Minimum standards for math "competency"

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Shawn Willden

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Nov 18, 1992, 11:51:57 AM11/18/92
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At Weber State University, Ogden, Utah, U.S.A (where I am working on a
B.S. in math and CS) there is a movement to change (lower) the
standards for math competency. The current policy states that every
student recieving a degree from Weber State must demonstrate his/her
mathematics competency by either 1) scoring a 19 or better on the
mathematics portion of the ACT or 2) passing a course in basic algebra
skills (called math 105) as taught by the mathematics department. The
proposed change (which, incidentally, was *passed* last year by the
faculty senate and only came up for reconsideration through the
efforts of myself, some other students and math dept. faculty) would
allow any department on campus to submit their own courses as
substitutes for math 105 in fulfillment of the math competency
requirement. The proposal specifies a list of topics that must be
covered by the course in order to qualify but makes no mention of any
standards with which the teaching of these topics is to be judged.
The proposal is championed by the departments of various social
sciences (Sociology, communications, etc.) who feel that math 105 is
simply too difficult for their students to pass. (Math 105 is
essentially a high-school algebra course).

I am completely opposed to this proposal on the grounds that it will
weaken degrees from WSU. (Just so there's no question about *my*
opinion of the matter :-)

I have heard that many other schools around the country are facing
similar problems. I would like to hear experiences from anyone who
has faced this situation and arguments both for and against such
proposals.

Also, (and this is really why I'm posting) I would like to find out
what standards are at other schools. I would like to be able to use
this information as ammunition for my arguments, so I would appreciate
it greatly if you would include your name, position and possibly even
a phone number where you can be reached if I need to verify any of the
info. So, please take a moment and answer the following questions
about your school's math competency requirements.

I am especially interested in colleges and universities with a makeup
similar to Weber's. Weber is basically a four-year educational
institution (we only recently became a university and though there are
plans for many master's programs in the works, currently we have only
master's in education and business programs) with a studentbody of
approximately 14,000 students, most of whom commute to school and many
of whom are non-traditional students (I believe the average age of a
WSU student is ~26 years).

Questions:

School information and demographics:

What is the name of your school and where is it
located?

Describe your studentbody (size, age distribution,
etc.)

What is the "purpose" of your school (i.e. education,
research, is your school an "elite" school, etc.)

Math competency requirements:

What math is required for entrance?

What math is required for graduation?

Is there an additional requirement for B.S. degrees
as opposed to B.A. degrees?

Are all math courses that count towards these minimum
requirements taught by the mathematics dept.?

If not, how are standards enforced?

General thoughts about math competency requirements:

What do you think should be a minimum standard for
a graduate of a four-year institution?

Do you think allowing departmentalized mathematics
courses is wise? Why or why not?

Any other comments?

Thanks for your time,
respond either on the net or by e-mail (e-mail preferred unless you have
something you would like to discuss with the net at large).

--
Shawn Willden
swil...@icarus.weber.edu


--
Shawn Willden
swil...@icarus.weber.edu

Robert J Frey

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Nov 21, 1992, 2:28:58 AM11/21/92
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In article <1992Nov18.1...@fcom.cc.utah.edu> swil...@icarus.weber.edu writes:
>At Weber State University, Ogden, Utah, U.S.A (where I am working on a
>B.S. in math and CS) there is a movement to change (lower) the
>standards for math competency...

>
>The proposal is championed by the departments of various social
>sciences (Sociology, communications, etc.) who feel that math 105 is
>simply too difficult for their students to pass. (Math 105 is
>essentially a high-school algebra course)...
>
>
>Also ... I would like to find out what standards are at other schools...
>
As someone with a Ph.D. in applied mathematics who has spend time as both an
academic and an applied mathematician in industry, I would like to offer you
an alternate question: What mathematics will students need when they get out
into the world REGARDLESS of what is or is not required in your or any other
university?

The answer in that case is clear. They need a lot more than they're getting!
It is serendipitous that I recently gave an invited paper dealing with this
issue at a recent conference. The title of the talk was "A View from Outside:
The Challenge of Mathematics Education." What it dealt with is the failure
of educational institutions in this country to produce graduates, at both
the secondary and postsecondary levels, who have the mathematical skills
required of workers in a modern industrial society.

We're not talking about math majors here, but of factory workers, maintenance
personnel, etc. who lack the skills to work with flexible manufacturing
systems, computer aided manufacturing, just-in-time inventory policies and
statistical quality control techniques. It is incomprehensible to me that a
professor of sociology, who is well aware of the role statistics plays in
his or her discipline, can not only suggest that someone graduate with a
B.A. in sociology without a solid statistics course but without even a solid
command of "high school" algebra.

If you want I can snail mail you a copy of the presentation. Here however are a
few facts:

o The Jobs Almanac's top 5 jobs are all mathematically based:
actuary, computer programmer, systems analyst, mathematician
and statistician.

o The Workforce 2000 report from the BLS estimates that 41% of
all new jobs will require "high" levels of skill in language,
mathematics and reasoning, compared with only 24% of current
jobs.

o Between '73 and '90 real per capita GNP increased 28% but real
hourly wages for non-supervisory personnel fell 12%. There
were many reasons for this, but the discrepancy was due in
large part to lower rates of productivity growth in the U.S.
compared to Europe and Asia.

o The math scores of the top 1% of American high school students
would place them in the 50th percentile in Japan (that's not
a typo). How can we expect to compete with Japan in high tech
manufacturing?

Thus, even if a sociology or communication major didn't already need a certain
amount of mathematical training, he or she would need competency in math simply
to qualify to work in a modern office or factory. At the conference, which BTW
was "A SUNY Conversation in the Disciplines - Applied Mathematics: Prospects
for the 1990's," a training manager for LILCO, the local power utility, stood
up and said that his company often had to put new workers through several
months of training before they could be productive.

My recommendations to you are as follows:

o Hit 'em with facts, HARD. Good sources: Lester Thurow, Head to
Head, Morrow, 1992; and National Academy Press, A Challenge of
Numbers: People in the Mathematical Sciences, 1990. These
contain extensive references which will point you further.

o Get the support of local industry. A representative from the
Really Big Corp. who is willing to support your position by
saying that innumerate graduates won't be getting jobs with
them is going to be VERY persuasive.

None of this means your original idea of comparing your university with others
is wrong. I'm simply putting these ideas forward as a more or less orthogonal
strategy that will greatly enhance your arguments.

