We are well into our second week of classes. It has been very gratifying to see how my 8th graders have stepped up to bat, so to speak, and really put great effort into learning algebra this year. They come well prepared, happy and enthusiastic. Many of them come to class a little early to drop off their materials so they can come in right after recess and begin the warm up. I am very excited about how the year is shaping up.
We started the year with my presentation of a new metaphor for learning algebra. Last year I tried out the idea that learning algebra was like learning the rules to a game. The example I used was backgammon, a game I enjoy and enjoy teaching to my students. This year, I came up a different metaphor as I was driving down long, endless roads in central Oregon over this summer: Learning algebra is like learning to drive. I am the driving instructor and my students are working towards their driving license, but first need to master the basics to obtain their drivers permits. To learn to drive, one must learn skills, such as turning on the car. These skills may or may not make sense per se, but they can be readily learned and applied without a deep understanding of why they work. In algebra, this could be live solving equations for a variable.
In order to drive, you must also learn concepts. For example, to take a left turn, you must learn why to use the left turn signal, when to use it, what to look for ahead and behind, how to slow to correct velocity and so on a so forth. Without a deeper understanding of why you need all this and how it helps, you may find yourself unable to make this turn safely. In algebra, I was thinking of the meaning of slope and how that is applied to word problems to represent aspects of growth that help us make reasonable predictions. If one sticks with a very mechanical understanding of slope, there is a very real limitation to using it in a variety of contexts.
Finally, there is the aspect of practice. Of course, in driving, there are many hours of practice, usually guided by an adult. In algebra, I also believe in hours of practice, either guided by an adult or done independently with adult guidance as needed.
After completing a driving training course, learning all the laws and regulations determined important by some authority, and sufficient practice, you can take the theoretical and practical tests. With a passing score, you receive your license, which is to say, it is legal to drive alone. Of course, the learning will continue on for a long time and mistakes will be made and certain laws will become vague (what is the difference between a double yellow line and single white one?). But with that license, you can travel far and wide and have many more options open to you.
I believe that algebra is very similar in its scope and its ability to open up options in the future.