*“You either learn your way toward writing your own script in life, or you unwittingly become an actor in someone else’s script.” ~ John Taylor Gatto*

An 11-year-old student recently asked me if we could set up a math class. I asked her why she wanted to study math. She replied, “Because I want to.” Usually this isn’t a good enough reason for me, but I know this student fairly well. She is very private and often takes her time to share what she is really thinking, so we set an appointment for the next day. I wanted to get a sense of where she was mathematically, so we went through the basics – addition, subtraction, multiplication, division, fractions, decimals, place values, and basic geometry. She seemed to have a solid foundation, so I told her we could move on to algebra or go deeper into geometry. She decided to pursue algebra because she felt she already knew a lot of geometry. We agreed to meet four days per week for half an hour.

What a pleasure it has been to work with this student. She always remembers to reserve the room, she is always ready to start on time, and she is always focused. She grasps math concepts quickly and can apply them immediately. I have to admit, for a minute or two I felt like a really good teacher. After a couple of days, however, I realized that I was doing very little teaching. The student already had a strong intuitive sense for math concepts. All I was doing was teaching her the *language* of math – a number next to a letter means that you multiply the two, a little raised number (an exponent) means that you multiply the base number by itself that many times, etc. I often reminded her that this language is just something invented to help people communicate mathematical thinking to each other.

Algebra also involves the use of variables and writing down the relationship between them. It’s a tool that is helpful in solving more complicated problems. A simple example is 3*x + 5 = y*. You can plug in a number for *x* or *y* and solve for the other variable. Solving for *y* in this case is fairly easy, but solving for *x* is a little more complicated. Learning algebra involves learning the steps to solve for *x *and *y*. I should add that these are the steps that *I* have to follow to solve a problem like this. And this is how most others have to do it too. But this student solves problems like this in her head!

At first I attempted to teach her some of the algebra “tricks” – isolate the variable, do to one side of the equation what you do to the other, etc. – and show her how to write these down step by step. After all, I can still hear my middle school math teacher saying, “Show your work.” But the student resisted and I reconsidered. She has an amazing ability to manipulate numbers and variables in her head. Why should I mess with her process? After all, she’s refining a talent that is really hard for most people, a talent that is really useful in areas outside of math.

Thankfully, I don’t take any pride in my “gifted” student’s math abilities. I sometimes think about what could happen to her in a more traditional education setting. I am sure that her math skills would be noted and rewarded, maybe even with trophies. She might even begin to believe that math is her “thing” – she’s good at it, most others think that math is the most important subject, and she often hears about the need for more scientists and engineers in the media. But is math really her passion? Does she really like it? And more importantly, is math her ticket to a happy life?

The student and I are still enjoying the class, but when and if she gets bored or her interest wanes, I will support her in moving on to something else and I’ll be happy that she is confident enough to do so.

*This blog post was partly inspired by this TED video by John Bennett – Why Math Instruction is Unnecessary – and this Psychology Today blog post by Peter Gray – The Most Basic Freedom is Freedom to Quit.*