DIY Geometry Definitions

I know one of the most important parts about Geometry is making sure all of our definitions are set up. I also know copying definitions down is brain-numbing and time consuming. As I was planning the first couple lessons of our Geometry half of the year, I turned to twitter with a general plea for help. Lisa  responded with how she started her year by synthesizing definitions with her students. She passed out a series of slips that had examples and non-examples of each of the vocabulary words, and had her kids create frayer boxes for each word.

For those of you not in the know, Frayer Boxes (or Frayer Models) are a literacy tool to help improve kids understanding of different vocabulary words.  The term goes in the middle, and then they fill in the rest of the boxes.

frayer model


It’s a really great model for building understanding, especially when you only give students some of the boxes and they have to fill in the rest. I started the activity by having the Examples/non-examples for “Angle” on the board, and then we filled in all of the boxes on a Frayer model together. This gave me a chance to explain to students exactly what I was looking for so I wouldn’t have to stop over and over again.

Then I passed out the first round of examples/non-examples to each group. There were 8 different terms I wanted students to work on, so I divided that into two sets of four terms. I made two copies of the examples/non-examples for each term so that two different groups were working on each term. After the smaller groups came up with a definition, they would find the other group that had the same term and collaborate on a final definition that they could share. They were to fill out an “official” Frayer box for each term that I could keep, and then copy it onto a giant box I put on the board.  We would then have a class discussion to iron out any kinks in the definitions. The groups that came up with the original definitions then had to add any revisions we made as a class to their “official” frayer box.

I really hate having activities where students are just asked to copy down definitions in class because it feels like such a waste of the precious few moments we have together.  So instead of taking the 15 minutes to copy down I scanned each of the “official” boxes that students gave me using a scanner app on my phone and posted all of the definitions on my website.  Over the weekend they had to fill in their glossary starter kits and I would check them on Monday.

Overall I was really happy with how the kids came up with definitions, and I think their definitions were fairly strong. The only thing I’d like to improve in the future is how quickly students changed groups.  It was all a little disorganized and some kids were not nearly productive enough and just started chatting. But that’s not an activity problem so much as a classroom management problem.


Geometry – Big Ideas

Now that my students have taken the Regents in Algebra 1 (to fair results – They all passed, but not by as much as I would have liked), it’s time for us to start Geometry full time.

Since we only have four months, I’ve been trying to figure out what the Big Ideas are for Geometry. Basically, I want 3 to 4 overarching skills that I expect everyone to be able to pull off by June. Maybe students can’t solve every problem, but they will have certain skills that will carry over to Algebra 2 next year and the IB curriculum after.

Some of this will seem like common sense to those that have taught Geo before, and I’m also very aware of how much these look like the Standards of Mathematical Practice.  For me it represents a shift in how I think about Geometry. When I took the course in 8th grade my largest impression was that we learned a lot about shapes and did some stuff with angles and maybe a proof or two.  It’s a similar shift that has happened in how I approach Algebra 2 as I try to make a more conceptual course than just procedural.

1) Use appropriate language to describe appropriate things: There is so much freaking vocabulary in Geometry, more than a lot of other math classes. Before we can really do anything constructive with proofs or analysis we have to understand what all of the vocabulary means. It’s like a second language. And anyone that has tried to define “Angle” understands how complicated the whole thing can get. So job 1 becomes Precision in Language and how to drive home the definitions, as well as how to build ironclad definitions for new terms.

2)  Seeing the Forest AND the Trees:  How many triangles are in the shape below? And how are all of those triangles related?


Understanding what pieces you have, and how they interact with each other, will help kids to build better proofs later on. And more importantly, it will help kids to look for structure in things when they transition back to more pure Algebra.

3)  Making a Strong Argument:  It’s not enough to say A is B, students need to practice defending WHY all of this is true. But many students haven’t had to create a watertight argument before. When writing papers in the Humanities, arguments tend to use Pathos, and even arguments that use Logos aren’t held to the same standard as proofs. Students must practice using all of the information they have in order to convince even a skeptic. This skill will help them make stronger arguments in other courses, not just math.