Good luck!!!
--
Dr. Robert J. Frey
Renaissance Technologies Corp
25 East Loop Rd.
Stony Brook, NY 11790
email: rjf...@rentec.com -- voice: (516)246-5550 -- fax: (516)246-5761

Randy Crawford

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Nov 22, 1992, 9:11:23 PM11/22/92
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In article <13...@kepler1.rentec.com> rjf...@rentec.com (Robert J Frey) writes:
>[...] an alternate question: What mathematics will students need when they get

>out into the world REGARDLESS of what is or is not required in your or any
>other university?
>
>The answer in that case is clear. They need a lot more than they're getting!
[...]

>If you want I can snail mail you a copy of the presentation. Here however are a
>few facts:
>
> o The Jobs Almanac's top 5 jobs are all mathematically based:
> actuary, computer programmer, systems analyst, mathematician
> and statistician.

A greater need is anticipated for systems analysts and mathematicians than for
nurses or accountants? First time I've heard that. Sounds dubious.

>
> o The math scores of the top 1% of American high school students
> would place them in the 50th percentile in Japan (that's not
> a typo). How can we expect to compete with Japan in high tech
> manufacturing?

Hoo boy! Does this statement need qualification!

In effect, this states that EVERY american student would be below average
mathematically in Japan.

I'll step out on a limb here and say: RUBBISH! Such a statement _has_ to be
completely wrong. If the margin between the US and Japan were that great, we'd
see vast differences between us in virtually every form of technology, including
patents and major prizes for scientific research, which we don't. We'd find
ten Japanese students for every American in every non-american and non-japanese
university, which (I'll bet) we don't.

But perhaps it's just my gross inadequacy in mathematics speaking...

>
>My recommendations to you are as follows:
>
> o Hit 'em with facts, HARD. Good sources: Lester Thurow, Head to
> Head, Morrow, 1992; and National Academy Press, A Challenge of
> Numbers: People in the Mathematical Sciences, 1990. These
> contain extensive references which will point you further.

More power to references.

--

| Randy Crawford craw...@mitre.org The MITRE Corporation
| 7525 Colshire Dr., MS Z421
| N=1 -> P=NP 703 883-7940 McLean, VA 22102

Steve Cunningham

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Nov 23, 1992, 12:55:27 AM11/23/92
to
craw...@boole.mitre.org (Randy Crawford) casts some doubts on the claims of
the original posting by rjf...@rentec.com (Robert J Frey) speaking of the
critical shortage of mathematically literate people (as well as mathematical
specialists) and doubting the low standing of American students in mathematics.

Without going to my references (I'm in my office late to staunch a roof-leak
flood and can't dig them out from the piles of materials under plastic) let
me assure Mr. Crawford that Mr. Frey's general points are entirely valid. For
references, consult the large literature on the subject from the Mathematical
Association of America and the National Research Council, who have documented
this situation well. It's real, and it's frightening -- if you can make time
to work with your local schools in bringing a sense of the reality and fun of
mathematics (oh, dear -- I said mathematics is fun, didn't I? It is, and it's
one of the most rewarding of human endeavors, IMHO...) to the students, you'll
do yourself, the students, the nation, and perhaps even humanity a favor...

Pierre VonKaenel

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Nov 23, 1992, 9:06:53 AM11/23/92
to
In article <1992Nov23.0...@linus.mitre.org> craw...@boole.mitre.org (Randy Crawford) writes:
>In article <13...@kepler1.rentec.com> rjf...@rentec.com (Robert J Frey) writes:
>>
>> o The Jobs Almanac's top 5 jobs are all mathematically based:
>> actuary, computer programmer, systems analyst, mathematician
>> and statistician.
>
>A greater need is anticipated for systems analysts and mathematicians than for
>nurses or accountants? First time I've heard that. Sounds dubious.
>

Yup, that's what the article states, I've seen it.

>>
>> o The math scores of the top 1% of American high school students
>> would place them in the 50th percentile in Japan (that's not
>> a typo). How can we expect to compete with Japan in high tech
>> manufacturing?
>
>Hoo boy! Does this statement need qualification!
>
>In effect, this states that EVERY american student would be below average
>mathematically in Japan.
>
>I'll step out on a limb here and say: RUBBISH! Such a statement _has_ to be
>completely wrong. If the margin between the US and Japan were that great, we'd
>see vast differences between us in virtually every form of technology, including

Perhaps you haven't visited a technical university lately. I recall
professors complaining that most of their students are oriental, and
where are the American kids? I'm not sure about the statement above,
but it's quite clear here in education land that American students are
pitifully deficient in math. Why a good number of them can't add
fractions together or interpret what a percent means. As to our
brightest.. there are way too few of them!

>
>But perhaps it's just my gross inadequacy in mathematics speaking...
>

--
Pierre von Kaenel | Skidmore College | pv...@skidmore.edu
Math & CS Dept. | Saratoga Springs, NY 12866 | (518)584-5000 Ext 2391

"Experience is the name everyone gives to their mistakes." Oscar Wilde

Steven E. Landsburg

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Nov 23, 1992, 11:27:55 AM11/23/92
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In article <By6E16...@cs.cmu.edu> jmo...@CS.CMU.EDU (John Mount) writes:

>In article <1992Nov23.1...@scott.skidmore.edu>, pv...@scott.skidmore.edu (Pierre VonKaenel) writes:
>|> Perhaps you haven't visited a technical university lately. I recall
>|> professors complaining that most of their students are oriental, and
>|> where are the American kids? I'm not sure about the statement above,
>
>I trying to imply you said the above (I even left a bit of your "I'm not
>sure about that"). But I think this kind of racist crud is intolerable-
>a good number of the Asian students ARE American kids.
>


I applaud the denunciation of the racist crud. But it doesn't go far
enough. So what if they AREN'T American kids?

Steven E. Landsburg
land...@troi.cc.rochester.edu

Polygon

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Nov 23, 1992, 1:12:02 PM11/23/92
to
craw...@boole.mitre.org (Randy Crawford) writes:

>>
>> o The math scores of the top 1% of American high school students
>> would place them in the 50th percentile in Japan (that's not
>> a typo). How can we expect to compete with Japan in high tech
>> manufacturing?

>Hoo boy! Does this statement need qualification!

>In effect, this states that EVERY american student would be below average

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>mathematically in Japan.
^^^^^^^^^^^^^^^^^^^^^^^^

>I'll step out on a limb here and say: RUBBISH! Such a statement _has_ to be
>completely wrong. If the margin between the US and Japan were that great, we'd
>see vast differences between us in virtually every form of technology, including
>patents and major prizes for scientific research, which we don't. We'd find
>ten Japanese students for every American in every non-american and non-japanese
>university, which (I'll bet) we don't.

>But perhaps it's just my gross inadequacy in mathematics speaking...

