Math Education

The AP reports ^[1] that the math skills of American students would be better if elementary school teachers had math skills to begin with. Now before we delve into this topic, let me state for the record that I am a high school physics teacher. From my position, it would be easy to blame the poor math skills of my students on their math teachers. I have students who can’t math their way out of a paper bag, and I take a lot of time every year to teach basic algebra (solve for x) to students who should have those skills before walking in my door. I sometimes resent that my time to teach my own subject is eaten up with mathematical remediation — and not just for a few individuals, but for a large percentage of even the honors students. There isn’t even an argument regarding whether my students lack sufficient math skills. But it isn’t their fault. I am not being facetious when I say that. The fact is that somebody along the way failed to teach them.

I do try to be reasonable. I am aware that I don’t resent the English teachers when I have to explain certain vocabulary or the Social Studies teachers when I have to explain the historical context of various theories and discoveries. But the math is somehow different. It might be because math skills build in a much more linear progression; if you can’t solve for x in an equation, you certainly can’t use trig identities to determine the initial horizontal velocity of an object when I give the velocity vector. While ignorance of a specific historical topic does not indicate ignorance of history in general, and ignorance of a particular word does not indicate an overall deficient vocabulary, in math it pretty much does.

So it is a problem.

Again, we can’t just blame students for being ignorant. We have to blame their teachers. But the study being discussed in the AP article notes that “education students should be taking courses that give them a deeper understanding of arithmetic and multiplication.” In other words, I can’t blame the elementary and middle school teachers my students have had. I have to blame their teachers. And according to Francis Fennell, a former president of the National Council of Teachers of Mathematics, I can’t even stop there:

To boost teachers’ understanding of math, the math departments at universities ought to place more emphasis on training educators, Fennell added.

The problem as far as I can tell is primarily a lack of desire to learn more. In this particular case we are talking about the lack of motivation among elementary school teachers to become more proficient at math on their own, but this occurs on a much larger scale in American culture. We have, as a society, accepted that math proficiency is innate. You’ve either got it or you don’t. Thus there is no shame in throwing one’s hands up and turning away from math to pursue other subjects. I have seen professionals, intellectuals, and educators with PhDs smile and tell a large group of people, “I don’t know, I can’t do math.” And the audience mostly chuckles and nods in understanding. Imagine if you will what the reaction would be if instead a school administrator were to announce “I’m functionally illiterate, I just don’t get letters!” I suspect chuckling would not ensue.

Children learn to value formal education when their parents and elementary school teachers overtly place a high value on it. But these role models often tell children that they don’t actually need certain subjects, including algebra — a case I specifically addressed two years ago ^[2] when a Washington Post columnist wrote an open letter to a high school dropout, explaining to her that while the columnist’s preferred field of writing is very important, algebra simply isn’t, and The System has ruined her life by expecting her to learn it. (I still can’t get over that this piece was published and endorsed.)

While it is certainly true that a university degree is not a requirement for success, it is also likely that parents who have degrees will raise children who have a greater desire to learn and who perform better in school because they value the education in the first place. Consider this map ^[3] showing state-by-state the percent of students performing at or above Proficient on the NAEP. For the 11 maroon states (the highest scores), how do you suppose they rank in terms of per capita college degrees? When checked against this data ^[4], we can see that 7 out of those 11 states are in the top quintile for college degrees (Bachelor’s or higher).

And for the 13 states that are yellow (the lowest scores) on this map ^[3]. They hold 9 of the lowest 10 ranks for per capita college degrees.

Now I certainly don’t believe that every student should go to college and pursue a degree. I don’t even believe that every student is best served by pursuing a regular high school diploma. I would love to see an increased focus on trade schools and other, more practical types of vocational education. But I think it would be a reasonable assumption that those who hold college degrees are more likely to expect “book learning” out of their children. The data does show some correlation. And even among the college educated, mathematical prowess is not generally pursued. This is the heart of the problem.

How acceptable is it in our society to be innumerate? According to recent polls ^[5],

Three-fourths of those surveyed believe schools place too much emphasis on the wrong subjects. Asked what subjects should be given more time in school, more than a third said math. English was a distant second, at 21 percent. A tiny fraction picked art, music and the sciences…

I don’t find that encouraging. Another way to state this would be, Nearly two-thirds said that math does not need to be given more time in school.

Numeracy is a vital skill that our schools and our society must promote at least as much as competency in any other subject. I am loath to ever assign the government responsibility for fixing anything, but if we are going to have government-run schools, then the government must be charged with running them well. As the first AP article I linked points out, the States set the standards for granting teacher licenses, and schools of education base their lax coursework on those government standards. That is where the changes can start. But in the long run, this is a cultural issue. Until math education and indeed all education is valued for its own sake by Americans in general and elementary school teachers in particular (and I mean education for themselves, not just their charges), we can’t expect our students to show proficiency on a level with students from cultures where it is valued.