Part of the problem is that no one has the slightest idea of what mathematicians actually do. Most

"I found myself in regular classrooms - no easels or tubes of color." We do not use colors before high school, one student told me. 'Seventh grade we mainly learn about colors and Brushes. Showed esic me a worksheet. Were on one side shades of colors with blank lines next to them. told them to fill the names., I like to draw, "said one student. 'tell me what to do and I do it.'s easy!'.
"After class I spoke with the teacher. 'So your students do not really draw at all?' I asked. "Well, next year they will have prepared for painting by number. This will prepare them for the main part of the coloring by number of high school.'s How they will apply what we learned here problems realism of the painting - dip a brush in color, wipe the brush, things like that. '
"Of course we are sorting students by ability., Some students simply do not connect esic with the material. Exactly Yesterday my neighbor asked me to give her son private lessons in painting. Is really difficult in art, he gets distracted and instead of listening to the teacher is just rattling notebook.'s My neighbor really want her son accepted grouping A, that artists who excel really - those who know the colors and the brushes really well - starting with drawing real little earlier, and most of them also will expand to five units in art., but especially esic at this stage we focus on giving students good foundations about the nature of drawing, esic so that when they reach the real world and have to paint their house, for example, they will get along. '
"'Oh well, you sound like one of my professors! They were always talking about self expression and feelings esic and things really abstract and advanced. I did a degree in painting myself, but never really worked with Knwasim parts. I just use kits paint by number school as ".
Unfortunately, the way mathematics is taught today is just a nightmare like this. In fact, if I had to invent a mechanism for the express purpose is to destroy esic the natural tendency for children in their curiosity and search patterns, esic there is no way I would be as successful as the current system can - just do not have enough imagination to ideas and stupid soul destroyers that are the current mathematics education. Everyone knows that something is wrong. Politicians esic say "We need higher standards." School says, "We esic need more money and equipment." All wrong. The only ones who really understand what's going on are the ones accused of the most and least listen to them: the students. They say "Maths annoying esic and boring." And they are right. Mathematics and Culture
The first thing to understand is that math is an art. The difference between mathematics other arts, such as painting and music, is that our culture does not recognize esic mathematics as an art. Everyone knows that poets, painters and musicians are producing art, and express themselves with words, images and sounds. Even architects, chefs and television director are considered artists. So why not mathematicians?
Part of the problem is that no one has the slightest idea of what mathematicians actually do. Most people esic think they are doing something having to do with science - may help scientists with their formulas, or put huge numbers into the computer for any purpose. There is no doubt that if he had to divide the world arty dreamy "and "mdanim rational", most people would put the mathematicians in the latter category.
But the fact is that math is something dreamy and artistic. At least as amazing math astronomy and physics (mathematicians thought the idea of a black hole long before astronomers actually found them), and gives more freedom of thought poetry, art or music (arts depends on the features of the physical world). Mathematics is the purest art, and most misunderstood. So let me start by explaining what math is and what mathematicians do. GH Hardy [2] said: "A mathematician, like a painter or a poet, creating templates. Whether more templates of their own immortality, it is because they are made of ideas." esic
So mathematicians sit and create templates from ideas. What kind of patterns? What kind of ideas? Ideas about rhinoceros? No, the ones we leave for biologists. Ideas about language and culture? No, not usually. All these things are too complicated mathematician's taste. If there is any one aesthetic principle of mathematics is this idea: It's pretty simple. Mathematicians like to think of as many things are simple, and the simplest things are imaginary.
I wonder how rectangle esic occupies the triangle. Maybe two - thirds? esic What is important here is to understand that I'm not talking about this painting of a triangle within a rectangle. I'm not talking about some kind of metal triangle that forms part of a system which has a bridge. I do not have any ulterior motive here. I'm just playing. esic This concept of mathematics - to wonder, think, play with imagination. Besides, the question of how rectangle occupies the triangle is not even logical real objects. Even the most accurate triangle composed of atoms generated still moving and changing all the time, unless you want to talk about some approximate measurements. And here enters aesthetics. All this will be complicated and ugly question hanging manufacturing all kinds of realistic details. Let's esic leave it to scientists. True mathematical question is about an imaginary triangle in an imaginary rectangle. Edges are perfect because that's how I want them - that shape which I prefer to think. This is a central theme in mathematics: things are what I want them to be. There are endless possibilities esic and reality should not bother us.
On the other hand, as soon as choosing the options (for example, I can decide my triangle symmetric) then my work doing what they do, and it's not up to me. This amazing thing creating imaginary patterns: they speak to us! Triangle rectangle occupies any part, and I have no control of what part. There is some number. Maybe it's two - thirds, maybe not, but I can not decide what he will. I need to find it.
So we can play and imagine esic and invent patterns