>>
>>My recommendations to you are as follows:
>>
>> o Hit 'em with facts, HARD. Good sources: Lester Thurow, Head to
>> Head, Morrow, 1992; and National Academy Press, A Challenge of
>> Numbers: People in the Mathematical Sciences, 1990. These
>> contain extensive references which will point you further.

>More power to references.

>--

>| Randy Crawford craw...@mitre.org The MITRE Corporation
>| 7525 Colshire Dr., MS Z421
>| N=1 -> P=NP 703 883-7940 McLean, VA 22102


If you think the Japanese are tough, try to beat the Singaporeans
first. Then you will know how far behind are the average American
high school students. When most of high school students in certain
Asian countries or areas start learning calculus in grade 10, some
of the American college students are still struggling with
trigonometry, if not algebra.

However, it is rubbish to claim that Asian students take advantages
over American students "absolutely". In the real world, it takes
a lot more than calculus to take advantage of others. Let's not
forget college student in Japan don't study hard-- at least not that I
heard of. I am not from Japan but all of my Japanese friends told
me that college students in Japan party most of the time. Doesn't
it explain something about the real world situation?

Peter, UIUC


David Rector

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Nov 23, 1992, 2:40:33 PM11/23/92
to
jmo...@CS.CMU.EDU (John Mount) writes:

>In article <1992Nov23.1...@scott.skidmore.edu>, pv...@scott.skidmore.edu (Pierre VonKaenel) writes:

>|> Perhaps you haven't visited a technical university lately. I recall
>|> professors complaining that most of their students are oriental, and
>|> where are the American kids? I'm not sure about the statement above,

>I trying to imply you said the above (I even left a bit of your "I'm not


>sure about that"). But I think this kind of racist crud is intolerable-
>a good number of the Asian students ARE American kids.

>--
>--- It is kind of strange being in CS theory, given computers really do exist.
>John Mount: jmo...@cs.cmu.edu (412)268-6247
>School of Computer Science, Carnegie Mellon University,
>5000 Forbes Ave., Pittsburgh PA 15213-3891

Your somewhat incoherent statement above makes even a staunch liberal
bemoan political correctness. Mr. VonKaenel's remarks imply no racist
views; they may simply reflect a current defect in American English
terminology: how to refer to the once dominant Euro-American cultural
group. You might try sticking to the subject.

Here in California the problem of poor math education is particularly
acute since California schools are a year or two behind the more
competent school systems in the nation. One characteristic of
California's much esteemed Asian American subculture is high respect
for education. Many parents, therefore, devote great personal effort
to overcoming the appalling defects in the educational system. In my
experience they succeed no better than the rest of the population in
overcoming the deficiencies in content, and may even exacerbate the
tendency of our schools to teach for the short answer test.

Incoming students to the University of California--all cultural groups--
share several characteristics:

1. They are bone ignorant.

2. They perform very well on short answer tests where they are
asked to regurgitate facts.

3. They will not reason.

4. They are willing to work very hard, but they are not willing
to be diverted by "theory" or the enjoyment of anything beyond
the required course syllabus.

5. They are totally at sea when asked to work independently.

6. They are very bright and can perform well if (big if) you
can dynamite them out of their careerist fortress.

7. They have no sense of humor--or wander--or beauty--or life.

We used to be able to beat some of the deficiencies out of the
students by the junior year (or at least get rid of some of the
students), but that is no longer possible. Since students come to us
without the prerequisite information or attitudes, we have inevitably
lowered our own standards so that much of the junior year is spent
(re)teaching freshman mathematics.

"Reforms" in education seem to have made things worse. California's
minimum standards tests seem to have become maximum standards. The
demise of the New Math, for all its faults, has meant that we can no
longer count on students having the basic vocabulary of mathematics.
Students have had no experience in numerical calculation, geometry, or
applying mathematics to a practical problem. Many have had calculus
in highschool and not understood it--hardly surprising since they have
had none of the experiences, mathematical or practical, that motivate
it. Most important, students are convinced that the point of
education is to collect isolated facts to parrot on a short answer
test so that they can get certification to apply for a high paying
job. Many--perhaps most--do not even like the course they study.

Some needed changes:

1. Competent teaching is an exhausting enterprise--about like
acting--requiring enormous emotional energy and extensive
preparation. No school teacher can perform well teaching more than
three hours per day--about half what is required in California
schools. University teaching is even harder. Teachers must be
professionals and paid--more important, respected--accordingly.

2. Education is not the same as job training and is much more
important. The great expansion of American industry in the nineteenth
century was based on well a educated (comparitively), flexible work
force. Business (and the Republican party) supported--AND PAID FOR--
education then--why not now?

3. Knowledge is not devided up into neat little packages that
can conveniently be translated into departments, bureaucracies,
and grant programs.

4. The most important requirement for good education is having
fun--both students and teachers. (One reason: a human brain does not
remember events unless signaled to do so by a certain control center.
Fun and fear are the most powerful ways to turn on that control center.
Fun motivates a person to repeat the experience, fear to avoid it.
The choice of motivation, therefore, ought to be obvious.)

5. Education is a social enterprise. Teachers need to talk to their
colleagues and students; teachers need to talk to each other. Class
discussion is very important to education. It has almost completely
disappeared from the California schools I am familiar with. Most of
my students would rather die than talk in class.


--
David L. Rector dre...@math.uci.edu
Dept. of Math. U. C. Irvine, Irvine CA 92717

John Mount

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Nov 23, 1992, 5:28:15 PM11/23/92
to
In article <drector....@math.uci.edu>, dre...@math.uci.edu (David Rector) writes:
|> jmo...@CS.CMU.EDU (John Mount) writes:
|>
|> >In article <1992Nov23.1...@scott.skidmore.edu>, pv...@scott.skidmore.edu (Pierre VonKaenel) writes:
|> >|> Perhaps you haven't visited a technical university lately. I recall
|> >|> professors complaining that most of their students are oriental, and
|> >|> where are the American kids? I'm not sure about the statement above,
|>
|> >I trying to imply you said the above (I even left a bit of your "I'm not
|> >sure about that"). But I think this kind of racist crud is intolerable-
|> >a good number of the Asian students ARE American kids.

|> Your somewhat incoherent statement above makes even a staunch liberal


|> bemoan political correctness. Mr. VonKaenel's remarks imply no racist
|> views; they may simply reflect a current defect in American English
|> terminology: how to refer to the once dominant Euro-American cultural
|> group. You might try sticking to the subject.

Just because you refuse to read carefully- doesn't mean what I said
was inchorent. Also, you are putting words in VonKaenel's mouth- he is
only reporting what he heard. Read the quote- do the professors seem
at all pleased that their classes are full of Orientals?

