Every now and then a student says something that makes me beam with pride. In my last post I asked my current students (particular those in MATH 280 and Calc II) to write and let me know what they needed to help finish out the semester strong. A large number of them responded, offering not only ideas for end-of-semester activities, but pep talks for one another and advice on helping each other across the finish line.
I wanted to pull a rather lengthy excerpt from one student's response that I thought did a better job of explaining what learning...and, in fact, doing...math is all about than anything I've ever said.
In this student's words,
Before college-level math, there was no wrong-to-be-right for a lot of students (myself included). A concept was explained and then you applied it and moved on. Right is right and wrong is wrong.The upshot: don't be afraid to be wrong; you'll almost certainly get it wrong before you get it right, and there's no consequence for going down a dead-end street. I could not have said it better myself. Literally.
Especially before this class I would have found it very hard to believe that I could spend 6 hours on a problem, and that 5 of them would be spent barking up the wrong tree. I then would have found it near-impossible to believe that those five hours were vital to the process.
As far as the group work goes, it helped a lot when every time I found myself up a wrong tree, there seemed to be another student or two up there with me, searching for some sort of elusive coconuts. We then climbed down together and gave each other a boost up the next (for better or worse!).
I get to hang out with these people all day, every day? I'm a lucky guy!