I think that is my point and Val's, though, Jon.
That without that emphasis on applied deductive reasoning, it is just sort of a jumble of memorized formulae having to do with areas and distances of plane figures.
That isn't what geometry should be teaching.
Yes, exactly. We water down the courses and then water them down some more and everyone smiles and pretends that our students are "learning geometry." They aren't. They're memorizing factoids so that they can pass simplistic multiple choice tests. And then everyone wonders why so many students end up in remedial math classes when they go to college. Please don't tell me that the colleges should have told the kids to study first: someone two or three months out of four years of solid high school math should be able to manage a bare scraping pass on a basic placement test, regardless of whether or not he spent some time the week before studying.
Seriously.
And all the while, the effects of this dumbing down are creating or exacerbating terrible problems in our society (e.g. two years of student loans paying for remedial coursework; the needs of bright and gifted students being sidelined) while people put the same hackneyed solutions in a shiny new box and label it "
Rigor (tm)
!"
