I wonder if teaching math should be made to look more like recess. Now that spring has sprung and the grass has dried out, my kids are doing lots of football and baseball after lunch. I've always been fascinated at the range of behaviors you can observe when a ball comes out .
Some boys never engage in these things. Others will only get involved if the ball hits them. Still others only engage when a group of similarly skilled boys coalesce. These kids aren't great at it but they have a good time with each other and almost never engage with the experts. The experts are at the top of this food chain. They exhibit skills that are simply amazing, given their young age (12-14)
The experts are usually (>80%) engaged and the others of course trickle down to no participation at all. There's a natural filter at work. The best are amazing, exhibiting a fluidity and naturalness that you can just tell is extracting the absolute best out of them. The worst (sorry) throw like girls. Actually I have a few girls who throw really well but they've never developed the requisite full motion skills to catch well. Might have to do with breaking a nail, sigh.
What's key is that everybody can throw and catch but there is an elite that clearly will go on to become accomplished athletes in football or baseball (or both). These kids will eventually get formal training in the underlying theory of what is making them excel naturally. For now they just excel and presumably they got that way from huge amounts of play (practice) that they chose (value proposition) because they were good (wired for it) at it.
You could easily conjure up a scenario where if bureaucrats were to see this (fortunately they mostly stay inside) they would be appalled at the disparities on display. They would retire to their offices and write a standard to ensure that no child is left behind in playing catch. Then they would set up classroom training to guarantee that every student has access to the new standardized curriculum. They would introduce nerf balls so that nobody gets hurt or breaks a nail. Then they could train us teachers to introduce mixed ability groups so that the experts are forced to play with the geeks. They would want to ensure that all sports were covered so they would schedule a new game every week in an elaborate multiyear spiral.
Before long every kid in school would hate recess as much as math. The playing field would be leveled and we would get the miserable equal outcomes that we are getting in the academic disciplines. Pretty far fetched, eh?
Well what if you thought of academics more like sports. In math maybe you work with calculators from day one and you make sure that every kid can do the kinds of things we all do with calculators, mastering every day mathematical application. As this process evolves you would see who has the passion and talent to go deeper. Along the way, kids who can't cut it get to drop out of the pursuit of theory and depth but they do so with a repertoire that ensures they can at least use the gadgets in their lives effectively. You could continue this natural filter throughout the K-12 years. Wouldn't every kid get what they need?
Right now we have a tendency to turn off kids at every step in the process by delivering theory first. Eventually the experts get what they need but only after suffering through 12 years of torture playing catch with people who can't catch. Many of the non-experts get turned off before they get the basics of application and leave school unable even to use a calculator properly. Wouldn't it be exciting to demonstrate some neat result and have kids jaws drop and quiz you on why that works? Wouldn't that lead to more interest than theory first?
Isn't it true that history and science are taught this way now? Two subjects that my middle school students love! Hmmmmmm.