In article <[EMAIL PROTECTED]>,
Robert Ehrlich <[EMAIL PROTECTED]> wrote:
>But Radford, most word problems address situations far from the
>studemt's potential field of application. They are seen to be as
>little more relevant that the more abstract problems.
This attitude is what has led to the incompetence of
American students. It is inappropriate to use applications
which the student cannot comprehend, but it is important to
get the student to realize that a large variety of subjects
can be applied in many ways, including some which might not
have been recognized yet. The old calculus courses used to
have examples mainly from physics, which required teaching
the concepts of physics to understand; this was not good,
and is not good even if the student is going to be an
engineer. A huge variety is needed, and also switches in
the use of variables.
In secondary
>school a common trig problem involves a tree, a river, and the tree's
>shadow leading to determination of the tree's height. Neat problem but
>not too much related to Fourier transforms.
How many high school students (or teachers) have the
mathematics background to understand what Fourier
transforms are, let alone how to use them?
IMHO few stats instructors,
>at least at the lower academic levels, have in fact analyzed and
>interpreted much real data tied to real world problems.
Learn theory, then apply it. For the one who only wants
applications, and does not have the time to learn the
theory, learn the concepts, formulate the problems, and
then go to someone who understands the theory to get the
practical answers. Learning methods without this leads
to misusing them, and being unable to later learn anything
but formalism.
Anyhow a
>blanket condemnation of the student reeks of the abdication of
>responsibility or the attempted teaching of students unready or
>unqualified for college.
Now how is someone expected to teach a subject to someone
without the necessary background? It is fraudulent to
reduce the course for those who are ready, and it is
fraudulent to state that students have learned the subject
matter of the course if it has not been fully presented.
Remedial courses are often needed, but they should be given
on the assumption that the student has not seen the important
material, not that it was not learned.
>Radford Neal wrote:
>>In article <[EMAIL PROTECTED]>, JW <[EMAIL PROTECTED]> wrote:
>>>From what I was able to tell, the thinking and mentality in the math
>>>department was just different. They liked theory and they liked formulas.
>>>They liked elegant solutions and proofs, even if they were irrelevant to
>>>application. I sensed a certain disdain for "word problems" and real world
>>>analogies and explanations to help the students conceptualize the theory
>>>because real math students don't need those crutches.
>>My experience, and that of other math/stat instructors whom I've
>>talked to, is quite the opposite. It's the STUDENTS who don't like
>>word problems, and resist applications (eg, to physics), because to do
>>them they have to actually understand the mathematical material (and
>>even some physics!), rather than just applying formulas without really
>>knowing what they're doing. This may not be true of "real math
>>students", however, who ought to be able to do the word problems (but
>>who may find the standard ones to be too easy to be interesting).
>> Radford Neal
It is true of many of the "real math students" as well. Many of
them have had their ability to understand weakened, or even
destroyed, by the elementary and secondary schools, and by the
cookbook courses at lower levels.
--
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
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
.
.
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