The intersection of people who struggle with basic algebra and the people who use Mathematica has a cardinality equal to the infimum of positive reals. :P Sincerely, Adam P. Goucher
--yes, but that is kind of my point. Does it have to be that way? Maybe they'd struggle less with appropriate computer help? I don't know. Partly, you cannot use such tools unless you already know what you are doing, so it is somewhat pointless... but those tools DO know what they are doing, at least about basic algebra, so it seems in principle, it ought to be possible for Joe Schmoe to do algebra even if fairly clueless, if has help from software that knows how. For example, Joe Schmoe can do long division with calculator aid, even though he himself unaided might have no idea how -- a fact the UK education system now agrees with. One time I was teaching calculus I wanted to tell them about Maclaurin series and was motivating them by asking "how does your calculator compute sin(50 degrees)?" The responses were all "duh! You press the 'sin' key! ...So since we can do that, why do we care?" Which was a quite defensible reaction from them all, even though not what I wanted to hear :( -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)