Re: [math-fun] NYTimes: Is Algebra Necessary?
I've been meaning to mention the article "What Is Mathematics For?" by Underwood Dudley. The title should be "What Is Mathematics Education For?" www.ams.org/notices/201005/rtx100500608p.pdf A short version of his case is "Is Mathematics Necessary?" at http://www.public.iastate.edu/~aleand/dudley.html Dudley refutes the claim 'Mathematics is Necessary for Work'. He aims a little higher than Algebra, but presents a good set of examples. The finale is a plea for 'Math as Art', asking readers to look beyond the pedestrian goal of preparing students for a job. (A tough sell during the Great Recession.) He does mention the justifications 'Math teaches logical thinking', and the general 'we want smart people here, and math is a good filter'. The issue came up in the Arizona CS department c. 1995, when the curriculum committee was debating whether to keep the Calculus requirement for the CS degree. (CS is a curious meld: programming skill and algorithm analysis, blended with the advanced math of Relative Computability.) Rather than reprise the arguments pro & con, I'd like to pose a puzzle: Why do so many people find math too hard? I think the toughest memorization task is learning the multiplication table, and the most complex widely taught algorithm is long division. Both of these are now 'calculator' jobs, which ought to make easier the problem of solving 2x = 5. Somehow, it hasn't. What's the difficulty? Rich ----- Quoting Henry Baker <hbaker1@pipeline.com>:
FYI -- I'm not fond of the way algebra is taught in schools, but I think it would be insane not to teach it at all. The comments on this article are interesting.
http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html
Opinion
Is Algebra Necessary?
Adam Hayes By ANDREW HACKER Published: July 28, 2012
A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? Ive found myself moving toward the strong view that we shouldnt.
On Sun, Jul 29, 2012 at 9:33 PM, <rcs@xmission.com> wrote:
Rather than reprise the arguments pro & con, I'd like to pose a puzzle:
Why do so many people find math too hard?
I think the toughest memorization task is learning the multiplication table, and the most complex widely taught algorithm is long division. Both of these are now 'calculator' jobs, which ought to make easier the problem of solving 2x = 5. Somehow, it hasn't. What's the difficulty?
Not enough people playing Dragon Box. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
I think the toughest memorization task is learning the multiplication table,
I disagree. Learning all of the methods to calculate the antiderivative (indefinite integral) of a function required far more memorisation. Of course, there is a very good reason for this: it's hard (in the sense of being undecidable in the general case). Although, I do wonder why people learn the multiplication table up to 12 * 12, since the table up to 10 * 10 together with any basic multiplication algorithm (which ultimately boils down to convolution of two sequences) is sufficient.
and the most complex widely taught algorithm is long division.
I believe that's been removed from the UK syllabus now, except for the equivalent algorithm for polynomials. I am in favour of this, since the only application of numeric long division is to prove that rational numbers have terminating or recurring decimal expansions. Sincerely, Adam P. Goucher
The whole point of mathematics is _abstraction_, but abstraction requires enough experience & sophistication so that the student is ready for it. In computer programming, we try to avoid "premature optimization". Mathematics education should avoid "premature abstraction". Only after a student has done the "same" problem in 3 different guises might they be intrigued by an approach that solves all three in the same way. This should be one of the reasons for teaching multiplication tables: to get the students bored enough to start appreciating abstraction. When you have to memorize a massive table, you start to look for cheats: notice that the table is symmetrical about the main diagonal... --- I'm about 1/2 way through the NYT comments, and have only seen one mention of the Khan Academy. This is a pity, as the Khan Academy does a pretty good job of teaching algebra -- probably better than 98% of the high school math teachers. Which brings us to the main issue: if _doing_ math is difficult, how difficult do you think _teaching_ math is? Why would a huge number of our lowest achieving (academically) students be capable of passing on this difficult subject to our next generation? A. They can't. Which is why our only hope is computerized education for math, at least. If we can take a very small number of our best & brightest -- e.g., Salman Khan -- and have them produce videos/animations/lectures/problem sets, etc., then we have a chance at getting high quality math education. At 09:33 PM 7/29/2012, you wrote:
I've been meaning to mention the article "What Is Mathematics For?" by Underwood Dudley. The title should be "What Is Mathematics Education For?"
www.ams.org/notices/201005/rtx100500608p.pdf
A short version of his case is "Is Mathematics Necessary?" at
http://www.public.iastate.edu/~aleand/dudley.html
Dudley refutes the claim 'Mathematics is Necessary for Work'. He aims a little higher than Algebra, but presents a good set of examples. The finale is a plea for 'Math as Art', asking readers to look beyond the pedestrian goal of preparing students for a job. (A tough sell during the Great Recession.) He does mention the justifications 'Math teaches logical thinking', and the general 'we want smart people here, and math is a good filter'.
The issue came up in the Arizona CS department c. 1995, when the curriculum committee was debating whether to keep the Calculus requirement for the CS degree. (CS is a curious meld: programming skill and algorithm analysis, blended with the advanced math of Relative Computability.)
Rather than reprise the arguments pro & con, I'd like to pose a puzzle:
Why do so many people find math too hard?
I think the toughest memorization task is learning the multiplication table, and the most complex widely taught algorithm is long division. Both of these are now 'calculator' jobs, which ought to make easier the problem of solving 2x = 5. Somehow, it hasn't. What's the difficulty?
Rich
----- Quoting Henry Baker <hbaker1@pipeline.com>:
FYI -- I'm not fond of the way algebra is taught in schools, but I think it would be insane not to teach it at all. The comments on this article are interesting.
http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html
Opinion
Is Algebra Necessary?
Adam Hayes By ANDREW HACKER Published: July 28, 2012
A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? Ive found myself moving toward the strong view that we shouldnt.
participants (4)
-
Adam P. Goucher -
Henry Baker -
Mike Stay -
rcs＠xmission.com