General Ideas for the Classroom

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.

Marbleslides, Squigles, Portfolios, Previewing: My Third TMC Recap Post

Another blogpost about takeaways from TMC17 which I may be able to use in my classroom.

Marbleslides Challenges

I love Sean Sweeney. He’s everything good in the world, packaged in humanoid form! He’s so welcoming and kind to everyone… he wants everyone to feel part of things. At the Desmos Fellowship, he was the person I felt most safe saying “I have no idea what the hell I’m doing” and he would hunker down and help. I think many others felt the same. Okay, enough of the love fest. I am going to share his my favorite which I desperately want to use in my classroom. First, a little note. There is a difference between reading something on a blog and experiencing it. More and more, I’m recognizing that. I think if I read about this, I’d think “cool story, bro” and be like “okay, I could do this, but is it really worth it?” But experiencing it like we did during his short presentation, it’s like “I MUST DO!”

Sean has made a number of Desmos marbleslide challenges (if you don’t know about this, google it). Here’s a gif from his blog. The idea is that the marbles drop and you have to create stuff on Desmos to make the marbles hit the stars.

marbleslideAnswerBlog

He shared one with us, and everyone in the giant room got obsessed with drawing functions that would let us “win.” For our challenge, people used ellipses, used lines, used piecewise functions, use quartics. It was inspired to see all the different approaches, and all the play that resulted.

What was lovely about Sean’s facilitation is that he paused us after a while (note: a teacher trick is to say “I’m going to pause your screens in 5… 4… 3… 2… 1…”). You knew from the cacophony of groans that we were in a good place. Then he shared out different approaches. The diversity of “answers” for the challenge was fascinating.

He made this a regular thing in his classes. I love his poster which shows the diversity of responses:

marble.PNGSo how can I use this? I’m not sure yet. I need a way to keep it light and fun, but also with all that my kids have on their plates and their lack of time, I don’t know if they would take the time to do it without some incentive. After teaching kids how to restrict the domain of a function/relation, and reminding them of all they have at their disposal that they’ve learned about (trig, circles, lines, parabolas, step functions, etc.), maybe I need to have a 10 to 15-minute in-class challenge (with kids working in pairs, so they are comfortable). And then do it again two weeks later, in class (but not in pairs). And then… announce that we are going to have regular marbleslides challenges. And the winner(s) will get the bonus question on the next assessment without having to do it. Or maybe buy some cheap plastic trophies which get displayed proudly in class? I want kids to work on the marbleslide challenges outside of class because part of this for me is that I want kids who might be slower at processing or coming up with ideas to have the time to execute their vision. I don’t want this to be a timed thing. Though maybe each time I introduce a new challenge, I give everyone 5 minutes in class to work on it.

What I have to make sure to do is share publicly the diversity of answers, like Sean did with his posters.

I also had an idea about how to score it. Something like 1 point for each star. But maybe if we’re learning about conics, or tangent, or something else, I’d give a bonus point for using those functions. And maybe an additional possible bonus point or two for any additional creativity (teacher’s choice)?

Sean’s posts are here and here.

SQUIGLES

David Butler also presented a my favorite on squigles. The poster and his blogpost are here.

sqwigles.png

I am not one for acronyms, really. They often are forced. But what I like is that these are used to teach student math helpers how to work with other students. From David’s post:

SQWIGLES is an acronym that we use to help our staff (and ourselves) when teaching in the MLC Drop-In Centre. It is a list of eight actions we can do to help make sure our interaction has a better outcome and make it more likely students will learn to be more independent.

It was originally Nicholas’ idea to have something like this. He wanted something to help the staff choose what to do in the moment, and also to help them reflect on their actions and choose ways to improve. We noticed that our staff (and ourselves) needed something focused on actions rather than philosophies, because then it could be used on the fly to choose what to do. Telling staff they need to be “encouraging” or “socratic” is not all that helpful when they don’t know how to put it into action. Yet this is what many documents giving advice to tutors do. So we decided to focus on the actions instead.

The reason I wanted to blog about this is because I think it might be helpful to share with the student tutors at my school. We have a peer tutoring program called TEACH (probably an acronym, since I always see it written in upper case… but for what, who knows!). And I haven’t inquired if and how students get trained. But I’d love to do a short 10 minute presentation on this, and maybe do a few scenarios where kids can practice tutoring while other kids watch (fishbowl?) and take notes on which of SQUIGLES happened. (Not all need to happen! Just look for them.)

I think I should also have this on my desk, since I work with students one-on-one a lot and having that reminder can’t hurt!

Porfolios

I went to Cal Armstrong’s session on documenting student learning. Over the years, I keep on getting inspired to have kids make portfolios that they turn in to show evidence of different traits. And this came up again in that session. James Cleveland has done it. Tina Cardone has done it. I want to do it. But aaaah! The time to make it into a reality! Argh! But I really would love to make explicit some values — maybe not standards of mathematical practice (… or maybe throw of a few of them in there…), but things like perseverance or active listening or seeing a problem in a different way or acting with courage or helping someone understand something by asking good questions or recognizing your own a misunderstanding or changing for the positive as a group member in somewayAnd have kids document these moments or interactions. And then at the end of a quarter, turn them in. (But have a check in halfway through the quarter!) It would mean that they are looking for these things, looking to do these things. And recognizing that I value these things. Maybe they have a choice of things they can include — not all of them? Maybe they can take videos or photographs or write paragraphs or draw a comic — it can open-ended how they demonstrated this quality or action.

