There is a certain case to make that American fundamental mathematics education is such crap. While we have some of the best universities in the world for mathematics research, disproportionate numbers of students there are foreign. Are there really not enough American born and bred students that are capable of doing mathematics?
So what is the root of the problem? I argue that we don’t teach enough mathematics to younger kids. As a young child in Hong Kong, attending school from first to third grade, I have found myself learning a lot at a very rapid pace. One of my worst fears upon immigrating to America was that I would fall behind in my education – a fear which did not come true even remotely.
I was not one of the best students or extraordinarily bright. Nonetheless, I learned a lot about basic arithmetic, basic algebra, and basic geometry before moving to America. I was able to perform all day to day computations then, and I was eight years old. We were trained to perform arithmetic rapidly and accurately, often through repeated practice.
Coming to America, I was very surprised to find myself way ahead of others. I was bored and forced myself to do algebra and geometry in 4th and 5th grade, moving upwards to trigonometry and calculus by middle school, as well as dabbling in number theory and other mathematics.
Needless to say, I excelled in the American system. Mathematics was such an easy subject that I did not think or worry about it at all until I went to college. What I observed after entering college, however, was disturbing. In spite of being placed in somewhat more advanced classes, I discovered that most of my cohorts were not able to perform simple arithmetic or algebra. We were, incidentally, taking differential equations.
I would readily assume that if people cannot perform algebra or take a simple derivative, they would not be ready for differential equations. It readily seems that our standards are way too low – too many kids are being promoted to take harder and harder courses without either understanding the material or at least be able to apply the material correctly.
Another problem is that we don’t teach the required skillset for real mathematics to kids. Mathematics isn’t about applying numerical operations – it’s about logical thinking, proofs, and critical thinking. Outside geometry, there is absolutely no proof-based mathematics education. Some kids are exposed to induction, but nothing more. Nonetheless, when we enter university, we are taught number theory, discrete mathematics, combinatorics, topology, analysis, algebra, etc. etc. Mathematics is far different the moment you jump into university, and kids are absolutely not prepared for it! I read an article a few weeks ago, in which some professors at (I believe Stanford) were asked what is the basic requirement for someone to be a math major there – and their answer was “bar none, ability to do proofs.”
Knowing how to do proofs is central to be able to do mathematics – mathematics is a very rigid science, and it requires a high level of organization, abstract and logical thinking, and kids need to be taught to think that way, and realize what mathematics is, before they enter university and discover this whole new world.
