Why People hate science
Herman Rubin
>In article <CFrxC...@mentor.cc.purdue.edu> hru...@snap.stat.purdue.edu (Herman Rubin) writes:
......................
>>You have now given a positive testimonial to his teaching. The goal of
>>a course should not be to be able to do certain things at the end of
>>the course, but that the material be usable in the long term. The
>By this criterion, I can give "positive testimonials" to the teaching of many
>high school teachers who couldn't teach their way out of a paper bag.
>Not to be unduly snide or anything, but please reread the first sentence of
>the last paragraph. *During the course*, I actually had a rather poor idea
>of what was going on. I ended up doing well overall, but as far as I can
>tell this was short term memory at work here.
>It was only *after* I had some time to actually think, as opposed to simply
>try to keep up with an overenthusiastic lecturer, that the ideas began to
>make sense (as a whole, that is, rather than hastily remembered and easily
>forgotten bits and pieces). This step came after I had taken this class.
>>>Moral: Small, seemingly insignificant differences in presenting style
>>>make a *big* difference. Good lecturers pay attention to both signal
>>>strength AND impedance matching.
>>Good teaching is what gets the students to learn the material in such
>>a way that it will be retained and usable in new situations. Now can
>Exactly. At the end of the class, I had neither retained as much
>as I would have liked, nor was I as flexible with it as I would have liked.
>Certainly not as much as I am now. Any subsequent improvement was by my
>doing, not the professor's.
If you retained as much as you liked, or could use it as well as you would
like, the course would have been below your level. They usually are below
the level of a good student.
>>you say, after the above, that you could clearly identify it? Remember
>>that you learned a lot from that "bad" teacher.
>
>No, I *learned* a lot from studying and reviewing, which are independent of
>the lecturer's ability as a teacher. Good teachers make this approach
>both easier and more productive, of course.
When I was a student at the University of Chicago, there was a professor
who most of the students thought was going way over their heads and that
they were not getting it while they were taking the course. But when they
took the following course, they found that they could use the material
well, and even had gotten the ideas of the subject, so that the following
course was much easier.
--
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)
hat...@msupa.pa.msu.edu
>In article <CFrup...@murdoch.acc.virginia.edu>,
>Cameron Randale Bass <cr...@watt.seas.Virginia.EDU> wrote:
>>
>> On the other hand, I think we're working them too hard. These people
>> are working far, far harder than I did as an undergraduate. They
>> appear to have no time for the natural reflection that accompanies the
>> assimilation of knowledge. The current undergraduates appear to me
>> to be no 'dumber' than the people I went to school with.
>
>What are we doing differently now than our predecessors did when we were
>in school X years ago? Or are you saying that there is more competition
>for students' time nowadays than there used to be?
>Jon Bell <jtb...@presby.edu>
I'm not sure that it's either of these alternatives, per say. Rather the
more obvious -fact- that there is an awfully lot MORE material that we
take as "basic" compared to what there used to be. My father ('5x EE MIT)
was always amazed at the "level" of material I had as a physics major
('83 Physics/Astronomy UC Berkeley) compared to what he had at the same
point in his schooling. So it needn't be either different teaching
techniques, nor time wasters/distractions.
-robert
Herman Rubin
>In article <CFqoC...@mentor.cc.purdue.edu>
>hru...@snap.stat.purdue.edu (Herman Rubin) writes:
>
>> In article <CFqGI...@dartvax.dartmouth.edu> Benjamin...@dartmouth.edu (Benjamin J. Tilly) writes:
>> >In article <1993Oct29....@Virginia.EDU>
>> >jp...@Virginia.EDU (James Prescott Ruffner) writes:
>>
>> I will put my comments at the beginning, as good editing of the material
>> quoted is quite difficult. It is all here.
>>
>> There are several problems involved. I believe that the major one is
>> attempting to get understanding of the concepts and structure. Now we
>> really do not know how to teach it, and even before the curriculum
>> decline about all that could be said is that it was somewhat presented
>> and reasonably well tested.
>>
>> Now when I teach a course in mathematics or statistics at ANY level,
>> I attempt to emphasize the structure and concepts. Do not think that
>> these efforts are well received by the students; they clamor for the
>> instructor to tell them what will be on the exams. Far too many of them
>> are so thoroughly brainwashed well before they get to college that they
>> consider it "unfair" to expect them to do problems of a type different
>> from those explicitly presented in the course, or to have to put several
>> aspects together. These people, even if they become scientists, and
>> many do, seem to think that everything is in essentially non-communicating
>> compartments. Compartmentalization is quite useful, but only if what is
>> in one compartment can be used elsewhere.
>
>What are the structure and the concepts? From my experience a
>mathematician is likely to give a different answer from a physicist. In
>truth I think that the answer should lie in between. For the student
>who is learning the material the important concepts IMO should *not* be
>the formalisms that are used to justify the procedures, but the ideas
>that the procedures attempt to let them deal with.
The formalism is rarely the concepts, and this confusion is far too
common. Also, concepts are only learned by being used, not by being
memorized. The student who can look at a concept and understand
"immediately" how to use it is already a potential mathematician.
Therefore I would be
>more happy with a group of students who remember that the integral that
>they run across in first year is a way to get at their notions of area,
>and who could give a reasonable explanation from that point of view why
>integration "undoes" differentiation, than I would be with ones who
>remember the entire formulation of the Riemann integral well enough to
>do that question on the test, but who have no idea *why* the integral
>would be defined that way.
A slightly redone Riemann integral captures the concept, but only it
more general measures are used. The concept is the sum of values
multiplied by measures, and limits obtained from that. Those who
learn that integral is antiderivative will have to have it beat
into them that area can be computed by integration, and never to
take that as the idea. But the special case of the length measure
obscures the basic concept, and as for choosing a partition for
approximation by a discrete measure, only the existence is needed.
When it comes to probability, there is no new basic concept needed;
expectation is automatically integration. But formalism should
never be the goal, and those not intending to be mathematicians
need not know the proofs.
The idea of approximating an area by counting squares, and getting
bounds by the inclusion principle, used to be presented in high school
geometry. This immediately generalizes to integral, and computing the
amount of a bill is much closer to the concept than merely the area
under a curve.
Nasser Abbasi
I want to throw this comment here.
from my experience in studying in US universities, is that the emphasis
seems to be on the quantities on the materials covered, weather students
really understand or not, do not seem to matter to the teacher, especially
the new, young teachers who go their PhD and are too eager to go out
show off to the students how much they know in that particular area,
so, in one quarter or one semester a huge large text is covered, one
chapter each lecture, the goal of the teacher is to get to the end
of the book before the end of the quarter because this is what the syllables
says to cover.
it is madness, students learn to memorizes how to do certain methods
without really knowing why because there is no time to learn why, just
do it, it works this way, and just to pass the exam and get that piece of paper
and get out.
I am not saying every course I took was like this, but many were.
I think these new PhD's who go to teach need to go first and learn
how to teach, and what teaching really means, and to learn what is
important is quality not quantity of material covered
It is better to learn 5 chapters and understand what is going on that
to cover 20 chapters and leave having little clue what you learned just so
the new teacher can show off to the head of the department how good they are.
Teaching in schools is becoming like a drive through burger places,
the important thing is how fast and how many burgers they can cook and throw
out of the window.
I have decided that the best way to learn is NOT to go to a university or
to a school, but to go to the public library instead. you learn more,
and it is much less expensive, actually it is free.
\nasser
Cameron Randale Bass
Jon Bell <jtb...@presby.edu> wrote:
>I can see that I can get the feedback just as well by having them
>discuss problems in class and observing their reactions. As for (b),
>well, one can argue that students have to learn the hard way, if
>necessary, that they have to keep up with the material themselves.
>
>I'm afraid to try to break the homework-collecting habit cold turkey,
>though. It seems to me that many of our students have really come to
>depend on that external stimulus, to the point where they don't try to do
>anything that isn't specifically assigned.
That's a problem. They seem definitely conditioned to
'just in time' learning. And if they went to the end of the
semester without many 'just in time's, I suspect some would
do badly. It might, however, teach them something more
important than anything we can teach directly. But I agree that
it is tough to wean them off of the collected sets.
dale bass
John Novak
[...]
>Now when I teach a course in mathematics or statistics at ANY level,
>I attempt to emphasize the structure and concepts. Do not think that
>these efforts are well received by the students; they clamor for the
>instructor to tell them what will be on the exams. Far too many of them
>are so thoroughly brainwashed well before they get to college that they
>consider it "unfair" to expect them to do problems of a type different
>from those explicitly presented in the course, or to have to put several
>aspects together.
If I may, I think the 'unfairness' is less a matter of being
forced to think independantly than a matter of being forced to be
creative or inspired at a certain time and place.
One of my general complaints with the engineering curriculum at
Bradley Univeristy (as regards 500 and 600 level courses) is the
lack of emphasis on project, and the overemphasis of short
homework problems and one hour test grades.
If you want your students to display an ability to connect
concepts, give them enough time. Give a take home test, or a two
week project, if the class size and composition warrant.
MHO, of course.
>The content of calculus courses is decried below. Many of the professors
>have given up trying to fight what the students demand. What is criticized
>here will bring complaints by the engineering students, and even many of the
>physics and chemistry students. And it is difficult to teach concepts in
>courses to students who only know manipulation, and to whom the notions of
>function and variable are ancient Sumerian, and of no importance.
