for the activity.) You can print this out and use this to help you come up with a specific list of things you want to talk about, and stop at those places (e.g. questions, places to pause, etc.)
  • After the session, I talked with Heather about this feeling I had when doing long activities with Desmos. Although I was constantly checking the dashboard, and walking around listening for conversations, I often felt useless and bored and like I was doing something wrong because I wasn’t … doing much. She let me know that she also feels this, but that’s part of it. Letting kids engage. But I realized that some of my best classes (without desmos) have me circulating and listening but not doing too much beyond that. I was “being less helpful.” So I think I just have to make sure that when I’m not doing much, it’s because kids are doing good things mathematically and conversationally, and that’s because I’ve orchestrated things to be that way.

As an interlude to this wall of text, here’s my favorite nerdy math picture from the day.

20180718_141146.jpgYes, indeed, you see a 3-4-5 right triangle, and a visualization of the oft-taught “Pool Problem.” In Starburst. My kind of math manipulative!

For the remaining two sessions, I worked on playing with Computation Layer and refamiliarizing myself with it (I spent 3 days earlier this summer spending huge swaths of time on this… a huge shoutout to Jay Chow who helped immensely with this). Having CL experts in the room and granting myself three hours to play with CL was amaaahzing. I first reacquainted myself with some of the basics (a lot of which I had forgotten, but it came back fairly quickly) and then I decided to start trying to “desmosify” this calculus optimization activity.). I didn’t get too far in, and so far this is no better than the paper version of the activity, but I am proud of what I was able to do with my CL chops! (You can see what I made here.)

The keynote session was given by Robert Berry (the new NCTM president) and he gave an overview of the recent NCTM book Catalyzing Change (which I have bought but haven’t yet read!), talked about some big picture NCTM things (advocacy, membership, financial health), and then told us what has been happening on the ground level. He ended his session talking about technology and what excites him about that. He said that “Technology that supports and advance mathematical sense-making, reasoning, problem solving, and communication excites me” and that “Competence is about being participatory in mathematics – with each other, with the teacher, and with the mathematics.” He then said technology can be used for good or evil based on how technology affects the following things in the classroom: 

  • Positionality [how students engage with each other, their teacher, the curriculum, the technology, etc.]
  • Identity [how students see themselves]
  • Agency [how students present themselves to the world? how do we create structures for that to happen?]
  • Authority [“shared intellectual authority”]

His latest NCTM President’s Message is precisely on this. Also, Robert is a totally awesome guy.

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That’s me on the left, him in the middle, and friend and TMC keynote speaker Glenn Waddell on the right.

Lastly, Eli (founder of Desmos and super nice guy) showcased a new desmos feature for teachers: SNAPSHOTS. You can read about it here, but what I love is that it allows teachers to facilitate discussions more thoughtfully in line with the 5 practices. (I’d love any help finding or coming up with problems at the high school level that work well with the 5 practices… Most examples that I’ve seen are at the middle school level so it’s been hard to wrap my mind around how to find/create problems for a precalculus or calculus class that might make this approach work super well.)

My favorite slide of his was:

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Eli keeps things simple, which allows me to read slides like this and think: “wait, in what ways does my teaching do that?”

And with that, it’s time to #pushsend.

 

Senior Letter 2017-2018

Every year that I’ve been teaching, And at the end of each year, when I start growing wistful (but also a little bit glad to get them out of school because their second semester-ness starts to take over), I write them a letter which I give to them on the last day of classes. The letter usually always says the same thing, hits on similar themes, but I write it from the heart.

Sometimes I remember to post it on my blog, sometimes I don’t. This year (obvs) I remembered!

Even though they got to be a bit punchy at the end of the year, I’m kinda missing my seniors right now.

 

A Secret Handshake

 

In one of my Advanced Precalculus classes last week, I saw a group of three students successfully figure something out. To celebrate, one group member taught his group how to do a three person handshake which was elaborate and awesomesauce.

Yeah, it moved me. Those are the things that get me.

Because what it showed me, in that moment, was how solid a group that was. They came to a collective understanding. They were having fun together — being wonderfully silly. And they were celebrating their success. It was a sign that the group had gone beyond being three people working together; they had created some sort of synergy. It was a lovely instantiation of that synergy.

Sadly for them, two days later, I changed groups. (My groups stay with each other for 6-7 weeks, usually.)

But inspired by this group, I changed what I did when I had kids sit with their new group members (in all four of my classes). They all said “Hi!” but then I dramatically and mysteriously had them hush up, and I showed them the first 11 seconds of this video.

They were entranced. So I asked if they wanted to see it again. They did, so I showed them the first 11 seconds again. They all thought they were going to learn that handshake. Fools! FOOLS!

Instead, I told them about how amazing it was to see this precalculus group develop their own handshake. I shared with them what that handshake meant to me, an outside observer… what it said about their group to me.

And then… I gave kids 3 minutes to develop their own group handshake together. The only thing I said was that the handshake had to involve everyone from the group. (Of course, this took 4 minutes, but saying you are giving them 3 minutes gets them working together very quickly.)

