This is my last week of tutoring before I go on maternity leave for the rest of the school year. As much as I’m ready for a break (and as much as I want time to prepare for the baby), I know I’ll miss my students.
The other day in both of my tutoring sessions I got to do one of my favorite things as an educator: make my students discover the answers on their own. When I was a full-time math teacher I tried to do this as much as possible, but with classes of students at varying levels and a long list of standards to “get through” before the end of the year, it wasn’t always realistic. In one-on-one tutoring, however, the “discovery” method is often the way to go.
I’m always telling my students that this is what real mathematicians do: they solve simpler problems and see if they can apply those ideas to more complex situations; they look for patterns and make theories; they test their theories and try different methods.
What I try to impress upon my Internet-age students is this: It’s okay if you don’t know the answer right away. It’s okay to try things that don’t work. That’s how you end up discovering what does work.
It’s similar to what I have to remind myself as a writer: it’s okay if my writing isn’t perfect on the first go-round. It’s okay if I write a whole chapter only to end up cutting it. (Or a whole book only to end up hiding it in a drawer.) It’s okay to take my time in order to discover what works.
The other day I came home and my physicist husband was bemoaning the fact that no one does math anymore – they’ve forsaken it for computer simulations that, he says, don’t always have as much meaning as old-fashioned pen-and-paper proofs.
“I don’t know if this will make you feel any better, but…” Then I told him about how I made both of my students discover the answers to their homework questions on their own.
“And when he figured it out,” I said, talking about my ninth grade student, “he got excited and was like ‘oh I see it! I see the pattern! That’s cool!’ He had a little light bulb moment, and those are the moments that make kids love math.”
“I guess that makes me feel a little better,” he said.
My husband loves math. Not only is it what he does for a living, but he actually reads math textbooks for fun. Sometimes I feel bad that I can’t talk to him more about his interests. I minored in math in college, so there was a time when I knew Multivariable Calculus and Analysis. But most of that has fallen out of my brain by now, and besides, Paul has a Masters in Applied Mathematics and a PhD in Physics. His knowledge of math is way deeper than mine ever was, even at the height of my mathiness.
Luckily, he likes hearing stories about my students and how I teach them math. One day I was telling him about a student of mine who is smart but always making careless errors. As I was describing him, Paul said, “I know exactly what his problem is – I used to do the same thing as a kid.”
Paul said when he’s working on a problem (both when he was in high school and now), he often intuits the answer long before he understands the nitty gritty of why it works. “I’ll be thinking about the problem, and then I suddenly see the answer, and my intuition says it’s right, but I have to figure out how to actually prove it. And that’s where I end up struggling and making mistakes.”
It occurs to me that the way people do math is not so different from the way people write. A few years ago I wrote a middle-grade novel. I knew how it would begin, and I had a very clear sense of how it would end, but I didn’t quite know how to get from point A to point B. Like Paul, the middle — figuring out the nitty-gritty details — was where I struggled.
Other times, I start out with a character or situation or inciting incident and have no idea where the story is going to end up. Like a mathematician, I try different things, writing scenes and doing character studies. I think about what might be possible for the story, I write and write and write to figure out what I’m trying to say, and then one day I have a flashbulb moment where I put the pieces together – I finally see the climax or conclusion I was searching for. Those moments are what can make writing so exciting.
In the end, the most important thing to remember in both math and writing is that it’s okay to make mistakes. Instead of being discouraged if you don’t get it right at first, learn from your failure and keep trying. The delight is often in the discovery at the end of the tunnel.