For teachers in Colorado, our most important metric is how much growth a student makes in a year’s time. How do you help students grow? There are so many pieces to that puzzle. I’m fortunate in that I work in a terrific, high-functioning team. We are very goal-oriented in our planning. We reflect often on how our lessons went and what we need to change.

I remind myself often that I don’t need to get all of my students to be proficient in every skill we teach; I am responsible for making sure my students grow from wherever they started to wherever they end up. To that end, I need to know from where they are starting. We do a lot of pre-assessing on my team. We group the kids every Friday into flexible math groups, and many Thursdays, they can expect a little quiz to find out what they know and what they need to know.

And yet there’s more to all that pre-assessing and data gathering. Sometimes, it helps me if I think of a particular student that I felt had a real turning point during the year. Last year, I had a student who I will call Aaron. Aaron was a very quiet, bespectacled kid who rarely made eye contact, never turned in homework, and only did minimal work at his desk if you hovered over him. His test scores had dropped steadily over the years, crossing into Unsatisfactory territory when he was in sixth grade. He was new to the school. In the fall, I decided a good first step would be to figure out if getting him to complete his homework would turn things around. I called his parents and set up a meeting to alert them to what was going on. I learned from them that he had a really difficult fifth-grade year in math and things started to go downhill then. I suggested he stay after school for homework help for a while until he started to find his feet.

The homework time was valuable for both of us. I used the time to gather information about his strengths and weaknesses. One afternoon, while he was working problems on proportions, he puzzled over the problem: 2/9 = x/27. I knew then that Aaron didn’t understand proportions, but I wasn’t about to teach him proportions unless he was ready to learn it. So I asked some questions to find out what he knew.

Me: “What if you think of it as equivalent fractions? Two-ninths equals how many twenty-sevenths?”

Aaron: “I don’t know.”

Me: “Maybe an estimate then. Is two-ninths greater than half or less than half?”

Aaron: “Less than half.”

Aha. Aaron did know some things about fractions as a portion of a whole. This was really helpful.

Me: “What would be less than half of 27?”

Aaron: “10?”

Me: “What made you say that?”

Aaron: “Well, 10 is half of 20. And 27 is more than 20 so 10 is less than half.”

It’s not a terrible estimate. Aaron’s numerical reasoning skills really weren’t bad at all, I realized at this point. He has decent number sense and this is a strength.

Me: “Okay. If we scale up the original fraction, we can find the value of that x. What’s 27 divided by 9?”

Aaron started counting on his fingers. But I wasn’t discouraged one bit. When he started counting on his fingers, I knew that Aaron, while not knowing his basic facts, did know a meaning of division. He knew it meant how many times a number goes into another.

I started the homework session with a student who had an unsatisfactory standardized test score and a string of failed tests. But I ended the homework session realizing I had a student that understood division and knew that a fraction represented a portion of a whole. He was ready to learn proportions, with the help of diagrams, manipulatives, grids, and some flash cards to help him with his facts. He wasn’t ready to abstract the proportions yet, but he was ready to learn about equivalent fractions and what they represented. We had a starting point. We worked from there.

When I gave feedback to Aaron, I told him about just what I’ve written here. I didn’t give him meaningless praise, but I told him I noticed his good number sense and his understanding of division. I said I thought he would make great strides this year and that he was ready to make a leap.

And he did. He grew a ton. Aaron’s standardized test score moved up a performance band, from Unsatisfactory to Partially Proficient. He failed tests less often. He talked in class and engaged in group work. He smiled more often. He may make another leap this year – I certainly hope he does.

I think of Aaron often and how in my assessments, I need to dig deeper to find out what the kids know – not just what they don’t know. From there you can grow.