Fw: [eddra] Arithmetic and Algebra
- Subject: Fw: [eddra] Arithmetic and Algebra
- From: gerald bracey <gbracey@EROLS.COM>
- Date: Sat, 23 Feb 2002 15:03:59 -0500
- Reply-to: Assessment Reform Network Mailing List <ARN-L@LISTS.CUA.EDU>
- Sender: Assessment Reform Network Mailing List <ARN-L@LISTS.CUA.EDU>
I didn't think it would take long to get a response from Waybe Bishop,
although I am surprise by his line of thought.
----- Original Message -----
From: "Wayne Bishop" <email@example.com>
To: "Gerald Bracey" <firstname.lastname@example.org>; <email@example.com>
Cc: "wbishop" <firstname.lastname@example.org>; <arn-L@listsrva.CUA.EDU>;
<email@example.com>; "Jay Mathews" <firstname.lastname@example.org>;
<email@example.com>; <firstname.lastname@example.org>; <email@example.com>;
<firstname.lastname@example.org>; "Lisa Black" <email@example.com>
Sent: Saturday, February 23, 2002 3:54 PM
Subject: Re: [eddra] Arithmetic and Algebra
> >Here's something a little different. I want to present some data and
> >ask a question. It's a real question, not a conclusion in the form of a
> What's different about it? It looks like the same tired rant. Algebra
> competence is fine for affluent white kids but not needed for the Bracey
> masses, the future McDonald's workers of the world.
> >Here's the question: Given FITW's overall stellar performance, do the
> >above data not indicate that mastery of "the basics" is not necessary for
> >the acquisition of advanced mathematical skills?
> Kumon, Sylvan Learning, Kaplan SCORE, etc., are growth industries in those
> affluent suburbs; I encourage you to invest. They're badly needed
> antidotes to Everyday Mathematics (so-called "Chicago Math", the FITW
> elementary school favorite that has almost no presence in Chicago itself,
> and with good reason), and along with it, Connected Mathematics, Core
> IMP, etc.
> > In the college town where I grew up, it was a cliche that
> > couldn't cope with arithmetic. Are arithmetic and math independent of
> > each other? My guess is yes. I await your responses.
> Better not to guess. "Couldn't cope" is a terrible, and perhaps
> deliberate, misrepresentation of reality. The ability to compute rapidly
> while remaining accurate is a nice ability to have, although it is not
> essential. However, I have never met, nor have you, anyone competent in
> any mathematics based discipline who did not know, and essentially
> understand, the rules of standard positional arithmetic, common fractions,
> and ratio and proportion problems. Mathematically knowledgeable people
> did not know, and essentially understand, the rules of standard positional
> arithmetic used to used to exist, the Greek geometers were the most
> and they only because positional arithmetic had not yet been invented or,
> more accurately said, were not yet widely known and were not known to them
> (some guy in India probably did know!). They would have soaked it up
> almost immediately and would have understood it and would have understood
> the power of this numeration system and how it follows easily from things
> that they did understand. My guess is that they would have invented a
> of algebra that would have looked much like ours had they had that
> fundamental insight. It is not entirely accidental that both "algorithm"
> and "algebra" derive from the "al-Khwarizmi" part of "Abu Abdullah
> Ibn Musa al-Khwarizmi". http://users.erols.com/zenithco/khawariz.html
> Find me one mathematician who didn't understand borrowing, carrying, long
> division, and the rest of the standard algorithms of arithmetic, and basic
> algebra including operations of rational functions and, almost innately,
> the graphs of obvious ones such as y = x^2/(x^2 - 1), and then we'll
> talk. Until then, please recognize that you are helping to keep
> underrepresented subpopulations from taking their rightful role in our
> supposedly egalitarian society. The bulk of our better students come from
> Asia and their schools really are FITW, not compensating for what should
> have been happening at school*.
> By the way, I somehow seemed to have been dropped from the EDDRA listserve
> and must depend on others to forward your posts to me. Please reinstate,
> Below is an editorial follow-up of a Lisa Black article on 4-13-00,
> "New-New Math Causes some Division". In that, she reported from one of
> those northwest Chicago suburbs:
> "Betty Underwood of Arlington Heights was PTA president of her daughter's
> elementary school when she was horrified to observe math students
> leapfrogging around the room. The pupils measured how far their classmates
> leapt and wrote down the mean and averages.
> '"The cutting edge is not necessarily the place to be in education," said
> Underwood, who pays $150 each month to enroll her children in a private
> math program that focuses on drill exercises."
> Chicago Tribune, May 15, 2000
> NEW-NEW MATH DOESN'T COMPUTE
> One plus one may equal two. Or about two. Maybe even an estimated three.
> It all depends on what style of math you fancy: Old math, new math, or
> new-new math, the latest entrant into the decades-old math wars, one that
> de-emphasizes rote memorization in favor of estimations and--Holy
> Under "new-new math," students are taught multiple ways to arrive at math
> solutions, but without the traditional encumbrances of worksheets or
> textbooks. That way, the thinking goes, they'll come to understand
> principles of math, and will choose which method works best for them.
> So much for carrying the 1s or figuring out the remainder.
> Advocates of the new-new method stress that students still are expected to
> familiar with the fundamentals of addition, subtraction, multiplication
> division. And indeed, some of the principles sound like good sense. For
> instance, fourth graders learn relationships between numbers, so that if
> know 6 x 8 = 48, they also know that 60 x 80 = 4,800.
> But then the stated program goals drift off into New Age-sounding
> in which students are "linking past experience to new concepts; sharing
> ideas; developing concept readiness through hands-on exploration." One
> second-grade exercise has students thinking up a lunch, drawing it on
> and cutting out the foods, all in the name of learning division.
> It's no wonder 200 mathematicians and scientists fumed publicly last fall
> after the United States Department of Education officially endorsed 10
> new-new math programs for kindergarten through 12 grades. Critics started
> calling the new programs names like "New-New Mush-Mush Math," "Algebra
> and "Placebo Math."
> New-new math programs such as Everyday Mathematics, designed by the
> University of Chicago, offer as proof of effectiveness the fact that 12 of
> the 25 top-scoring Chicago-area schools on last year's 3rd grade Illinois
> Standards Achievement Test used its method--along with 1.5 million
> nationwide. But then there's that pesky rule of advanced statistics that
> correlation doesn't necessarily mean causation.
> If old style math, the "drill-and-kill" kind, was stupefying students into
> lifelong aversion to math, then new-new math, with its engaging word
> and hands-on exercises, may hold some promise at least in keeping young
> peoples' attention. Or, it may confuse them to such a degree that while
> they'll have fun playing "Frac-Tac-Toe" and "How Would You Spend a Million
> Dollars," when they grow up they won't be able to figure out a restaurant
> Old, old, old math guy Pythagoras had it right: The shortest distance
> two points is a straight line.
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