On Oct 1, 2012, at 12:40 PM, Wayne Bishop <wbishop@calstatela.edu> 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.

Bob Hansen