Sunday, October 31, 2010

Alphabet Books, and A is for Abacus

I used to like making alphabet books for my son. He and I made a book together we called the Cool Car Alphabet Book. We mostly used Wikipedia for photos, and managed to find a type of car for every letter. I use a program called ClickBook to get the pages to come out right. (Pages 1 and 2 go with 19 and 20, and then 3 and 4 go with 17 and 18, etc. Staple and fold, and you've got a book!)

Today I got the urge to do a math alphabet. It's been done before -  G is for Googol: A Math Alphabet Book looks pretty fun. But I thought I'd have fun doing it, and maybe I'll come up with something a bit different. I think I might write a short blog post for each letter. (Sue, do you know how to write short blog posts?) Some letters look more fun than others. I hope you'll enjoy coming with me on my journey from
A is for Abacus and
B is for Binary, through
Z is for Zero.

A is for Abacus
Many years ago my mom got me an abacus for Christmas, just like the one you see here. It had a little booklet with it called Bead Arithmetic, with lessons on all the basic operations. I learned to add and subtract, and began learning to multiply. I had fun with it, but didn't go very far. (I never learned to divide, and have no idea how one would find a square root on it.) I still have it, though I haven't played around on it for years.

This is a Chinese abacus (suanpan). The five bottom beads are ones (times a power of ten) and the top beads are fives. To start, you clear it by pushing all bottom beads down and all top beads up. To represent 57, the second rod from the right would have one top bead down for the 50, and the last rod would have one top bead down and two bottom beads up, for the 7.

If I remember correctly, the procedures for adding and subtracting sometimes used all of the beads on a rod, although the final form of a number never uses all five bottom beads or both top beads. (I just now learned from Wikipedia that this bead configuration can actually be used for hexadecimal numbers (base 16), since you could represent any number up to 15 on each bar.)

Expert abacus users can perform arithmetic on an abacus faster than most of us can do it on a calculator. Here's a sweet video of some kids in Japan taking classes to learn how to do mental math while visualizing the abacus (the Japanese abacus is called a soroban).

It might be fun for kids in this country to learn to use an abacus when they're working on addition and subtraction problems. Feeling the beads while thinking about the numbers would be  grounding. Elementary teachers might enjoy learning to use the abacus along with their students, approaching arithmetic from a new angle. I think the best thing parents can do to help their kids with math is to learn some math themselves. If you're up for it, get yourself an abacus. Here's an online abacus to play with for now.

My son goes to a mini-school with just 5 kids in it, currently held in our friend Felicia's home. After I started writing this, I asked her if she'd like to teach some math on the abacus and she said sure. Yesterday I went to Oakland's Chinatown and bought 6 of them, for \$6.50 each. (Available online here.) I'm hoping she gets the kids intrigued enough that they'll try to teach their parents!