Isn't it ever so satisfying when your hard-earned taxes are spent on something useful and constructive, such as the report of the National Mathematics Advisory Panel, which was charged with answering the question of why American students are falling behind the rest of the world in mathematical preparation. Of course, enormous piles of research has been done on mathematics education, and any math or science professor can tell you about the abysmal preparation of students who have gotten into college (and who are thus high school graduates).

The task of the advisory panel was basically to collate all the knowledge out there into a plan of action for fixing the disaster of math education in this country. Wouldn't it have been nice if math education researchers themselves brought all this knowledge together? Indeed, the mere existence of the panel shows that our problems go much, much deeper than any set of recommendations in a report can solve.

Fixing the problems with math education in this country will involve breaking a cycle that goes back decades at least. Until education professors face up to the elephant in the room, that poor students find an elementary education major an easy alternative, a million reports and recommendations like this one will be meaningless. All the experts in the world can make absolutely correct statements such as this:

Teachers and other educational leaders should consistently help students and parents to understand that an increased emphasis on the importance of effort is related to improved mathematics performance. This is a critical point because much of the public's self-evident resignation about mathematics education (together with the common tendencies to dismiss weak achievement and to give up early) seems rooted in the erroneous idea that success is largely a matter of inherent talent or ability, not effort.

But if elementary teachers consider themselves inherently "bad" at math, as I guarantee you many (if not most) of them do, they cannot possibly make their students understand that no one is just born bad at math.

There is a fundamental problem that has created this crisis to the point where any solution is at best decades away, if it is possible at all. Culturally, math illiteracy is not considered a deficiency. In fact, many people (including undergraduates taking required math courses) seem to wear it as a badge of honor. How did it get this way? We seem to take language illiteracy much more seriously (which is not to say that students are adequately prepared in reading and writing either). After all, while I have heard dozens of people proclaim their math illiteracy, I have never heard one person proudly announce that they cannot read or write. Parents don't think math is important, so their kids don't. Some of those kids go on to be elementary teachers. How do they get the degree when they continue to be illiterate in math? They do it within a system that gets many of the worst students, because instead of making them meet high standards, it accepts them adjusts courses accordingly. Minimum grade levels to graduate are meaningless; they just result in grade inflation. Programs focus more time on "methods" teaching than on content; even while all the skills in teaching methods in the world are useless if you do not have a firm grasp of what you are teaching.

Why are we passing poor math students through unchallenging courses that result in teaching degrees? One, because of the cultural stigma tied to proficiency in math. Two, because the profession of teaching today provides little rewards, even for the saints among us, which results in a high demand due to high turnover. Most teachers will tell you that it is not even about the pay and benefits - although the pay discrepancy between the teachers and administrators is a travesty. It is about a lack of autonomy in the classroom - due to government's and administration's love of relentless standardized materials and testing, which prevents even the smartest and most motivated teachers from using their abilities to teach creatively. It is also about parents who think schools are daycares for their snotty, insolent, bored-without-TV brats, instead of a controlled environment for children who have been taught respect to participate in the excitement of learning.

Thus, we have classrooms of teachers who know little content in certain areas and are even taught about teaching math in a way that reinforces its stigma:

Teachers and developers of instructional materials [added emphasis] sometimes assume that students need to be a certain age to learn certain mathematical ideas. However, a major research finding is that what is developmentally
appropriate is largely contingent on prior opportunities to learn. Claims based on theories that children of particular ages cannot learn certain content because they are "too young," "not in the appropriate stage," or "not ready" have consistently been shown to be wrong.

How is it that the people creating instructional materials have no idea what all the research has been telling us for years? This is a fundamental disconnect in most areas of education. The educational research that has been done decades ago and today is emphatically ignored by the people charged with actual education, such as school boards and administrators. For example, everyone knows that the best time for language acquisition (single or multiple) is early childhood. Yet, when is foreign language instruction begun in the U.S.? High school.

Another fairly futile recommendation:

...teachers must know in detail and from a more advanced perspective the mathematical content they are responsible for teaching and the connections of that content to other important mathematics, both prior to and beyond the level they are assigned to teach.

This seems to be a bizarre concept to students in math education. Even those at my campus planning to teach high school math - and thus who are essentially getting a content degree in mathematics with a few education courses - are known to complain, "why should I have to take this high-level math course when I will never teach this material?" The utter lack of interest in their major subject is astounding. Why are they math majors then? Because with such a shortage of math teachers, they are certain to get a job. And with teachers relatively uninterested in the subject they are teaching, the cycle of poor preparation continues.

And let's not forget that there is seemingly always a role played by big business when policy makes no sense:

Mathematics textbooks are much smaller in many nations with higher mathematics achievement than the U.S., thus demonstrating that the great length of our textbooks is not necessary for high achievement. Representatives of several publishing companies who testified before the Panel indicated that one substantial contributor to the length of the books
was the demand of meeting varying state standards for what should be taught in each grade. Other major causes of the extreme length of U.S. mathematics textbooks include the many photographs, motivational stories, and other nonmathematical content that the books include.

Why all the extra garbage in these math books? (For an extreme example of textbooks with gratuitous material that schools should definitely avoid, see this YouTube video.) Interestingly, the panel's report does not spell out the obvious reason: publishers' profits. The textbook industry has gotten completely out of control, filling books with junk to make them longer to justify the cost, and coming out with new editions every couple of years, which forces school districts to spend the money to replace their entire inventory, rather than order a few replacement books. In science, this can be justifiable given the rapid increase in knowledge and thinking that occurs - textbooks that define only two biological kingdoms, for example, would not be useful in preparing students in biology. But school-level math has been the same for decades, if not centuries. Discoveries on the frontiers of mathematics do not change how you do long division.

There are so many problems that the panel's report goes on and on. One suggestion the panel makes that has merit is the idea of having math specialists teaching at the elementary level. Like art and music teachers, they would travel from class to class an alleviate the burden of teaching math from all the teachers who hate it. The only way to break our current cycle of math phobics creating more math phobics is for kids to realize at an early age that math is interesting, and fun for everyone, not just for geeks. Math is part of what makes us human.

Another more radical suggestion is that there be no mathematics teaching at all until middle school. This may seem counterintuitive to the recommendations of the panel, but the main reason most students are terrible in math when they get to middle school is that their aversions have been so reinforced they are already lost causes - poor teaching at the elementary level has already convinced them they are no good at math so they don't even try. What if we waited to teach math, so that students haven't already closed their minds before they have a teacher who is actually interested in math? Why not use the time in elementary school to teach a foreign language? Since many current college students today cannot do middle-school-level math, no one can claim that it would be impossible for students to catch up at that point. As the report points out, the same simple concept is often taught year after year after year in elementary school, which adds to the boredom factor.

Whatever we do, it must somehow involve changing the greater American culture that looks down on the enjoyment of math as geeky, and the hatred of math as cool. Maybe someone could make some Einstein and Von Neumann action figures for Happy Meals. If the culture does not change, the performance of American students in math will not either.

Labels: education, mathematics