I'm an engineering student, and my _only_ complaint is that a one
hour, high pressure exam is not the right arena for me to display
any particular creativity. It is an adequate arena for me to
display my familiarity and competance at the material through
which I have already worked.
--
John S. Novak, III
dark...@camelot.bradley.edu
dark...@cegt201.bradley.edu
m...@waikato.ac.nz
[...]
>
> One of my general complaints with the engineering curriculum at
> Bradley Univeristy (as regards 500 and 600 level courses) is the
> lack of emphasis on project, and the overemphasis of short
> homework problems and one hour test grades.
>
> If you want your students to display an ability to connect
> concepts, give them enough time. Give a take home test, or a two
> week project, if the class size and composition warrant.
>
> MHO, of course.
>
[...]
>
> I'm an engineering student, and my _only_ complaint is that a one
> hour, high pressure exam is not the right arena for me to display
> any particular creativity. It is an adequate arena for me to
> display my familiarity and competance at the material through
> which I have already worked.
>
Presumably you will have no objection to paying the extra fees to
support the much more labor-intensive evaluation teaching and
evaluation methods that you favour?
--
Murray Jorgensen, Maths & Stats, U of Waikato, Hamilton, NZ [m...@waikato.ac.nz]
-------------------------------------------------------------------------------
Doubt everything or believe everything: these are two equally convenient strat-
egies. With either we dispense with the need for reflection./ Henri Poincare'
Cameron Randale Bass
>I'm not sure that it's either of these alternatives, per say. Rather the
>more obvious -fact- that there is an awfully lot MORE material that we
>take as "basic" compared to what there used to be. My father ('5x EE MIT)
>was always amazed at the "level" of material I had as a physics major
>('83 Physics/Astronomy UC Berkeley) compared to what he had at the same
>point in his schooling. So it needn't be either different teaching
>techniques, nor time wasters/distractions.
That is true from the 50's to now, but
I think they're being forced to work substantially harder
than I did on the same material.
dale bass
Cameron Randale Bass
Nasser Abbasi <abb...@star.enet.dec.com> wrote:
>
>I have decided that the best way to learn is NOT to go to a university or
>to a school, but to go to the public library instead. you learn more,
>and it is much less expensive, actually it is free.
What university, and what public library? I might have sympathized
if you had said 'University library'.
However, it is easy to become badly mislead when reading books
without the benefit of experience. Consider professors an
adjunct to your reading, and force them to teach you if you
are not satisfied. Ask questions...
dale bass
stephen voss
> In <CFqoC...@mentor.cc.purdue.edu> hru...@snap.stat.purdue.edu (Herman Rubi
>
> [...]
>
> >Now when I teach a course in mathematics or statistics at ANY level,
> >I attempt to emphasize the structure and concepts. Do not think that
> >these efforts are well received by the students; they clamor for the
> >instructor to tell them what will be on the exams. Far too many of them
Have you ever considered that many of your students(especially with
the lower level courses) are not math and science majors. The only
reason they are in the class is because they have to be. These are
students whose real goal is graduate school(law,business,etc.) and
cant get in without extremely HIGH grades and when you throw in unplanned
stuff it lowers their grades and they resent it.
Herman Rubin
The comments made here are completely relevant, but the poster has the
reasons all wrong. The pressure to follow a specific syllabus and
concentrate on memorization does not come from the faculty. New PhD's
have mostly been teaching assistants and told that this is the way it
is done.
But the biggest problems in remedying the madness you mention in your
third paragraph, with which I agree fully, comes from the students and,
in service courses, from the other departments. The students ask, demand,
clamor for "relevance" and "how do I do the problems on the tests."
Attempts to teach WHY are met with active hostility. The engineering
departments want the mathematics and physics and chemistry departments
to prepare the students to do the "standard" problems from those fields;
the physics department wants the calculus course to cover the manipulations
before they will occur in the physics course: everybody wants the first
course in statistics to teach the students how to solve an arbitrary
statistics problem, without having the slightest idea of what anything
means, etc.
I do not believe in following a syllabus, in that I will not do such-and-such
a topic on a given day, but if the material is not covered, what are they
going to do in the next course?
Herman Rubin
>In <CFqoC...@mentor.cc.purdue.edu> hru...@snap.stat.purdue.edu (Herman Rubin) writes:
>[...]
>>Now when I teach a course in mathematics or statistics at ANY level,
>>I attempt to emphasize the structure and concepts. Do not think that
>>these efforts are well received by the students; they clamor for the
>>instructor to tell them what will be on the exams. Far too many of them
>>are so thoroughly brainwashed well before they get to college that they
>>consider it "unfair" to expect them to do problems of a type different
>>from those explicitly presented in the course, or to have to put several
>>aspects together.
>If I may, I think the 'unfairness' is less a matter of being
>forced to think independantly than a matter of being forced to be
>creative or inspired at a certain time and place.
>One of my general complaints with the engineering curriculum at
>Bradley Univeristy (as regards 500 and 600 level courses) is the
>lack of emphasis on project, and the overemphasis of short
>homework problems and one hour test grades.
>If you want your students to display an ability to connect
>concepts, give them enough time. Give a take home test, or a two
>week project, if the class size and composition warrant.
You will get no arguments from me on this. Now how do we implement this?
In a low-level course, the cheating problem is bad enough on in-class
tests; take-home is essentially impossible. This is not something
which an individual teacher can do much about.
Herman Rubin
>In article <2b28fb$l...@cegt201.bradley.edu>, dark...@cegt201.bradley.edu (John Novak) writes:
>[...]
>> One of my general complaints with the engineering curriculum at
>> Bradley Univeristy (as regards 500 and 600 level courses) is the
>> lack of emphasis on project, and the overemphasis of short
>> homework problems and one hour test grades.
>> If you want your students to display an ability to connect
>> concepts, give them enough time. Give a take home test, or a two
>> week project, if the class size and composition warrant.
>> MHO, of course.
>[...]
>> I'm an engineering student, and my _only_ complaint is that a one
>> hour, high pressure exam is not the right arena for me to display
>> any particular creativity. It is an adequate arena for me to
>> display my familiarity and competance at the material through
>> which I have already worked.
>Presumably you will have no objection to paying the extra fees to
>support the much more labor-intensive evaluation teaching and
>evaluation methods that you favour?
If we want the teaching and the grades to mean anything, we must be
willing to spend the time grading the exams. If this means that the
students will not get their grades the next day, or even in the next
three days, so what? If something is worth doing, it is worth doing
well, and the students and society should get as meaningful evaluations
of what the students know and can do as we can manage.
Herman Rubin
>> [...]
I very definitely consider it. I am also quite aware that the only way
that they are likely to use the material, and many of them are, is to
formulate problems and interpret the answers that are obtained with the
aid of computers. Do the "real world" problems they will encounter follow
the routine in the textbook? Not at all! But I do not teach the course
to them as I would to science, and especially math, majors.
As for lowering their grade, how does this happen if all are graded the
same way? I grade according to standards for that particular course, as
I interpret them. Those who are taking a course, if they are honest
students, will try to acquire an understanding of that course.
Craig Graham
In article <1993Oct29.1...@kpc.com>, a...@kpc.com (Alberto Moreira) writes:
> Have you tried reading the book and spending some 2-3 hours
> a day on it ? Science - Math - they're just like learning
> to play a difficult classical instrument such as violin or
> cello. You can't possibly do it unless you put a lot of
> commitment and weight on it. And that's I suppose why a
> lot of people don't like science, and they don't like
> classical music either: it's very hard to conquer.
>
> -Alberto-
And like an instrument, maths & such are Talents. If you are great at them,
you will love them and find them easy. Few do. But people can be shown how to
appreciate them all the same, without having to slog it out. I love music,
but I don't pretend I could ever do it myself - this doesn't lessen my
appreciation of it. My talent for Maths is on a par with this - but I despise
maths as it has been forced on me at a level I could not comprehend.
Teaching people to appreciate, does not mean forcing them to hate a subject
^^^^^^^^^^
that they have no talent for, which is something which many lecturers & teachers
should bare in mind if they want more sympathy from Joe Public.
Craig Graham (Masters Degree, Microelectronics)
Craig Graham. /\ E-mail:Craig....@newcastle.ac.uk
BAe Space Systems || Phone : (UK) 091 4883098
Stevenage,England.|| Snail-mail: 2 Sun Street, Suniside, Newcastle, England.
-----------------/__\-----------------------------------------------------------
SPACE the final^^^^frontier. Seen it,done it,read the book,got the T-shirt....
Mike Dowling
you all think that people hate science? In fact, since most of you seem to be
actively involved in science, the whole theme seems to be rather paranoic!
My students, who are mainly maths and computer science students, seem quite
well motivated. Perhaps I am fortunate, as, if they did not like what I teach,
they are under no compulsion to attend.
I have taught engineering maths repeatedly over the years. They tend to be
quite a mixed bunch. My experience again is that they are mostly well
motivated, despite the fact that they are a captive audience. There are quite
a number present who don't want to persue a mathematical career, and many of
these have difficulties. In my experience, though, even these don't hate maths
and/or science. They generally recognise that maths and science have their
merits even if they don't share my enthusiasm for it.
