*Caution: this is an inspirational story of a child overcoming obstacles to succeed beyond anyone’s expectations. So at the bottom I’ve drawn out two lessons I learned from this student that teachers don’t often talk about.*

In my first three years of teaching, I taught a girl named, let’s say, Ana, who started 6th grade as a terrified, anxious student on the verge of failure and ended 8th grade by placing out of Algebra 1 and into Geometry for high school. Since that time, she has continued to make remarkable progress as a math student, beyond even what I thought she was capable of doing.

The funny thing is, her transformation happened so slowly that I almost didn’t notice. Her improvement during her three years in my class was so steady and gradual that I didn’t fully recognize it until the spring of her 8th grade year.

Ana walked into my class in 6th grade with a crippling math anxiety. Her struggles in math were so profound that she had been diagnosed with a math-related learning disability. She hardly knew any of her multiplication facts (she struggled with 4*3, for instance), and the sight of word problems on a math worksheet terrified her into paralysis.

But over the course of the year she got to work. She never spoke up in class, but as I walked by her seat she started asking me questions. She completed her homework every night and came in before tests to ask me questions. She still failed many of those tests, but she retook them until she passed them.

In seventh grade, she opened up a bit. She still didn’t like talking in class, so I told her that I would only call on her when I knew she knew the right answer. With that assurance, she started sharing her ideas in class more and more. Her work improved, but was still marred by years of conceptual gaps that she was still struggling to overcome. She was moving in the right direction, but she had a long way to go.

I remember working with her after school one day. After a few warm-up problems, I told her we were going to try something different. “Here comes the boulder” she said. I asked her what she meant, and she said “You’ve been giving me the pebbles. Now you’re going to give me the boulder.” She always had a way with words.

In eighth grade, Ana took Algebra 1 because it was the only course offered at our school for 8th graders. We knew that this would be a struggle, so I met with Ana and her mom and assured Ana that this would be a great year to build a foundation in algebra so that when she went to the public high school, she could take Algebra 1 again and feel very comfortable.

Ana took this as a personal challenge. She started working in small groups, sharing her thoughts and asking her classmates to critique her work. She became an advocate for her own learning. At the end of the school year, she took the placement test for high school and placed out of Algebra 1! I didn’t know what to say, so I met again with her and her mother. We all agreed that if the high school felt that she was prepared, she should give it a try.

I kept in touch with her mom since that time. In 9th grade she did so well in Geometry that her teacher recommended that she move up into the honors program, an almost-unheard-of advancement in this challenging school. She continued to succeed in the honors course and recently earned a score on her Math ACT that places her in the 95th percentile nationally.

This is just staggering progress. This girl went from being one of my biggest strugglers to being among the top math students in the country. Pebble by pebble, she built a mountain.

Because of Ana, I can’t believe that kids who struggle in September are damned to struggle for the rest of their lives. Because of Ana, I know that kids’ brains truly are capable of remarkable growth, and that we don’t truly know a child’s potential until we give them a sustained opportunity to find out for themselves what they are capable of achieving.

Ana is the reason I don’t write kids off as lost causes. If I did, I would have written Ana off pretty quickly. And she would have continued to struggle, and she would have stayed in the low track, and she never would have found out that she is actually a very good math thinker. And I’d be another teacher who talks about “high kids” and “low kids” as if those are two distinct and immutable categories.

So yes, this story is inspirational. But that’s not why I wanted to share it. I have two other reasons.

### Lesson One

If I hadn’t taught Ana for three years in a row, I never would have known this story. I just happened to be the only math teacher at this small private school, so I just happened to teach the same students in 6th, 7th, and 8th grade. As a result, I got to see Ana blossom into a strong math thinker.

But if I had only taught her in say, 7th grade, I never would have seen that transformation. I would have seen a girl grow from a weak math student to a somewhat-less-weak math student. And I never would have recognized the enormity of the shift that she was undergoing.

That’s because learning doesn’t always move at the pace of the school year. Sometimes it happens glacially, and only those adults who know a kid for several years get to see the full trajectory.

I worry about this fact because the vast majority of middle and high school math teachers do not loop with their students. Most of us only get to see our students for one year. Most of us miss these types of stories, which means we are more likely to believe that “low kids” stay low forever. That worries me.

### Lesson Two

In the past I’ve told this story as inspiration for my students, but I realized last year that I needed to ask Ana for her perspective. So I emailed her and asked her for her side of the story. Something she wrote to me really stuck out:

Man, does this hit me so much harder than a generic inspirational story. And it rings truer. Math is still hard for her. But she's made a commitment to improve. She made it in 6th grade, then again in 7th, again in 8th, and in every year since then.

I mention this because I want teachers to remember what we are asking our struggling students to do. We are asking our students to work harder than their peers to catch up in math, and then *continue working harder than their peers for the rest of their educational lives.* That's a huge thing to ask of an 8 year old, or an 11 year old, or a 15 year old. But that's what we're asking.

I believe that kids can grow smarter with hard work and dedication. I've seen it firsthand. But now, thanks to Ana's email, I know just how hard that hard work can be.