On Oct 24, 2012, at 11:47 AM, Paul Tanner <firstname.lastname@example.org> wrote:
> I suspect that you will show the same type of hostility to such ideas > as these that make things so much easier and quicker for so many > people, the same hostility I have received from so many in terms of > making it easier and quicker to perform various skills.
This is because your critics (including myself) don't view math as a collection of rote tricks to be taught "easier and quicker". Their view of teaching arithmetic involves a true sense of arithmetic being transferred from teacher to student. They view "pretending to teach algebra" as superficial and damaging to that sense. They know that without the sense, the student will be unable to apply any of it.
You did mention struggling students and grades. I have tutored students in algebra before and had to pretend, but these were not students working on some math intensive degree. Algebra was a requirement and the last math class they would ever take in their life (maybe with a pretend statistics class as well). That does change things. By hook or by crook you try to get them through the course, so that they can go on with what they are really interested in.