Friday, November 14, 2014

Fall 14 - Book Club

In my senior capstone history of mathematics class, I had had good luck with having students choose books to read and then sharing and swapping. (Previous post.) I thought it might be worth trying with my preservice elementary teachers, who in the past would all read one book. Currently, if I was picking just one it would be Boaler's. No more than 5 per book; choices included:
  • Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement, Steven Leinwand, (Amazon) [Practical, pre-service teacher approved)] (3)
  • Intentional Talk: How to Structure and Lead Productive Mathematical Discussions, Kazemi & Hintz, (Amazon) [Applies to more than math; good support for helping students learn to converse productively] (2)
  • Making Sense: Teaching and Learning Mathematics with Understanding, Carpenter, Fennema, Fuson, Hiebert, Murray & Wearne (Amazon) [Writers and researchers of the best elementary math curricula around tell what they think is important.] (FULL)
  • Math Exchanges: Guiding Young Mathematicians in Small Group Meetings, Kassia Omohundro Wedekind, (Amazon) [Similar to intentional talk, more strongly based in literacy routines.]
  • Math for Smarty Pants, Marilyn Burns (Amazon) [Collection of entertaining problems across all kinds of math from a master math teacher.] (FULL)
  • A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form, Paul Lockhart (Amazon) [Not sure about putting this on. Many readers are disappointed in the 2nd part, but the 1st part people see as a powerful argument for why math teaching has to change.] (FULL)
  • Powerful Problem Solving, Max Ray (Amazon) [New book from a very deep thinker about how to teach math.]
  • What's Math Got to Do with It?: How Parents and Teachers Can Help Children Learn to Love Their Least Favorite Subject, Jo Boaler (Amazon) [If I was picking one book for everybody this would be it. Dr. Boaler is doing a lot to research and shares how to make math better.] (FULL)
I was disappointed no one chose Kassia's or Max's great books - there was a bit of a follow the leader effect in choosing books. 

What follows is a poor transcript of the group discussion. On book club day, I ask students to bring in enough snacks for four people. They start in small groups with people who read the same book, then we have a discussion circle where each group shares and fields questions and I try to keep my mouth shut unless asked a direct question. (Group questions in italics.)

What's Math Got to Do With It? Jo Boaler
Anyone else hear Tina Turner
when they see this book?
I rated this book as must read, because it talks about what we grew up with, and what we should do. Connected with this class really well, and I’ve never had a class like this. The other way separates you by ability, makes the kids feel dumb or come to hate math. So then in life later, they can’t even think about careers that use them. “I wasn’t good at it I didn’t like it.”
Any specific lessons? Talked about research on the effects of this.
Also had kid perspective.
Did it address grading? Not as much as they could have. Did talk about what doesn’t work with tests and encouraged smaller assessments that aren’t a big deal. 

From Mark Bennet's visual reading notes
A Mathematician's Lament, Paul Lockhart Our book talked about teaching styles, too. His big point was that math is an art. Example: triangle area and formula. By giving problem and answer in one you’re cheating the kids. 2nd part was all about how he loves math. Redundant or over my head.
Students need to get to play around with it. Example of art class, where students aren’t told how to do each brush stroke. I like that, but 
It wasn’t very practical. We don’t have time to have each kid discover the area of a triangle. It really connected with me how I was taught. My high school geometry… my face got red as I read. 
Any solution at all? Really, no.
Also not fair to teachers to blame them entirely. Brought up issues, just wish there was more solution. I liked the book but kinda hated it. 
Was he a teacher? Sort of… 

How is he teaching?
Lockhart says, 'I want to know what you think of this. If you’re a student I send my condolences. Ignore the absurdity you’re taught in your math class.' 
You can’t be a teacher and tell students to ignore their teachers. I hated math, ignored my teacher, and got switched to a slower class - it didn’t work.
Kind of puts himself on a pedestal. 
Talked about textbooks, and how math is stuck in the 19th century. We can’t get out of it because then schools adopt these books. You read that, get fired up, but then what do you want to do. 

Talking Heads
Making Sense, by Fennema, Carpenter,  Fuson, Hiebert, Murray, Wearne  
We want to teach all students so that they make sense of mathematics. 5 dimensions. How to communicate teacher to student.
The book was helpful, set up logically, good examples of classrooms, but then repetitive. Everyone should read the first chapter, and then read more about one dimension.
At the end, giving examples of classrooms in different modes. But just stories - a detailed description would be better. Got tedious, chapters 7-10 were repetitive. Nice, but can’t tell the difference between some of them. Did tell how each related to topics in chapters 2-6. 
It was good. 

