Strong Students Aren't Always Ready for More
Though sometimes they are
A few years ago I taught a kid that I’m going to call Sophia. In the past, Sophia always told her parents that math was her favorite subject. As a 3rd Grader she was already comfortable with multiplication, division, subtraction and addition, and had a great foundational understanding of fractions.
And yet, her parents were concerned, because Sophia seemed to have lost her enthusiasm for math at school.
She complained at home that math was too easy. She told her family that she was finishing everything faster than her peers. Sophia said that the class moved too slow. She didn’t have a problem with her teacher—me—but she wanted to know when I’d be getting to the new, harder stuff.
When I learned about this, I have to admit, I smiled.
In class, Sophia definitely did finish worksheets quickly, though a bit sloppily. She was what Bowen Kerins and Darryl Yong call a “speed demon,” eager to fly through problem sets.
Her arithmetic skills were, without a doubt, exceptional.
But she skipped problems that she didn’t initially understand. When I came over to try to help her, she would quickly tell me she understood to end the conversation. She expressed boredom when given extra, personal challenges.
There was only one exception to this: algebra. She loved solving equations with letters instead of numbers. She wanted to know, when would we be doing more algebra? Would we get to algebra soon? What grade do people typically study algebra? So are we doing 7th Grade work?
Even though I’m talking about Sophia, I could also be talking about David, Rory, Chandra, or any number of other kids in my “accelerated” 3rd and 4th Grade math classes. They were very accomplished with the grade-level material, but often not at all ready for more.
Outside of math education, I think people sometimes see math as a stacked pyramid you can ascend or a faucet that you can simply turn on (for more) or off (for less).
Why not let students climb higher if they’re ready for it? Why not simply give them more?
I’m not saying that this attitude is wrong—I was trying to give Sophia more, after all. But what it misses is that Sophia had both completely mastered K-4 mathematics content, and was also not really ready for broader mathematical growth.
Oh sure, I could have shown her some “5th Grade skills.” She could have continued computing stuff with decimals and fractions. She could have learned some equation-solving moves to really dig into the algebra. She would have been happy with all that.
She was completely ready for any computational problem that resulted in a numerical answer, but algebra involves a lot more than that. She didn’t want to make a table. She didn’t want to turn a description into an equation. She wasn’t ready to graph, to sketch, to prove or make arguments. She was at her happiest when she had 10-30 similar problems of moderately increasing difficulty—not a bad thing at all! But also not ready for problem solving challenges and sophisticated reasoning.
Mathematics isn’t a continuous flow of material, even in school. First comes whole numbers and arithmetic, and then comes everything else. And here is a truth that I have observed over and over again: some kids just LOVE whole numbers, and until they get older want nothing else.
When my oldest, who is going into 3rd Grade, was younger he used to wake us up with a multiplication problem. He’d run into our room at 6 AM and shout, what’s 19 x 15? And at first we thought this was cute and then we told him that it was obnoxious, but he still did it and we were sort of proud.
My boy has his obsessions, and this one lasted for a while. For about a year, maybe two years, it was multiplication, division, and factors, all the time. He wanted us to give him math problems—though it turned out that he was interested in a fairly limited chunk of math. Much like Sophia, my attempts at turning him on to puzzles or problems was not entirely successful.
Look, I love math. Math is great. But even I have my limits, and I was quickly getting tired of giving him arithmetic problems to solve.
The boy has since moved on to Rubik’s cubes, NBA stats, Harry Potter, Percy Jackson and Greek mythology. He still likes math, but the obsessive streak that pushed him to independently explore the K-5 arithmetic curriculum is thankfully over.
And, since he only showed limited interest in the broader mathematical things that I’ve shown him, we don’t often find ourselves talking about math.
The other day, though, he was saying that he was bored, and I looked at my shelf and pulled down a Number Theory textbook. The first chapter was mostly about least common factors and “relatively prime”—20 and 30 are not relatively prime, because they share many factors, but 20 and 21 only share the factor “1,” so they’re relatively prime.
I shared started working through that first chapter with my boy, and I saw that old spark again. For the rest of the day, he wanted to keep talking about this stuff.
But then, the next day, he dropped it, and moved on back to Percy Jackson.
Maybe the way to put the pieces together is like this: the world of arithmetic is a world of skills, not concepts. But the broader mathematical world has many, many new concepts. The same brains that show enthusiasm about K-5 arithmetic are not necessarily going to show that same enthusiasm for graph theory, number theory, probability or anything else. Because that is new conceptual terrain.
In fact, some especially rigid kids love K-5 arithmetic because of the narrow conceptual repertoire. It’s familiar, unchanging, and they can play with it without having to worry about new ideas that will require them to be flexible.
Parents need to know that this is common, and that a slowdown after a child masters whole number arithmetic isn’t a sign of trouble. It’s also not a sign that the school is failing the child—it’s natural, in a way, though there are better and worse ways for a classroom teacher to manage it.
The best? Offer real challenges that warmly nudge students out of their comfort zone, to get them closer to real mathematical sophistication. But the worst is to capitulate to the child’s desires and simply give them more, more, more, more of what the child already knows. That’s not teaching, that’s something else.