Mathimatics has been always a horrow subject to me. My brain blocks when I only see numbers and formulas… It’s a wonder how I could have survived so far with such an attitute towards maths!
Renecetly I came across an amazing article on mathematics, which literary has blown my mind. A Mathematician’s Lament, is written by Paul Lockhart in 2002. Paul is a mathematics teacher at Saint Ann’s School in Brooklyn, New York. His article has been circulating through parts of the mathematics and math ed communities ever since. His point is that much mathematics education is hijacked by people who know nothing about it.
Here are some quotes:
“The first thing to understand is that mathematics is an art. The difference between math and
the other arts, such as music and painting, is that our culture does not recognize it as such.
Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound.
In fact, our society is rather generous when it comes to creative expression; architects, chefs, and even television directors are considered to be working artists. So why not mathematicians?
Part of the problem is that nobody has the faintest idea what it is that mathematicians do.
The common perception seems to be that mathematicians are somehow connected with
science– perhaps they help the scientists with their formulas, or feed big numbers into
computers for some reason or other. There is no question that if the world had to be divided into the “poetic dreamers” and the “rational thinkers” most people would place mathematicians in the latter category.
Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical,
subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or
physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depend heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood.
So let me try to explain what mathematics is, and what mathematicians do. I can hardly do
better than to begin with G.H. Hardy’s excellent description:
of patterns. If his patterns are more permanent than
theirs, it is because they are made with ideas.
So mathematicians sit around making patterns of ideas. What sort of patterns? What sort of
ideas? Ideas about the rhinoceros? No, those we leave to the biologists. Ideas about language and culture? No, not usually. These things are all far too complicated for most mathematicians’ taste. If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary. . . .”
Or this one:
“Sadly, our present system of mathematics education is precisely this kind of nightmare. In
fact, if I had to design a mechanism for the express purpose of destroying a child’s natural
curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being
done– I simply wouldn’t have the imagination to come up with the kind of senseless, soul-
crushing ideas that constitute contemporary mathematics education.
Everyone knows that something is wrong.
The politicians say, “we need higher standards.” The schools say, “we need more money and equipment”.
Educators say one thing, and teachers say another. They are all wrong.
The only qustion that arises after that article: “Why hasn’t anybody talked about math like this before???”
P.S: waht about a solution? does the author suggest soemthing worthy? Oh, yes! Check this dialog out!
Paul Lockhart created a dialogue between two made-up characters.
SIMPLICIO: Are you really trying to claim that mathematics offers no useful or practical applications to society?
SALVIATI: Of course not. I’m merely suggesting that just because something happens to have practical consequences, doesn’t mean that’s what it is about. Music can lead armies into battle, but that’s not why people write symphonies. Michelangelo decorated a ceiling, but I’m sure he had loftier things on his mind.
SIMPLICIO: But don’t we need people to learn those useful consequences of math?
Don’t we need accountants and carpenters and such?
SALVIATI: How many people actually use any of this “practical math” they supposedly learn in school? Do you think carpenters are out there using trigonometry? How many adults remember how to divide fractions, or solve a quadratic equation? Obviously the current practical training program isn’t working, and for good reason: it is excruciatingly boring, and nobody ever uses it anyway. So why do people think it’s so important? I don’t see how it’s doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them. It might do some good, though, to show them something beautiful and give them an opportunity to enjoy being creative, flexible, open-minded thinkers— the kind of thing a real mathematical education might provide.
SIMPLICIO: But people need to be able to balance their checkbooks, don’t they?
SALVIATI: I’m sure most people use a calculator for everyday arithmetic. And why not? It’s certainly easier and more reliable. But my point is not just that the current system is so terribly bad, it’s that what it’s missing is so wonderfully good! Mathematics should be taught as art for art’s sake. These mundane “useful” aspects would follow naturally as a trivial by-product. Beethoven could easily write an advertising jingle, but his motivation for learning music was to create something beautiful.
SIMPLICIO: But not everyone is cut out to be an artist. What about the kids who aren’t “math people?” How would they fit into your scheme?
SALVIATI: If everyone were exposed to mathematics in its natural state, with all the challenging fun and surprises that that entails, I think we would see a dramatic change both in the attitude of students toward mathematics, and in our conception of what it means to be “good at math.” We are losing so many potentially gifted mathematicians—creative, intelligent people who rightly reject what appears to be a meaningless and sterile subject. They are simply too smart to waste their time on such piffle.
SIMPLICIO: But don’t you think that if math class were made more like art class that a lot of kids just wouldn’t learn anything?
SALVIATI: They’re not learning anything now! Better to not have math classes at all than to do what is currently being done. At least some people might have a chance to discover something beautiful on their own.