Autobiography should not be only about the things to happened to me. If that was all it was, I would appear to be devoid of agency. It's also not only about the places I've been and events I have witnessed. That might rather be a travelogue. I believe my autobiography should reveal who I am...or have been...maybe even who I will be or might have been.
So I was looking for some essays I will be sharing in the next few days concerning Crises 1 and 2, when I stumbled upon something I wrote in April of 2006 and published to the 21st issue of Teacher's Lounge, which some may recall that I created and operated in the way back. It was a bit of a rant...and a bit of me.
|An educated mind is an opened mind. An opened mind is a liberal mind. Teachers don't have to intend to create liberals, it happens naturally.
I am totally aware that the subject matter may chase away some of my readers. But any subject matter contains the seeds of that possibility.
On Thursday (April 13, 2006) plf515 posted a diary entitled, Why teach math? I'll give my response a little later, but first off I feel like I need to address some of the commentators, the ones who apparently didn't care for that question or thought the question was other than what it was. Of course, the diarist himself changed the question to, "Why teach math so freakin' BADLY?"
There were a lot of comments concerning the question, "How should we teach math?" and "What is wrong with mathematics education?". There were
complaints about expressions of the perception that math was all about memorization. And there was a lot of tiptoeing around the real problem, with only a few commentators who clearly understood.
So first, to address some of the comments. A disclaimer is in order, or maybe rather an aside. I do not really understand why people are bad at mathematics. I've never experienced the situation. I've always been the best in every class I took, up until I was in graduate school, when I finally encountered people who were as smart as me. Since I have an IQ of around 160, I don't encounter a lot of folks smarter than me. That's okay. Left to my own devices, I'd also be one of the laziest people I know. But the sense of guilt I would feel about not using my talents keeps me plugging along, trying to become an expert in anything I encounter that I think will keep my life interesting. And even though I have this tendency towards laziness, I don't like to waste time, so I finished my undergraduate degree in 2.5 years with no grade below an A. I majored in math because it was the most challenging of my subjects, but I could have just as easily majored in creative writing or foreign languages or art. On the other hand, I have no musical talent to speak of, so when I need to understand failure to be good at something, I try to view it from the standpoint of me learning music.
- Mathematics is not arithmetic. Thinking that it is is a huge part of the problem. It's equivalent to saying, "Science is a rock." Now, we know that science includes the study of rocks, but science is not the rock itself...or even geology. Science is much larger than the rock and a totally different kind of construct. The same can be said for the relationship between mathematics and arithmetic. That said, there is a beautiful theory of arithmetic that includes the arithmetic we learn in grade school as a special case, but you would need graduate school level mathematics to learn it, so I won't go there right now.
- Mathematics is not rote memorization. I offer you sincere apologies in the name of teachers of mathematics everywhere if you were given that impression. Memorization is not learning. It never has been and it never will be. I know that is the impression given by some/many of our elementary school teachers, but that's because they themselves don't understand mathematics. Mathematicians almost never teach elementary school. We try to teach elementary school teachers, but these students are not as a general rule, mathematically gifted...or even mathematically adequate (we'll get back to this later). Doing mathematics requires "knowing." Memorizing is a poor substitute for knowing, if it is even any kind of substitute at all. Arithmetic is about pattern recognition. If you recognize the patterns (and know the language, but that's another point), then arithmetic is easy, even fun, and doesn't need to be memorized. If you don't have a clue there even are patterns, then you are stuck with memorizing and this is not fun, so you learn to hate math. If you didn't even realize this was the case, then you have been mathematically abused by someone, and there is a whole lot of blame to go around. The point of the tables (matrices) was to help you recognize the patterns, not to abuse you by requiring that you memorize all the individual facts. Eventually, however, the train has to leave the station, and such is the case with mathematics: eventually your cohort is supposed to move on to the next stop along the line, and you will be required to use some of those facts that some people didn't learn, and hence they resort to memorization to fill the gap.
