Saturday, August 27, 2011

If Math was Taught Like Art

The class is algebra. The students are divided into two groups. There are those who aspire to be mathematicians and those who took it because it seemed fun.

The professor will walk in. He will be a man who wanted to teach and is, or he will be a guy who wanted to do math and isn't. One will be an excellent teacher who knows nothing or an excellent mathematician who can't teach.

He will strut to front of the class and tell them what mistakes they are going to make on their assignments. This announcement can range from extremely accurate, "You will forget to carry the one," to very arbitrary, "You should never use a pen." The more arbitrary, the more the students will proceed to hear about for the rest of the course. “She wasn’t wrong for trying to use a completely different equation, but that she did it in ink.” In a different class (if she ever does try to take algebra again) the teacher will tell her that it is important she does the opposite. "Use a pen. I want to see when you did something wrong."

The lessons will be based around previous teaching methods. Exercises, lecturing, techniques, and homework will be identical to the professor’s styles. The work will not be based around how the teacher himself actually does math, but how a person who is bad at math should do it. He will often say, “The professionals never use this technique, but you need to learn the rules before you break them.”

The techniques will have great benefits, but only in certain circumstances. Due to overexposure and irrational force, the students will brace against the "absolute" lesson and never use it. When Susie is bad at multiplication, using paper clips as a visual suddenly makes it clear. When Jimmy is slowed down by having to use paper clips for every problem, he decides the teacher doesn't know what he's talking about.

That belief will be furthered when the teacher continues the busy work taught to him. Games and exercises meant to make the situation more fun will be played without thought as to actually how it will help the students now. The procedures have merit, we can directly understand how they intend to benefit us, but they are often taught more because they’re easy for the teacher to occupy attention with than that they're useful.

On the homework itself, the teacher will hand it back with the solutions written on it. He may go so far as to find where the equation turned sour and say, “This should be this.” She makes the changes, but won't be able to do it herself the next problem. If the student’s lucky, the teacher will try to not just hand her the answer, he will try to lead her there. But even in that case, more often than not, she will spend her time trying to figure out what he wants as he asks her, “What did you do here?” rather than trying to figure out to fix the mistake.

And, of course, the teacher has no answer key, so he’s sitting there trying to solve the equations in his head as he helps her. He realizes that if she catches him not knowing the answer, she may dismiss him as an expert, so he must pretend to know exactly what he’s doing as he goes.

The main way he attempts to grade homework is by giving it to the other students. He believes this will demonstrate their mistakes if they can see it in others. They will get together in a group and talk about what everyone did wrong, but, of course, most of them have no idea.

The people who are there who want to do math for the rest of their lives are too busy trying to prove they should be there and they do know what they’re doing to really look attempt for problem solving, on their own or others. Like the professor, they don’t want to be caught in a mistake.

The students who came in for fun want it to be fun and don’t want to have hostility. They will stick to the safe route of what the teacher told them, so they’ll often just repeat back what he’s said a million times: “Is that a pen?”

The organization structure of the class causes minimum teaching efficiency. Because algebra is the math class that non-majors and majors have to take, the students find themselves with varying levels of interest and knowledge.

More often than not, it can be the only math class offered. In freelance classes outside of the university, such as an opportunity at a library or a paid tutor or an independent class offered at a community college, the student finds herself retaking the same algebra class over and over again, despite having gone to many different places.

Because it has this mix, the class becomes geared towards the common denominator. It teaches the basics (addition) for the entirety of the course. For those who are trying to get better at math, this proves frustrating. Those who wanted to have fun, didn't, and they flee.

Because of this constant repeating of "beginner courses," class searches become less about the subject matter and more about the quality of the teacher.

The best math teachers are the ones who care. If they are more interested in math itself more than teaching, no matter if they are great at it or not, they are more likely to end up hurting their protégés in the end.

A bitter teacher can ruin a student. He will tell her that she will never use math in the future. He will tell her that she will not get anywhere with it. He may even “lovingly” inform her that she is so terrible at it that she should go into another field. He is, of course, telling her this for her own good. So she "doesn't waste her time."

If a student is younger than average, some people may go as far to say, “You shouldn’t try to do algebra yet. Wait until you’re older.”

The outside world does not consider the best mathematicians the ones who went to school for it. Having a degree in mathematics doesn’t mean the student is any better than the man who’s been practicing since he was three. There is a reason why most aspiring mathematicians don’t bother going to school.