Myth and Truth about Mathematics
As I see it, math is viewed by majority of students in America as an unneeded subject. Indeed, they realize that in their practical life they will unlikely have to solve a system of linear equations or calculate an area of a trapezoid. In 99% of the cases they are right, so they are negatively predisposed to math and consider it to be just a bunch of facts they have to memorize to pass an exam and then they can happily forget it. Nothing is left from this knowledge after a year or two. Looks like the system of education focused on giving the students prepackaged recipes to as many math topics as possible fails because students do not go any deeper in understanding these topics, just learn a rule "if you have to find ... do ...", which, as I mentioned before, is easily forgotten as unneeded. As one person characterized it, this system is "a mile wide and an inch deep". Not withstanding some memory training, this system bears no useful purpose.
So, the need to drop all the mathematical facts onto student's head counting that something will stick and might be useful in their future life is a myth.
What I think the focus of math education should be is the development of the mind. Does not matter what math topic is studied. What matters is, how does it help to develop abilities of a student's mind. What differentiates math from other subjects is its completely artificial character. It's a product of bright minds. No other subject has this degree of brain participation because all other subjects are dealing with real objects. Studying chemistry or literature, foreign language or biology - it's all about what exists in the world, already created. Studying math allows to get a student involved in the creative process. Prove this theorem, solve this problem, construct this geometrical figure - these are creative assignments not available anywhere else. Artificial character of math allows to train the student's mind to be logical, analytical, creative, intelligent. Math is an ultimate form of art because it is completely a product of artful minds.
If I were a teacher, I would start my first lesson from asking students about why should they study math. I am sure there will be very few, if any, who would answer that it's needed to develop their mind or simply to get smarter. Most likely, I would hear no answer at all. And then I would compare studying math to develop the mind based on problem solving approach to exercises in gym to develop the muscles, stamina and other physical abilities. What gym is for physical development, math is for intellectual development. I realize that not many students will be interested in their intellectual development, after all people in general are not satisfied with their physical appearance but quite satisfied with how their brain functions, but whoever will be interested, will benefit tremendously.
So, mathematics is a tool to develop a student's mind. This is the truth. And to accomplish this, a student must be challenged with proofs of theorems, problem solving, logical approach to theory and creativity. This approach is not in the focus of most schools and UNIZOR.COM attempts to compensate for this.
Our goal with Unizor is not as much to change an entire system of education, we realize impossibility of this, but to present a choice for those real knowledge seekers, who are still there in the world, deprived from proper intellectual development by existing educational system.