It is racist to imply that Asians can not be Americans. You are right
in that one of the most offensive aspects of PC is that they try to
redefine words on the fly- but I don't think "American" ever meant the
dominant Euro-American cultural group. It has always meant "citizen"
and the term you are looking for is "WASP".

How do you think Asian Americans feel when somebody says to white kids
"why can't you American kids do as well as these Orientals?" I'll bet
they don't feel proud that they are busting the grade curve, they
probably feel excluded and we are not talking nit picky little
language questions ("should I say Asian or Oriental?"). Many of them
are Americans and have the right to be lumped in with the local
idiots (if that is what they are into).

Real harm has been done by the "Asians are smart" myth. An example:

At UC Berkeley there are a two really good minority tutoring programs:
PDP and MEP. One is a tutoring program for minority high school
students (so they will be competent enough to get into UCB) the other
is a minority peer tutoring for engineers. Both were based on Uri
Triesman's (sp?) work on how successful Asian students formed study
group. Both groups work very hard, and do not do remedial tutoring.
Neither group (to my knowledge) has the ability to admit students.
This was great. Triesman recently got a MacArthur award and you are
correct when you say the group he studied does (as a whole) perform
much better than average.

Now here comes the funny (unless you think all people are individuals
deserving a chance at success) part. Around 1986 or 1987 Filipino
Americans were dropped off some "minority list" by the university
administration. This meant they were no longer eligible for tutoring
from PDP or MEP. The nasty part is the Filipino Americans even though
they look like all the other Asians have one of the worst retention
rates at UCB- so they really needed the help.

Read Amy Tan or Maxine Hong-Kingston about how much it sucks to be an
artisticly inclined Asian American when all your teachers think you
should be taking extra math classes.

|> Here in California the problem of poor math education is particularly
|> acute since California schools are a year or two behind the more
|> competent school systems in the nation. One characteristic of
|> California's much esteemed Asian American subculture is high respect
|> for education. Many parents, therefore, devote great personal effort
|> to overcoming the appalling defects in the educational system. In my
|> experience they succeed no better than the rest of the population in
|> overcoming the deficiencies in content, and may even exacerbate the
|> tendency of our schools to teach for the short answer test.

I am of European ancestry and I went to UC Berkeley undergrad, so you
can consider my experiences as a data point- or you can ignore it so you
can safely draw any conclusion you want.

|> Incoming students to the University of California--all cultural groups--
|> share several characteristics:
|>
|> 1. They are bone ignorant.

Not all- I took night classes in 2nd year college DiffEqs while in
high school so I wouldn't make a fool of myself in college. I *never*
took any course (public or private) on how to take the SAT or any
other test.

|> 2. They perform very well on short answer tests where they are
|> asked to regurgitate facts.
|>
|> 3. They will not reason.
|>
|> 4. They are willing to work very hard, but they are not willing
|> to be diverted by "theory" or the enjoyment of anything beyond
|> the required course syllabus.

I was pure math- so there was nothing but the "theory".

|> 5. They are totally at sea when asked to work independently.

I did a large senior project.

|> 6. They are very bright and can perform well if (big if) you
|> can dynamite them out of their careerist fortress.

You think there is big money in theoretical CS?

|> 7. They have no sense of humor--or wander--or beauty--or life.
|>
|> We used to be able to beat some of the deficiencies out of the
|> students by the junior year (or at least get rid of some of the
|> students), but that is no longer possible. Since students come to us
|> without the prerequisite information or attitudes, we have inevitably
|> lowered our own standards so that much of the junior year is spent
|> (re)teaching freshman mathematics.

In my senior year almost half my course work was graduate courses in
math and CS.

I have no desire to talk any further with you either...

|> --
|> David L. Rector dre...@math.uci.edu
|> Dept. of Math. U. C. Irvine, Irvine CA 92717

--

Randy Crawford

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Nov 23, 1992, 4:53:55 PM11/23/92
to


In article <1992Nov23.1...@scott.skidmore.edu>, pv...@scott.skidmore.edu (Pierre VonKaenel) writes:
> In article <1992Nov23.0...@linus.mitre.org> craw...@boole.mitre.org (Randy Crawford) writes:
> >In article <13...@kepler1.rentec.com> rjf...@rentec.com (Robert J Frey) writes:
> >>
> >> o The Jobs Almanac's top 5 jobs are all mathematically based:
> >> actuary, computer programmer, systems analyst, mathematician
> >> and statistician.
> >
> >A greater need is anticipated for systems analysts and mathematicians than for
> >nurses or accountants? First time I've heard that. Sounds dubious.
> >
>
> Yup, that's what the article states, I've seen it.

I don't doubt the accuracy of the quote, only the accuracy of the article.
Just because the book of Timothy says the Bible is the word of God doesn't
necessarily make it so.

>
> >> o The math scores of the top 1% of American high school students
> >> would place them in the 50th percentile in Japan (that's not
> >> a typo). How can we expect to compete with Japan in high tech
> >> manufacturing?
> >

[...]

> >I'll step out on a limb here and say: RUBBISH! Such a statement _has_ to be
> >completely wrong. If the margin between the US and Japan were that great, we'd

> >see vast differences between us in virtually every form of technology, [...]
>
> Perhaps you haven't visited a technical university lately. [...]
> Why a good number of them [US students] can't add


> fractions together or interpret what a percent means. As to our
> brightest.. there are way too few of them!

I don't doubt that US students don't perform as well in math as they should, but
when a scholarly article equates 99% here with 50% there, that is one hell of an
assertion in itself. This implies that the entire bell curve of US student
scores belongs in the 0-50% range in Japan. Before we all start self-flagellating,
why don't we ask for clarification?

What test was this, administered in both english and japanese? SRA? SAT?
Do other tests reflect this level of disparity? Was it repeated over several
years using large samples of students? Exactly what did it test? Or is this
just a magic number meant by the author to strike fear into the hearts of stout
men (and women)? Where oh where is Alan Bloom when we need him?

It seems to me that ready acceptance among educated americans of so improbable a
claim may be evidence that the claim itself is true.

To misquote two for the price of one: "If it's in print, then however improbable,
it _must_ be true."

Frank Adams

unread,
Nov 23, 1992, 3:04:03 PM11/23/92
to
In article <13...@kepler1.rentec.com> rjf...@rentec.com (Robert J Frey) writes:
> o The Jobs Almanac's top 5 jobs are all mathematically based:
> actuary, computer programmer, systems analyst, mathematician
> and statistician.

