Math Girls: A Novel Way to Learn Some Deep Math

I asked for a review copy, but I can't even wait until I finish it to tell you about this marvelous book. Math Girls was published just yesterday. (How I love the internet, let me count the ways!) My thanks to Robert Talbert for his blog post on the book, and to Bento Books for sending me a review copy so I can satisfy my desire for immediate gratification. You can download a sample (first two chapters) from Bento Books here.


Math Girls has gone through 18 printings in Japan, and the English translation has just been released. There are lots more books in the series, but those of us who don't read Japanese will have to wait for those.




Here's a bit for flavor:

When you’re doing math, you’re the one holding the pencil, but that doesn’t mean you can write just anything. There are rules. And where there are rules, there’s a game to play—the same game played by all the great mathematicians of old. All you need is some fresh paper and your mind. I was hooked. 

I had assumed it was a game I would always play alone, even in high school. It turned out I was wrong.

Our protagonist, a high school student, is intrigued by Miruka, an elusive girl at his school who gives him challenging math problems to ponder:

“Forget about the matrices for now,” she said. “Here’s a problem for you.”

Problem 3-1
Give a general term a_n in terms of n for the following sequence:
n     0 1  2 3 4 5   6  7···
a_n    1 0 −1 0 1 0 −1 0 ···

“Think you can you do it?” she asked.
“Sure, that’s easy. All you’re doing is going back and forth between 1, 0, and −1. Sort of. . . oscillating between them.”
“That’s all you see?”
“Am I wrong?”
“Not wrong, exactly. Go ahead and give me a generalization.”

And our protagonist (I don't know his name yet) helps another student, Tetra, with her math. So you get to see the same ideas played out at higher and lower levels. When Miruka kicked Tetra's chair out from under her, I had to skip the math to find out what would happen next between the characters. I'm not sure the storyline will make complete sense to me, but I am so loving it!

Tony, the rep from Bento books made a request:

If you blog about Math Girls, please be sure to let your readers know that this is a pretty advanced book. We’ve had many inquiries from parents looking for fun books for their middle school and younger children who love math, but Math Girls is probably best suited to, at a minimum, talented high school juniors and seniors who want to go beyond what they’re likely to be exposed to in a high school curriculum. The “sweet spot” for our readership will probably be first or second year college math majors who are looking for a more relaxed treatment of some of the stuff that they’re plunging into.

I'm counting the math lovers on my holiday gift list, and planning to buy each of them a copy. I'll be reading the rest of the book on the plane to Seattle this evening. And I'll let you know soon whether the adult content extends past the math.

===

It's Friday now. I just finished. My review copy is a pdf, and I need a paper copy to study the math. I just bought 4 copies; one for me, and 3 for the math lovers in my life. (Oops! I just thought of someone else I need to get it for.)

The topic I'm most interested in studying more closely is called the "Basel problem". It asks for an exact sum (in closed form) of the series . I knew the answer, but had no idea, until I read Math Girls, how it was derived. I've started to see it, and I love what I'm seeing through the mist. The coolest thing is how connected it is to what I'm teaching in Calculus II.

The only complaint I have about the mathematical exposition is when derivatives are given with no real explanation in chapter 9. I think that could have been fleshed out a bit more.

I would highly recommend this book for anyone at the level of pre-calculus and above who enjoys math. (There is no adult content besides the math.)

Risk: Betting on Your Expertise

I wrote last year about using a game called Risk to help my students review before a test. Sam Shah wrote about it recently, and today seemed like a good time to try it again, since tomorrow is their big test on trig functions. I had my handout almost done (it was 10 minutes before class), and Word crashed. No, I hadn't saved it...

So I gave them a blank template, and put the problems on the board, mostly from memory. It actually worked better than handing out all the questions at the beginning. It raised the energy level, and kept the best students from working ahead. The best way to do this would be to have the blank template for the students, and one that fills in one question at a time on a powerpoint deck. (But I don't have a smart classroom for this class.)

My students loved it, and worked way harder on the problems than they otherwise would have. I hope their enthusiasm leads them to study enough to do well on the test tomorrow!










Edit: I seem to be getting a lot of credit lately for this game. I learned it at the 2010 AMATYC conference, where Janet Teeguarden used it to spice up her presentation on the history of pi. It's my understanding that she created it. I'm glad all us bloggers are spreading a fun idea.

A More Personal Post: Considering Our Options

This is not about math. It's about finding a good experience for my son.

My son is 9. He was at a freeschool for Kindergarten through 2nd grade, where he got to play all day with lots of friends, and zoom around on bikes and scooter, and it was mostly good. When the school closed in 2010, one parent opened a mini-school in her home. That was a good experience too. She was hoping to expand, but that didn’t work out. There was a different teacher involved this school year, and the location has changed a bunch. They have just now decided that it’s not sustainable (there were only two students for most of the fall), and will end in December. So I am looking for a good situation for my son. I see 3 options:

1. Start a mini-school in my home, contract with a marvelous teacher / mentor, and find other students to join my son. I like the idea of schools as community centers, which I wrote about here. (Pros: I get to find just the right person, and if it works out really well, I can encourage other working parents to try it; cons: this will take lots of time.)

2. Send him to a school with a good philosophy: Diablo Valley School (pros: kids make the decisions, $760 a month is affordable; cons: far away, not much outside play space) or Crestmont (pros: close, almost affordable; cons: so different from what he’s used to; unknowns: how much choice do the kids have, how much playtime, what is their day like? And there may not be any openings...).

3. Find an unschooling family who’d be interested in having him join them 3 days a week (TWTh).  I’m not sure what the pros and cons are, but I am excited by this possibility.  If a family you know (close to Richmond, California) would enjoy having another kid around, we’d like to talk with you.

If you can see any other options, I’d love to hear them. (Public school is not an option on my list, because academics are pushed too early to be developmentally appropriate, there's way too much testing, etc.  I know of one public school I think would be good for my son, but it's in Minnesota. I can’t afford most private schools. I am a single parent, and I love my work, so staying home is not an option for me.)

My son is very smart, but is 'behind' academically because he's never done conventional school. He loves biking, trampoline, cars, taking photos and videos, and being silly. I sometimes imagine him becoming an engineer or inventor, but there are so many possible paths, I mostly want him to fill his days with adventures, learning what he's moved to learn.

Got any ideas for us?

What does a good classroom look like?

 

You might not expect it, but the desks make a big difference.









One of my favorite parts of the Math and Technology Workshop run by Maria Andersen in August was her session on what she called ELITE classrooms. And the best thing I learned in that session was how much the desks/tables mattered. Maria said:

In a classroom with desks in rows, you're pushed to lecture more, that's what the room tells you to do. People have taught the same class in this room and in a traditional room, and it makes the 2 classes completely different. They hated the traditional room.

 I'm doing well with having students push the standard desks into groups of 4, but I would be delighted to work in a room with tables like these.

Maria also recommends walls covered in whiteboards, a document camera, and a smartboard. I think the least high tech (desks and whiteboards) will make the most difference. Maria has just posted a summary of her recent presentation on all this.