Bread Crumbs and the Endorphin Rush

 Bread Crumbs and the Endorphin Rush

By Bobby Neal Winters

In my last column, I wrote that we resist learning.  In this one, I would like to continue in that same direction by talking about ways we combat that resistance.

The main perspective I can speak to this from is that of a math teacher.  While the resistance to learning I wrote about last week was with regard to topics other than skills, I do think I can add some value to the conversation.

Most people hate mathematics.  Indeed, it takes an odd breed of duck to love it. But it is useful and it is essential that at least a few people know it.  Within mathematics, our topics separate into two streams: techniques and problem-solving.  By techniques, I mean the mechanics of solving for x.  We call it “plug and chug” amongst ourselves. While most people find it difficult, it is not held in high regard amongst many in the practice of mathematics.

The ability to problem solve is much more prized, and much more difficult to teach.  It is a chicken-and-egg problem: We teach students to problem solve by having them problem solve. The best teachings do this by laying out bread crumbs for the students to follow.  

For those of you who aren’t familiar with the bread crumb metaphor, you should think of a trap having been set for a bird. Say, you have a box propped up by a stick.  You lay out a path of bread crumbs so that the bird will follow the trail and find itself under the box, and then wham! The box falls.

In math, we’ve no boxes and no bread. We have a problem we’ve solved ourselves, and we’ve broken it into pieces.  We then ask the student questions that will lead them to understand the pieces.  The trap slams shut when they put all of the pieces together to see the big picture.

This works because we like to solve puzzles.  Our brain gives us a little chemical reward whenever we solve one; whenever we come to the right conclusion ourselves.  So mathematical traps are nice; a box doesn’t fall on you, but you get an endorphin rush instead.  

Why do you hate us so?

We can learn other things this way as well. That is to say, we can come to it ourselves.

The poets figured this out a long time ago.  The poets, the good ones, visit truths for which they have no precise language, but lead us there anyway.  We spend an amount of time wrestling with their words that we would never spend on something that was written out plain.

If you don’t believe me, think about how much time you spent trying to figure out “The Hotel California” or “Stairway to Heaven.” (Or “The Love Song of J. Alfred Prufrock” if you didn’t grow up with Rock Music.) There have also been untold thousands of hours spent wrestling with the symbolic language of the Book of Daniel and the Book of Revelation.

The best teachers won’t just give you the answer. The best teachers will put scaffolding in place and let you come to it on your own.  Give a man a fish; feed him for a day. Teach a man to fish; feed him for a lifetime.  Lead a man to a way to teach himself; and he will be able to eat things besides fish.

I fear for this method of teaching during a time when there are so many tests in school. (Though that trend seems to have abated somewhat.) Those who have money and power will have it for their children, but not so much for those who work in the factories they own.

But I’ve laid this out too plainly.  You won’t believe me.  You’ll not take it up as your own idea. I have failed.

Bobby Winters, a native of Harden City, Oklahoma, blogs at redneckmath.blogspot.com and okieinexile.blogspot.com. He invites you to “like'' the National Association of Lawn Mowers on Facebook. Search for him by name on YouTube. )