It appears that a number of people are doubting this, based on the
assumption that these are the jobs which [will] have the most jobs opening
up. On that basis, it is very dubious. A more plausible assumption is that
these are the jobs with the greatest *shortfall* of qualified applicants
compared to positions to be filled. (Although I would still wonder about
including "mathematician". Maybe it's the *ratio* of jobs to applicants.)

Then again, the Almanac may be using some other criteria entirely.

Michael Somos

unread,
Nov 23, 1992, 6:28:34 PM11/23/92
to

Is everyone else fed up with this thread too? There have always
been and always will be students who don't have any clue when it
comes to mathematics? Aren't you just quibbling over the relative
percentages? And finally, if the situation is really so bad, then
why are there so many people with a lot of mathematical knowledge
who are underemployed or unemployed? For details look at recent
issues of Notices of the AMS. Something is very wrong, but it is
not what people are saying it is.

Also realize that there is no consensus on this. There is a wide
variety of opinions. If everyone agreed on what the problem was,
there would be rapid progress on solving it. This is absolutely
not the case now. I won't bore you with any of my own opinions,
but point out that this has nothing to do with mathematics per se.
It is a general cultural problem and pervades many areas. Let us
drop this thread, and let us enjoy mathematics while we can. At
least that is what I think this news group is for. There are many
other news groups for other kinds of discussion. Shalom, Michael
--
Michael Somos <so...@alpha.ces.cwru.edu> (* No, I don't work for CWRU *)

USENET News System

unread,
Nov 23, 1992, 6:23:00 PM11/23/92
to
I think the point intended is that American schools are not producing
enough good university students. Whether or not you agree with this,
there is nothing racist about it. The fact that there are still able foreign
students is praise to the education system in other countries and evidence
that it is possible to produce students of a sufficient standard. I have no
idea how many Asian students ARE American, but if the situation is
similar to New Zealand, you will be getting a lot from Asia. The aim
was not to complain about getting too many of these, rather, it was to
complain that the American education system is not producing enough
local students. Again this is in no way racist - it is a simple statement
of the perception of the writer. (This may be fact or fiction).

It seems to me that any mention of race seems to raise a howl from
the politically correct. Perhaps the politically correct readers can
try to read the context and not just pick out isolated sentences.

Shawn Willden

unread,
Nov 23, 1992, 8:12:16 PM11/23/92
to
so...@ces.cwru.edu (Michael Somos) writes:
: Is everyone else fed up with this thread too? There have always

: been and always will be students who don't have any clue when it
: comes to mathematics? Aren't you just quibbling over the relative
: percentages? And finally, if the situation is really so bad, then

No, I don't think we're "quibbling over the relative percentages."
The present discussion concerns (among other things) the validity of
an article that claims that 99% of American students would be considered
below average in Japan (I'm ignoring the discussion about Asian American
students vs. Asian students, which should be dropped). Those percentages
are downright frightening if true.

: why are there so many people with a lot of mathematical knowledge


: who are underemployed or unemployed? For details look at recent
: issues of Notices of the AMS. Something is very wrong, but it is
: not what people are saying it is.

This is a different issue entirely. We aren't talking about the
demand for people with a lot of mathematical knowledge, we're
talking about the requirement of an industrialized society that
all individuals have an understanding of basic mathematical
concepts -- something that is just not true in America today.

: Also realize that there is no consensus on this. There is a wide


: variety of opinions. If everyone agreed on what the problem was,
: there would be rapid progress on solving it. This is absolutely

I disagree that posession of a definition of the problem implies
rapid progress toward a solution. Sometimes solutions aren't that
easy to come by. A mathematician above all others should know
that :).

[ Other (somewhat valid) complaints about the crosspost to sci.math
deleted. ]

: --


: Michael Somos <so...@alpha.ces.cwru.edu> (* No, I don't work for CWRU *)

Now, to see if I can turn this thread in a more useful direction, here
are some questions.

1) Do you disagree that innumeracy is a problem?

Now, supposing the answer to that question is no:

2) What math do you think an "average" citizen should
know?
3) What math skills should an employer be able to expect of
a college graduate?

--
Shawn Willden
swil...@icarus.weber.edu

Keith Ramsay

unread,
Nov 23, 1992, 8:27:31 PM11/23/92
to
In article <13...@kepler1.rentec.com> rjf...@rentec.com (Robert J Frey) writes:
| o The Jobs Almanac's top 5 jobs are all mathematically based:
| actuary, computer programmer, systems analyst, mathematician
| and statistician.

In article <1992Nov23.2...@Cookie.secapl.com>


fr...@Cookie.secapl.com (Frank Adams) writes:
|It appears that a number of people are doubting this, based on the
|assumption that these are the jobs which [will] have the most jobs opening
|up.

...


|Then again, the Almanac may be using some other criteria entirely.

I suspect that this is based on the same job survey as was cited in
the newspapers, which rated these five jobs highest on some
combination of pay scale, working conditions, stress, possibility for
advancement, and job security. I don't think availability of the job
was among the criteria, just security (once one has it). I dimly
remember wondering whether the method of combining the criteria was
reasonable.

I suspect that mathematics rated well as an occupation because of
tenure (for academic mathematicians), and because it is an indoor job.
By contrast migrant farm work and fishing were near the bottom of the
same list.

Keith Ramsay
ram...@unixg.ubc.ca

David Rector

unread,
Nov 23, 1992, 8:43:18 PM11/23/92
to
jmo...@CS.CMU.EDU (John Mount) writes:


>In article <drector....@math.uci.edu>, dre...@math.uci.edu (David Rector) writes:
>|> jmo...@CS.CMU.EDU (John Mount) writes:
>|>
>|> >In article <1992Nov23.1...@scott.skidmore.edu>, pv...@scott.skidmore.edu (Pierre VonKaenel) writes:
>|> >|> Perhaps you haven't visited a technical university lately. I recall
>|> >|> professors complaining that most of their students are oriental, and
>|> >|> where are the American kids? I'm not sure about the statement above,
>|>
>|> >I trying to imply you said the above (I even left a bit of your "I'm not
>|> >sure about that"). But I think this kind of racist crud is intolerable-
>|> >a good number of the Asian students ARE American kids.

>|> Your somewhat incoherent statement above makes even a staunch liberal
>|> bemoan political correctness. Mr. VonKaenel's remarks imply no racist
>|> views; they may simply reflect a current defect in American English
>|> terminology: how to refer to the once dominant Euro-American cultural
>|> group. You might try sticking to the subject.

>Just because you refuse to read carefully- doesn't mean what I said
>was inchorent. Also, you are putting words in VonKaenel's mouth- he is
>only reporting what he heard. Read the quote- do the professors seem
>at all pleased that their classes are full of Orientals?