There is something that I think happens in my school. Kids form facebook groups (or maybe on some other kind of social media) for their classes, and I suspect lots of backchannel communication about the class happens on this group. I suspect a lot of it is positive and uplifting and helpful. I would love to encourage kids to submit that sort of stuff in their portfolio also, if it demonstrates whatever qualities were asked for!

I don’t know if I’m going to do this this year. But maaaaaybe?

Preview, not Review: Student Intervention

Kat Glass gave a my favorite on intervention with students who were failing. Part of it was a powerful and important note about language and using code-words instead of saying what you mean. We don’t have many kids that fail classes in my school. But one thing that did strike home was that sometimes when working with kids who are struggling, we put all our emphasis on remediation and it’s like we’re always playing catch up. But sometimes we need to remember that with a struggling student, one tack that we can’t overlook is previewing upcoming material. It can help kids be more engaged and confident in class, and it sets a good tone moving forward.

I do this sometimes, but I need to remember to do this more frequently. Although I do lots of discovery based work, I don’t think that previewing some of it with a kid, and working through some of the discovery with them one-on-one, and then them seeing some of it happen again in class is a bad thing. I’ll just have to remind them that they need to be careful about not letting other kids have the same insights they had — and their role is to help without telling.

 

Play! Create! Adult!: My Second TMC17 Recap Post

Here are some more TMC17 notes!

Don’t play with your food, damnit! Play with your math!

I love the idea of having kids engaging in recreational math. I don’t have much time to encourage that in my curriculum — or at least the only way I’ve found for that to happen is with my explore math project [posts 1, 2, 3; website]. Some kids get some extra math problems to work on at math club (usually problems from math competitions or brilliant.org), and kids do math problems on our math team. But that isn’t the spirit of what I want to bring to my school. I want to get kids just fooling around with math for fun! Tinkering! Thinkering! Building! Collaborating! So that’s why I fell in love with Joey Kelly (@joeykelly89)’s my favorite presentation. Where he shared with us Play With Your Math.play

He and a friend created it. Right now it has 15 sheets of paper that can be printed out, each with a challenge. The name, inspired. Design wise, fantastic. But the problems are captivating, easy to dive into, and many have this open-endedness that can lead to obsession. When I was at the Desmos Fellowship a couple weeks ago, they had these for us to work on as a way to get to know each other. Each table had a different one and we were encouraged to play, and meet others who were playing, and then move to a different table and meet and play when we felt like it. The one I spent all my time on, trying to come up with a strategy? One that I know will get my kids in competitive mode? Poster 5:

genius.png

I liked getting to know people and I liked these problems! At TMC we were given poster 14 and I became obsessed. And eventually, I solved it (and a second more complicated one). But it took A LONG TIME and I DIDN’T CARE. I refused to go play boardgames at gamenite until I had climbed this mountain!

I need to brainstorm if and how I am going to use these in my school. Some initial ideas:

1. Leave copies of these in the library for kids to use. Or put many copies of all of them on a bulletin board for kids to take, so when they’re board and standing there, they just grab one and start thinking.

2. Use these when I need to fill a long block (we have double periods one out of every five times we meet our kids) and I don’t have a good idea.

3. Plan an Upper School math night, where we gather at a space in the school, do math, order pizza. Like PCMI’s “pizza and math” (was that what it was called? we can do better!). These can be the amuse bouche or the main event!

Math Art!

Speaking of recreational math, at TMC17 there was so much math art. I just wanted to share some of it!

Captivating! I hope at some point to learn how to make crochet coral. It feels like once I get in the rhythm, it could be so soothing. Actually, I wonder if it would be fun to have a MAKER MATH club where we make math stuff together. And create our own math art gallery. Things like the things shown here, but also like these, and origami (demaine and lang), and a menger sponge made of business cards, and design and 3d print these optical illusions, and carefully color in pictures from Patterns of the Universe, and create our own mathart coloring pages. If you are reading this and have ideas of things that we could make, let me know in the comments! You probably can tell this is something I’m actually totally *feeling* (FYI, for me, the definitive math art page is @mathhombre’s page here.)

How To Adult: Let’s Buy A House

So @rawrdimus gave a my favorite on how to adult. He was teaching calculus and wanted to keep his seniors engaged. So he came up with this project that had kids pick a few houses and figure out what they’d need to buy it. He was the banker (a hilarious banker) and gave them two different mortgage options (a 15 year and a 30 year, with different interest rates) and they had to figure out their monthly payments.

I know come the spring, the kids in my calculus class will have their attention wane. So I think something like this could work (this investigation on wealth inequality worked a few years ago)! But right now it’s a little bit like trying to put a square peg into a round hole. I need it to have some more calculus before I do something like this though. Maybe we’ll spend some time talking about e or we’ll do something with summing (in)finite geometric series, and maybe seeing that as a riemann sum? I think it’s totally doable — I just need to think a bit more! But if you want to get a sense of why I’m trying to make this happen, just watch Jonathan’s presentation and you’ll totally get it. (Here’s his blogpost.)