Intentional Talk, Hintz and Kazemi

Sets up different strategies, open discussion, targeted, gave strategies to assess and fix discussions. The examples were actual dialogues. Then they looked back and identified, here she was identifying goals, here she was introducing math ideas. Good strategies on how to make the classroom safe for discussion. The ideas and participation of all students are valued. So even wrong answers, it gave you lots of ways to use that and build from it. 
The book showed how you plan discussions. Gave a template, helped you think about how to plan it before, going from what you think they are going to say. 
I gave it a 5 because it was really helpful, I want to reread before I student teach. You wanted to take notes as you were reading.
Open strategy sharing. Like kids giving different ways to multiply, we need to think about different strategies so everyone has a way to learn.
That’s like at Family Math, we have 5 pizzas with 4 pepperonis. What’s a math problem like that? “Well we have 5 groups of 4…” I never thought about it that way when I was kid.
They give you talk moves, so you have ways to move it forward. 

Smarty Pants, by Marilyn Burns
On Etsy.
Our book was not about how to teach. It was just problems. Different kind of problems.  Listening to other people talk - I didn’t get that much out of this one. It was interesting, and fun to read through, but you don’t get a lot out of it except different kind of problems. 
Each part has a ton of new problems and cartoons.
Parents could use it as a supplement. 
My sister doesn’t know my nephews math, he’s like 14. They call me… could parents use that to practice.
This is younger, but more about abstract thinking. They got me thinking, but it doesn’t explain why it works out.
How do they take into account kids who are not ready for abstract thinking. They have specifics to do in the problem, but then it abstracts…
It is literally just a book of problems. I liked it. It was interesting. I enjoyed reading it.
Would it show them how to teach, like addition? There was a section on tricks to multiply, but it was just hints and different strategies.
It reminds me of problems of the week. I used to get my family doing them.
Even the answers were hard - upside down and backward. 

Accessible Mathematics, by Steve Leinwand
We played his Ignite on
"It's Instruction, Stupid!"
afterwards, so they could read in his voice.
This gives what’s wrong with math and gives different positive approaches. 
I really liked it. So straightforward, 10 shifts to do. Emphasizes how to always be asking questions. I’d recommend reading it. So practical, check homework more effective, using problems of the day. 

(Not much discussion, but a lot of interest in reading it afterwards.)

Their Summary My questions for them for the summary.

What would you like to read?
I’d want to read Accessible Mathematics. Like music ed, know the beats as a pattern… that’s doing math.
I’d want to read intentional Talk, because of good ways to get you to get students thinking. For teachers that are just starting out, it has very practical.
What’s Math Got to Do With It - practical, actual ways to teach.
Smarty Pants - I want to see the activities. How could you incorporate them into the classroom.
Variety or one book? Variety!  
Assigned or pick your own? 
Choice! Now we know multiple books, which one connects, time thing. 
We get to focus on one book, get more in depth, get to borrow.

My Summary
This worked out well.  I'm going to do it again, and try it in more classes. They did a nice job with this summary day, and I was convinced of their interest and investment.

I ask them to make a reading plan once books are chosen, with the end date in mind. I ask them to keep reading notes, for accountability and retention, that include a summary and a response to each session of reading. I don't grade those, but just check when done. I emphasize this as a rough draft of doing book studies as teachers, and like that we're arming them with some different book choices for those future book clubs. 

Thursday, November 13, 2014

Array Maker 9000

This is probably a stupid little post.

The other day I was making some math games, and I needed a rectangular array for a board. As one often does. So I made a quick GeoGebra sketch. And rather than make it so it only made one board, I made sliders so that it could make any rectangular board. Of course sometimes you'd have to zoom out to see the whole thing. A little clunky.

Then Tim Cieplowski (the BGU prof with the beautiful GeoGebra stuff) tweets:

Which makes me feel like I should do a proper job.

One of the things I love about GeoGebra is that you can make the window dynamic, so that it automatically fits what you want to show.

The problem with doing the array is that fitting it to the window will make it non-square and change the game board. So here's my workaround.

The array is just a ratio to compare a window of array plus a border of .5 to the actual graphics window. Corner[1] is the lower left corner around counter-clockwise to the upper left Corner[4]; those are helpful for making things that go right to the edge. Corner[5] gives the (width, height) in pixels of the graphics window. (You can even ask for Corner[2,5] if you have the second graphics window.) So these definitions make the window fit the height if that is taller than the width is wide, relative to the window.

Bonus: this is the closest I have come to doing the Border problem in real life. (Which is so well known that it comes up ahead of immigration stories, even.)

Here's the sketch on GeoGebraTube.

Can you think of a quicker or more elegant way to do this?