The Failure of Math Education in the United States

Let's not mince words: Math education in the United States is a failure. Yes, we are better than some countries, we have some good teachers, and we do produce some world-class mathematicians, but when regarded on the whole, one can only conclude that as a system it has failed Americans. The institutions that should be most concerned, the Schools of Education have not been effective in addressing the issue.

One response has been denial through demolishing an appropriately erected straw man. Apologists will explain falling SAT scores in Mathematics by pointing out that a much larger fraction of the student population takes the test now than in the past, and so this group necessarily will include more underprepared people. Perhaps this is the case, although even this argument is not completely clear. The perceived premium on scoring well has led to the creation of an entire industry to prepare students for this test which one would think should improve scores. Other factors also cloud the issue, but even if this argument is correct it misses the point.

The appropriate comparison is with other countries, and here there is little doubt that our international standing is middling at best. A PISA (Program for International Student Assessment) study in 2006 placed the average score for 15 year-olds on math literacy statistically significantly under 31 countries, higher than 20 (mostly third world( countries, and on the same level as six countries. The TIMSS studies which assess the 4th and 8th grades rank us higher, but the comparisons, taken together, give the impression that the longer students attend our schools the more they fall behind students from other countries, since our comparative standing drops from 4th grade to 8th grade to 15 year-olds. Given the fact that we have far more resources and the illusion that we are devoted to equal opportunity, it makes clear these results are unsatisfactory. Unfortunately even when the problem is recognized, the standards of scholarship are so low in the Departments of Education that no effective plan to attack the problem has emerged.

Math failure has significant consequences. As a nation it cripples our ability to compete internationally. Thus far, we have been spared the full consequences of our ineptitude because our economic position has attracted talented immigrants to fill the gap of what we should produce, but this will change as our economic prominence diminishes. Even more importantly, it short-changes our people economically. We have always felt that US citizenship should guarantee at least an opportunity to compete equally with others in the world, but an inability to understand mathematics has severe economic consequences that often are not recognized by those with the handicap.

No one doubts the crippling effect of illiteracy but, but in the US too many people think that to be inept mathematically--well join the crowd. You won't perceive math illiteracy to be a problem when it seems that most are in the same boat. But the loss to are citizens can be seen in all the immigration loopholes we create in order to get technically qualified employees. These represent losses of well-paying jobs for Americans. It is also remarkable that so many small businessmen come from the ranks of new immigrants rather than natives. One cannot help but think that the former gained the math savvy to assess business opportunities, while far fewer of the latter have those skills.

Finally, it seems to me that many of our political difficulties stem from the fact that so many eligible voters vote fail to recognize their own economic interest, and are thus susceptible to outrageous distortions.

The mathematician as an artist

Mathematics represents the highest form of art. To those of you who perceive mathematics as simply the manipulation of numbers, such a statement seems, at best, a wild exaggeration. To justify this statement we need to consider what we mean by art.

The American Heritage dictionary (3rd edition) defines an artist (meaning 2) as "A person whose work shows exceptional creative ability or skill." Few would dispute the idea that mathematicians need exceptional skill, but many who do not practice mathematics are surprised to learn that creativity is the most important talent for a mathematician.

There is a notion that creativity means coming up with weird, shocking, but somehow pleasing things. Creative work can indeed seem weird, shocking and pleasing, but it is essential that an underlying concept lie behind it, giving it unity and purpose. Third rate artists can concoct weirdness and shock, but they lack the talent to make their work profound. That is what differentiates pseudo-art from true art. The art lies in having work transcend the strangeness and shock to give us something of beauty or understanding.

A mathematician is an artist in the sense that he or she creates structure from a set of concepts that he or she defines. The mathematician must define a concept in such a way that allows the construction of a structure that clarifies the relationships that exist between the elements. Every mathematical entity, from the most mundane to the most esoteric, is in reality a unifying concept. Take the number three. This is not something you can hold or feel in the same sense that you can a book, but it does describe a unity about a collection of objects or even concepts. Similarly, a mathematical group, describes a structure imposed on a set and an operation.

A mathematical proof can be beautiful in the same sense a painting is beautiful because it reveals heretofore unsuspected relationships between objects that are themselves concepts. It is the ability to conceive of new concepts that allow the structure to be revealed. For this reason mathematics represents the most exalted expression of human creativity

Beginnings

Dragged kicking and screaming into the 21st century. Here is my first experiment with blogging since the best way to learn about something is to do it. Even though it's Halloween it shouldn't be scary, although it is at this time, confusing. Is this a way to make your voice heard? Well time will tell.