Now I’ll be honest. I thought this could go either way. I thought kids might be hesitant to do something corny/dorky like this, and it would be a huge flop. But in all four classes, every group did it. [1] And they were doing SUPER COOL THINGS including pounding the table, incorporating fistbumps, incorporating dance moves, and creating beautifully symmetric hand formations. It was super fun to watch. And some kids wanted to share their handshakes publicly, so those who were comfortable (and that was most of them) demonstrated their handshakes for the rest of the class.

What is going to happen with this?

I don’t know. Maybe nothing. At the very least, it was a great quick way to get kids working as a team on something when switching groups. And if the group can use it when celebrating a collective success, it will make visible and public what fun and friendly groupwork can look like. And that might just inspire other groups to do the same. I like an atmosphere where kids are propping each other up, patting each other on the back, and see themselves working as a team. And the more structures that I can develop that promote this [2], the better.

 

[1] Okay, one of my calculus classes was a little less enthusiastic as the others, but they all did it too! I didn’t get the same JUMP RIGHT IN feeling in all groups I got from the other classes. Some groups had it, but not all.

[2] Like the hotel bells

The DIY Math Curriculum: Simple tricks to make creating your own material feel less onerous

Math teacher friend Bowman Dickson and I presented a session at NCTM in Orlando on Friday. I have never given a public talk about math teaching before. Well, that’s not precisely true. I’ve led a couple of sessions at Math for America on the online math teacher community known as #MTBoS (as part of a larger thing that MfA was doing for new teachers). And at TMC, I have led some workshops. But this felt more official. The program committee for the Orlando meeting contacted me about presenting, and it wasn’t a workshop but a talk. And upon advice from a friend who said “you need to do this because it terrifies you,” I decided to do it. But only if my friend Bowman would do it with me. And of course he did.

This post is going to share the talk. If you scroll to the bottom, you’ll get access to the slides and the handout.

Title: The DIY Math Curriculum: Simple tricks to make creating your own material feel less onerous

AbstractDon’t like the way the textbook approaches a concept but are intimidated by creating your own content? Bowman and Sam both write their own content from scratch. We’ll share the simple lesson-design tricks we use to write investigations that lead to vibrant discussions and a-ha moments. You will leave ready and excited to write your own content!

Hack #1: Old Problem, New Problem
The Important takeaway:
This is the simplest of all the hacks. You might already do this naturally, and textbooks sometimes have questions that switch what students are traditionally given and what they are asked to find. If you’re hankering to see if students have gotten what they’re doing conceptually, mix things up. Just look at a problem and see if you can’t refurbish it by maybe giving them some information and “the answer” and asking them for some other piece of information that they traditionally are given. When you do this, kids will think harder, talk a heck of a lot more with each other (because the problem is more abstract), and you’ll often have many different responses that lead to great whole class conversations.

My favorite slides (one content, one funny):

 

Relevant blogposts:

  • Give students right triangles and have them associate the correct trigonometry equation that corresponds with those right triangles: http://bit.ly/NCTMSamTrig
  • Come up with the equation for a parabola given a focus and directrix, and the backwards question: http://bit.ly/NCTMSamParabola
  • Give students definite integrals and signed areas but missing the function, and see what functions they can draw: http://bit.ly/NCTMSamIntegral
  • Play Rational Function Headbandz with students, where students have a rational function (or trig! or logarithm! or whatever!) on their forehead so they can’t see it, but they ask each other yes and no questions to determine the equation of the graph: http://bit.ly/NCTMSamHeadbandz
  • Students use protractors to attack forwards and backward questions on inverse trigonometry on the unit circle: http://bit.ly/NCTMSamInverseTrig
  • Instead of giving students visual patterns and ask them to come up with the sequence, why not have them come up with their own visual pattern using blocks?: http://bit.ly/NCTMSamBlocks
  • Mathematical Iron Chef using group-sized student whiteboards: http://bit.ly/NCTMBowmanIronChef

Hack #2: Thinking Before Mathing
The Important takeaway: 
Too often, mathematical notation and premature abstractness get in the way of student thinking instead of being the tool for efficiency and communication that it is for those of us that already understand the concept. Let students play around with ideas in their heads, with their own framing, and own vocabulary, before you develop abstract structures. Let them do it their own, inefficient way before you show a better, more efficient, “correct” mathematical way – the right way won’t stick unless they’ve created something in their brain to stick it to!

My favorite slides (one content, one funny):

 

Relevant blogposts:

Hack #3: Make Math Magical Again
The Important takeaway: 
This hack takes some time, but it is worth it. You are trying to build up a moment of surprise and curiosity for kids – something that will make them want to learn more. (It’s like watching a magic trick. You’re in awe, but you desperately know how the trick was performed because magic isn’t real.) You have to think about something you find interesting and really dig deep to figure out for yourself why it is interesting. That takes some thinking! But once you find the answer, I’ve found it often points directly to a way to get kids to appreciate that thing. Often times, I’ve found that having kids explore uninteresting things is powerful because it gives context for the interesting outcome (e.g. appreciating that the complex solutions to polynomials when plotted aren’t that interesting, but solutions to xn=1 are interesting). Also, like in magic, misdirection can also work. Have kids think they are working on one thing, but actually have them accidentally stumble upon another thing can be powerful (e.g. algebraically finding properties of very different looking trig equations like x-intercepts and vertical asymptotes, but as students work, they find out the very different looking equations actually produce the same graph).

