On Oct 1, 2012, at 12:40 PM, Wayne Bishop <firstname.lastname@example.org> wrote:
> My concern with Dave's problem (and his expressly as well) is that someone can know Algebra 2 well and still miss the trick unless a hint is given.
I would have to have more on what you mean by "know Algebra 2" well.
The reason this problem seems like a trick is that we do not teach algebra this way. If a few students pick up on this element of algebra, all the power to them, but we don't teach algebra this way.
> That has never bothered me. Out of that hundred, how many will need to know or ever use who Carl Sandburg was? And a ton of other such stuff. What really does bother me - and leads to the huge inequity at later stages - is being genuinely algebra ready at algebra time. At that point, becoming algebra competent or not (especially at the Algebra 2 level) is probably irrelevant for those whose ambitions lie other directions (if known; if not known??) Hence my huge interest in quality K-7 mathematics with K-5 (both math and reading) being the most important and 6-7 having lots of ratio/percent/etc. word problems that have to actually be read and understood for the mathematical content and how to interpret it back in terms of the original setting.
I think most here believe that a student that can't work with fractions is like a student that can't read. I am only saying that if you set out to teach algebra at least teach it. I don't mean the quadratic formula, I mean the cleverness and the solving. That part is transferable and underlies the complexities of STEM.