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From: bjal_ltd@uhura.cc.rochester.edu (Benjamin Alexander)
Newsgroups: comp.edu,sci.math,sci.physics
Subject: Re: Student and Course Integrity  (was Rising cost of textbooks)
Summary: Where did you go to school?!
Message-ID: <484@ur-cc.UUCP>
Date: 13 Dec 88 21:27:10 GMT
References: <1131@osupyr.mast.ohio-state.edu> <1887@sun.soe.clarkson.edu> <1057@l.cc.purdue.edu>
Reply-To: bjal_ltd@uhura.cc.rochester.edu (Benjamin Alexander)
Organization: University of Rochester
Lines: 178

In article <1057@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes:
>In article <1887@sun.soe.clarkson.edu>, jk0@clutx.clarkson.edu (Jason Coughlin,221 Rey,,) writes:
>> 
>> [Things are bad in the mathematics classrooms]
>
>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.

Just an idle question: How do you confirm this "rule"?  I'm not sure that
you are quite justified in stating these bland accusations at all of the
mathematics students across the country.  I certainly don't find this the
case with myself or my peers.

>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.

I'm sorry, I don't understand this.  You seem to be say the following
Educationists have a major claim.  They say the following:
	"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."
I would be surprised if anyone would take such a claim seriously, if I could
only find a sentence in there somewhere ....

>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

Perhaps regurgitation exams should not be given as finals.  As midterms,
yes.  Understanding methods is as important to other fields as concepts are
to mathematics.

>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.

Oh, you are sooooo wrong.  Concepts CAN be tested on multiple choice and
true false tests!  The hardest math test I ever had was a true false test.
It asked things about the reasons certain intervals were open or closed in
certain proofs.  And the "trivia" must be mastered.  Just like algebra must
be mastered.  Adding and subtracting is trivial (my calculator can do it)
but if you can't add 5x and 8x (my calculator can't do that) then you're in
serious trouble!
>
>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.

Don't you think that is severly and painfully wrong!  My high school teachers
would be morally offended if they heard you!  They taught me all the math I
know (I'm a freshman, not a Ph.D) and I understand concepts!  Proofs must be
memorized, because if you misremember the hypothesis and misapply the
theorem, you will get wrong answers!  Using L'Hopitals rule on an expression
that is of a form 6/2 might give you the wrong answer entirely.  Or hadn't
you though of that!  I never thought it an imposition when a problem was
given on a test that hadn't been covered umpteen times in class.  I have
always resented it when a teach takes too much time going over stupid
examples and not enough time explaining how this type of problem needs to be
approached.  If my teacher only explains one way of doing a problem, I ask
for, or suggest, another.  That is the important thing!

>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.

I think I agree with you, but I am not sure.  What do you mean by "knowledge
prerequisites"?  Do you mean a big multiple choice exam at the beginning of
every semester?  I don't think you do, and I don't think it would be easy to
implement.

>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.

Finally!  Here I agree with you.  It is important to know how to approach a
problem.  That skill is not exercised if a student is asked:
	y = 7a + b.
	What happens to y if a = 3 and b =2 and a is then doubled?
There are more important things to teach and to learn.

>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.

What school did you go to, anyway!  I don't understand why you even mention
this.  Are you trying to say that this is unusually.  I certainly don't feel
any different.  It's scary to think how much more stupid I would look and
feel if all the *really* smart people in my class had this advantage.

>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.

It is EXCEEDINGLY important for an average person to learn how to add.
Recognizing addition in daily life makes living that much easier.  If adding
is some kind of mystery black box machine (push the buttons for the first
number; push the holy and sacred Plus sign; push the buttons of the second
number; push the almighty Equals key) then ordinary people like Johnny will
be deceived by clever people throughout his entire life.  Polititians will
lie to him not with clever words and non answers, but they will say to him:
"Don't worry, it all Adds up".  Salesmen will tell him about their wonderful
Patented Snake Oil, Addition version -- "It will Add to you".  Why make
Johnny any more at a disadvantage than he already is?  And if Johnny is
going to be a Mathematician when he grows up, he will need to know how to
add.  How can you stand there and say it is not important whether or not
Johnny can add.  Figuring out when to add and what it really means can only
be done with practice.  You can't think for Johnny, so leave him alone and
let him figure it out for himself.
>
>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?

Oh of course, sir.  Of course students won't know what they've been taught.
They have no way of understanding if you have misled them or if you have
confused them in class.  How could they tell if one of your lectures was
well prepared or informative.  After all, your lectures aren't going to lead
them to a higher plateau of reasoning.  Your lectures aren't going to
explain the map of the forest to your students!  Why should they have any
valuable ideas on what confused them at the beginning of class, because your
lectures aren't going to change that, will they!  After all, oh most
venerable sir, the students are not the reason your lecturing in class, are
they.  No sir, you're in the classroom for "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.

I must admit that I have no suggestions.  I find fault with what you have
said here, but have no better solution to this problem, which you are
convinced exists.  I feel that the problem lies not with the institutions,
but rather in the apathy of individual students.  I am not apathetic, and I
don't see this problem around me.
>-- 
>Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907
>Phone: (317)494-6054
>hrubin@l.cc.purdue.edu (Internet, bitnet, UUCP)

Benjamin Alexander
Freshman at University of Rochester
bjal_ltd@uhura.cc.rochester.edu