A story

A few days ago my 3rd grader and I were walking the dog when she spontaneously began to ask our dog multiplication questions: “Charlie, what is 9 x 5?” It wasn’t entirely clear to me what my role in her imaginative game was supposed to be. Did she want me to answer for him? Was she planning on answering in Charlie’s voice? So when she asked the question again, I stalled, and said, “If you’re going to ask Charlie math questions, you need to know the answer. Do you know what 9 x 5 is?”

One weird trick

Now, I have a theory about my daughter, and there’s no way to substantiate my theory, and I am completely aware that it’s the theory I want to be true, which is maybe why I believe it. But my theory is that my daughter’s current very positive relationship with mathematics (a very recent development) is almost entirely due to “one weird trick” that we’ve been using in our home since she and her older brother were very, very young.

This is not click-bait. I’ll tell you the trick. The trick is a question:

“How do you know that?”

If I could give parents exactly one piece of advice for helping their kids learn and love mathematics, it would be to ask that question, early and often, with genuine curiosity.

My 5th grader is great at memorization, has a natural curiosity about numbers and patterns, and learns quickly when it comes to mathematics. My 3rd grader, on the other hand, has a hard time even remembering what she went up the stairs to do, is curious about a great deal of things but not particularly curious about numbers or patterns, and does everything at her own pace, which is usually slower than the adults in her life are comfortable with. In a typical classroom, none of this bodes well for her math learning, and in fact up until this year she hasn’t really cared much for school math.

But she does enjoy doing math at home with me. When I asked her about this once, in second grade, she said that at home, I always ask her how she got her answer, and listen to her. At school there are just so many other kids in the class, and no one is asking her that. ¹ My interpretation of that explanation was that at school, she feels like the math is being handed down to her, and she doesn’t always understand it. At home, she feels like her thinking is centered, and that she has interesting and important things to say.

I’d like to say that, as a math teacher with a particular interest in children’s mathematics, I spend a lot of time designing cool math activities and looking for math in the world around us, and yes, I have great ambitious to do just that. But mot of the time it’s a problem here or there, a conversation on a walk with the dog, a moment after dinner going over the worksheet her teacher sent home. It’s really not about the amazing math activities we do. It’s almost all about the question.

Why does it work?

Asking “How did you do that?” or “How did you know that?” is a simple switch, but it doesn’t mean it’s a natural one. As adults, our inclination when doing math with kids is to

• validate correct answers and correct incorrect answers, and
• teach correct solution methods.

Changing the response also changes the entire nature of the adult-child conversation. It puts the child’s thinking first instead of the adult’s, which is a much more effective way to build a child’s confidence, support their learning, and find joy in doing mathematics. Here are some ways I have seen this with my own 3rd grader:

• Building Confidence. A. is not the fastest mathematician in her classroom, and she is very, very quiet in class. Recently I took my college students to her school to interview children about their math strategies. I requested that my daughter be one of the children, and her teacher looked hesitant and said, “But A. never talks.” Five minutes later, A, was sitting on the floor with two complete strangers, happily solving math problems and explaining her thinking before my students could even ask.
• Supporting Learning. My daughter is resistant to being told what to do if she doesn’t already have buy-in. If I try to tell her, “here’s my way to solve this problem,” she generally doesn’t care, and it won’t stick. But if we begin with her thinking, she’s much more excited about learning. For example, when she shared with me how she solved 9 x 5, I asked if she could do the same thing for 9 x 6, and she wasn’t sure. It took more thinking and an incorrect answer along the way, but when she got there (“Oh, it’s 54!”), she was so delighted to realize that her strategy worked for any multiplication fact with 9s.
• Finding Joy in Mathematics. More than anything, this is fun! Last year in 2nd grade A. was supposed to regularly compete problem set worksheets for addition and subtraction within 20 at home. Initially, I did not love the idea. It was just rote practice, week after week, with no variation in the types of problems. But here’s where the “one weird trick” description is, well, weirdly appropriate. Because asking, “How did you know that?” completely transformed what could have been mathematical drudgery into something delightful. I have so much more to say about this particular experience, and maybe someday I’ll write about it, but suffice it to say now that the thing I thought would be stressful or tedious for us became, at least most of the time, a joyful experience.

How to

It’s so easy! Just ask the question, and then be genuinely curious about what you’ll find out.²

Ask the question about interesting math problems. Ask the question about math problems that don’t seem all that interesting, and see if they become interesting.

Ask the question when your child gets a wrong answer. Maybe they’ll figure out the right answer as they respond, or maybe you’ll learn something about the right ways they’re thinking even if they didn’t get all the way there.

Ask the question if you know a lot about math. Ask the question if you don’t know much about math. Your kid knows things differently than you do, and you may be surprised how much they learn.

And ask the question early and often, because this one weird trick is not a quick trick. It’s a question that works well now, but gets better with time.

1. This is not in any way a critique of her teachers. No matter how good they might be, no teacher in a class of 29 kids can give the kind of one-on-one attention a child is going to get in the home. Which is why this is a strategy I recommend especially for parents. ↩︎
2. Or ask a variation on the question: “How did you figure that out?” “How did you get that one so fast?” “How did you think about that?” “How did you know that…?” “Why did you choose to do it that way?” ↩︎