2011 June 13: No more help needed on this one. Thanks for piloting this study for me, team.
If you're still in school, if you still have students around, I'd be thrilled if you'd help me answer a question that's nagging me.
If you pose this question to a student:
It took Michael Benson six minutes to run one mile in a timed trial at his school — his fastest time ever. How long would it take him to run a 26-mile marathon?
Does the student multiply six by 26 getting 156 minutes? Or, more sensibly, does the student multiply six by 26 getting 156 minutes and then add some time to compensate for the fact that Benson isn't going to be able to maintain his fastest time for one mile over 25 more of them?
My speculation is that math class pretty effectively conditions that sensibility out of a student by the fourth or fifth grade. It's very difficult to succeed at math class if you don't train yourself to ignore entropy, gravity, friction, and a million other factors mitigating these tidy word problems.
But does the medium matter? If you present those two sentences in black and white on paper, are the results worse than if you present them in a medium that's more befitting the context? Like a video? Or a newspaper clipping?
How You Can Help Me
- Print out equal numbers of these four pages. They're four different versions of the same question.
- Shuffle the four versions and pass them out randomly, in equal numbers, to your students. (Doesn't matter to me if this is calculus or sixth-grade math. The more classes the better.)
- Tell them you can't answer any questions about the problem. They should write those questions down. Let's leave calculators off the table. Ask them to do their best and to be sure to write down their reasoning.
- Give your students as much time as they need to do this one problem.
- Collect the papers.
- Get the papers back to me:
- via email: email@example.com
- via fax: 831.325.0095
- via mail: PO Box 429, Mountain View, CA 94040
I'll need to know the letter grade of each student, too. And the course they're taking. Can I get any volunteers to raise a hand in the comments? I'm not going to pretend this isn't a huge favor. You can consider me in your debt.
2011 June 7. To clarify, would you be sure to send the forms back without the student names. Feel free to just attach numbers to the top. ("Student #1," "Student #2," etc.) Or anonymize them in some other way. I only need some way to link the student's response to her overall class performance.