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Re: Pseudo-education marches on
Posted:
Feb 12, 2001 9:55 PM
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I don't know how much of an indictment of education your examples of student
work represent, nor have I ever been introduced to these type of strategies
at any math conference I've attended.
It appears that the student who worked on the salesperson's wages did a very
good job of translating the word problem to an algebra problem and was able
to solve the problem, but was unsure how to work the problem backward. It
also appears the student was careless in forgetting that he had to account
for the flat weekly salary.
Without being told anything about the class or what level this student was
at, I would guess this is the work of a first year algebra student who is
stubborn with the belief that he has a perfectly good way to solve a word
problem and he didn't want to monkey around with a method he hadn't studied
thoroughly and/or he didn't trust.
I don't understand the problem with the fourth grade problem. Let s = price
of sweater and c = price of coat, s + c = 80, and s + 50 = C, then the
problem is simply: s + s + 50 = 80, 2s +50 = 80, 80 - 50= 2s, 30 = 2s, s =
15. This is exactly the same as the solution you described without the
algebra. For 9 year old students, the approach described is perfectly in
line. Testing fourth graders for mastery on this type of problem is
inappropriate. I think this problem would be good for developing students
ability to use a sequence of calculations to reach the answer to a specific
type of word problem. In short, it could be an example of a teacher saying,
"hey, look kids, here's a messy old word problem that has several problems
inside it, but it is doable. Here's how we will do the first one...."
Without touching on algebra, a level of abstraction that would be too
distracting for little kids, it would be in the kids developmental interests
to solve a very similar problem where they would have to identify the number
to subtract from the total, and to identify the item that is the cheapest,
etc. Remember, kids that young are trying to read and translate text to
math, skills the average adult takes for granted.
The first problem seems to be a simple problem from first year algebra, and
the student hadn't shown complete mastery of the concept of translating and
manipulating algebra problems, falling back on a trick he had used in the
past in an earlier math class.
Guess and Check is a valid strategy for solving problems, not the only one
all the time, but perfectly valid. A good example of a guess and check
problem is "You wish to buy a car that costs $18,000 with tax and license.
You put $3000 down and finance the rest at 7% over 48 months. How much will
your montly car payment be?"
"Domenico Rosa" <domrosa@snet.net> wrote in message
news://jeu68t8cpnhikmlopqkure9sr6utgk0pmo@4ax.com...
> Last year, in a message posted at:
>
> http://forum.swarthmore.edu/epigone/k12.ed.math/gleeswoxvax
>
> I described how guess-and-check appears to be the "strategy" of choice
> that is being taught for solving simple problems. Another amazing
> example is how students handle a problem like the following:
>
> A salesperson receives a base pay of $160 per week plus 12% of the
> weekly sales.
> (a) Determine the equation for the total weekly pay (define the
> variables).
> (b) Find the weekly pay if the sales are $4,750.
> (c) If the salesperson earned $820, how much were the weekly sales?
>
> One student wrote the following:
>
> (a) Let x = weekly sales
> 160 + .12x =
>
> (b) 160 + .12(4,750) = 160 + 570 = $730
>
> (c) about $6,834
> [The student multiplied 0.12 by the successive guesses of 6500, 6600,
> 6700, 6800, 6900, 6850, 6840, 6830, 6835, 6834, 6833]
>
> Two years ago, one of my older students told me that her fourth-grader
> was doing problems like the following: A person bought a sweater and a
> coat for $80. If the coat costs $50 dollars more than the sweater how
> much does each cost?
>
> The fourth-graders were taught to subtract 50 from 80, and then divide
> by 2. $15 is the cost of one item. When you add back the 50, $65 is the
> cost of the other item.
>
> These "strategies" are becoming more and more widespread under the guise
> of "solving algebra problems" and "algebra for all." In my opinion, far
> from teaching any meaningful concepts, these mechanical calculations are
> doing little more than enhancing the pseudo-education of American
> students.
>
> This type of pseudo-education is being promoted--at conferences,
> workshops, minicourses, and training sessions--by assorted "experts" who
> promise to boost scores on assorted "mastery tests" and other
> standardized tests. These promotions are being adopted mindlessly by
> administrators and teachers, whose bonuses and other financial rewards
> are based on the results of these tests.
>
> As long as this rampant pseudo-education continues to be promoted, the
> situation in the U.S. will only worsen.
>
> Dom Rosa
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