Throughout elementary, middle and high school mathematics is quite merely about memorizing concepts and formulas, understanding the theorems (without their proofs) and applying acquired knowledge in examinations. It is not perfect, I concede, but it is almost as good as is needed. I am a graduate student who is devoted to pure mathematics, and I have about 4 years of teaching experience with a great variety of students. I hope that this is gives me enough credit to discuss a matter of this sort.
It is (to some extent) true that mathematics is “art”; it is about creating patterns and connecting them with each other, etc. This is what most professional pure mathematicians like to think and say to the public. Now, there is the harsh truth that a great portion of pure mathematics undergraduates drop out or, after graduating, either run away to some applied area of mathematics or decide to teach mathematics in middle or high schools; “real” mathematics is very difficult even for people who were very good/excellent in high school math. Moreover, many of the students who safely land in graduate school find it difficult to get accepted in the graduate programs they wanted to get in because of their incompetency, and so they end up doing something they did not really want to do. I am not trying to suggest that advanced pure mathematics is a nightmare, but my point is that if the education in school was made so that students would learn to “appreciate” the beauty of mathematics and get motivated to pursue pure mathematics, most of them will fail later on.
One asks: why, then, are most professional pure mathematicians discontent with the current style of math education? In my opinion, the answer is: most of them are geniuses and have no idea what mathematics looks like to inferior beings, and the rest simply forgot what kind hard work is required for learning and digesting advanced concepts and are unaware of how it might be much more difficult for less capable people.
My conclusion is that mathematics education is in a fine state in today’s world. It is not “fundamentally wrong” and “delusive”; it is just realistic. If you are not extremely comfortable dealing with numbers, elementary functions and geometric figures, you do not stand a chance in advanced mathematics.
To make this a question, allow me to pose following:
Do you disagree with this? What important points am I missing in my defense of the current school education system?