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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