So those are my big three foci for the rest of the year. Every other skill and exercise we do should tie into those three skills somehow.  We’ll see how well I can pull that off

It’s a fine, fine line OR How to make me Rageful

Previously in my Math Class: One of the essential features in my department are short presentations that we expect students to give in small groups. They have five minutes to Frame a problem, Explain a problem, and then Take Questions. In case you can’t tell by my awkward capitalization, that means there are three roles: Framer, Explainer, and Question Taker. We are currently doing these presentations as a form of midterm exam review. Groups of three are assigned a problem from the midterm that many students struggled with, and then they are given a day in class (plus however much time at home) to prep for their presentation.

Now: A group was giving a presentation. The Framer did an OK job, the Explainer wasn’t the best presenter but their math was correct. The Question Taker stood up and started trying to field questions. The first question asked if the way the group solved the problem was the only way to solve a problem. The QT said yes, that’s the only way and other ways are wrong. Everyone started laughing.

Then I lost my shit.

Obviously ignore "June 13"

Obviously ignore “June 13”

Here’s the thing. The student that was Question Taker has a certain way of speaking. The best way to describe it is to compare his intonation to that of an old time radio announcer (think kind of like the narrator from Legend of Korra). He’s not the strongest student and he’s not the weakest. But when he talks like that, it’s really difficult to tell if he’s being goofy on purpose (i.e. he’s getting the answer wrong to get a laugh) or he’s using his goofiness as a shield because he doesn’t know what’s going on (i.e. the likely situation). Other students find his tone to be very amusing, and I think he is hamming it up because it’s better to be laughed with than laughed at.

I totally get that reaction. I am goofy and sarcastic and self-deprecating, and I laugh at myself a lot. My instinct when I make a stupid mistake is to call myself an idiot. I don’t mind if kids laugh at my stupid mistakes because I make a lot of them. But I know that this sends a mixed message when I’m also like “Don’t laugh at others”. I don’t know what to do about that.

I once saw on Twitter someone tell some version of the following anecdote from their class: A student was at the board, and had to choose another student to do the next problem. First student chooses a second student, but second student says they don’t know how to do it. First student says “That’s ok, we’ll help you!”  This is what I want in my class.  Everyone helping everyone, everyone understanding that none of us are experts (even me) and we all make mistakes (especially me), everyone feeling safe to make mistakes.

So…how the hell do I make that happen? I’ve had numerous conversations that I don’t like it when we laugh at others in my class. Even today I was like “Not nearly enough of you got this question right that you should be amused that someone else didn’t, and even if you did get it correct you shouldn’t be laughing. You’d feel like crap if someone laughed at you, I’d feel like crap if someone laughed at me, so why are you laughing at someone else?” And I ended with “I don’t know how else to make you all buy in. I’ve told you I want this to be a safe space and yet here we are. I’m tired of it and it has to stop”. I was upset. I’m still upset thinking about it. It ruins my day when I have to have these conversations.

But I don’t know how to constructively address it. Stern talking-to’s aren’t helping. Pleas for compassion aren’t helping. I brought this to a consultancy group last month and they were all like “Well it sounds like you just haven’t set up the classroom culture you want”.  Well yes, apparently. But how do I fix it?

Here are my ideas:

– I have a mid-year survey that I’m asking students to fill out. One of the questions is “What can Mr. Baker do to make it a safe space?  What can YOU do to make it a safe space?” The goal is A) To get ideas from the kids about things they see that I’m not doing but could be, and B) to get students to realize that it’s not all on the teacher.

– Bribery: I’m going to start a table points system. This was originally to get kids on task more quickly, but what if I also use it to reward groups that are supportive and helpful?

– Supportive Shout-outs: Acknowledge kids that are already being supportive and awesome. Maybe even a “Most Supportive” weekly award?

The cynical, jaded, bitter part of me feels this is cheesy, but I have to try something or I’m going to go crazy. I welcome any suggestions as to what has worked in your classrooms in the past.