On Mon, Jun 3, 2013 at 12:13 PM, Robert Hansen <email@example.com> wrote:
> > On Jun 3, 2013, at 2:01 PM, kirby urner <firstname.lastname@example.org> wrote: > > There should be no teaching of algebra as it was taught in say 1964. They > had no decent way to program personal computers back then, no Google Earth, > no GPS. > > > > Algebra has nothing, zero, zip, to do with computers. Algebra is entirely > about thinking. This is what I mean about the purpose lost. >
That's entirely incorrect Bob. Plus you're quite inconsistent as you've written here a number of times that 'Mathematics for the Digital Age and Programming in Python' is a respectable math-learning text as text books go. It had better be, as families frequently pay the big bucks to have their students go to such schools that use it.
Computer programs (as much as on-paper forms as "human computers" used to fill out, such as when computing a geodesic domes angles and edges) are in part about standardizing algorithms -- meaning you need to know right away what's a constant and what's a variable. Then you learn about what variations in input produce what variations in output. Again, that's functional analysis and ratio-ing deltas, the basis of diffy-Q.
Whipping out programs is a great way to study the properties of mathematical objects, including Pascal's Triangle, which has everything to do with the Binomial Theorem (still part of pre-calc algebra the last I checked).
Computers are a tool, like calculators. Nowadays it's still about using calculators. That's part of what's criminal. Teachers are at least a decade behind on average and getting further behind by the day. SQL relates to boolean algebra or has "boolean algebra" nothing to do with "algebra" despite the truth tables the alegbra books commonly feature.
The algebra you had as a kid is not something I'm keen to perpetuate. Conway's and Guy's 'The Book of Numbers' is more in the ballpark, but then so is 'Godel Esher Bach' in providing a more "lexical" idea of precise rule following (the kind of appreciation helps make chess a part of maths, as much as Conway's Game of Life, which it isn't only for ethnic reasons, no "pure reason" at work -- English has a way of dumpstering a lot of good thinking thanks to mind-numbing antibodies).
But lets just say for the sake of argument that there's nothing in the newer STEM curriculum that's recognizably "algebra" the way you remember it, with just such a list of topics, just such a table of contents.
That would be, is going to be, a very good thing, a blessing. My thesis is we can't afford to hold kids back to the degree you would like to, for reasons of nostalgia perhaps.
When you have a language that permits operator overloading so you-the-student get to define a meaning for multiplication, addition etc., and think about properties of multiplicative and additive inverse in the abstract, you're inherently in a better position to really learn algebra than some late 1900s 8th grader with no access to such tools.