-----------------------------------------------------------------------------
Dr. Michael L. Dowling (__) moocow.math.nat.tu-bs.de
Abteilung f|r Mathematische Optimierung (oo)
Institut f|r Angewandte Mathematik \/-------\
TU Braunschweig || | \
Pockelsstr. 14 ||---W|| *
D-3300 Braunschweig ^^ ^^ Ph.: +49 (531) 391-7553
Germany
on.do...@zib-berlin.de
----------------------------------------------------------------------------
James Prescott Ruffner
> Now when I teach a course in mathematics or statistics at ANY level,
> I attempt to emphasize the structure and concepts. Do not think that
> these efforts are well received by the students; they clamor for the
> instructor to tell them what will be on the exams. Far too many of them
I know exactly what you are talking about, and you are quite
right. Most students (I know a lot of my cohorts were this
way) were interested in learning by rote only what they were
going to be required to regurgitate on an exam, this hardly
seems a scholarly attitude to say the least.
> The content of calculus courses is decried below. Many of the professors
> have given up trying to fight what the students demand. What is criticized
I wouldn't say I was decrying the content of Calc. courses. In
fact, I'm very sorry I didn't work harder and learn more of the
things which were covered. No doing so only meant going back
and pulling out the textbook and learning it later when I
needed to use it. I am saying that I wish more of the
professors and grad. students who taught me in my first calc.
courses had made as much of an effort to explain/emphasize
structure and concepts as you seem to.
> 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)
Scott Ruffner
john baez
>,,,,there is an awfully lot MORE material that we
>take as "basic" compared to what there used to be. My father ('5x EE MIT)
>was always amazed at the "level" of material I had as a physics major
>('83 Physics/Astronomy UC Berkeley) compared to what he had at the same
>point in his schooling.
Good point. My uncle, a physicist, once asked me if theoretical
physicists really needed to know the correspondence between Heisenberg's
matrix mechanics and Schrodinger's wave mechanics. Clearly he thought
it unlikely, and I felt quite embarrassed about having to say that this
was basic stuff any theoretical physicist would know. (Perhaps not
under that name - perhaps under the name of "solving the harmonic
oscillator.")
MADIGAN KEVIN M
>
>So why do I assign, collect and grade homework (in the upper-level
>courses, anyway... it's too much work in large introductory courses)? I
>guess for two reasons: (a) to give me and the students some feedback on how
>well they understand the material, (b) to force them to do the stuff in a
>reasonably timely fashion instead of waiting till the last night before a
>test.
>
>I can see that I can get the feedback just as well by having them
>discuss problems in class and observing their reactions. As for (b),
>well, one can argue that students have to learn the hard way, if
>necessary, that they have to keep up with the material themselves.
>
>I'm afraid to try to break the homework-collecting habit cold turkey,
>though. It seems to me that many of our students have really come to
>depend on that external stimulus, to the point where they don't try to do
>anything that isn't specifically assigned.
>
In freshman level classes I never collect homework (too easy to cheat,
pain to grade), but I always begin class with the same phrase:
"Any questions?" Few students have any questions, because they don't do the
homework. I tell them repeatedly that they must do the homework in a timely
fashion. It is not my responsibility to make sure they do. If they are
legally old enough to vote, get married and join the military, then they
don't need a babysitter.
I know many people think this attitude is callous, but I don't care.
I make it clear to the students what thier responsibilities are, and I
am always availiable for help. It is up to them to do the work.
By the way - many students seem upset that I don't collect homework.
They seem incapable of doing it unless it will be collected - very strange.
I got my BS in 1986, and RARELY had to turn in homework until I took my
senior real analysis course.
-
Ron Maimon
|>
|> Teaching in schools is becoming like a drive through burger places,
|> the important thing is how fast and how many burgers they can cook and throw
|> out of the window.
|>
|> I have decided that the best way to learn is NOT to go to a university or
|> to a school, but to go to the public library instead. you learn more,
|> and it is much less expensive, actually it is free.
|>
I heartily agree.
I would hate physics if I would have learned it in school.
Ron Maimon
Ron Maimon
|>
|> And like an instrument, maths & such are Talents. If you are great at them,
|> you will love them and find them easy. Few do. But people can be shown how to
|> appreciate them all the same, without having to slog it out. I love music,
|> but I don't pretend I could ever do it myself - this doesn't lessen my
|> appreciation of it. My talent for Maths is on a par with this - but I despise
|> maths as it has been forced on me at a level I could not comprehend.
|>
|> Teaching people to appreciate, does not mean forcing them to hate a subject
|> ^^^^^^^^^^
|> that they have no talent for, which is something which many lecturers & teachers
|> should bare in mind if they want more sympathy from Joe Public.
|>
Oh come on!
There's no such thing as talent.
Believe me, I know. I met a lot of supposedly talented people and they're dumb
as posts for the most part.
I was also called talented at math/physics at one point in my short life, but
I could remember the hours I spent at the physics library trying to understand
a concept I could just rattle off in class, and I got a lot humbler. I remember
when I was a kid, I didn't know _anything_, I had to learn it all, damn it, and
I didn't do it any faster then anyone else (I just seemed to 'cause I spent my
entire waking life learning physics)
There is no math talent, there is no physics talent. There is interest in math
or physics, or art for that matter, and there is luck.
But you will never find the "math genes"
Ron Maimon
MADIGAN KEVIN M
I took Abstract Algebra (in grad school) from a man that made us work damn
hard and demanded we see things his way. Most students didn't like that
approach, and dropped. Two years later, when I took my written Algebra prelim,
I found I didn't have to study very hard, because this man had taught me
all I really needed to know. Figuring out the rest was a piece of cake.
Josh Vander Berg
%Oh come on!
%
%There's no such thing as talent.
Oh, really?
%Believe me, I know. I met a lot of supposedly talented people and they're dumb
%as posts for the most part.
Really? I have met people like that also. I have also met people whose
ability to grasp complex concepts FAR exceeded my own, and not through any
hard work on their part.
%I was also called talented at math/physics at one point in my short life, but
%I could remember the hours I spent at the physics library trying to understand
%a concept I could just rattle off in class, and I got a lot humbler. I remember
%when I was a kid, I didn't know _anything_, I had to learn it all, damn it, and
%I didn't do it any faster then anyone else (I just seemed to 'cause I spent my
%entire waking life learning physics)
So everyone does it at exactly the same speed? There is no one on this
earth who is any faster at comprehending complex subject material than
anyone else? Hmmm... I KNOW that such is not the case.
%There is no math talent, there is no physics talent. There is interest in math
%or physics, or art for that matter, and there is luck.
And then there are people who just seem to "understand" math, who grasp
concepts intuitively. I have met people like this. They were not arrogant
asses trying to pass off their secret hard work as natural talent, they were
TRULY gifted.
%But you will never find the "math genes"
And I suppose genetics have absolutely nothing to do with intellectual
ability...
%Ron Maimon
-josh
//========================================================================\\
|| "Genius: the intelligence that knows ||Josh Vander Berg||Never stop ||
|| its frontiers" ||k08...@kzoo.edu||asking "why?"||
|| -Albert Camus ||KalamazooCollege|| Why? ||
\\========================================================================//
Daniel E. Platt
|> In article <2arpuf$7...@anaxagoras.ils.nwu.edu> cle...@ils.nwu.edu (John
|> Cleave) writes:
|> >$ In article <wa2iseCF...@netcom.com> wa2...@netcom.com (Robert Casey)
|> >$ writes:
|>
|> >$ Math is a wonderful subject. It has the most intrinsic beauty of
|> >$ of anything around. I teach quantum mechanics to chemists. I find that
|> >$ they don't seem to appreciate much of it ... probably because
|> >$ of a poor math background. It's really sad to try to teach
|> >$ such a beautiful subject, year after year, to a bunch of logs.
|>
|> >This is definitely _your_ problem. Math may be "beautiful" to you,
|> >but it is your job as a teacher to make your students enjoy it, which
|> >means showing them how it is relevant to and useful for them. The fact
|> >that you refer to them as "logs" makes me think you aren't taking this
|> >aspect of your job seriously enough.
|>
|> Let me agree with Cleave here and emphasize that the job of the teacher
|> is to figure out why his or her current approach seems to be failing and
|> do something about it. Insulting the students is a sure sign that the
|> teacher is doing his or job wrong. Certainly I can wish that my
|> students were better taught in high school, or were just more
|> intelligent and curious people (like me, the bad teacher mentally
|> adds), but if they are not, TOUGH. One has the students one has and
|> ones job is to teach THEM, not some fictional ideal students.
|>
|>
Well, as someone who has had several years in a broad range of courses,
I can say that there is a problem getting kids who are there via
required (compulsory) credits. I've done it successfully on some
occasions, but failed on others. The worst I've done was just to
help them get by doing something they really didn't want to do.
For example, I taught a modern physics course to chemistry, math,
and engineering majors, and that went over very well. None of them
expected it to be much fun; they rated it as the best course they'd
ever taken to date (I was *very* proud of that). I also taught
college algebra during the summer. That was *painful*. They just
weren't interested, and hoped to get by it without dieing.
