On Aug 26, 2013, at 1:16 PM, Wayne Bishop <email@example.com> wrote:
> The real key is algebra readiness; basically competent computational skill through ordinary fractions and percent with lots of straightforward ("cookbook" if you will) word problems of mixed nature through ratio and proportion problems so that students have to actually read the problem to understand which and how the numerical aspects are relevant, (have the requisite "tools " to) set up and solve the resulting mathematics problem, and interpret the results back to the original setting.
I agree, but if the student has kept up with *all that* and can prove it then we are probably saying the same thing. They are thinking. At least enough to take it to the next level. I still say we have to be careful. If your proof of *all that* consists of tests that are only half of *all that* and the other half just rote recitation of facts and/or concepts and your cutoff scores are half of all of this, then there is no proof.
It shouldn't come as a surprise to anyone here, especially the older teachers, that as they have targeted more and more students with these courses the tests and grading standards have lost more and more of their value. For every action there is an equal and opposite reaction.