In article
<e9d04345-2183-4656-a4c3-fdafd3cfb287@[EMAIL PROTECTED]
>,
Beliavsky <beliavsky@[EMAIL PROTECTED]
> wrote:
>http://www.nytimes.com/2008/04/25/science/25math.html
>Study Suggests Math Teachers Scrap Balls and Slices
>By Kenneth Chang
>New York Times, April 25, 2008
>'One train leaves Station A at 6 p.m. traveling at 40 miles per hour
>toward Station B. A second train leaves Station B at 7 p.m. traveling
>on parallel tracks at 50 m.p.h. toward Station A. The stations are 400
>miles apart. When do the trains pass each other?
>Entranced, perhaps, by those infamous hypothetical trains, many
>educators in recent years have incor****ated more and more examples
>from the real world to teach abstract concepts. The idea is that
>making math more relevant makes it easier to learn.
>That idea may be wrong, if researchers at Ohio State University are
>correct. An experiment by the researchers suggests that it might be
>better to let the apples, oranges and locomotives stay in the real
>world and, in the classroom, to focus on abstract equations, in this
>case 40 (t + 1) = 400 - 50t, where t is the travel time in hours of
>the second train. (The answer is below.)'
The most im****tant part of algebra for the non-mathematician
is formulation. The position of the train leaving station
A at time t ( >=6), relevant to station A, is 40*(t-6).
For the train leaving station B, the position, relative
to station A is 400 - 50*(t-7), assuming t >= 7. One
sets these two equal and solves for t.
Then comes the solution; showing how to do it deserves
most of the credit even if the arithmetic is bad.
The most im****tant part is formulation. If one can
formulate the problem correctly, it can be fed into
a sufficiently advanced calculator and get solved.
If it is not formulated correctly, who cares if the
student knows how to do the rest.
The solution for this problem, and for most, follows
the rule of equality, which states that the same
operation done on equal entities gives equal results.
It this is used, any calculator can be used to get
the results. If it is not known how to use it, the
process of getting from the formulation to the use
of arithmetic is likely to produce wrong answers.
Finally comes the arithmetic. Knowing how to do the
arithmetic was not even that im****tant BC (before
computers) and is of little im****tance now; it may
be useful, and I see no reason not to teach it.
A student (as distinguished from a warm body occupying
a space in a classroom) will try to learn the useful
materical, and should be discouraged from overdoing it.
>If the study is correct, I wonder which math curricula are most
>consistent with it. It appears to contradict the philosophy of
>Everyday Mathematics (EM), which our public school use. The EM site
>http://everydaymath.uchicago.edu/about.shtml#curriculum
says
>"Students acquire knowledge and skills, and develop an understanding
>of mathematics from their own experience. Mathematics is more
>meaningful when it is rooted in real life contexts and situations, and
>when children are given the op****tunity to become actively involved in
>learning. Teachers and other adults play a very im****tant role in
>providing children with rich and meaningful mathematical experiences."
:
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
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