The difference between the two groups was astounding. I tried the
same kind of things in both groups, but one went for it, and the
other didn't... Oh well...
I've come to a place where I can be sympathetic to having a bunch
of 'logs.' It literally happens that regardless of what you try,
you just won't get a response. It's worse if they don't bother showing
up (I had a few who did that... and then they tried to pass a final).
If they're not there, there's nothing you can do.
Dan
--
-------------------------------------------------------------------------------
Daniel E. Platt pl...@watson.ibm.com
The views expressed here do not necessarily reflect those of my employer.
-------------------------------------------------------------------------------
Alberto Moreira
>>> In <CFqoC...@mentor.cc.purdue.edu> hru...@snap.stat.purdue.edu (Herman Rubin) writes:
>
>>> [...]
>
>the routine in the textbook? Not at all!
"Real world problems" depend on the eye of the beholder. A partial
differential equation may look outlandish in the math class, but when
you meet it in Electromagnetic Theory or Fluid Mechanics
sometimes later you'd better not have treated it too antagonistically.
Math is a set of techniques and by definition must be general enough
to be usable by people from different paths of life. I'm into
computer science - I could easily make the point that calculus is
is completely irrelevant and that undergrad math courses should consist
of Discrete Math, Lattices and Number Theory. But like a math
teacher once told me, you don't learn this and learn that in a pointwise
way, you must have breadth of scope and master a variety of techniques.
The important thing is not to know what application you're gonna have
for math, but when you meet something that hasn't been met before,
you know what kind of math you're going to try so that your problem
becomes tractable; and when you need to read a paper or a book on
some aspect of your profession, you know math enough to at least be
able to read it.
If you concentrate in just teaching those things that your students
can see an application right in front of their noses, you're not
giving them what they need. Students don't have enough experience
to tell you what is or isn't useful, it's up to you to get a good
balance. "Real life" is as much inventing the next programming
language or developing the next wing shape as it is knowing your
odds in the lottery or balancing your checkbook.
When I was an electrical engineering undergrad, for four years
in a row my math curriculum was dominated by a very demanding
head of department. He got us to learn complex variables, group theory,
topology, logic and advanced geometry. A lot of people squirmed
like mad - "there's no real world application for this stuff!". Funny
enough, what he taught me gave me the basis for my professional
career. It allows me to open any book, read any paper, digest any
information, without being afraid of the math involved. It gave me
focus and became my scientific security blanket for life. I have no
application today for the calculus and the statistics and the trig
and all the other "real life" stuff I was taught, as I have for the
things that that guy taught us.
Bless him...
-Alberto-
Ron Maimon
|> rma...@husc9.Harvard.EDU (Ron Maimon) wrote:
|> %Oh come on!
|> %
|> %There's no such thing as talent.
|>
|> Oh, really?
really.
|>
|> %Believe me, I know. I met a lot of supposedly talented people and they're dumb
|> %as posts for the most part.
|>
|> Really? I have met people like that also. I have also met people whose
|> ability to grasp complex concepts FAR exceeded my own, and not through any
|> hard work on their part.
well, I guess youve been hanging around all these exceptional people, because
I have never met anyone whose ability to grasp complex concepts exceeded my
own by even one iota.
and, believe me, this has nothing to do with me.
|>
|> %I was also called talented at math/physics at one point in my short life, but
|> %I could remember the hours I spent at the physics library trying to understand
|> %a concept I could just rattle off in class, and I got a lot humbler. I remember
|> %when I was a kid, I didn't know _anything_, I had to learn it all, damn it, and
|> %I didn't do it any faster then anyone else (I just seemed to 'cause I spent my
|> %entire waking life learning physics)
|>
|> So everyone does it at exactly the same speed? There is no one on this
|> earth who is any faster at comprehending complex subject material than
|> anyone else? Hmmm... I KNOW that such is not the case.
Well, I know that it is the case that anybody who is born with a normal brain
can know physics as well as Glashow, Witten, Hawking, or any other physicist.
They just have better things to do with their time, and I can respect that.
|>
|> %There is no math talent, there is no physics talent. There is interest in math
|> %or physics, or art for that matter, and there is luck.
|>
|> And then there are people who just seem to "understand" math, who grasp
|> concepts intuitively. I have met people like this. They were not arrogant
|> asses trying to pass off their secret hard work as natural talent, they were
|> TRULY gifted.
I have _never_ met anyone like that. I have never seen anyone "intuit" math
through some oracle. At times, of course, I see someone solve a problem through
an ingenious trick, but this is not so impressive, since its usually a trick they
have seen someplace before, and the same result can almost always be gotten by
a more brute force approach, which is the way I solve things.
|>
|> %But you will never find the "math genes"
|>
|> And I suppose genetics have absolutely nothing to do with intellectual
|> ability...
I certainly don't think so.
Or at least, if they do, count me as one of the dumb ones.
because I know how hard I had to struggle to understand physics.
Ron Maimon
Benjamin J. Tilly
Craig....@newcastle.ac.uk (Craig Graham) writes:
> In article <1993Oct29.1...@kpc.com>, a...@kpc.com (Alberto Moreira) writes:
> > Have you tried reading the book and spending some 2-3 hours
> > a day on it ? Science - Math - they're just like learning
> > to play a difficult classical instrument such as violin or
> > cello. You can't possibly do it unless you put a lot of
> > commitment and weight on it. And that's I suppose why a
> > lot of people don't like science, and they don't like
> > classical music either: it's very hard to conquer.
> >
> > -Alberto-
>
> And like an instrument, maths & such are Talents.
I disagree strongly. It is true that there is a modicum of natural
ability that shows up, as in all things. However other factors seem to
be far more important than raw talent. However many people will use the
claim that it is talent as an excuse to not really try and see if they
can do it. It takes a substantial investment of time and energy to
become good at either. It also takes spending your time well. But it is
not just raw talent. I think that it was Gauss who said that he was
good at math because he spent _all_ of his time at it. You cannot get
by with just being talented and never working.
If you are great
at them,
> you will love them and find them easy. Few do. But people can be shown how to
> appreciate them all the same, without having to slog it out. I love music,
> but I don't pretend I could ever do it myself - this doesn't lessen my
> appreciation of it. My talent for Maths is on a par with this - but I despise
> maths as it has been forced on me at a level I could not comprehend.
>
I think that it may have been presented in a way which you *did* not
follow, but that does not mean that you *could* not learn to comprehend
it at that level. All to often people will say that if they do not get
it right away that they are just not capable. This is usually wrong.
There is nothing wrong with you, you can learn the material. I have
seen too many cases of people thinking that they just plain had not
talent at something like singing who later found that they could learn
to sing quite well. IMO talent is _very_ unlikely to be your problem.
> Teaching people to appreciate, does not mean forcing them to hate a subject
> ^^^^^^^^^^
> that they have no talent for, which is something which many lecturers & teachers
> should bare in mind if they want more sympathy from Joe Public.
I agree that more could be done to make people appreciate things.
However I disagree that the material in question is likely to be
material that the students in question are _fundamentally_ incapable of
learning.
Ben Tilly
Benjamin J. Tilly
mike@MooCow (Mike Dowling) writes:
> After reading so many contributions to this thread, I feel compelled to ask why
> you all think that people hate science? In fact, since most of you seem to be
> actively involved in science, the whole theme seems to be rather paranoic!
>
You are hearing a specialized group of people. Believe me when I tell
you that in the US most people think that they are really bad at math
and science, that both topics are just beyond them, and that they are
really unpleasant topics. (Especially math.) Given attitudes like these
it is not suprising that the level of math illiteracy is shockingly
high.
However it is also true that this topic has wandered from what the
title says. But I have not changed it as a courtesy to those who want
to keep it in their kill-files.
> My students, who are mainly maths and computer science students, seem quite
> well motivated. Perhaps I am fortunate, as, if they did not like what I teach,
> they are under no compulsion to attend.
You are fortunate. Most students in the US do *not* really care about
the material that they are supposed to be learning.
> I have taught engineering maths repeatedly over the years. They tend to be
> quite a mixed bunch. My experience again is that they are mostly well
> motivated, despite the fact that they are a captive audience. There are quite
> a number present who don't want to persue a mathematical career, and many of
> these have difficulties. In my experience, though, even these don't hate maths
> and/or science. They generally recognise that maths and science have their
> merits even if they don't share my enthusiasm for it.
Ben Tilly
Benjamin J. Tilly
hru...@snap.stat.purdue.edu (Herman Rubin) writes:
> >What are the structure and the concepts? From my experience a
> >mathematician is likely to give a different answer from a physicist. In
> >truth I think that the answer should lie in between. For the student
> >who is learning the material the important concepts IMO should *not* be
> >the formalisms that are used to justify the procedures, but the ideas
> >that the procedures attempt to let them deal with.
>
> The formalism is rarely the concepts, and this confusion is far too
> common. Also, concepts are only learned by being used, not by being
> memorized. The student who can look at a concept and understand
> "immediately" how to use it is already a potential mathematician.
>
Agreed. However I think that one of the biggest problems that the
students have is understanding how the concepts relate to the
formalism. If they had a better sense of this then it would bring the
subject home, give them a better sense for the theorems, and avoid a
lot of the errors that they make because the mix up formulas that they
do not understand.