- 1 + 1 = 2 is truly a profound a statement for the common man. That's not precisely true. Yes, the mathematics behind the statement can be profound, but the utter truth of the matter is that 1 + 1 = 2 because that is the definition of "2", given understanding of the symbols "+" and "=". And 3 is defined to be 2 + 1. And 4 = 3 + 1. This is not an exercise in mathematics, but rather an exercise in vocabulary. I think we would all agree that vocabulary of words is important. So is the vocabulary of symbols. It's just that we like to pretend these are different things, when they are not.
So what is wrong? Why do people struggle with mathematics?
People hate it when I say this, but original sin lies with our society. Simply put, people are bad at mathematics because it is okay in our society to proudly proclaim that fact. Parents teach this to their children, using the claim that they are bad at math as an excuse to abuse their children when the children most need their parents' help. People attempt to hide from everyone the fact that they are poor readers or can't write a meaningful sentence, but will proudly proclaim, "I was never any good at math."
This is reinforced by too many elementary school teachers who also hate mathematics and suck at hiding this fact from their charges. It is also reinforced by socialization that teaches that being smart is anathema to being popular, especially among the young. And nobody is geekier than a math nerd. Even science nerds are more popular than math nerds. It is a sad fact that elementary teachers most often would not strive to become elementary school teachers if they had any skills at mathematics at all. The door to knowledge and learning on higher levels is open to those who truly understand mathematics, and they tend to choose other career paths. Those left behind often are the ones who decide teaching on the elementary level is something they can do. [Note: Some elementary teachers do in fact overcome this disability and learn to teach mathematics adequately, even well. And some people do decide to become elementary school teachers because that is what they always wanted to do and didn't change targets just because they were good at math. But that's still not enough of the population to meet the demand.]
On top of that, we insist on teaching mathematics in our schools in English, even if that is not the native language of the students. Mathematics is an adventure in words. Teaching mathematics in a language that is, if not foreign, at least not very well understood by those attempting to learn it is going to have about the same success rate as teaching Spanish literature to someone who doesn't speak Spanish beyond being able to order food at a Mexican restaurant.
These are huge problems to overcome. They are American problems, thought they may exist other places as well. They are cured by instituting fundamental change in the society. It requires the collective will of the people and leadership by people who we would never elect because being smart is a force against electability in this country.
So why teach math?
We finally get to the topic of plf515's diary. To me, this is the fun part. We teach mathematics because it is the ultimate expression of human accomplishment. It is the one language that all humans share. And all aliens, too, if we ever encounter any. It is the language of science. It provides the logical basis for discourse. It engages the human brain in a pursuit of Truth. Whether or not it has applications in what many call the "Real World" is irrelevant. It's nice that it is the language of science and that science is the language of engineering, but the dance of the symbols is art. I do not have a Bachelor of Science degree or a Master of Science degree, I am an abstract algebraist. I have a Bachelor of Arts degree and a Master of Arts degree along with my PhD. My pursuit, when I was working as an algebraist (I am currently a professor of computer programming...long story), was Truth. I taught people how to pursue Truth. I taught people how to decide what was true and what was not and how to prove it. To my great surprise, my pursuit of Truth led me to discover Beauty. The dance of the symbols is every bit as beautiful as the movement of a person; the arrangement of the words and symbols into a proof is just as beautiful as a painting by Leonardo da Vinci, a sculpture by Michelangelo, a symphony by Tchaikovsky, a poem by Walt Whitman, or dancing by Mikhail Baryshnikov. The mathematical canvas is the world of possibility enclosed in the imagination that is possible in the human mind. The levels of understanding, cognition and metacognition that are in there/out there are so mind expanding that no drug can approach inducing the euphoria that can be experienced.
Why teach math? Indeed. Why live?
--(Now) Professor Emerita, Bloomfield College, NJ
FTW: What did Vinci, Michelangelo, Tchaikovsky, Whitman, and Baryshnikov have in common?