Reflection & Discussions in Grade 8, Part 1

Woo, blogging! As I start work on high school curriculum, I thought I would go back and revisit the grade 8 units that I’ve spent the past 18 months working on and share some of my favorite things. This gives me a chance to think about what sorts of things I really want to keep in mind as I write new stuff and gives folks a way to take a peek “under the hood” at how some activities came about. A new curriculum can be a daunting thing to jump into, so hopefully this is a friendly way to dip toes in. Let’s start in grade 8, unit 1, shall we? Oh, and some of the links are going to be to the online curriculum, which you’ll need to sign up for. Signing up is free and you can do that here.

Discussion in math class between students is important to me. My happiest days teaching were spent listening to students develop their abilities to articulate points with precision and clarity. While working on the Illustrative Mathematics 6-8 Math curriculum (fancy title, no?), one thing we did was start by focusing on familiar ideas that students would feel comfortable talking about in their own words. From that launching point, we could then build toward the main mathematical idea(s) of the lesson while also giving opportunities for students to practice engaging in mathematical discussions.

For example, one of my favorite new words that I learned while working on the curriculum is chirality. Left hands and right hands are examples of two things that are chiral. In order to orient both hands so that they line up perfectly, we have to use a reflection. While we don’t use the word chiral in the materials, in lesson 11 we have this image in the warm-up:


After students take time to identify all the right hands in the image, in the synthesis they are asked to “think about the ways in which the left and right hands are the same, and the ways in which they are different.” What ways do you think your students would come up with? (No really, what do you think they would say? What do you think you would have said as a youngster? I want to know!) Depending on how students define “the same,” they may focus more on the differences or more on the similarities. Both ways of thinking have justifiable responses, and this is purposeful. For this warm-up we want to engage as many students as possible early on and give them opportunity to articulate their thoughts so they can refine their ideas throughout the lesson about what it means for two things to be “the same.” Additionally, a teacher can use student words and ideas from the warm-up to fuel the rest of the lesson as the class makes steps toward a precise mathematical idea of “the same” (*cough*congruent*cough*).

Do let me know how younger you would have answered the question! Or, if you happen to have some handy students sitting around that don’t yet know what it means for two figures to be congruent, ask them and let me know in the comments.


Session Thoughts: Shadow Con, Part 2

Shadowcon2015 Laila

So now you’re in your classroom and getting students to talk is akin to squeezing rocks for water because math. Mathematics is serious business, no? But what if the quiet of the classroom is tearing at your soul? Sure, they’ll respond when you pull out a popsicle stick with their name on it, but the hesitation you see in Adelaide’s answer doesn’t make sense when you know she’ll have her friends in stitches the moment the bell rings. How do you break through this miasma of reserve that settles over the room at the ring of the bell?

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Session Thoughts: Shadow Con, part 1

Session Thoughts Shadowcon header 2015

For those on the twitters and reading blogs, there was a nice build up in advertising to this event. I really didn’t know what to expect from Shadow Con until the day before when I got to ask some folks that were speaking at it during the math games night. The ‘TED-esque, but with a call-to-action’ description ended up being most spot on for me. This was probably one of my favorite events from my time in Boston and I greatly enjoyed each speaker. Let me tell you why.

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Session Thoughts: Contexts for Complex Numbers

Wow was I torn about what session to attend at 12:30 on Thursday. I ended up going this route since I’ve been poking (slowly–every so slowly) at the book Visual Complex Analysis by Tristan Needham, which came highly recommended by a mathematician friend of mine when I voiced wanting to learn more about Complex Analysis.

sketchnotes from the complex numbers sessionYou know a session is pretty awesome when the person sitting behind you lets out a genuine “Holy sh*t!” when he sees the path the presenters have set us on. For those deciphering my color-coding above, blue = Michael Pershan, orange = Max Ray (like that was a choice), and green = everyone else. Except for Ralph, who was also sitting behind me and commented about 40 minutes in that how complex numbers were being built up by the presenters “eliminates thinking about i as a variable”. Because how many of us have had students that do treat it like some unknown thing? i is not a made up number, and this session laid out a compelling argument for students to see why.

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Session Thoughts: Adapatation

sketchnotes of Geoff Krall's session, Adaptation

Geoff Krall, who has posted all the things from his talk over on his blog, lead a session Thursday on thinking about how to adapt the tasks you have. Due to the work I do for Illustrative Mathematics, adapting tasks is something I think about a lot and something IM does with teachers at PD conferences frequently so it was great hearing Geoff’s perspective of the Why, How, and What of task adaptation.