> Therefore I would be
> >more happy with a group of students who remember that the integral that
> >they run across in first year is a way to get at their notions of area,
> >and who could give a reasonable explanation from that point of view why
> >integration "undoes" differentiation, than I would be with ones who
> >remember the entire formulation of the Riemann integral well enough to
> >do that question on the test, but who have no idea *why* the integral
> >would be defined that way.
>
> A slightly redone Riemann integral captures the concept, but only it
> more general measures are used. The concept is the sum of values
> multiplied by measures, and limits obtained from that. Those who
> learn that integral is antiderivative will have to have it beat
> into them that area can be computed by integration, and never to
> take that as the idea. But the special case of the length measure
> obscures the basic concept, and as for choosing a partition for
> approximation by a discrete measure, only the existence is needed.
> When it comes to probability, there is no new basic concept needed;
> expectation is automatically integration. But formalism should
> never be the goal, and those not intending to be mathematicians
> need not know the proofs.
>
I agree that this is a much better explanation of what the concept of
the integral is in higher math. I also agree that students who are used
to thinking of the integral as the antiderivative are unlikely to have
a real understanding of many of the applications. However I would be a
little bit more reserved about what the concept that I want them to
learn in a first calculus class is. From my point of view I *want* them
to think of the basic integral as some sort of area so that they can
have a sense of it. I also want them to have an understanding of what
the properties of area are. I actually was lucky enough to get this
sense in my first calculus course. Later when they learn about the
generalizations of the first integral that they learned they can
abstract out the important properties. It actually *helped* me when I
was learning about the Riemann-Stieltjes integral, and again it helped
me when I learned about the Lesbegue integral that I had a good sense
of the integral as being a way at getting at the concepts of area.
Because with that background I could see how the more abstract concepts
were really attempts to push the concept that I was familiar with into
new directions, and I had no problem in understanding that the
generalization could be about something very different than the
original idea that I had started with.
> The idea of approximating an area by counting squares, and getting
> bounds by the inclusion principle, used to be presented in high school
> geometry. This immediately generalizes to integral, and computing the
> amount of a bill is much closer to the concept than merely the area
> under a curve.
I agree that this sort of intuition about the area is important, and I
think that it should be taught in schools also. However I think that in
a single-variable calculus class I would say that thinking of an
integral as a way of computing the amount of a bill would be less
valuble than thinking about it as an area. But that is just my opinion
based on my own experience.
Ben Tilly
Benjamin J. Tilly
sbr...@symcom.math.uiuc.edu (Scott Brown) writes:
> >Actually I would say that a good teacher *does* adjust for what the
> >students in the classroom know. That is they set the background to that
> >level and then do what they can.
>
>
> This works well once the teacher knows the level of the
> various students. As a calculus instructor at the university
> level, I find that it frequently takes a few weeks to get
> to know my students' abilities and limitations, and by then
> the semester is almost half over (quarter system is even
> worse). It's very frustrating; it's like cranking students
> through an assembly line. If I notice someone a few
> stations up the line missed a bolt, there's no time to
> fix it _and_ do my part. And there are, it seems, lots
> of loose bolts. :)
>
I agree. However does the level of the class really vary from year to
year? IMO one good idea would be to have some sort of tutorial that was
being run by a grad student or advanced undergrads, and then having the
person running it make a list of what the significant gaps seem to be.
The reason for this is that the students will often be more willing to
admit their problems to someone who is closer to their age, and the
other thing is that the problems that the class has are often not what
you would expect. Thirdly there is the advantage of written feedback,
which is always useful when you are trying to learn from your
experience. In any case an example of what I, as a grad student running
a tutorial noticed that the prof was unaware of, is the following. In
multivariable calculus the single biggest stumbling block was the fact
that the students never really got down how you could express the same
surface in parametric form, as a function, or as a level curve. It was
always a mystery to them, and when it came from switching from one form
to another, then they were totally lost. And the sad thing was that it
is not a hard thing, but the three were described briefly in class, the
prof (and the text) did not stress the point, or explain the
advantages/disavantages of each, or go over how to convert between
them. As a result the students did not get it down, and from then on
they never really understood the connection between their formulas and
the actual surfaces in space that the subject is about.
> What I would give for a class of third-semester calculus
> students, all of whom could define "limit", "derivative"
> and "continuous"! For some reason, although I don't show
> it, it really pisses me off to ask a bunch of students in
> vector calc "Ok, now how do we find the equation of this
> tangent line", and get 33 blank stares.
I would care less at that point about any of those definitions than I
would care that they understood what a tangent line is and why it is
important! Although by that point I would want them to get some idea of
what the other things were other than formulas that they had been
taught.
Ben Tilly
Scott Brown
>Scott Brown writes:
>> This works well once the teacher knows the level of the
>> various students. As a calculus instructor at the university
>> level, I find that it frequently takes a few weeks to get
>> to know my students' abilities and limitations, and by then
>> the semester is almost half over (quarter system is even
>> worse). It's very frustrating; it's like cranking students
>> through an assembly line. If I notice someone a few
>> stations up the line missed a bolt, there's no time to
>> fix it _and_ do my part. And there are, it seems, lots
>> of loose bolts. :)
>I agree. However does the level of the class
>really vary from year to year?
The average level is probably about the same, but each
student comes in with a different set of strengths and
weaknesses. Some are weak in algebra, others can't see
the connection between pictures and formulas, and some
do fine but are always worried they are doing worse
than they are (and of course some come in well-prepared)!
It is in trying to help with these individual weaknesses
that I run out of time. It takes a while to get an idea
of where each student is coming from. In the meantime, a
lot of them are using the "I'm not good at math" excuse
to place the blame for their difficulties on something
out of their control, and their problems compound. *sigh*.
>> What I would give for a class of third-semester calculus
>> students, all of whom could define "limit", "derivative"
>> and "continuous"! For some reason, although I don't show
>> it, it really pisses me off to ask a bunch of students in
>> vector calc "Ok, now how do we find the equation of this
>> tangent line", and get 33 blank stares.
>I would care less at that point about any of those
>definitions than I would care that they understood what
>a tangent line is and why it is important!
I agree, and my point is that once they have the
intuitive notion clear they will be able to answer
the question about the equation for the line. When
I say, for instance, define "continuous", I'd like
to have them able to explain that a function is
continuous if the graph has no "holes" (f(a) not
defined), no "jumps" (limit not defined at a)
and no "hops" (for want of a better term) (limit
at a not equal to f(a)), then the part in parentheses
is easy to remember. If they understood that the
tangent line and the instantaneous slope are essentially
equivalent, and the derivative is the instantaneous
rate of change giving the best linear approximation,
they'd have no trouble finding its equation.
Scott
>Ben Tilly
--
Jon Bell
MADIGAN KEVIN M <km9...@phoebe.albany.edu> wrote:
>
>By the way - many students seem upset that I don't collect homework.
>They seem incapable of doing it unless it will be collected - very strange.
Some of them may also figure that the homework will help pull up their
final grade. Last year, as an experiment, our instructors in first
semester General Physics collected and graded homework. For _some_
students, the homework grade made a big enough difference in the final
average to raise their letter grade from, say, a C to a B. These were
students who were conscientious about doing all the homework, of course.
--
Jon Bell <jtb...@presby.edu> Presbyterian College
Dept. of Physics and Computer Science Clinton, South Carolina USA
Jon Bell
Mike Dowling <mike@MooCow> wrote:
>I have taught engineering maths repeatedly over the years. They tend to be
>quite a mixed bunch. My experience again is that they are mostly well
>motivated, despite the fact that they are a captive audience. There are quite
>a number present who don't want to persue a mathematical career, and many of
>these have difficulties. In my experience, though, even these don't hate maths
>and/or science. They generally recognise that maths and science have their
>merits even if they don't share my enthusiasm for it.
Aren't university students in Germany a more "select" group than in the
USA, because of the limited number of Studienplaetze? Here, just about
any high school graduate can go to college _somewhere_. Perhaps not MIT
or Michigan, but if they have the money, they can get into someplace like,
well, here... :-) ... and if they don't have a lot of money, there are
many middle- to lower-rung state-supported colleges.
That might account for some of the difference in motivation between
"typical" American and German students.
Mark Yeck
wa2...@netcom.com (Robert Casey) writes:
>I remember having to fight my way thru calculus classes. I used to like
>Math in high school, but I learned to absolutely hate it in college.
>The calculus profs seemed to go out of their way to make it hard to figure
>out. Especially those who thought showing a proof on the blackboard
>tells you anything useful to do test problems. Proofs don't mean sh*t
>to me. "I enjoyed math so much, I took it twice". I did make it to
>graduate with a BSEE, but I never felt too happy with calculus, in the
>sense that I would ever *want* to try to solve a problem by making up
>calculus equasions and solving them and feel that I didn't screw it up.
>I imagine that those who didn't survive to graduate in engineering
>and did graduate in something else would feel worse than I did with
>calculus.
I had the same experience in my math classes, enjoying them in high school,
and hating them in college. I actually learned very little in any of the
classes that I took in the math department. I did end up learning most of the
math from my engineering classes, though. I took differential equations twice,
but didnt learn them til we reviewed them in some electrical engineering class.
