Tuesday, September 11, 2012

Solving Life's Equations

School recently started again and that means i get to go back to one of the things in my life that gives me great pleasure — volunteer tutoring. I tutor math to kids from elementary school through high school and the teacher in me never, ever tires of watching them "get" a topic that was previously thought impossible. :-)

One of the kids i work with this semester is in Algebra 2, and, not unexpectedly, she popped the question on our first meeting: "What good is all this stuff? Is there any use for it outside of the classroom?" I can't blame her really, it was our first meeting and i had her working through some word problems, which she told me were impossible and that she hated them. At the end of the hour she was all smiles and was saying: "That's it? That's all there is to solving these?" I wanted to hug her, but figured that wasn't a great way to keep my job.

But, i digress. In answer to her original questions, i thought i gave her a reasonable answer. Yes, there are uses for Algebra outside the classroom, although most people don't use it. I even gave her a few examples. She didn't laugh or argue, so i think she accepted my point. But, i upped the ante and pointed out that research has shown that students who do well in high school Algebra do better in all subjects when they move on to a university.

What i wanted to tell her, though, was that one of the greatest benefits of Algebra is that it teaches you to think abstractly and this improves the way you live your life. You may not like Algebra, you may not do all that well, but you learn to think outside the box, as they say, you learn to look at problems more abstractly and less linearly, and this directly affects the way you approach problems in all areas of your life.

I'll introduce these kinds of lessons little by little as we work through the semester, but one of my favorite lessons will come when we get to a procedure called "Completing The Square," a method for solving quadratic equations.

In case you don't know what that is, i won't try and explain it mathematically but it goes something like this:

  • Start with an equation you want to solve.
  • Find the piece that makes it difficult to solve.
  • Get rid of that piece. Move it out of the way. You can't really get rid of it so just set it to the side and leave it alone for now.
  • In its place add something that would make what's left over easy to solve.
  • Solve that (now) easy part.
  • Apply the fix to that piece you set aside earlier. It will also modify that.
  • Put the two pieces back together, and voila, you have a solution to your problem.

So what, she will say, does that have to do with life? Well, i'll say, that is life in a nutshell. You will have problems throughout your life and some of those will seem absolutely impossible to solve at first glance. You may see no way out from under it, but that doesn't mean there isn't a way.

What to do? Rarely is the entire problem the real problem. So, find that piece that is messing everything up and set it aside. Ignore it. Don't worry about it for awhile. In the meantime, look at what's left of the "problem" and figure out what you could do, what you could say, what you could add that would make it easy to deal with, easy to solve. Then do that, say that, add that. And stand in amazement when that piece of the problem disappears.

Now take that fix and apply it to the piece that you set aside. Since it was isolated from everything else that was going on it should be an easy fix. Once that is done, stand back and look at the whole "problem" as it originally hit you. You'll be amazed that it wasn't as unsolvable as it had first seemed.

Yes, math can be used in real life, i will point out.

And that's another of my pleasures when i tutor. Watching them roll their eyes when i give them yet another "life" lesson but seeing that they got it. They may not admit it, but we both know it's in their heart as they walk out the door.

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