So I have thought about this and Lou has provided some input and Dave has provided some input. To be honest, this wasn't the type of question I was expecting, but I am grateful to Dave for supplying it. I was expecting the "put the blocks together in the correct order" type question.
Is this problem too clever?
My feeling is that your typical algebra class, even a typical good algebra class, stops short of asking students to solve clever problems. To me that has always been like teaching chess yet never putting the students to the task of playing a game of chess. Prior art is important as well but prior art goes with the territory. But if students are not put to the task to create art themselves (to figure out the tricks), they will not appreciate, retain nor find useful the art of algebra.
I posit that this is one of the reasons that very very few people know algebra after school. They never actually knew it in the first place. They were never put to the task. I note also that no one here had a problem with Dave's problem so why is it that we feel obligated to hide this art from students? We do not do this in language arts, we ask students to write. We do not do this in music, we ask students to play. We do not do this in art, we ask students to paint, sculpt and draw. Why then do we do this in algebra?
Lou says that there is a utilitarian usefulness to algebra, but if that were true wouldn't we see it in everyday life? I see it no where. I see people doing spreadsheets galore and when they get stumped by something, like a moving average, they ask me or someone like me what to do. And I am not complaining, I like answering questions and solving problem, who here doesn't? But I do think more people could do what I do if they had been put to the task in school. My algebra teacher did put emphasis on solving but even she held back. The truth is, mathy students, the ones that use this stuff after school, are pretty much on their own.
Are we conditioned this way? It would seem so.
On Sep 28, 2012, at 5:51 PM, "Dave L. Renfro" <firstname.lastname@example.org> wrote:
> Robert Hansen wrote: > > http://mathforum.org/kb/message.jspa?messageID=7897638 > >> I want to try something different. I want everyone to contribute >> problems for a hypothetical algebra 2 exam. You can contribute >> just topics if you wish though I would like see examples as well. >> I am going with algebra 2 rather than algebra 1 because I think >> the line is more well defined. > > I only have a few moments before I need to leave to tutor > someone, but here's a somewhat silly one off the top of > my head: > > Determine the exact value of a^2 - b^2 if > > a = 7.0241132301442003123012230341430201 > b = 6.0241132301442003123012230341430201 > > Calculators are allowed. > > Dave L. Renfro