Mathematics at 5 Miles per Hour

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Remember learning how to drive? Remember those early teenage years when you thought, “Why do we need permits and all that behind the wheel time? I’ve watched people drive my whole life! I’ve totally got this!”

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Then you sit behind the wheel. Adjust the seat and the mirrors, secure your seatbelt…and then ossilate between the gas and the brakes until your dad yells at you to keep your eyes straight ahead of you and stop hovering over the brake pedal and good lord, girl, I’m gonna throw up if you don’t stop jerking the wheel. My God, you drive like your mother, and don’t go that fast on this road, I don’t care if the speed limit is 55, the car behind you can go around you. I don’t remember a whole lot of what my parents told me as I learned to drive. My mom probably said something like “changing lanes isn’t a right turn and a left turn. It’s a fluid movement.”
But I couldn’t learn to drive until I got out on the road and navigated it for myself. I needed to make sense of how the steering wheel worked together with the gas and the brakes. I needed to experience stopping distance and highway merging, white knuckled and fearlessly. I needed to drive on ice and in the rain. 30 miles per hour city streets and 65 miles per hour freeways. In short, observing my parents for 15+ years didn’t have nearly as much effect on my ability to drive as a few months behind the wheel myself. My parent now a guide rather than a presenter of information.

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I hope the parallels to teaching math are fairly obvious here but I think too often we feel that because a student can follow our examples and imitate in practice, they’ve learned mathematics. In the short term, that might be true. But in the long run, do they know how soon they need to apply the brakes when approaching a stop sign at 45 mph? Or just that the brakes make the car stop?

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But don’t kids need to practice their skills? Surely sense-making mathematics can’t completely replace routine practice, right? Here’s another antecdote: my high school had something called a Driving Range. Only a few high schools had them at the time, which was impressive until I realized that this Driving Range is not related to golf and wasn’t really that cool. During driver’s education class, we would go out to the driving range and practice our “skills.” At 5 miles per hour. Left turns, right turns, 3 point turns, yielding, merging, all done slower than an average runner. Sure we “practiced” all kinds of “skills.”

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Could we apply them to any problem-solving situation on, for instance, a real road? Not a chance. Most math practice is just like the driving range. We explain to our students how the left turn works versus the right turn and then send them off to practice at 5 miles per hour on the driving range. And then wonder why they have no idea what to do when they they venture out onto the road when it’s snowing.
Many who have ridden with me might
disagree that I’ve mastered driving, but they keep letting me renew my license and operate a motor vehicle anyway. And I’m thankful my parents let me venture out past 5 miles per hour.
Kids don’t need more mathematical driving range practice. They need more behind the wheel. With an adult sitting next to them, encouraging them and guiding them. Because I believe that everyone with a driver’s license can drive at the highest levels.

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*Quotes from Principles and Standards for School Mathematics, 1998.

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