Normally I would consign your posting to /device/null, but you have
read into my previous posting all sorts of racist garbage that I did
not intend and cannot leave unanswered. Could you perhaps turn down
termperature of your postings and stop deliberately misunderstanding
people? You have even, in your last line

>I have no desire to talk any further with you either...

stooped to being intentionally rude.

Perhaps there was a transmission error but you said:

>I trying to imply you said the above

which is incoherent. Pierre VonKaenel has already denied the intent
you ascribe to him. His language was perhaps ill chosen, but he
does not rate your worst case assumptions. I appreciate your
desire--which I share--to combat racism, but you went too far.
(I regret to say I have done the same in other circumstances.)
It is impossible to function if one has to examine every casual
phrase for the worst case someone might read into it.

"If you have to watch everything you say, you won't get much
said." --Lucy Van Pelt-- --(Charlie Schultz)--

>Real harm has been done by the "Asians are smart" myth. An example:

>At UC Berkeley there are a two really good minority tutoring programs:

> ...

>Now here comes the funny (unless you think all people are individuals
>deserving a chance at success) part. Around 1986 or 1987 Filipino
>Americans were dropped off some "minority list" by the university
>administration. This meant they were no longer eligible for tutoring
>from PDP or MEP. The nasty part is the Filipino Americans even though
>they look like all the other Asians have one of the worst retention
>rates at UCB- so they really needed the help.

You have an excellent point. The essence of racism is to treat
individual cases according to membership in some group. All Asians,
and all Asian nations are not alike. Indeed, since Asia extends from
East Asia--the current common usage in California--to Istanbul, there
is at least as much difference between Asian groups as between those
groups and Europeans. ALL words are subject to the same problem, and
we simply have to muddle through. AVERAGES DO MATTER in some
contexts. For example, in

>|> Here in California the problem of poor math education is particularly
>|> acute since California schools are a year or two behind the more
>|> competent school systems in the nation. One characteristic of
>|> California's much esteemed Asian American subculture is high respect
>|> for education. Many parents, therefore, devote great personal effort
>|> to overcoming the appalling defects in the educational system. In my
>|> experience they succeed no better than the rest of the population in
>|> overcoming the deficiencies in content, and may even exacerbate the
>|> tendency of our schools to teach for the short answer test.

I implied and intended NO universality of behavior. But enough
people behave as I stated to make a large difference in the
ethnic composition of California's Universities--as a number of
very vocal ethnic lobbying groups will point out.

Cultural differences are real and cannot be ignored, or we cannot
deal with a highly varied world. Besides, cultural differences
are interesting and often enjoyable. They add spice to human
interaction. The cultural diversity of California is one of
its strong points.

>I am of European ancestry and I went to UC Berkeley undergrad, so you
>can consider my experiences as a data point- or you can ignore it so you
>can safely draw any conclusion you want.

One cannot draw general conclusions from individual cases or even
refute statements based on averages. I used "all" nowhere in my
attempt to indicate current conditions in UC.

>|> Incoming students to the University of California--all cultural groups--
>|> share several characteristics:
>|>
>|> 1. They are bone ignorant.

>Not all- I took night classes in 2nd year college DiffEqs while in

> ...

Average conditions strongly influence a classroom. A few years ago
I decided to stop lecturing to my lower division classes since lecturing
is a poor way to teach a routine course. I had tried that a few years
before with great success. To my surprise, the class would have none
of it. They were not interested in working problems and asking questions
about those the did not understand. There were several outstanding
students in the room, including an eleven year old boy, but their
presence was not enough to overcome the general tendency of the class
to be spectators. This tendency has gotten worse since then.

David Petry

unread,
Nov 23, 1992, 9:23:27 PM11/23/92
to
In article <1992Nov23.0...@linus.mitre.org> craw...@boole.mitre.org (Randy Crawford) writes:
>In article <13...@kepler1.rentec.com> rjf...@rentec.com (Robert J Frey) writes:
>>If you want I can snail mail you a copy of the presentation. Here however are a
>>few facts:
>>
>> o The Jobs Almanac's top 5 jobs are all mathematically based:
>> actuary, computer programmer, systems analyst, mathematician
>> and statistician.
>
>A greater need is anticipated for systems analysts and mathematicians than for
>nurses or accountants? First time I've heard that. Sounds dubious.

Maybe the jobs are "top" jobs in the sense of the satisfaction they bring to
those who have the jobs?


>> o The math scores of the top 1% of American high school students
>> would place them in the 50th percentile in Japan (that's not
>> a typo). How can we expect to compete with Japan in high tech
>> manufacturing?
>

>I'll step out on a limb here and say: RUBBISH! Such a statement _has_ to be
>completely wrong.

It wouldn't surprise me much if the MEAN score of students in the American
high schools which rate among the top 1% of all American high schools is
about equal to the MEAN score of students in the Japanese high schools which
rate in the 50th percentile among Japanese high schools. That's the kind of
statistic which appears in the recent Scientific American article comparing
Asian and American students.

David Petry

Martyn Thomas Quigley

unread,
Nov 24, 1992, 2:10:52 AM11/24/92
to
dre...@math.uci.edu (David Rector) writes:
[,,,]

>"Reforms" in education seem to have made things worse. California's
>minimum standards tests seem to have become maximum standards.

This is inevitable. It has been a fact of life for at least 3000 years.

Mart

John Mount

unread,
Nov 24, 1992, 10:29:40 AM11/24/92
to

In article <drector....@math.uci.edu>, dre...@math.uci.edu (David Rector) writes:
|> Perhaps there was a transmission error but you said:
|> >I trying to imply you said the above

I would never stoop to such an excuse- it was a dumb (by me) typo that
killed off the "am not" that obviously should have been there- but you
should have been able to read through it.

Carl Zmola

unread,
Nov 24, 1992, 12:11:13 PM11/24/92
to
jmo...@CS.CMU.EDU (John Mount) writes:

>In article <drector....@math.uci.edu>, dre...@math.uci.edu (David Rector) writes:
>It is racist to imply that Asians can not be Americans.

^^^^^^ ^^^^^^^^^

It is not racist, just incorrect. Asians are the
inhabitants of Asia, Americans are the inhabitants of the Americas:-)


Isn't it fun to take things out of context:-)


Carl
zm...@cicero.spc.uchicago.edu

Mark Purtill

unread,
Nov 24, 1992, 12:37:42 PM11/24/92
to
rjf...@rentec.com (Robert J Frey) writes:
> o The Jobs Almanac's top 5 jobs are all mathematically based:
> actuary, computer programmer, systems analyst, mathematician
> and statistician.
I'm not familiar with the Jobs Almanac, but there certainly is
currently in no shortage of mathematicians, as the 12% of last years
class of Ph.D.s who are unemployed can attest. (Source: latest issue
of the Notices of the A.M.S., which also mentions that many of the
employed had part time or one year positions). People have been
predicting shortages for years and years, but they haven't happened
(and there's really no sign that they ever will).

