Kids asked to physically gesture at math problems are nearly three times more likely than non-gesturers to remember what they've learned.Taking that at face value, and assuming that is works at the university level too, how long would it take this knowledge to seep into the practice of teaching college math?
On the other hand, what if one were to persue the practice of science to its logical end? Without rigorous standardization, it's very difficult to separate out potential causes from effects. Is such a rigid scheme appropriate or desirable for an educational setting? It would be a radical transformation. Such a transformational middle school math program is being tested in New York City, according to the website GothamSchools.org:
Students in the new pilot program [...] take a quiz every afternoon, and then receive a computer-generated schedule each morning, called a “playlist.” A student’s playlist might tell him to begin the day by meeting with a tutor, then to complete a set of online tasks, and then to work on a project with his classmates.This robotic-sounding instruction method was concocted by the same group who came up with a rigid curriculum delivery described in a 2005 New York Times article, where this description of a teacher's work under the system is described:
But in his classroom, he was not designing anything; instead, he was following the balanced literacy script. In a 90-minute period, actual imparting of knowledge was restricted to a lesson as short as five minutes. Then pupils broke into small groups for independent guided work, and reconvened to share their efforts. School administrators made unannounced visits to ensure that teachers were using their rugs and abiding by the "flow of the day" schedule posted in each classroom.This reminds me of fifth grade. For at least part of the year, our math lessons came from a purple SRA box. This program is now online, of course, but in the old days a student was suppose to start at the front of the box with division problems (there were probably other types of problems, but I remember only division). Our brains are not designed to do long division--an example of Moravec's Paradox, I'm sure. As a consequence, it's a hard slog to grind through what I learned later is basically an inverse convolution. (I now wonder if it could be done more easily by just inverting the convolution matrix... Have to think about that during the long meetings today.) At any rate, it was a real pain for an energetic fifth-grader, and probably turned many off to the idea of math entirely.
There was a system to the problems. Everything was self-scored, and if one did better on a particular test, the next one would be more challenging. The reverse was true too--if you missed many of the problems, the next set would be easier.
You can imagine what I did. I quickly discovered that if I "forgot to do" several of the hard problems, the next batch would be much less taxing. I shared this secret with my friend Ronnie, and soon we were working our way through the problem cards without breaking a sweat. While the other kids were trying out 14589/235, Ronnie and I were doing stuff like 256/16. Unfortunately he got caught. Fortunately he didn't rat me out, but I had to go back to the slog out of fear of being sent to the gulag.
The point is that systems can be hacked, cheated, and gamed. Any system. We hominids have faced that problem ever since people have lived in groups, probably, and have very good on-board apparatus for detecting cheats of all sorts. Computers and card systems aren't so good at it. Not yet, anyway.
Read what happens when a teacher in the teaching system described in the Times article employs a little flexibility and gets off track:
To avoid being caught if they did not follow the schedules, some teachers began "actually training their kids to switch subjects on command," [a teacher] says. "They can be doing a reading lesson, and if somebody walks through the door, all of a sudden they're doing the writing lesson."This sort of side effect to standardization is inevitable. If we're going to go this route, it's imperative that we do the meta-analysis and ask: how can our beautiful system be gamed? It's the equivalent of building a new operating system to unleash on the world's computers. It needs to have safeguards against hacking, right? But no system is completely hack-proof, so in practice there's always a race between the hackers and fixers. (Computer people call malicious hackers "crackers," actually.) And this race, I think, is computationally so complex that it is out of the realm of prediction: that is, it's not a subject that can be easily made scientific.