Xref: utzoo comp.edu:1513 sci.math:5058 sci.physics:5090
Path: utzoo!utgpu!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!bloom-beacon!bu-cs!purdue!i.cc.purdue.edu!k.cc.purdue.edu!l.cc.purdue.edu!cik
From: cik@l.cc.purdue.edu (Herman Rubin)
Newsgroups: comp.edu,sci.math,sci.physics
Subject: Re: Student and Course Integrity  (was Rising cost of textbooks)
Summary: My diagnosis of the reasons
Message-ID: <1057@l.cc.purdue.edu>
Date: 9 Dec 88 12:37:13 GMT
References: <1131@osupyr.mast.ohio-state.edu> <1887@sun.soe.clarkson.edu>
Organization: Purdue University Statistics Department
Lines: 94

In article <1887@sun.soe.clarkson.edu>, jk0@clutx.clarkson.edu (Jason Coughlin,221 Rey,,) writes:
> 
> 	Enough professors now (like try to find one who hasn't!) have stated
>   that they feel their courses and the books that they use have degenerated,
>   and they attribute this degeneration to their students.  So what's really
>   happening here?  Are all the professors wrong?  Do the professors expect too
>   much of us today?  Or is it really the students?  And if it IS the students,
>   what's happened?  Is it a loss of motivation (, and just what are we
>   motivated to do these days)?  I think this is a VERY important issue which
>   needs to be addressed, and maybe solved?

1.  The courses have degenerated.  I do not trust the students coming out of a
mathematics course to know the manipulations presented, not to say the
concepts.  It is too easy to confirm that this is the rule.  I am not saying
that things were good N years ago, but one could expect the students who had
the calculus course to be able to do the manipulations 1-2 years later in a
course with an explicit calculus prerequisite even on an in-class exam then,
but cannot get it on a take-home exam now.

2.  I believe that the major reason for this is that the teachers of
mathematics courses have allowed themselves to be hoodwinked by the claims
of the educationists.  The major one of these claims is that it is unimportant
what is learned in the course is essentially irrelevant, and only for the
purpose of getting a relative standing.  Also, even this is not important.

3.  It is not just a problem of mathematics, but the idea that one learns for
the future, and not just for the grade in the current class, seems to have
disappeared.  People are taught how to study for grades, but not how to learn
the material.  It is possible to put enough in short-term memory to get an A
on a regurgitation exam.  Thus

4.  There is pressure to examine the trivia.  At the college level, this means
that methods of routine manipulation are emphasized on examinations.  One
reason for doing this is that the examinations are easy to grade.  Concepts
cannot be tested on multiple choice examinations.  It is more time-consuming
to read through the work to see if the method was essentially correct, but a
minor arithmetical error gave the wrong answer.

5.  The teachers at the elementary and secondary levels can only teach
plug-and-chug operations.  Even proofs are memorized.  The students expect
such, and object to a teacher even mentioning anything else.  They consider
it an intolerable imposition on them if an examination question is given 
which cannot be done by following exactly the steps of a problem in class.
There is resentment of taking class time to give an understanding of the
material.  Any statement made by the teacher is at least implicitly 
challenged by "Is this going to be on the final?"  Not whether it will
help in doing the exams, but whether it will be explicitly on the exams.

6.  At the college level, it is politically difficult to require that the
students have knowledge prerequisites.  That someone got A's in their high
school mathematics courses is no guarantee that s/he know anything from 
high school mathematics.  That someone got an A in last term's calculus
course is no guarantee that the material of that course can be used in this
one.  I have advocated that knowledge prerequisites be used, and that 
remedial courses be provided, and even taught with the understanding that,
while it may be on the students' records, some of the students may not even
have seen the relevant material.

7.  Emphasize "word" problems.  I would make the ability to formulate word
problems at the high school algebra level of arbitrary length THE mathematics
requirement for non-remedial entrance to college.  And do not make the 
mistake of teaching or expecting parsimony in the use of variables.  The
high school algebra courses do much damage by asking the students to 
formulate problems in one variable.

8.  Encourage students to think, and to ask questions.  "The only stupid 
question is the one which is not asked."  Encourage reasoning.  Encourage
the recognition of structure; while it is sometimes necessary to look at
the trees, it is important to see the forest.  This is not limited to
mathematics.

9.  We can, and should, teach concepts without manipulation.  The concepts
and the manipulations are largely separate.  The student who has the
impression that antidifferentiation is integration cannot learn the 
easy concept of integral, which can be taught at the high school algebra
level.  Facility with arithmetic calculations does not help in learning
the structure of the integers; I think it can interfere.  Whether Johnny
can add is not particularly important; what is important is whether Johnny
knows what addition means, and when to add.

10.  We must fight the attempts to reduce out courses to what the badly-
taught students want.  Can a student judge the quality of teaching in a
course, especially if the student does not have the prerequisites?  Can
a student steeped in plug-and-chug appreciate the importance of learning
concepts?  Should the evaluations by such students be considered in
deciding promotion, salary, and tenure?

At least 10 more paragraphs can be written.  The situation is BAD.  Our
Ph.D. programs are now dominated by foreign students, because the 
American ones do not exist.  I have put forth some suggestions.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907
Phone: (317)494-6054
hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)