^.-.^ Mark Purtill, pur...@ccr-p.ida.org || purtill%ida...@uunet.uu.net
((")) \@_: IDA/CCR-P, Thanet Road, Princeton NJ 08540; (609) 924-4600.
Alternate email: purtill%ida...@princeton.edu UUCP: uunet!idacrd!purtill

Robert J Frey

unread,
Nov 24, 1992, 1:47:15 PM11/24/92
to
In article <1992Nov23.2...@linus.mitre.org> craw...@boole.mitre.org (Randy Crawford) writes:
>
>> >> o The Jobs Almanac's top 5 jobs are all mathematically based:
>> >> actuary, computer programmer, systems analyst, mathematician
>> >> and statistician.
>> >
>> >A greater need is anticipated for systems analysts and mathematicians than for
>> >nurses or accountants? First time I've heard that. Sounds dubious.
>> >

You are misinterpeting what I (and the BLS) meant by "top". They used a scoring
system which took into account such variables as pay, demand, stress-level and
working conditions to measure the overall desirability of each career. It is
under this measure that these jobs came out on top.

Obviously, one can argue about whether this weighting or that factor was
handled correctly, but it is suggestive that these occupations did score so
well given what was probably at least a reasonable scoring scheme.

>>
>> >> o The math scores of the top 1% of American high school students
>> >> would place them in the 50th percentile in Japan (that's not
>> >> a typo). How can we expect to compete with Japan in high tech
>> >> manufacturing?
>> >
>

>> >I'll step out on a limb here and say: RUBBISH! Such a statement _has_ to be

>...This implies that the entire bell curve of US student


>scores belongs in the 0-50% range in Japan. Before we all start self-flagellating,
>why don't we ask for clarification?
>

I've posted a response to this elsewhere on this thread. This claim, however,
is not unreasonable given the nature of secondary and postsecondary
education here versus Japan.

BTW, a little constructive self-flagellation is exactly what we need. We are
doing an absolutely awful job educating and training (different things) our
youth. We had better wake up.

We spend only slightly less of our GNP on education on education than do
Germany and Japan. We screwing up because we are not spending that money
wisely, because we treat teachers like dirt and students like idiots, because
we lack any coherent form of educational standards, because we have too many
dollars spent in administration and too little in teaching, because we have
lost the will, the vision and compassion to do the damn thing right.
--
Regards,
Robert

Allan Adler

unread,
Nov 25, 1992, 1:39:37 AM11/25/92
to

People are taught in school that the way capitalism works is that people
make a living by providing goods and services. That is not true. Actually,
people make a living by withholding goods and services. The proof of this
is that if you give away food, you are providing goods and services, but
you are not making a living. It is only when you make it clear that you
are prepared to let everyone starve to death that you start to make a living.
Naturally, this only works if you have something to withhold and that is
the motivation for manufacturing the goods and preparing oneself to provide
the services.

Well, if you withhold food, that works pretty well, because people die without
it. Ditto for shelter. But no one dies if they can't get enough mathematics,
so when you withhold it, you don't make a living (at least I didn't when
I tried it).

However, that doesn't mean that there is no shortage of mathematicians.
Mathematicians meet a need that people can get away with pretending is
not a vital need, that's all.

Allan Adler
a...@altdorf.ai.mit.edu

Robert J Frey

unread,
Nov 24, 1992, 1:23:21 PM11/24/92
to
In article <By6L8...@news.cso.uiuc.edu> pkk3...@uxa.cso.uiuc.edu (Polygon) writes:
>craw...@boole.mitre.org (Randy Crawford) writes:
>
>>>
>>> o The math scores of the top 1% of American high school students
>>> would place them in the 50th percentile in Japan (that's not
>
>>I'll step out on a limb here and say: RUBBISH!

I'm the one who originally posted this comment. I took it from Lester Thurow's
new book, _Head to Head_. I don't think it is rubbish; unfortunately it's true.


> I am not from Japan but all of my Japanese friends told
> me that college students in Japan party most of the time. Doesn't
> it explain something about the real world situation?

At the high end, the U.S. is still first-class, but of the ~ 4,000,000 students
who take math in the 9th grade only ~400 end up with Ph.D.'s in math -- that's
only 0.01%. It is from that group (with similar, though less dramatic, numbers
for other fields) that most of the new inventions, research results and
prizes come from. That's why the 1% - 50% comparison is not as unlikely as it
first sounds. Our top 0.01% *is* better than almost everyone else's, but
that wasn't the point I was making.

In Japan students who have entered university are just about done. This is
in sharp contrast to the U.S. where students are for the first time asked
to do real work.
--
Regards,
Robert

Jim Wissner

unread,
Nov 24, 1992, 6:06:38 PM11/24/92
to

Whoa! Wait a minute folks, wait wait wait... You are missing the point
entirely. I believe the intent of the statement was that the students
coming from oriental schools are much farther ahead than are the students
coming out of American schools. I don't see even a trace of racial
overtone from Mr. VonKaenel; I see him describing the frustration of
professors over the lack of high quality students coming from our schools.

Haven't you been following the thread? I don't understand why you are
so quick to scream "racist?" C'mon, I don't want to see this thread
turn into a flame war.

(Back to the real topic)

I came out of high school with a gross deficiency in mathematics. The
sad part of this was that I /didn't care/. Not only was it easy for me
to slide through without really learning anything, but none of my
teachers ever really explained the importance and depth of mathematics.
It was a remarkably bland, one-dimensional topic. I hadn't a clue.
It wasn't until after two or three years of studying computer science
at a University that I began to realize the importance of math (and
that, gee, it really wasn't that bad. In fact...)

So I guess my viewpoint is that we're missing some key motivation. It's
easy, of course, to speculate about the problem. I don't know, however,
what needs to be done to fix it. I guess I'd be rich if I did. 8-)
But at any rate, I think this is an important topic and as I said before,
could we please keep it focused? I'm very interested in hearing what
others think about what I consider to be quite a crisis that we have.

- Jim Wissner

Brian Harvey

unread,
Nov 25, 1992, 10:13:03 AM11/25/92
to
wis...@perlis.mcs.gvsu.edu (Jim Wissner) writes:
>So I guess my viewpoint is that we're missing some key motivation. It's
>easy, of course, to speculate about the problem. I don't know, however,
>what needs to be done to fix it.

