On the whole I agree with simon17 although I also know from my own experience that taking advanced placement math courses is no guarantee that a student is ready for college level mathematics. I've been on both sides of math education in the United States and right now it is in very bad shape as our friend has noted. Rigor has been thrown out the window in favor of passing badly composed standardized tests. (I've also worked as a grader of state standardized tests and know just how bad many of them are.) If a person aspires to be an engineer, mathematician, actuary, technician or scientist, then mathematics is an essential. Everyone knows that. What is missing in much of math education today is why something is done or true. Emphasis is placed on how and even then that emphasis is very narrow in its focus and reach.
When you take calculus and higher mathematics at the college level, you must know how to prove things. You must know what a definition, axiom/postulate, and theorem are. This isn't being taught in high school mathematics anymore, not even in Euclidean geometry classes. I was appalled at the textbook used in the Honors Geometry class I taught that skipped over Euclid and his axiomatic method for the bulk of the course, mentioning both only in passing and only at the very end. So when a student gets into a college calculus class and has to learn the epsilon/delta approach to limits, or reason why a maximum or minimum of a function over an interval depends on calculating its derivative, he is at a complete loss because he doesn't understand how to construct a simple proof. I've seen many a high school math whiz fall flat on his face in a differential calculus or real analysis class because of that ignorance.
Students are given calculators in third grade but don't understand the basic arithmetic used to solve problems. They don't know the relationship between decimals and fractions. Hell, they can't even do the four basic operations of arithmetic if fractions or decimals are involved! And when I interviewed for teaching jobs, I was asked what was my attitude about calculator use in the classroom. My reply that I banned their use until my students could demonstrate basic math competency disqualified me for the job I sought right then and there. I've said before the fault lies, not with the kids, but with bureaucrats, parents, employers and others who don't demand competency and the meeting of high standards from our students. I know of many teachers who don't even teach multiplication tables anymore saying, "To drill is to kill"!
All the standardized testing in the world isn't going to fix the problem of math education until real math teachers are welcomed back into the classroom; get paid well for their services; and are backed up by administrators and parents when they demand and enforce the kind of mental discipline the study of mathematics must have. Then and only then will our kids and others get the math education they deserve.
Quendi