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Session Thoughts: Project Based Learning

sketchnotes from the session

Through coincidence I met Anthony Rodiguez the previous week in Chicago at an unrelated meeting and while exchanging our session titles I realized he was already on my calendar for NCTM Boston. After getting to spend a few days with him in Chicago I was looking forward to this session even more as Anthony has an enthusiastic and grounding presence and I really want to spend some time picking his brain over a meal.

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Session Thoughts: NCSM Ignite!

I always enjoy a good Ignite talk so I headed to the NCSM one after dropping things off at the MTBoS booth. This was my first attempt at live sketchnoting, and wow is an Ignite a trial by fire with how fast some of the presenters talk! If you’ve not seen an Ignite before, you can catch video from prior ones here. My sketchnotes and thoughts below the cut.

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in which I sketchnote all the things

Quick Links to Sketchnote posts from NCTM 2015:

I’ll be working through these of the course of this week. I plan to post the sketchnote itself and then some of my thoughts on the session along with any relevant links. If you are interested in reading more about how I got into sketchnoting, head below the jump.

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In which British comedy is investigated

While my grades in Algebra 1 and 2 may lead one to believe I knew what was going on, those classes were agonizing for me. I can still vividly remember the frustration I felt because nothing seemed to make any sense and my ability to memorize steps is sub-par. To this day I find it easier to remember only the formula for the volume of a sphere and then use calculus to find the formula for surface area rather than actually memorize to formula for surface area.

Strange, I know. But it works for me.

In my last post I was thinking about what it’s like to not know something. But in addition to not knowing, I think the utter confusion one can feel in a classroom is also something important to keep in mind while teaching and lesson planning and working with students. To that end my mental index popped out the card for a skit from the British sketch comedy show That Mitchell & Webb Look called Numberwang. Yes, yes, I know it sounds like I am leading you to a dark place on the internet, but I’m not. Look:

There are other episodes along with A History of Numberwang, which I recommend watching as well. Go ahead. I’ll wait.

I asked some tweeps if they had seen the skit before, and Carl Oliver came back with this:

As that kid without conceptual understanding in algebra, this skit is pretty much exactly what it was like in class for me. Confusing, almost no stated rules I understood, and at any moment the scene might change or I might be shoved in a box for not achieving Wangernumb.

Next time I go to make lessons for others, I need to keep this skit in mind and think about how I can plan for conceptual mental grappling and not just learned memorized performance in front of a live studio audience.

That’s Numberwang.

In which sticky notes are examined

If you ever see my desk you will find a bunch of sticky notes. They are not reminders so much as errant thoughts and little quotes I like enough to write down to ponder while I avoid over work. In example:

“He doesn’t get mad when things are hard. He just works. And I think that’s something I don’t have and not enough people do have.” – John Green on his brother, Hank

Yesterday I was looking through the app from Cuethink and admiring how it seems focused on getting students to communicate their mathematical understanding. Many of the things I enjoy most in the math sphere involve articulating mathematical understanding. The Math Forum‘s Notice and Wonder. Number talks. Task Talks. Doing math with others. Listening to my niblings explain how they figured out a puzzle. Crouching down at a group’s table in class to just listen. The following sticky note resulted:

“I think adults sometimes forget what it is like to not know something.”

When I think back to most of my math classes in middle and high school, they were warmup, homework checkoff, lecture with 3ish examples, homework time. Pretty much every day. I have no memory of ever doing a project in math. Not getting math meant going in for help and listening to an explanation again. Watching a new example. Sometimes trying to explain my understanding was involved, but having so little experience articulating my own conception of mathematics that was usually a non-starter. Not knowing to knowing was just a matter of listening more carefully or repeating some more examples, no?

When I think back to my first few years in the classroom as a teacher I can say it looked a lot like that. But I still didn’t give space for student’s to articulate their understanding (at least not students beyond those with Hermione-esque tendencies). I went into teaching because I enjoy working with teens and I love math. I stayed in teaching because I started learning how to give space for students to communicate their understanding and found that listening was fascinating. Watching a student going from not knowing to knowing and figuring out their path is one of my favorite things. Especially when they take paths I would never see because I know.

I’m curious how many people out there yelling one thing or another about education and classrooms and educators remember what it’s like to not know something. Or perhaps it’s better to ask if they remember what it’s like to not know something and also not know how to get to knowing something. As much some claim school is about content I will argue it’s more about going from not knowing to knowing and the many strategies life will demand one learns to survive and do good and be awesome.

So what stickies do you have at your desk?