More precisely, when the approach we're using keeps on not working, instead of doing more of it, maybe we should rethink the whole approach and give up the way that keeps not working.
I had four years of math beyond calculus and tutored many students, so I feel qualified to present an opinion on the subject.
I love math and science. I'm very pro math.
But, I'm also pro reality. Reality is good, even when it's inconvenient.
Most people don't like math. That's also reality.
Why is that?
I think the main reason math is so hard is that you can't get by being "mostly correct" - you have to be entirely correct.
An English paper with a grammatical error can still be excellent. A math equation with an error is completely wrong.
Surprisingly, if you are compulsively neat and organized, math itself is easy, and, I love it because problems have correct answers that don't depend on what the teacher thinks. On the other hand, I can't stand problems like "What did Hemmingway really mean by the image of the fish?" because the answer depends on the instructor.
The reason math is difficult is that most students today have no experience being the type of compulsively neat detail-obsessive workers that it demands in order to work at all. Unless you get 100% of an solution's steps correct, the answer isn't "mostly right", it's totally wrong.
It is as if we are trying to lay precise rail-road tracks across a thinly-encrusted swamp of sloppy behavior, and, frankly, that simply does not work, and cannot be made to work.
So, the implications of that strong assertion are enormous. So everyone is playing "Let's pretend."
Either we bite the bullet and figure out what it takes to accomplish "self-discipline", or we should abandon all pretense that we can "teach math and science" without it. It cannot be made to work.
There is no point trying to teach concepts to students who don't have sufficient self-control to keep a column of numbers straight on a page. It may in fact be possible to teach the concepts, but it won't by itself result in them being able to ever "do" math or science in any socially useful sense.
If my analysis is correct, then to get STEM education to work, we need to have wide-spread specialized remedial courses in structured work and self-discipline. It's absurd to expect our math and science teachers to have to do that on top of teaching math and science.
In mathematics, the passing score for any concept should be 100% - - the only exceptions being questions that were poorly designed. "Sort of knowing" something will not cut it. Getting "most of the equation right" except for that one term there will not get most of the answer right.
This seems to come as a surprise to people, students and teachers alike.
Yes, in the long run, we should improve things, but in the short run, don't bet on it working.
If we cannot make our individuals reliable, that doesn't mean we are unable to make combinations of individuals reliable.
And, just like SEAL teams in the military, maybe these teams should persist across years, learn to work well with each other, and then go apply for jobs as a team, not as an individual, and stay together on the job.If we're going to go that direction, then the dollars, priorities, and emphasis in education needs to change from attempting to maximize individual skills and reliability to maximizing combined skills and reliability of small treams of people working on problems together.
On the job front, one way to handle the logistics would be to incorporate the team as, say, an LLC and have the LLC take a job slot as a "consultant." That can be done with today's technology.
The problem is the educational system, oriented almost entirely around work-units of size 1, that is, "individuals."
Not only should that be "fair", it should be encouraged.
- We could try to back-fill remedial high-quality self-discipline into our students and culture and also "learn math", or
- We could try to remove the "do your own work separately" constraint and start tackling problems as pairs of somewhat-sloppy but cooperating individuals.
My point is, if we want to be sloppy about our personal work habits, and we appear to take that as a cultural norm, and if we HAVE to be concerned about product reliability, which is demanded by the mission or a competitive marketplace, then we have no choice that I have seen so far besides figuring out how cancel out that sloppiness by working together.
While we're at it, let's say the dyad should be allowed to have permanent full-time access to the internet during any portion of training, education, examination, or activity during the actual job. That's realistic these days.
Here's a crucial point: if we demand students perform amazingly well as individuals and graduate high-school and college as "singlets" before considering them for inclusion in a work team, there are two guaranteed results:
- People who would make great team members and totally boost team energy and morale, say, but are mediocre working alone will never get a chance, as they'll drop out early as "failures".
- The people who do succeed as singlets are then supposed to do a u-turn and work as team members, which they just spent 12 or 16 years learning to avoid.
So now the question is, can dyads of Americans, with access to the world wide web, working just with each other and learning over time how to operate as a team, trained as a team, operating as a team, outperform Chinese singlets working with what they learned and stuffed in their heads, without access to web?
My thought is, yes.
I guess, when you're coming from behind, "whatever works" is a good philosophy. We have a lot of sports where doubling-up on your opponent is a winning strategy, don't we?
Besides .. it sure beats having to learn algebra for real.