Even though I’m dyslexic, I’m gifted in math. In fact, in second grade I was at the top of the class in math and the bottom of the class in reading and spelling. I thought it averaged out and I was doing okay. Unfortunately, it did not work that way.
It was also in second grade that my teacher informed me that if "I didn’t show my work, I would never be a good mathematician". Of course I never showed my work. But I already knew I was a good mathematician. This began my battle with the industrial–educational complex over showing my work.
For many years, I enjoyed this battle. However, in high school this began to change. At this time, my sister asked me to help her with her geometry problems. This was very exciting to me for a couple of reasons. First, my sister was wicked smart and she often helped me. Also, she had spent endless hours playing rhythm guitar to Wild Thing, while I invented different guitar leads. This took the patience of a saint. Importantly, she never ratted me out to my parents.
When we sat down at the kitchen table, I looked at the problems in triumph. I then proceeded to tell her the answer to each problem. At first, she looked amazed but then her expression turned to shock. She said, “I can’t turn these in without showing my work.” I was devastated. For the first time, I wanted to be able to show my work, but I couldn’t.
The question is, why couldn’t I show my work? I was obviously doing something right. I just didn’t know how to communicate it. I do not work out most math problems using a step-by-step process. I just see how it works. The more I talked to people and thought about how I do mathematics, the more I began to understand it. Most often, I see movies in my head, groups and bundles of things that shift and flow. Sometimes I see geometric shapes.
For example, if someone read me the following problem;
John bought a video game for two thirds of what it cost new. He paid $20 for it. How much did it cost new?
I know the answer instantaneously. I don’t do the computations. The best way for me to explain it is to show you.
I start out picturing $20.
$ $ $ $
$ $ $ $
$ $ $ $
$ $ $ $
$ $ $ $
Then I break it in half.
$ $ $ $
$ $ $ $
$ $ $ $
$ $ $ $
$ $ $ $
Then I add a third half.
$ $ $ $ $ $
$ $ $ $ $ $
$ $ $ $ $ $
$ $ $ $ $ $
$ $ $ $ $ $
I have my answer. I don’t think about the steps, it just kind of happens.
The irony is that this creativity and visual thinking is exactly what makes a gifted mathematician. Teachers should promote it instead of discouraging it.
However, I do understand the teacher’s dilemma. She needs to know that the student didn’t copy the answer. If the answer is wrong, she needs to understand why the student made a mistake. I have a couple of recommendations.
- Ask the student to explain how he got the answer.
- Ask the student to draw a picture.
- Let the student use manipulatives to demonstrate how he got the answer.
We also have a responsibility. We need to be able translate our unique ideas and visions into words. I believe learning to do this is a lifelong process. The earlier you can start, the better. It helps if you understand why you are practicing this skill. It is not for your teacher or your parent. It is for you. No matter how brilliant you are, without this skill you’ll end up being isolated and ineffective.
Be well and make a bit of noise,
Dr. Michael Ryan
