On Jul 7, 2013, at 4:22 PM, "Clyde Greeno @ MALEI" <email@example.com> wrote:
> It often happens that highly formal, strictly didactic, direct instruction is sufficiently common-sensible for the intended audiences ... and often it miserably fails. It often happens that "indirect instruction" is contra-productive because it tangentially goes off into the la-la land of irrelevance ... likewise failing to make foundational mathematics common-sensible to students.
Did it ever occur to you that the level at which this stuff is of any use or even works requires that the student be able to get it from direct instruction? In other words, if you came to me and said "Bob! I successfully turned this student around and they have succeeded in Algebra 1." I would say "Great Clyde. I will fully believe you if they attend that traditional direct Algebra 2 honors course and succeed." If algebra is clicking through their minds then there is no reason that should be a problem.
Why? Because that is how it looks in real life when you use this stuff. You have to be able to fill in a lot of blanks. I have never said that you must start there. I agree that many students suffer by not being ready for that experience. However, you do have to get there at some point to be successful. You can't say "He or she is really getting it, but they still don't get it in a lecture." People are going to ask you "Well, then what do you mean by "really getting it"?"