Aren't there things everyone needs to know?
I'm not sure about that. When pressed to answer their own question, most people say things like "basic math" or "how to read" and then have trouble thinking of much else. Even if I conceded that these two things were absolutely necessary for every person to know, that would hardly justify me sending my kids to school, as schools try to teach a whole lot more than just those things.
Every hour I spend tutoring students makes me wonder even more about the things that are taught in school. Just in the past few weeks, I have helped kids learn how to do polynomial long division and to use the three different methods for solving quadratic equations. Also, I have student who is in Geometry this year, and this week I helped him memorize all the different formulas for the length of an intercepted arc of a circle. Why?! Why does every child need to know these things?
And what does it mean to "know" something? In school, I think it means "getting a good grade on the test." It requires remembering something just long enough to answer a few to a lot of questions correctly. As I pointed out in my first post about tests, these forced testing situations are unique to school.
When I tutor a child who is not a "natural mathematician," I notice that sometimes it can seem like he understands a concept as I work with him. But even sometimes the very next day I talk to him about it, it is like he has never heard of it before. If he happens to take a test a few hours after our session, and does reasonably well on it, does that mean he knows it?
What about the child who definitely understands the concept, but does poorly on the test because he forgot to show his work (because he didn't need to do any work to get the answer)? Or because he is sick? Or distracted because of some tragic situation going on in his life? Does that mean he does not know it?
What do you think everyone needs to know? And how long does someone have to remember something before he qualifies as "knowing" that thing?