NateD26 wrote:I don't understand who decides those seemingly arbitrary and wholly illogical
rules for what to teach first.
I may put up a thread sometime about teaching. Like almost everything, there is a spread when it comes to teachers and textbook writers. Only about 15% are good. And maybe less than 5% are extremely good. There are no rules for when things get introduced. A great teacher anticipates problems students will have. But that is path dependent. By taking one path through the material, different problems will need to be anticipated.
Fortunately, serious students can learn even from mediocre teachers. What kind of efficiency is at issue? 2-1 perhaps. The extremely good teacher leads the student through the material in half the time.
What I may start a thread about is this: Why the hell don't Greek textbooks make extensive use of all the words in English with Greek roots? Even if a very good teacher has a good reason, the burden of proof surely is on him to expain himself because prima facie it seems quite absurd
not to. Teachers in the sciences make appeals to our intuitions about nature all the time. But Greek teachers refuse to avail themselves of all the Greek we already know?!?!?! I'm tempted to use very strong language right here. They may follow tradition, but tradition should not be the primary guide in the class room. Even if somebody gives me some devils advocate BS for why it is OK to not use all the Greek we already know, it is too late
. That case needed to be made in the introduction to the book.
There are no rules for how to teach. But there are lots and lots of bad teachers. Indeed, maybe the lack of rules explains all the bad teaching.
I could tell you stories about other fields where everybody does the same dumb things simply because most people are rank conformists. They can't imagine that they all have been doing things the wrong way forever. Consider, for example, doctors and their residency ritual where they work 16 hour shifts. Is that a rule? No, just rank human conformist stupidity.