EE classes like Signals and Systems are very math intensive, but I didnt hate
them and actually learned stuff, but if they were taught by math professors,
i'm sure that i would have flunked them or something. Not necessarily a cut
on math profs. Maybe math majors understand them. who knows.
-mark
(my...@andrew.cmu.edu)
John Novak
>>Have you ever considered that many of your students(especially with
>>the lower level courses) are not math and science majors. The only
>>reason they are in the class is because they have to be. These are
>>students whose real goal is graduate school(law,business,etc.) and
>>cant get in without extremely HIGH grades and when you throw in unplanned
>>stuff it lowers their grades and they resent it.
>I very definitely consider it. I am also quite aware that the only way
>that they are likely to use the material, and many of them are, is to
>formulate problems and interpret the answers that are obtained with the
>aid of computers. Do the "real world" problems they will encounter follow
>the routine in the textbook? Not at all! But I do not teach the course
>to them as I would to science, and especially math, majors.
And here, I have to agree with Mr. Rubin.
Whether or not a student resents having to learn some material is
not an excuse for waiving the level of their understanding, nor
an excuse to dumb down the course.
Presumably, some 'wise' administrators somewhere have decided
that the courses are necessary for either general education or
specific major requirements. Presumeably, there are reasons for
this.
>As for lowering their grade, how does this happen if all are graded the
>same way? I grade according to standards for that particular course, as
>I interpret them. Those who are taking a course, if they are honest
>students, will try to acquire an understanding of that course.
Again, I agree.
Had the University not stipulated a non-Western Civilization
requirement for me (for example) I would not have taken a survey
course of eastern religions. However, once in the course, I did
not expect to be graded on a different caliber, or a different
expectation, than the serious RLS students.
Now, this analogy is slightly off, because the requirement I
filled with that course was general education, not
degree-specific. For a degree-specific requirement (like stats
for business and/or psych majors) I would agree that some changes
in the course motivation might be in order, but not the
introduction of a new standard for non-majors.
John Novak
>After reading so many contributions to this thread, I feel compelled to ask why
>you all think that people hate science? In fact, since most of you seem to be
>actively involved in science, the whole theme seems to be rather paranoic!
<Chuckle>
Look at the distribution line... :-)
I for myself give these reasons:
o I know, from experience, that a lot of people _don't_
like math, or science, and I believe that in large part, this is
learned behavior. Granted, its anecdotal evidence, but many of
the people I know are frighteningly innumerate, yet consider
themselves well educated. And the attitude toward math extends
even into some of the technical majors. A CS senior I know is
_constantly_ complaining about the math courses he is required to
take. (Which boggles my mind-- that's all computers _do_ is
math...!)
o Since I found, and started participating in, this
discussion, I've gotten mail from people telling me that any more
math is useless.
>My students, who are mainly maths and computer science students, seem quite
>well motivated. Perhaps I am fortunate, as, if they did not like what I teach,
>they are under no compulsion to attend.
[...]
You may have hit the nail on the head-- you teach technically
oriented people, who in general know the value of mathematics and
science.
However, the disdain for learning cuts into the engineering
departments as well. Most of my colleagues are openly annoyed at
the fact that they have to take the occasional history course, or
(God forbid) humanities course.
And I've heard a number of fellow students laugh off their
English and speech courses with the statement, "I'm an engineer--
I don't know how to write/speak publicly." I would silently
chuckle, do the work to the best of my ability, and I've landed
myself a part time assisstantship as a grad student. Because my
lab and project reports and memos are in readable, uncluttered,
clearly written English, and because I stand up in front of my
peers and professors, speak for a half an hour and answer
technical questions without _looking_ self-conscious, nervous, or
amateurish. (My skill at avoiding run-on sentences is less than
perfect, however... :-)
(My only complaints with most of my non-major requirements was
that they didn't go into enough depth.)
I wonder if your students are as well-motivated in non-major
classes. If they are, then you are a particularly lucky
instructor. I look forward twenty-five to thirty-five years, and
see myself teaching-- I hope my students are as enthusiastic as
yours.
John Novak
>Oh come on!
>There's no such thing as talent.
>Believe me, I know. I met a lot of supposedly talented people and they're dumb
>as posts for the most part.
I disagree with you, very strongly.
There _are_ people who have a talent or a knack for certain
subjects. This can certainly be augmented by, and sometimes
mistaken for, diligence.
I, personally, have a small amount of mathematical talent. I'm
no god, especially not by professional levels, but of my
classmates as an undergrad, I picked up the pure math concepts
more quickly than most other people. I also spent far less time
on the homework, and I got better grades.
But I have no ability for languages, other than English. I can
_learn_ other languages. At one point, I spoke German, and could
puzzle through written (and slowly spoken) Latin. I even got A's
in the classes (this was high school.) But I only learned them
by spending twice as much time as anyone else, and I can't
remember much of them today. An old acquaintance of mine,
however, used to pick up languages like nothing. A true
polyglot.
Anecdotal evidence, but she had a talent for languages.
I have a talent for math.
[...]
>But you will never find the "math genes"
I remember hearing a report, about a year and a half ago, which
tracked math ability in young students. It seems that
mathematical ability (and particularly three-dimensional
visualization and conceptualization) was strongly correlated with
the child's exposure to particular hormones (testosterone?) in
the womb.
If someone else remembers hearing the report, or better yet can
point me to it, that would be non-anecdotal evidence.
Alan Morgan
>In article <1993Nov1.2...@hobbes.kzoo.edu>,
> k08...@hobbes.kzoo.edu (Josh Vander Berg) writes:
>|> rma...@husc9.Harvard.EDU (Ron Maimon) wrote:
>|> %There's no such thing as talent.
>|>
>|> Oh, really?
>
>really.
Do you consider that to be true about physical ability also? If
so, do you really believe that you could have been a good a high
jumper as Javier Sotomayor? If not, why is mental ability so
different?
I have no trouble believing that Carl Lewis is just *faster* than
me and that Anthony Gatto is a better juggler than I will ever be.
Similarly I have no trouble believing that Donald Knuth is smarter
than I am.
>|> Really? I have met people like that also. I have also met people whose
>|> ability to grasp complex concepts FAR exceeded my own, and not through any
>|> hard work on their part.
>
>well, I guess youve been hanging around all these exceptional people, because
>I have never met anyone whose ability to grasp complex concepts exceeded my
>own by even one iota.
>
>and, believe me, this has nothing to do with me.
Maybe it has to do with the people you hang out with. I count myself as
a pretty bright guy all around and I have certainly met people who can
run little tiny mental circles around me. Not many, but they certainly exist.
>Well, I know that it is the case that anybody who is born with a normal brain
>can know physics as well as Glashow, Witten, Hawking, or any other physicist.
How do you *know* this? I haven't heard any final word from the
psychologist over the nature vs. nurture battle. Maybe you should
pop over to sci.psychology and inform them you have the answer.
>They just have better things to do with their time, and I can respect that.
I tutored someone in high school. She was really earnest and wanted
to do well because she was very close to not graduating because she
couldn't pass math. She (and I) spent several hours a day for the
last few weeks of the year going over algebra. You will no doubt
find this hard to believe but SHE JUST DIDN'T GET IT. It wasn't that she
wasn't interested or didn't want to spend the time on it, she just
didn't understand it. She finally passed with a C- and was overjoyed
to get that. I'm sure she would be happy to hear she could have been
the next Godel if she had just had the inclination.
>|> And then there are people who just seem to "understand" math, who grasp
>|> concepts intuitively. I have met people like this. They were not arrogant
>|> asses trying to pass off their secret hard work as natural talent, they were
>|> TRULY gifted.
>
>I have _never_ met anyone like that. I have never seen anyone "intuit" math
>through some oracle.
I presume you have heard of Ramanujan? Most mathematicians that I have
met consider him a "natural" mathematician. The people who he worked
with thought that of him. He certainly could "intuit" math and I don't
believe that just anyone can demonstrate that ability. Even if (by
some miracle) that was possible, I still think that Ramanujan would
become a Ramanujan^2 under those circumstances.
>|> %But you will never find the "math genes"
>|>
>|> And I suppose genetics have absolutely nothing to do with intellectual
>|> ability...
>
>I certainly don't think so.
You don't think genes have *anything* to do with intellectual ability?
I am prepared to believe that nurture plays a major role, but that nature
plays *none*?
>Ron Maimon
Alan
----
EFI agrees with me 100% on matters of fact. The above isn't and they don't.
-----> Mail abuse to: al...@efi.com <-----
Alias 'C Frog'. Keeper of the alt.tasteless song and part-time evil genius.
George M. Kierstein
>a...@kpc.com (Alberto Moreira) writes:
>
>that there are a lot of crummy books for science and math out there where
>the author assumes you have allready failed this class before and therefore
>have a general knowledge of it. It is up to the prof to make the class
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>enjoying and, failing that, at least innovative.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^. !!!!!!!!!!!!!!!!!
