It's no surprise that many Americans, young and old, express frustration with math and skills of numeracy. As a teacher, I hear far more people note how they "hated math" and struggled with it than people who express the same feelings about language arts, humanties, sciences, and electives. However, because of where I work and because of the truly gifted mathematical mind of my son, I have a window into the world of mathletes and mathematically-talented students. My school has four classes past AP Calculus, and that's because some students accelerate to the level of calculus by sophomore or even freshman year. These students are usually highly-ranked math and science competitors who score in the top 1% on tests like the AMC8/10/12 and the AIME. It is a pleasure to work with these kids and coordinate their incredibly advanced talents and schedules. However, the achievements of students like these can lead to an unintended consequence - a "math acceleration arms race," where other advanced students want to accelerate quickly, even skipping classes, because they believe they must keep up. As a GT coordinator, we look at a body of evidence for true giftedness, and we see clearly the difference between hard-working, advanced students and truly gifted kids. In speaking with kids and families about math advancement, it always seems to be focused on advancement as the key to an Ivy League college admission. And that's so sad.
For many years, my wife and I have listened to parents of other mathletes ask us "How do you get him to do that?" And that is the key. We don't. It's also the key difference between a smart kid pushed by zealous parents and a truly GT kid. We have never done anything as parents to push our son to achieve. And he does not attend endless math camps or have private tutors. We are certainly open to opportunities, and we encourage him with his participation in competitions such MATHCOUNTS and A/JMO, as well as his work in the mathlete community on AoPS, the Art of Problem Solving. But we haven't pushed him to excel - he excels precisely because he is gifted, passionate, and engaged. You can't create gifted, and parents absolutely must stop trying to do so. In a recent discussion with kids about "skipping math classes" to get ahead, I was turned on to a fascinating treatise on math and math education - Paul Lockhart's A Mathematician's Lament. For those interested in the world of advanced math, it's worth reading his essay.
Mathematics and Culture - The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such. Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound. In fact, our society is rather generous when it comes to creative expression; architects, chefs, and even television directors are considered to be working artists. So why not mathematicians? Part of the problem is that nobody has the faintest idea what it is that mathematicians do. The common perception seems to be that mathematicians are somehow connected with science— perhaps they help the scientists with their formulas, or feed big numbers into computers for some reason or other. There is no question that if the world had to be divided into the “poetic dreamers” and the “rational thinkers” most people would place mathematicians in the latter category. Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depend heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood.
Additionally, the Lament was eventually developed into a book, which expounds on Lockhart's ideas and his concerns.