Help is on the way. A couple of years ago, the National Council of
Teachers of Mathematics issued a document called _Curriculum and Evaluation
Standards for School Mathematics_ (everyone calls it the "NCTM Standards")
that calls for less memorization, less focus on algorithms (how to multiply
three-digit numbers), more questions requiring thought, more discrete math,
statistics, more participatory learning, less lecture, more experiment.

In parallel with that, people are inventing lots of ways to use computer
technology to turn mathematics into an experimental science. This includes
both the use of programming languages (a lot of work has been done in Logo
but there is also a new spurt using ISETL, a language that's more directly
"math-like" in its notation) and more narrowly focused environments such as
Geometer's Sketchpad, Derive, etc.

Of course it's going to take a lot of time and money to get these ideas
and these tools into the hands of most teachers, but the money situation
may start getting better in light of the recent election -- who knows?

Herman Rubin

unread,
Nov 25, 1992, 11:12:23 AM11/25/92
to

This is almost like the fox telling us how to guard the henhouse. There
is little change; there is nothing on the teaching of concepts; there is
more on frills than on substance.

I have seen some of the suggestions on discrete math; they are still nothing
more than manipulations. I am a statistician of long standing; I do not see
how they can teach any meaningful statistics--it requires an understanding
of the concept of probability, not combinatorics. ISETL is not math-like;
formal manipulations with sets are still formal manipulations.

Teach the use of variables, the notions of function and relation, formulation
of word problems, logic, the structure of the integers and the reals, and how
operations fit into that. A first-grader can understand the Peano Postulates.

Show them that intuition, while useful, is also dangerous, and that careful
proof is needed. However, point out that there are times when they will
have to accept the idea that someone else has found a proof.

--
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hru...@snap.stat.purdue.edu (Internet, bitnet)
{purdue,pur-ee}!snap.stat!hrubin(UUCP)

Robert J Frey

unread,
Nov 25, 1992, 5:19:13 PM11/25/92
to
In article <92Nov24.07...@acs.ucalgary.ca> qui...@acs.ucalgary.ca (Martyn Thomas Quigley) writes:

>dre...@math.uci.edu (David Rector) writes:
>>California's minimum standards tests seem to have become maximum standards.

>This is inevitable. It has been a fact of life for at least 3000 years.

Unfortunately, this is true. It is precisely the reason that "minimum"
standards have to be TOUGH standards if they're to be of any use whatsoever.

The point isn't to needlessly torture students but to prepare them for the
world they'll need to live in.

Regards,
Robert

Robert J Frey

unread,
Nov 25, 1992, 5:50:41 PM11/25/92
to
In article <17...@idacrd.UUCP> pur...@idacrd.UUCP (Mark Purtill) writes:
> I'm not familiar with the Jobs Almanac, but there certainly is
>currently in no shortage of mathematicians, as the 12% of last years
>class of Ph.D.s who are unemployed can attest.

First of all, given the current recession it is not surprizing that a
high percentage of new grads are unemployed, even among fields which
are considered desirable.

Second, many Ph.D.'s in math display the distressing tendency of viewing
positions outside of academia with distain. I recall a recent conversation
with a colleague who was bemoaning the lack of vacancies for new Ph.D.'s.
When I gave him examples of firms on Wall St. that were hiring "quants"
who would love to get some these people, he gave me a surprized look and
said, "I wasn't talking about THAT."

Another example. We approached a department about recruiting some
recent Ph.D.'s. The response was, "Sure, maybe the ones not good
enough to get a post-doc will be interested." Sorry, we want the best
ones, and we pay accordingly.

There are a lot of jobs out there that those new Ph.D.'s should be looking
at that they're not!

Brian Harvey

unread,
Nov 26, 1992, 11:18:33 AM11/26/92
to

While I agree with everyone who's been posting messages to the effect that
people ought to know a lot of stuff, I don't agree with the establishment
of specific standards, minimum or otherwise, to achieve that. The trouble
is that that makes for assembly-line education in which the standards
become the purpose instead of learning to think.

Although it's important to know a lot, there is no one single thing that
everyone has to know. For example, I've managed to accumulate five
college degrees including a PhD without ever taking a statistics course.
(I mention this example because everyone's been using statistics as an
example.) I *have* learned a lot of math -- back in high school I was in
an NSF-sponsored Saturday program where I studied stuff like Hilbert spaces
and point set topology.

My point is that the math I've studied stretches the same "mental muscles"
as statistics. If I needed to learn statistics I could do it easily because
I speak the language. It would be different if I had no math at all; that
would be a serious failing in my education. But there is no particular
mathematical topic that's crucial.

The same is true about every kind of learning. When people make lists of
Great Books they always put in things like Plato's _Republic_, but they
don't usually list Alasdair Macintyre's _After Virtue_, a book I read in
graduate school that completely changed my life. So should we add that
one to the list? No, it's hopeless to list all the great books. A better
approach is the one my high school took: They had us fill out forms on
which we listed all the books we read, and they didn't care which books
they were, as long as there were *enough* of them. (If it seemed that
someone was only reading one kind of book, the teachers would suggest ways
that that person might branch out, of course.)

Charles Geyer

unread,
Nov 26, 1992, 11:54:54 AM11/26/92
to
In article <1f2tcp...@agate.berkeley.edu> b...@anarres.CS.Berkeley.EDU
(Brian Harvey) writes:

> Although it's important to know a lot, there is no one single thing that
> everyone has to know.

I couldn't agree more.

> For example, I've managed to accumulate five
> college degrees including a PhD without ever taking a statistics course.
> (I mention this example because everyone's been using statistics as an
> example.) I *have* learned a lot of math -- back in high school I was in
> an NSF-sponsored Saturday program where I studied stuff like Hilbert spaces
> and point set topology.
>
> My point is that the math I've studied stretches the same "mental muscles"
> as statistics. If I needed to learn statistics I could do it easily because
> I speak the language.

No so, but I'll excuse your ignorance. The primary difficulties in statistics
are not mathematical. That's why it was such a struggle to invent. Much of
what we teach in introductory statistics courses is less than 100 years old
and has no earlier antecedents. The bulk of the subject was created since
1920. That's also why it is such a struggle to learn. Most of it is highly
counterintuitive.

> It would be different if I had no math at all; that
> would be a serious failing in my education. But there is no particular
> mathematical topic that's crucial.

I agree with that. I don't know much about abstract algebra or complex
variables and I've never felt that either was a "failing".

It is much more important to learn some mathematics well than to have
a knowledge of many areas that is too shallow to be of any use.

--
Charles Geyer
School of Statistics
University of Minnesota
cha...@umnstat.stat.umn.edu

Gary Martin

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Nov 26, 1992, 12:36:25 PM11/26/92