Unfortunatly this tells us as much about the reason that people
hate science as his comment. The responsibility lies with the student,
not the prof. If your E+M book sucks, find another (I suggest, found.
of Electromag thoery, by ____, ____, and christy (sorry forgot the first
two names) In any case your responsibilities as a student include
finding any way possible to learn, including going to class, and possibly
even *gasp* doing so many problems that they dribble out your nose. (by the
way, what would the force exerted by the drops be ?) As a wonderful prof.
of mine told me, Teachers are a public resource. A RESOURCE meaning that
you are to use them as an aid to teaching yourself the material. Mr Sutherland's point was that science must be practiced and practiced and practiced.
through problems and problems and then some reading to do more problems,
and perhaps a little thought... OK a LOT of thought, not just re-reading
things. If a teacher is boring to you well that is unfortunate, and if he
makes his class inovative then great, but those things are mainly asides to
where the learning is really done.
(Whew' now that that is out.. 8-)) -George
>
>
>
>--
> How many docs does it take to get to the center of AmigaDOS 3.0?
> The world may never know.
> The Fly Boy <| E-MAIL: tay...@hubcap.clemson.edu |>
>+--<| Activating peril-sensitive sunglasses! |>--+
Kouhia Juhana
>cle...@ils.nwu.edu (John Cleave) writes:
>>but it is your job as a teacher to make your students enjoy it
>
>is to figure out why his or her current approach seems to be failing and
>do something about it. Insulting the students is a sure sign that the
>teacher is doing his or job wrong. Certainly I can wish that my
>students were better taught in high school, or were just more
>intelligent and curious people (like me, the bad teacher mentally
>adds), but if they are not, TOUGH. One has the students one has and
>ones job is to teach THEM, not some fictional ideal students.
A few days ago it were posted following by <U27...@uicvm.uic.edu>
(Thaddeus L. Olczyk) which annoyed a bit me -- the above quotes does
save me in posting a reply. :-)
==clip==
5) ( I hope the numbers scrolled passed) With A students a teacher has little
effort. With B and C students you can push them into learning more and
make them into A and B students.
But with D and F students ( not all some fall into the B C category) you have
a problem. Basically they are idiots. I don't mean that they can't handle the m
aterial. I mean that they get up to go to the bathroom every night and each nig
ht they walk into the door. They rarely ask for help. They don't withdraw
from a course when they get 10 and the passing grade is 60 on a midterm, becaus
e they know they can do better on the final. etc...
these people take the fun out of teaching, and unfortunately they are growing i
n number. this is probably a result of our poor primary and secondary
educational system. Unfortunately the higher ups push us to go easy on these
people making them comfortable with their stupidity ( for example
pushing to lower the passing grade on exams ).
==clip==
So, we have good students and poor student, say. I have heard about
this problem since elementary school. The problem was tried to solve
by helding courses of different level.
But, helding courses of different level in material content is no no,
since everyone (at least math major) would like to learn the same stuff.
Since, those good students learns fast, I could try to teach them
separately and fast -- basically, good students hate slowness of the
lectures. And use more time for not good students; for example, more
example exercises.
Natural solution is to held reasonable fast lectures for all, 'explaned
example exercises'-hour for people not getting the stuff, and normal
home-exercise-hour for all.
Good students could get the extra exercises with solutions on paper
for selfstudy.
In above article, it is written: "they rarely ask help".
Well, I will not ask any help in front of tens of people, if there's
possible that the lecturer do not take the simple questions of "idiots"
seriously.
The point is that the above kind of teachers often overlook the
"idiots" and starts blaming or ignoring them.
Good way to solve the asking-problem is to create a local newsgroup
where students could ask any questions they want -- they probably get
the reasonable answers from the other students and staff people
instead of overlooking teachers.
In such newsgroup I have presented few exercises in higher or
different detail than they were presented in the home-exercise-hour
by individual students (corrected after by exercise-keeper).
Those, who read the newsgroup get the extra material offered.
Juhana Kouhia
E. Spitzberg
What about stopping these Crosspostings ?
E. Spitzberg
Dept. of Chemistry
University of Constance
Germany
chst...@nyx.uni-konstanz.de
Jim Carr
Then I feel sorry for you and your limited experience. I have known
several people with this talent, and it is a striking thing to observe.
In one case, it created quite a problem for a graduate student who was
set a proof as a thesis-related problem. The prof *knew* it was true
(and it proved to be true) but could not provide even a hint of guidance
as to how the problem should be attacked. He had not reasoned out any
part of it from some angle, he had seen the answer.
Too little is understood about thinking to consider whether this is
a result of an unconscious process of reasoning or some independent
pattern formation process. I might also add that one person I have
in mind was a truly awful teacher. You see, he could not explain
physics to anyone because his way of knowing it had little to do
with the sort of analogies or images that can be conveyed verbally.
You had to understand the material quite well before you could
talk about it with him.
--
J. A. Carr <j...@scri.fsu.edu> | "The New Frontier of which I
Florida State University B-186 | speak is not a set of promises
Supercomputer Computations Research Institute | -- it is a set of challenges."
Tallahassee, FL 32306-4052 | John F. Kennedy (15 July 60)
Craig Graham
In article <2b3j2n$d...@scunix2.harvard.edu>, rma...@husc9.Harvard.EDU (Ron Maimon) writes:
>Oh come on!
>
>There's no such thing as talent.
>
>Believe me, I know. I met a lot of supposedly talented people and they're dumb
>as posts for the most part.
>
I think you confuse talent & intelligence - the two do not necessarily go hand
in hand.
Craig.
MADIGAN KEVIN M
> of mine told me, Teachers are a public resource. A RESOURCE meaning that
> you are to use them as an aid to teaching yourself the material. Mr Sutherland's point was that science must be practiced and practiced and practiced.
> through problems and problems and then some reading to do more problems,
> and perhaps a little thought... OK a LOT of thought, not just re-reading
> things. If a teacher is boring to you well that is unfortunate, and if he
> makes his class inovative then great, but those things are mainly asides to
> where the learning is really done.
>
In grad school I always viewed the professors as tour guides, giving me
a very guided tour of the material, showing me where it is, what it does,
how to use it. It was up to me to take it in.
-
MADIGAN KEVIN M
>In article <2b3j2n$d...@scunix2.harvard.edu>, rma...@husc9.Harvard.EDU (Ron Maimon) writes:
>>Oh come on!
>>
>>There's no such thing as talent.
>>
>>Believe me, I know. I met a lot of supposedly talented people and they're dumb
>>as posts for the most part.
>>
>>Ron Maimon
You sir, speak from ignorance. Ever met Charles Fefferman?
Ron, you don't have all the answers. I have been to conferences and met
people so smart and so talented at Mathematics it almost makes one feel
inadaquate.
kevin
emil rojas
>In article <2b1v3s$s...@jac.zko.dec.com>,
>Nasser Abbasi <abb...@star.enet.dec.com> wrote:
>>
>>I have decided that the best way to learn is NOT to go to a university or
>>to a school, but to go to the public library instead. you learn more,
>>and it is much less expensive, actually it is free.
> What university, and what public library? I might have sympathized
> if you had said 'University library'.
> However, it is easy to become badly mislead when reading books
> without the benefit of experience. Consider professors an
> adjunct to your reading, and force them to teach you if you
> are not satisfied. Ask questions...
Along this line, while in college, I would refer to my professors
as "coach." I did this mostly with peers, but also with a few
professors that did not take themselves to seriously. For me, a
coach is someone that is helping me develop my own talents,
rather than someone imparting truth.
--
Emil Rojas em...@shell.portal.com There is truth,
(408) 973-0603 but no one knows what it is.
Cognisys -- Software Systems Development My opinions are my own,
San Jose, CA 95129-2205 nobody else works here.
John Novak
>>>I sympathize quite a bit with the original poster. I've been in
>>>the same kind of math courses described, and remember feeling
>>>much the same way. One, in particular, was our third calculus
>>>course, which concentrated on vector calculus and multivariate
>>>calculus. The prfessor was a technically brilliant man, whom I
>>>have no doubt understood the content of the course (and far,
>>>far beyond!) But he could not teach it in a way which mattered.
>>>The course was filled with physicists, math majors, and
>>>electrical and mechanical engineers. He insisted on giving us
>>>lectures of proof after proof in class, yet providing us with
>>>numerical problems on the tests. This is _non helpful_ to people
>>>who don't already have a grasp of the material.
I wrote the above, so I will respond to the response.
>Are you sure that this is what happened? Now I agree that the
>presentation might have seemed formal, and it is quite possible
>that the proofs may have been overemphasized, but if anyone is
>to understand the use of mathematics, s/he must be able to take
>an idea and apply it to problems which are not like those worked
>out in class or in homework.
Had this professor displayed any tendency to demonstrate the
formalisms through numerical (or better yet, practical numerical)
examples, I would not be complaining. I agree whole heartedly
that every student of mathematics, even engineers, need exposure
to, and understanding of, the formalisms.
I do not think it is overwhelmingly unfair to give problems
slightly different than the material covered in the lectures.
I _do_ think it is unfair to give problems vastly different on an
hour exam. Mainly because, I don't _think_ that fast, when
running over unfamiliar mental terrain. I will try to associate
it with something familiar. I will make wrong turns and
mistakes, and likely have to go back to previous points and try
new things.
None of which I have time for when I am given five problems
of an unfamiliar nature to answer in fifty minutes.
> If he graded on the correctness of
>the numerical answer, which many do, that is bad, but if he graded
>on the application of the ideas, that is what should have been doen
>in elementary school and high school, and it is not his fault, but
>the fault of your previous teachers, that you found this to be
>even slightly unexpected. I suspect also that other kinds of
>manipulations were involved on the test; that much arithmetic
>would be difficult for anyone not a rapid calculator.
