Deep inside the math box

Don't let the reality in!

This is depressing. I gave my intermediate algebra students the following problem. It's a standard distance-rate-time exercise (I added some emphasis to some important words):

Jane rides her scooter 6 miles to the mall to buy some shoes. Eager to get them home, she drives 2 miles per hour faster on the way back, traveling the same 6-mile route. The total travel time for Jane’s round trip to and from the mall is 2.5 hours. How fast did she travel on her way to the mall?

It's not a catchy, exciting, and engaging application problem, but it's comfortingly mundane. Certainly people live in a world where distance, rate, and time are not entirely foreign. Most of my students drive and know that traveling for 2 hours at 60 miles per hour equates to a 120-mile trip.

It's not scary stuff. Not rocket science.

One of my students—and not an indolent homework-shirking student either—quite innocently asked me (after she screwed up the problem), “What words in the problem were supposed to tip us off that we had to add the two times together to make an equation? How we were supposed to know that 2.5 was their sum?”

No, I didn't slam my head on the board multiple times, even though I felt like it.

How about “total time”? How about “round trip”? How about “to and from”?

Would it have helped to include “Hint: Add the freaking times!”?

This particular student (among quite a few others) has put math in a box. The real world isn't allowed to leak in. Don't think about how things operate in reality. It's not permitted! Math is a pure mind game that doesn't mean anything. It's just a formal system that you have to beat if you're going to graduate.

I answered her question with a question: “If it takes you ten minutes to get to school and seven minutes to get back home, how long did you have to travel?”

“Seventeen minutes,” she answered instantly, her expression suggesting that I had asked a dumb question.

I waited for the light to dawn.

Still waiting.