## Wednesday, April 12, 2017

### Sometimes It's an Accident

We are learning about angles in grade 7.  Yesterday, I asked students to draw 10 different angles (at least 3 acute and at least 3 obtuse) and measure them with a protractor.  Historically, I've been really bad at teaching students how to use a protractor, but they made their best pass at it.

Today, I drew random angles around the classroom on our whiteboards and was going to ask for volunteers to walk up with their protractors and measure them at the board.  But before doing so, I went around the classroom asking the class to classify the angles as acute, obtuse or right.  When we came to a right-is angle, the class was divided; some said acute, some obtuse and a few said right.

"Ok, so what do we do?"

Sam picks up his protractor, holds it out in front of his face, closes one eye and peers through the hole at the bottom of the protractor.  I stepped back and watched what he was doing.  He was peeking at the vertex into the hole, while lining up one of the rays with the guides at the bottom of the protractor.  He then says, "Mr. Cox, it's pretty much 90 degrees."

Now, I loved this for reasons.  1) This kid invented a hack for doing a little better than estimating 2) The entire class understood what he was doing and started using his hack and 3) I had never thought of doing this before.

But that isn't even the good part.

I had drawn three straight angles that had a second ray breaking it into two supplementary angles.  We argued a bit about whether there were two or three angles shown.  Everyone eventually agreed that there was an acute, obtuse and straight angle represented.  Then we got to the measures.  Glad to say, the pairs they measured were all supplementary.  Then came the two students who made mistakes (on purpose).  We discussed how some students use the wrong numbers on the protractor, but if they classify the angle first as acute or obtuse, that helps them know which number to use.

That wasn't the good part either.

I wanted to start a conversation on supplementary pairs and I was going to use the drawings of straight angles broken into two supplementary angles that were on the board.  But then I thought about Sam and his protractor hack.  Change of plans.

"Ok, take a look at your protractors and look at the pairs of numbers.  What do you notice?"

We created a list of numbers.

170   10
160   20
150   30
140   40
130   50
120   60
110   70
100   80
90    90

Then I added one more entry:

34   ?

"Without using your protractor, make your best guess about the number that should be paired with 34."

154   146   156

Argument 1:  "I think it's 154 because 150 and 30 are paired together.  Since we added 4 to the 30 to get 34, we need to add 4 to 150 to get 154."

Quick check of the class to see who understood the argument. I was careful to let them know that saying they understood the argument was different than agreeing with it.  They understood.

Argument 2:  "I disagree with 154 because on one side the numbers are increasing and on the other they're decreasing.  34 is between 30 and 40, so our answer needs to be between 150 and 140.  So, I think it's 146."

Homework:  Who do you agree with and why?  If you think the answer is something different, make an argument.

Can't wait until tomorrow.

## Friday, January 13, 2017

Dawson is the oldest.  Aidan is the musician/artist.  Bohdan is the baby.  And Jabin is, well, Jabin.

But my second son, Nevan just finished his first semester of high school.  He hadn't been in a classroom since the end of his second grade year and he hadn't done traditional math course work in years.  Instead, he did a lot of interesting math problems.

So, I has a little hesitant when the local high school recommended he take math 2 and chemistry as a freshman based on a single placement test.

Our conversation went a little like this:

Me:  Nevan, I know they say you're ready for these classes, but remember, you're being asked to take math 2 and there's a lot of content in math 1 that you haven't done.

Nevan:  I know Dad, but I want try it.

Me: Ok, that's good enough for me.

I mean, he wanted to challenge himself.  And even though I have reservations about acceleration in general, I knew Nevan would have support at home.   So, we decided he could give it a shot on the condition that he could always move into a math 1 class if he felt overwhelmed.

Yeah, that didn't happen.

Suffice it to say, he has done very well in both his math 2 and chemistry classes so far.

The takeaway for me here isn't that my wife and I have done anything extraordinary.  The takeaway is that my son has learned how to learn.  He reads everything that he can get his hands on, is curious and is willing to take risks.

The fact that he had some content gaps didn't matter because he was willing to do what he needed to do in order to fill them.

This really makes me wonder about all of the time we spend worrying about "gaps" in student's knowledge.  I realize that claiming this as a mindset win would be shortsighted as Nevan has advantages that most of my students don't.  However, it's a clear indication that habits of mind matter.  They matter a lot.