Friday, October 16, 2009

Math methods

When I was in school, I was pretty consistently a math underachiever, always scoring in the top percentiles on standardized tests, but rarely succeeding in class. My mother blames this tendency on my second grade teacher, who liked to announce to the whole class when I made a mistake. Some of it may also be due to gender bias -- girls weren't supposed to be good at math. But whatever the reason, it was my own lack of confidence in math that kept me from achieving well. I second guessed myself all the time. Frequently I would look at a problem and know the answer, but without knowing exactly why I knew it. Then, in trying to prove it to myself, I'd make a mistake. It wasn't until I was in sixth grade, while at the American School in London, where my math issues were identified appropriately. I didn't need remedial math. I needed more challenge and confidence. So along with 3 or 4 other kids in my grade and the grade above, we were pulled out of our regular math class and put with Mrs. Heumann.

Mrs. Heumann was one of the very best teachers I ever had. She was tiny and wildly energetic, one of those people who seemed to inhabit her whole body and also several inches of the space beyond. I had thought I'd been thrown into remedial math, but Mrs. Heumann didn't seem to know that. She worked us hard. On the very first day, she took away our pencils and paper. "We're doing math in our heads. Because you need to know that you can." And I could. We all could. And we were good at it. I moved away before the end of that school year and I was very sad to say goodbye to Mrs. Heumann. But amazingly, some of her lessons stuck, especially the one about "you can do it." I still battered my head against the wall sometimes with math, but I kept at it. I was even on my junior high math team for a year. I couldn't believe it.

But after high school calculus, I never took math again. I went to a college without distribution requirements outside the major. The closest I ever came to math again was a microeconomics class that was so bad, I stopped going to class after the first month. The teacher was canned after a single semester and I got the only D on my college transcript. Pretty good, considering I only ever showed up on test day and rarely cracked a book.

But as I see AJ struggling in similar ways, I've been thinking about all this again. AJ has a brain that absorbs higher math concepts readily. He's had a good understanding of complicated issues since preschool. But those things that require memorization or tedious practice often give him enough time to talk himself out of the simple solution and into something more complex and erroneous.

One of the things that can, I think, help students like AJ and like me back then (and maybe me now) are some alternative ways of thinking about the problem. One of the great strengths of the Everyday Mathematics curriculum that AJ's school uses is its support of multiple solving methods. But as the curriculum is actually taught, there are not that many methods endorsed. I've been digging around for other possibilities to help. AJ is very visual and physical, so here are two that have interested us in particular.

1. Finger Math. At one point in my own math struggles, my mother came home from the library with this book, or one very much like it.

I was fascinated. Based on a system used in Korea, Finger Math takes counting on your fingers to a new level by assigning different values to your fingers. The fingers of the right hand are worth 1; the thumb is 5. The fingers of the left hand are worth 10; the thumb is worth 50. This allows you to count to 99 on your fingers. The book also explains how to use fingers for adding, subtracting, multiplying and dividing, although I no longer remember the methods. I need to reacquaint myself with it. Here is a website that explains the same system.

2. Chinese method. Earlier this week, Dedicated Elementary Teacher Overseas posted a video of a Chinese method of addition that fascinated AJ and I. It involves drawing lines to represent the columns of numbers and adding the points of intersection. AJ and I were both fascinated and need to play around with this a little. Here's a video explanation:

Do you have any alternative math methods or tricks you like to use? Fill us in!


FreshHell said...

Dusty has started learning geometry and I am no help whatsoever.

I don't even understand the Finger Method.

Anonymous said...

My eighth grade teacher did not assign any girls to the advanced math track at the high school. Consequently, it was not until my sophomore year that my amazing geometry teacher, Miss McDonald, said "Why are you in this class?" But it was really too late -- honors adv. math didn't fit in my schedule and I never did take calculus. But I wish I had. N knows she's good at math and M though she wasn't, but all of a sudden she loves calculus. So there's hope.

Anonymous said...

I'll have to check out this Korean finger math! Thanks for telling us about it.

Eileen, Dedicated Elementary Teacher Overseas