Most of us remember that (a+b)^2 = a^2 + 2ab + b^2
I’m willing to bet none of us were taught it like that, and yet once you see it it’s so obvious. It’s one of those “A-HA!” type moments.
It reminds me of reading about KIPP schools in Work Hard, Be Nice and reading that the schools had turned the multiplication tables into sing-song ditties that the entire class sings, which of course makes it much easier for children to remember. (I still remember the torture it was to learn multiplication tables as a child, and I still don’t know them. If you ask me what 4×8 is, I do the math in my head.)
There’s of course an important policy point to be made about all this: I’m willing to bet all the money in my pocket that if a fry cook at McDonald’s comes up with a faster way to make a Big Mac, his manager will notice, who will get his team to use it, and the information will trickle up to his manager and so on, and then trickle down and a year later all McDonald’s fry cooks around the world will be using the new, faster Big Mac cooking technique.
Such are the virtues of the competitive sector. Not all private sector companies are like that. Much has been written in the business literature about
kanban kaizen the process of continuous incremental improvement which was so instrumental in the trouncing of US automakers by Japanese automakers. Elsewhere, I’ve described bureaucracies as “Institutions which do not see themselves as being under competitive pressure.” In the case of Toyota vs GM, GM became a bureaucracy because it forgot it was under competitive pressure, while Toyota was very aware that it was competing with GM and so the impetus to innovate and then broadly apply best practices was felt throughout the organization.
Forgive me for thinking this is precisely a feature public educational systems lack.