[math-fun] We don't need no stinking algebra
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)
On 7/31/2012 2:45 PM, Warren Smith wrote:
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,
They know what *they* are doing - but they don't know what you're doing...and if you don't know either...
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.
The trouble is he won't know what should be divided by what. An engineer friend once said, "I didn't really learn algebra until I took calculus. And I didn't really learn calculus until I took differential equations." You don't really learn stuff until you use it.
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 :(
The original thread though was about requiring algebra in high school (at least for college prep) and weren't we filtering out a lot of good history and art and lit and poli sci majors? I think that's bunk. Algebra, of the kind taught in high school, should be an integral part of the math curriculum starting about the 4th grade. It's just a matter of becoming comfortable with abstractions. As for what is actually useful to those art and lit and poli sci majors, I'd say probability and statistics is what the educated voter should know, but you need *some* algebra and calculus (not much) for that. Brent Meeker
On Tue, Jul 31, 2012 at 3:57 PM, meekerdb <meekerdb@verizon.net> wrote:
The trouble is he won't know what should be divided by what.
An engineer friend once said, "I didn't really learn algebra until I took calculus. And I didn't really learn calculus until I took differential equations." You don't really learn stuff until you use it.
I know that I didn't understand any thermodynamics until I took solid state physics. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
participants (3)
-
meekerdb -
Mike Stay -
Warren Smith