Articles:What are these things called variables? and On the learning and teaching of algebra.

Two thought-provoking articles. I didn't agree with everything, but both gave me specific ideas on some problems I've noticed in my algebra support class.

At the end of the "Variable" article, the author rejected the notion of a lecture on all the meanings of the term "variable". I don't know about a lecture, but I think more specificity is exactly what some students need. "So if you have one variable in an equation, you can solve for a specific value. Two or more variables in an equation, it's spelling out a relationship that can have many solution pairs." And so on. I will be taking this tack in my algebra support class.

The other article talks about the "reversal" process of solving algebraic equations. I have actually used this before in test prep--encouraged students to circle a term and treat it as one entity, ignoring its complexities and looking at the big picture. While I like this method, it's hard to get students to see the equation at this simpler level. However, I just realized that I can use the "reversal" process to help my algebra support students with one of their great archenemies: working with negatives. For example, 5-(-2) can be reversed. If 5-(-2) equals something, then something + (-2) equals 5. Most students can get to 7 from there. I'm going to try that next week.

I did dislike the doom and gloom tone of the second article, mainly because I don't think these articles about the sad, sad state of math affairs are accurately reflecting reality. For example, three paragraphs on the horrors of the bus problem. So the heck what if a lot of students didn't register the actual question, as opposed to the underlying problem? The important thing is that they knew the right method to solve the problem. Do they really think that the students wouldn't figure out that they'd need 32 buses in real life? Of course not. They're just fussed because a student who really cared about completeness and accuracy and applying math to real life would realize that 32 buses were needed. Well, boo me a big old hoo. Many, many people just don't care enough. Once they've solved the underlying problem, the relief is so huge that they don't want to look back. They're done! They got an answer! Leave them alone!

But the important thing is they knew the underlying problem, and they knew how to solve it. The authors are focused on a failure that has nothing to do with math itself--again, unless they want to argue that the students wouldn't quickly figure out they needed that extra bus in real life.

I'm similarly skeptical of the other examples and think the case is overstated. I do think learning algebra is difficult and that concrete thinkers are going to have an even tougher time. I just don't think the state of math knowledge in this country is as bad as they paint it.

Still, both articles gave me some valuable teaching ideas and so I forgive them their occasional dramaqueeniness.