I have written before about my philosophy of learning math. I tell my students that one needs to do math wrong first, before one can figure out how to do it right. This, after all, is the logic of doing homework. Homework gives students a chance to mull over problems and possibly go down blind alleys, only to eventually learn how to solve a problem in a way that works. I have also seen such a theory applied to many areas in life. It is often the case that we need to make our own mistakes so as to learn how not to make those same mistakes again. I thought of this last weekend as my daughter learned how to ride a two-wheel bike without training wheels for the first time.
As the neighborhood children began to shed training wheels last summer, I admit that the competitive mother in me came out as I decided to teach my daughter how to ride a bike, too. The best model I had for teaching a child to ride a bike was one taken from movies and entertainment. I convinced her to let me run next to her holding the bike for a short distance, after which I would let go. In theory, she should then continue on, riding without anyone helping her. It would be that easy, I thought.
But when I tried to teach her this way, she had difficulty learning. Every time I let go, she would go for a second or two before realizing that she was riding without help, and then, looking at the wavering ground below her legs, would fall. Before she could learn to ride a bike, the summer ended. The bike was soon replaced with a “flying saucer” sled, something she had no difficulty driving.
This past weekend brought with it not only Easter, but also beautiful weather in our part of the country, and this time it was she who decided she wanted to learn to ride a bike. She looked up at me, still recovering from my injuries, and announced that she wanted to learn to ride. I laughed at myself as I stood there, with the help of a crutch and two limbs in splints. “Go ahead”, I told her, “but I can’t help you. You might want to start on the lawn, so you don’t get hurt very much if you fall.” And so she did.
The most difficult challenge for her was getting up on her bike seat, which my husband adjusted to the new correct height, since she had grown quite a bit over the winter. And then, with me standing by helplessly, she began to peddle. Yes, she fell down a few times, but it was less than a half hour before she had taught herself how to ride a bike on the lawn. And before long, she was off to the driveway and then the sidewalk. I was never so happy that we had bought a house with sidewalks in front of it. To think, I had grown up without them!
She fell a few times, scraping her knees, but always getting back up on the bike. I have to compare her efforts to those of my students who struggle with math problems, often making mistakes before finally solving the problem. I know that someday she will study math and many other subjects in college, and I believe that the confidence she gained from teaching herself how to ride a bike will carry over into her academic studies.
When she finally was able to ride down the driveway and onto the sidewalk several times, she stopped for a second and came inside and triumphantly announced “I did it! I did it!” Yes, she did, and it took only a few scrapes on her elbows and knees. If only I could convince my students that Calculus could be just as easy!