Why the kids don't know no algebra

Gene ExpressionBy Razib KhanJul 3, 2012 6:36 PM


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A few days ago I stumbled upon a really interesting post. And I'm wondering if my readers are at all familiar with the phenomenon outlined here (it was a total surprise to me), The myth of “they weren’t ever taught….”:

Stage One: I will describe this stage for algebra I teachers, but plug in reading, geometry, writing, science, any subject you choose, with the relevant details. This stage begins when teachers realize that easily half the class adds the numerators and denominators when adding fractions, doesn’t see the difference between 3-5 and 5-3, counts on fingers to add 8 and 6, and looks blank when asked what 7 times 3 is. Ah, they think. The kids weren’t ever taught fractions and basic math facts! What the hell are these other teachers doing, then, taking a salary for showing the kids movies and playing Math Bingo? Insanity on the public penny. But hey, helping these kids, teaching them properly, is the reason they became teachers in the first place. So they push their schedule back, what, two weeks? Three? And go through fraction operations, reciprocals, negative numbers, the meaning of subtraction, a few properties of equality, and just wallow in the glories of basic arithmetic. Some use manipulatives, others use drills and games to increase engagement, but whatever the method, they’re basking in the glow of knowledge that they are Closing the Gap, that their kids are finally getting the attention that privileged suburban students get by virtue of their summer enrichment and more expensive teachers. At first, it seems to work. The kids beam and say, “You explain it so much better than my last teacher did!” and the quizzes seem to show real progress. Phew! Now it’s possible to get on to teaching algebra, rather than the material the kids just hadn’t been taught. But then, a few weeks later, the kids go back to ignoring the difference between 3-5 and 5-3. Furthermore, despite hours of explanation and practice, half the class seems to do no better than toss a coin to make the call on positive or negative slopes. Many students who demonstrated mastery of distributing multiplication over addition are now making a complete hash of the process in multi-step equations. And many students are still counting on their fingers.

The author is involved in education personally, so is posting their own reflections as well as what others report to them. In personal correspondence they explain that this phenomenon is common among children of average intelligence. The lowest quartile presumably would never have been able to master many of these rules in the first place. Some of the information resembles the stuff that a friend of mine experienced when he went in to do tutoring for disadvantaged students in Boston when he was getting his doctorate at MIT. At first my friend was totally taken aback at the level of ignorance (e.g., the inability to see the relationship between 1/10 and 10/100). Today he works at a major technology firm as a scientist, but continues to be involved in mentoring "at risk" kids. At some point you have to muddle on. He does his best, and does not indulge in the luxury of shock and disappointment. That helps no one. This matters because American society is notionally obsessed with education. All this isn't too clear or important to be frank when you aren't a parent. It's somewhat in the realm of the abstract. That changes when you become a parent. Suddenly you become immersed in the data of your local schools, and begin to weight various options to optimize your child's schooling experience. Of course the real differences in school metrics have not only parental relevance, they matter in terms of national policy and attention. Both the political Left and the Right have their own pet solutions. More money, reform teachers' unions, charter schools, vouchers, etc. But the biggest problem at the heart of the matter is the fundamental populist drive to ignore human difference. American schools were designed to produce the citizen, and the citizen has the same rights and responsibilities from individual to individual. In some ways the public school system as it emerged in the 19th century was a project by the Protestant establishment to assimilate white ethnics, in particular Catholics (who of course created their own alternative educational system to maintain cultural separation and distinctiveness). In the 21st century the drive to produce H. Americanus seems quaint, rather, we want to citizens of the world with skills and abilities to navigate an information economy. What American society on a deep philosophical level, no matter the political outlook, detests acknowledging is that a simple and elegant public policy solution can not abolish human difference. Some children are more athletic than others, and some children are more intelligent than others. Starting among conservatives, but now spreading to some liberals, is a rejection of this premise via blaming teachers. The premise is bewitching because it presents tractable problems with solutions on hand. Here is John B. Watson, the father of behaviorism:

Give me a dozen healthy infants, well-formed, and my own specified world to bring them up in and I'll guarantee to take any one at random and train him to become any type of specialist I might select – doctor, lawyer, artist, merchant-chief and, yes, even beggar-man and thief, regardless of his talents, penchants, tendencies, abilities, vocations, and race of his ancestors. I am going beyond my facts and I admit it, but so have the advocates of the contrary and they have been doing it for many thousands of years

I think if Watson were alive today he'd have to admit he was wrong. Your ancestors are not destiny, but they are probability. If your father plays in the N.B.A., the probability that you will play in the N.B.A. is not high. But the probability is orders of magnitude higher than if you are a random person off the street. With all this I am not saying conditions which are non-hereditary are irrelevant. What I am saying is that we can't ignore the shape of the pre-existent landscape before we attempt to reshape it to our own image. Excoriating teachers for having pupils who can't master mid-level secondary school mathematics is in some cases like excoriating someone for the fact that their irrigation canals from the plains into the mountains are failures. You need to level the mountains before your canals can work (or, barring that design and implement a mechanical system which will move water against the grade). Easier said than done. E. O. Wilson said of Communism, "Great Idea, Wrong Species." The reaction of Communist regimes to this reality was brutal and shocking. Obviously the modern rejection of unpalatable aspects of human nature are not so grotesque. But they have a human toll nonetheless. I'm skeptical that this generation will pass before we have to acknowledge these realities and calibrate our policies accordingly.

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