My favorite slides (one content, one funny):

 

Relevant Blogposts:

Hack #4: Toss ‘Em An Anchor
The Important takeaway: 
Math instruction doesn’t always need to go from skill to practice to application. Instead, application to some interesting context, whether that be abstract or “real world” can actually drive student learning, and help them learn the more mundane skills and contexts. Great anchors are both natural to the mathematical context, and sticky – tangible, novel, memorable, easy to refer back to.

My favorite slides (one content, one funny):

 

Relevant Blogposts:

Photos of Me and Bowman Presenting:

 

 

A photo of Bowman, me, and my colleague who came to support me!

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Some Tweets about the Presentation:

 

This slideshow requires JavaScript.

Resources: 

NCTM Orlando Handout PDF

Slides (with one taken out…):

Exploding Dots! Global Math Week 2017!

Hi all,

Life is getting away from me with some tough personal stuff. So I haven’t been as active with the online math teacher community/twitter/blogging/etc. for a while, and I sadly probably I won’t be for a while.

That being said, I really wish I could participate in this initiative that Raj Shah (no relation!) shared with me a while ago. But because of life stuff I might not be able to. But one of the biggest things I want to do is bring joy into the math classroom as a core value, and this does that. And I love the idea of a collective joyful math moment for students and teachers all around the world! I’ve done a bit of exploration with this initiative — exploding dots — and I think it’s fabulous and full of wonderment. What it takes? At minimum, 15 minutes of classtime! I highly recommend you reading the guest post I asked Raj to write (below), and joining in this worldwide effort to celebrate the interestingness of mathematics!

Always,

Sam

***

The Global Math Project is an invitation to students, teachers, and communities everywhere to actively foster their sense of wonder and to enjoy truly uplifting mathematics. Math is a human endeavor: It’s about thinking creatively, exploring patterns, explaining structure, and solving real problems. The Global Math Project will share a unifying, joyful experience of mathematics with people all across the world.
Our aim is to thrill 1 million students, teachers, and adults with an engaging piece of mathematics and to initiate a fundamental paradigm shift in how the world perceives and enjoys mathematics during one special week each year. We are calling it Global Math Week.
This year, Global Math Week will be held from October 10–17. The focus of Global Math Week 2017 is the story of Exploding Dots™ which was developed by Global Math Project founding team member James Tanton, Ph.D.
Exploding Dots is an “astounding mathematical story that starts at the very beginning of mathematics — it assumes nothing — and swiftly takes you on a wondrous journey through grade school arithmetic, polynomial algebra, and infinite sums to unsolved problems baffling mathematicians to this day.”
The Exploding Dots story will work in any classroom, with a variety of learning styles. It’s an easy to understand mathematical model that brings context and understanding to a wide array of mathematical concepts from K-12 including:
  • place value
  • standard algorithms for addition, subtraction, multiplication, and long division
  • integers
  • algebra
  • polynomial division
  • infinite sums
  • and more!
Teachers routinely call Exploding Dots “mind-blowing”!
“I am still amazed by this. Exploding Dots has changed my fifth grade class forever!” – Jo Anna F.
 
“This makes me WANT to teach algebra!” – Kristin K.
 
“YES!” Hands up in the air in triumph! Decades of believing I couldn’t do math—poof! Exploded!”  – Jennifer P.
Join us for Global Math Week, October 10 – 17, 2017!
 
During Global Math Week, teachers and other math leaders are asked to commit to spending from 15-minutes to one class period on Exploding Dots and to share their students’ experience with the Global Math Project community through social media.
You can join the movement in four easy steps:
 
1) See Exploding Dots for yourself
Here’s a brief overview: https://youtu.be/KWJVAjONqJM
2) Register to Participate at globalmathproject.org
3) Conduct an introductory Exploding Dots experience with your students during Global Math Week
All videos, lesson guides, handouts are available for free at globalmathproject.org. Since everything is available online, inspired students (and teachers) can continue to explore on their own.
4) Share your experience on Twitter during Global Math Week using #gmw2017
That’s it!
The power of the global math education community is truly astounding. To date, over 4,000 teachers have registered to participate in Global Math Week (#gmw2017) and they have pledged to share Exploding Dots with over 560,000 kids from over 100 countries! We already over half-way to our goal
Help us reach and thrill a one million students!
The Global Math Project is a collaboration among math professionals from around the world. Spearheaded by popular speaker, author, and mathematician James Tanton, partner organizations include the American Institute of Mathematics, GDayMath.com, Math Plus Academy, and the National Museum of Mathematics.