Well, summer officially ended on Thursday as we went back to school. This year I have my normal load of honors pre-calculus classes along with one section of algebra 1. All the classes are off to a good start, but the first “real” discussions won’t happen until Monday, so we’ll see how things go. Yes, this includes the algebra 1 classes. While I’m not running my section in as independent and discovery-driven a way as we do with the honors pre-calc kids, I am still infusing a lot of discussion into a relatively small amount of lecturing. In particular, the emphasis is going to be on the applications as opposed to being on the mechanics of algebra. That doesn’t mean that we’re not going to work on the mechanics, because we are. Obviously, it’s a little difficult to do a basic algebra problem without the mechanics. However, I thought of/realized something over the summer about the mechanics of high school mathematics that seems to have struck a chord with everyone to whom I have mentioned it.
Grammar is important in English class. No one disagrees with this. Grammar is important and it needs to be emphasized. However, proper grammar is not the point of English class. The point of English class is to improve the communication skills of the students, in terms of their ability to both take in and interpret information and to share information with others. Proper grammar is a point of focus and an important aspect of attaining this goal, but it is not the actual goal.
Now, let’s look at a typical algebra 1 class. Are the mechanics of algebra important? Absolutely. We really can’t do much without them. However, the mechanics of algebra are the “grammar” of the subject. The point of algebra 1 (or of any high school math class, in my opinion) is to improve the problem-solving skills of the students. Solid mechanics can certainly help the students reach this goal. But if all the students can do is push the symbols around while having no idea about how to use the mechanics to solve a problem, then we haven’t really done much in terms of realizing the actual objective. For that matter, the mechanics of algebra are not the only means available to the students to solve a problem. Geometry and statistics play a vital role in helping the students become well-rounded problem solvers. Sadly, I experienced several conversations in different settings over the summer where a person solving a problem got to the correct answer without algebra and described the process they used as “not really involving any math” precisely because there was little to no algebra involved. Some used well-drawn pictures and a healthy dose of geometry, some used data tables and graphs, but since there was a lack of creating an equation and pushing the symbols around, the conclusion was that there wasn’t really any math going on.
So, in addition to incorporating a healthy amount of discussion into my algebra 1 class, my goal for the year is to get the students in all of my classes to see everything they are doing as they attempt to solve an exercise as “doing math”. I want the kids to realize that drawing a picture, creating a table, making and testing a conjecture, making a quick calculation, and yes, writing and solving an equation are all “doing math”. All are valuable tools to have at their disposal in order to reach the goal of improving their problem-solving skills.