
Areas of Mathematical Thinking
Posted:
Jun 13, 2000 5:28 PM


People have made a viable K12 curriculum but the one's in power won't let it be. You can't give it away!
Firstly, the teachers from the 50's knew what the basic curriculum for k8 should be  it was just what they were teaching. Yes, there were many things missing, like how to handle your finances and pick stocks. But, essentially they taught you what a sentence was and how to write a complete composition, or essay. They taught you basic arithmetic, algebraic operations, how to solve equations, etc. they taught you history, geography, etc., etc.
As I see it nobody back then really knew what a sentence really was (They told it was a group of word that expresses a complete thought) it took me thirty years to find out the real meaning of a sentence. They told me that a polynomial is an algebraic expression that is rational and integral in the literals. I didn't know what they were talking about. I now know that the teachers didn't know, either. No, the teachers were telling the kids things they read in a book, but didn't understand. The problem with the education system today is based upon the fact that teachers had jobs whether they knew the material or not. The principal never went into the class room to find out if the teacher knew what he was talking about or not. So, who suffered? It was us kids. How? Well, I had to rummage through the books in libraries until I found that every book was a copy of other books before it. Not one book I ever ran through had an explanation of what a polynomial is and why you need one. The book writing business is pathetic in this country, actually, its pathetic all over the world. Well you've heard it and I know that I am right. Why should teachers learn what a polynomial is. They still get paid whether they know what it is or not.
Now I learned what a sentence is, what an essay is, and what a polynomial is by intense perseverance. All without pay. That's the answer. Alexander Pope said that nothing great has been ever achieved where there was a want for money. Thats it. Money, money, money is the reason why our education system is so bad. Everybody is writing a book by copying somebody else. And, the teachers are only teaching from the books. This is called rote learning. It is only a repetition of what is in a book. Real learning through genuine understanding is gained through dedicated analysis of a problem motivated by genuine interest in educational things.
The "math wars" between California and the NCMT are sparked by real mathematicians, people who broke their backs to understand math concepts like differential equations, Green's functions, Legendre polynomials, hyperspaces, hypergeometric functions, matrix theory, curl, divergence, etc. These are all topics that were discovered because the great master had the problem by the seat of the pants and understood all aspects of them. I defy one person to tell me what a Green's function is in plain words. There is nobody. I wanted to know what one was since the 60's and never was able to find out. Finally, I figured it out. Recently, I contacted the University of Nottingham for information on the Green's function and they sent me a reply stating that "Based on what you have told us you know more about the Green's function than we do and we would look to your help. So, the root of the problem is: let the experts develop the curricula for the high school students, not the graduates of teacher's colleges who know about as much about what a polynomial is as I did when I came out of high school in September 1950.

