On Sun, Nov 11, 2012 at 5:41 PM, Robert Hansen <email@example.com> wrote: > > On Nov 11, 2012, at 8:01 PM, kirby urner <firstname.lastname@example.org> wrote: > > So I'm still wondering if your touristic excursions into math teaching > pedantry is "formal reasoning". > > > Yes. The excursions are data gathering and all the writing I do here is to > sort out my thoughts. > > > Apparently you're not equating it > with "formal logic" ala the logic of Frege - Russell - Wittgenstein > (the latter in fragments, as by Philosophical Investigations it's > mostly prose, though deeply worked to be grammatical in a certain > way). > > > Formal reasoning is different than formal logic. It uses logic though. > > > I am good with the extra for experts inserts, but you have to get the > algebra first before you can teach the student the why behind it, otherwise > > > I think saying you're not needing to give "the why behind it" up front > is what too many teachers are saying: we'll tell you later what this > is for, "just trust us" or "you need to know it because it's on the > test" (a smug tautology -- don't let your teacher get away with such > cheap and easy retorts, have some standards!). > > > There is a why behind group theory and a why behind that why as well.
Turtles all the way down. Wittgenstein investigated these beginnings and found not justifications but agreements in doing.
> Are you suggesting that we start at the end of all that and work our way to the > beginning?
More previewing and big picture certainly. Give more of a road map. Show where it's going.
Here's another thing:
As soon as you insist students use scientific calculators to do assignments, you *must* be ready to explain every key.
Giving students technology and then saying half the keys will not be explained this year is deliberately mystifying.
Therefore we need at least small forays into trig (SIN COS TAN) immediately upon introducing the device. This is mandatory.
Of course I'm not the czar. And of course I have no interest in imposing this doctrine on the unwilling.
Just, if you want to be on my team, don't ever introduce a device you're not prepared to rather completely explain.
> First you said a small intermission of some group theory topics.
I didn't say "small intermission".
Rather, I think the concepts of totient, totative and modulo arithmetic belong woven into the fabric of Algebra, along with Euclid's Method.
I've shown ways this might be done many times, many ways. That's probably why you think I'm a con man, because you can't find anything wrong with the math.
I think the Algebra we have now is relatively poor and insipid.
It's obvious that I think USAers are conned into a really inferior education for the most part, and in that sense I agree with Haim. As adults, they're mostly deeply misinformed not only under-informed, no fault of their own. They still have native smarts, many of them, so all hope is not lost.
Sometimes they only come to us after suckering for another war (a bait and switch racket, where they lure you with high-sounding language, a con).
However, I think the Education Yakuza (unlike Haim's Mafia) is well positioned to effect reforms. The Quakers (some of them) are on our side. That's already encouraging. Asia is not just more Europe, praise Allah.
> Now you seem to suggest that we put the whole cart before the horse. Help us > out here. Post what you think the sequence should be. Something tangible > like my elementary sequence I posted earlier. I am not asking for a
is something I came up with a long time ago. Not specifically "elementary school" but then my background is teaching high school and older adults.
I've been publishing curriculum writing for 20 years or so, free to the Internet.
It's not at all difficult to see what I'm advocating. Only the laziest reader on earth would need to say "lets take it from the top" as if I hadn't left a record.
> paragraph or two about Martian math. I am asking for a list of topics for an > algebra 1 class. Grab an algebra 1 book, copy the topics down, rearrange > them, add to them, delete them, do what ever you want, and present what you > think the topics should be. Without that it is rather pointless having a > discussion with you concerning the sequencing of an algebra class, since I > seem to be the only one bringing a sequence for an algebra class to the > table. >
Sorry guy, I work in my own manner and have plenty of details out there if that's what you're looking for.
As for dictating THE sequence I don't think that needs to be done, that's my point.
There are infinitely many permutations. Any teacher worth her salt should be able to cook up a bunch that work.
Here's another interesting Physics curriculum (in sketch):