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
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. Are you suggesting that we start at the end of all that and work our way to the beginning? First you said a small intermission of some group theory topics. 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 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.