He did grade on correctness of the answer, but he also gave
partial credit, as well. Incidenatlly, I got a 'B' out of the
course. I would have gotten an 'A' had I not taken one of the
hour exams under very adverse personal conditions.
The following is no longer a response to my text. My own
following text is merely general commetary.
>You have now given a positive testimonial to his teaching. The goal of
>a course should not be to be able to do certain things at the end of
>the course, but that the material be usable in the long term. The
>problem of prerequisites is also a major one; at least in mathematics,
>I cannot trust anything on the student's transcript. Possibly your
>teachers did too much, and in trying to make it more palatable to you,
>left out too much.
Hmm.
I think I agree, in general.
However, examinations are typically geared to measure what can be
performed and what is understood _right now_. The grades, of
course, reflect that. And every student in the world is
concerned with his grades, out of sheer practicality.
>I remember reading about a small college which one year turned out a
>large number of students who did quite well in graduate work in physics.
>The only explanation found was that the instructor of the senior honors
>physics course was ill most of the year.
<Chuckle>
>Good teaching is what gets the students to learn the material in such
>a way that it will be retained and usable in new situations. Now can
>you say, after the above, that you could clearly identify it? Remember
>that you learned a lot from that "bad" teacher.
I realize that this was not aimed at me, but I will apply it to
my situation in calculus III anyway. I would claim that the
professor who over-emphasized proofs failed in his job by your
criteria above. It was not he who taught me multiple
integration, or spherical coordinate systems, or vector calculus.
Some of it I knew when I walked in the class (I had an
_outstanding_ math teacher in high school) and the rest I learned
on my own. I collect math books, so I had enough sources to
teach myself from a variety of books.
Herman Rubin
>In article <CFqpw...@mentor.cc.purdue.edu>
>hru...@snap.stat.purdue.edu (Herman Rubin) writes:
>> In article <1993Oct30.1...@sarah.albany.edu> km9...@phoebe.albany.edu (MADIGAN KEVIN M) writes:
>> >In article <2as3ie$m...@galaxy.ucr.edu> ba...@guitar.ucr.edu (john baez) writes:
>> >>adds), but if they are not, TOUGH. One has the students one has and
>> >>ones job is to teach THEM, not some fictional ideal students.
>> >One also has a departmentally derived syllabus that should be adhered to,
>> >and must also retaiin some integrity. This, of course, makes the job more
>> >difficult. I agree, one must make every effort to teach the students
>> >which are actually enrolled, but, as someone said in the 19th century,
>> >"a lesson is never given, but taken." You can't teach differential equations
>> >to a room full of students that don't know how to integrate and don't
>> >really know what a derivative is.
>> And this is essentially what we are being asked to do. The idea that one
>> must adjust a subject to those individuals which happen to be placed in the
>> classroom, whether or not they have the necessary background or ability, has
>> been foisted on us by the schools of education, and is unfortunately the
>> current practice in the elementary and secondary schools.
>Actually I would say that a good teacher *does* adjust for what the
>students in the classroom know.
This can be done only to a small extent. One can fill in small gaps, and
state what is assumed. But one cannot maintain a curriculum if the students
are incapable of learning what is supposed to be achieved in the course.
I have no objection to providing remedial work. Nor would I insist on
taking N credits per term. But once it is considered appropriate to
reduce the content of a course because the students are not up to learning
that course, the curriculum becomes meaningless.
BTW, I also will not use any background material NOT assumed if any of the
students in the class does not have it. A student with the knowledge
and ability explicitly assumed for a course should be able to take it
without having some other material which the others in the class know.
Doing this also violates the idea of a curriculum. I would even avoid
using such material if all of the students have had it, as it would
still compromise the idea of a curriculum.
--
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)
Keith Robison
>In article <2b403i$a...@scunix2.harvard.edu> rma...@husc9.Harvard.EDU (Ron Maimon) writes:
>>
>>I have _never_ met anyone like that. I have never seen anyone "intuit" math
>>through some oracle. ...
>Then I feel sorry for you and your limited experience. I have known
>several people with this talent, and it is a striking thing to observe.
>In one case, it created quite a problem for a graduate student who was
>set a proof as a thesis-related problem. The prof *knew* it was true
>(and it proved to be true) but could not provide even a hint of guidance
>as to how the problem should be attacked.
Let me guess -- his words were "I have discovered a truly remarkable
proof of this, but this margin is too small to contain it" :-)
Keith Robison
Harvard University
Department of Cellular and Developmental Biology
Department of Genetics / HHMI
Herman Rubin
>In article <CFqpw...@mentor.cc.purdue.edu>
>hru...@snap.stat.purdue.edu (Herman Rubin) writes:
>
>> In article <1993Oct30.1...@sarah.albany.edu> km9...@phoebe.albany.edu (MADIGAN KEVIN M) writes:
>> >In article <2as3ie$m...@galaxy.ucr.edu> ba...@guitar.ucr.edu (john baez) writes:
..........................
> Personally I think that we should test ideas as well as
>math. Here is a _radical_ suggestion, why not have a test or homework
>question which was to explain the underlying heuristic idea behind some
>theorem, or one case of a theorem. That is part of the material in the
>sense that they will not be able to understand how and why that
>material is applied, or what motivates it, until they can try to answer
>questions like that. So why *not* test them on that. Perhaps they would
>learn it because we told them that it was on the test! That might make
>them integrate the material more, which would help them understand it,
>apply it, and would make the subject make sense.
>
While I most definitely agree that we should test ideas, the only good
way to test them that I know is to ask the students to use them, preferably
in situations they have not seen. But I have made the mistake of asking
students to explain ideas on a test; they either have the definitions
memorized, or they provide some words without meaning.
John Novak
>>If you want your students to display an ability to connect
>>concepts, give them enough time. Give a take home test, or a two
>>week project, if the class size and composition warrant.
>You will get no arguments from me on this. Now how do we implement this?
>In a low-level course, the cheating problem is bad enough on in-class
>tests; take-home is essentially impossible. This is not something
>which an individual teacher can do much about.
Ugh. I just took a look at your address, and I can see why we
might be looking at this from different angles. Purdue, to the
best of my understanding, is a _large_ school. Bradley is a
small school. In our general calculus I course, the average
section size was some thirty students. (Of course, there were
multiple sections of the class.)
I imagine the attitudes and approaches for both students _and_
professors are quite different at Purdue. We're small enough
that at the upper levels (3 and 400 level courses) we can afford
to give take home tests or small group projects, on occasion, and
have them graded in reasonable amounts of time. And small enough
that people working to gether on the tests will be almost
blatantly obvious. I grade papers of a 500 level engineering
course, and I can spot people who work on their homework together
very easily. (They're lucky we don't consider that a crime...)
In some cases, I just take out the three students' homeworks and
grade them together. Usually with the same comments on each
paper.
The only reasonable question left for me to ask at this point is
the following. Is it possible to construct a test with one or
two questions which test the ability to synthesize the
information, one or two difficult, but familiar problems, and the
rest routine problems?
Of course, this brings the question of grading criteria into the
picture. I'd say that being able to perform familiar questions
quickly, under pressure, is worth a 'C' grade, while performing
complex familiar problems is worth a 'B'. Being able to
synthesize knowledge on the spot should merit an 'A'. Again,
IMHO. (My interest in this thread is double edged-- I'm trying
to land a teaching assistantship, and if I actually get it, I'd
like to be the best I can possibly be.)
John Novak
>|> %Believe me, I know. I met a lot of supposedly talented people and they're dumb
>|> %as posts for the most part.
>|> Really? I have met people like that also. I have also met people whose
>|> ability to grasp complex concepts FAR exceeded my own, and not through any
>|> hard work on their part.
>well, I guess youve been hanging around all these exceptional people, because
>I have never met anyone whose ability to grasp complex concepts exceeded my
>own by even one iota.
Personally, I think you're crocked.
While IQ tests are by no means a perfectly accurate or
precise measurement tool, they do have some weight.
Saying that no one has any greater or lesser ability to learn is
tantamount to saying that everyone has an IQ of 100.
>|> So everyone does it at exactly the same speed? There is no one on this
>|> earth who is any faster at comprehending complex subject material than
>|> anyone else? Hmmm... I KNOW that such is not the case.
>Well, I know that it is the case that anybody who is born with a normal brain
>can know physics as well as Glashow, Witten, Hawking, or any other physicist.
>They just have better things to do with their time, and I can respect that.
And how, exactly, do you know this?
And, do you also 'know' that people can learn physics as quickly
Hawking?
I'd also like to see an operating definition of a 'normal' brain.
Whose is the standard?
>I have _never_ met anyone like that. I have never seen anyone "intuit" math
>through some oracle. At times, of course, I see someone solve a problem through
>an ingenious trick, but this is not so impressive, since its usually a trick they
>have seen someplace before, and the same result can almost always be gotten by
>a more brute force approach, which is the way I solve things.
I suspect that you're simply unobservant in this respect.
John Novak
>Presumably you will have no objection to paying the extra fees to
>support the much more labor-intensive evaluation teaching and
>evaluation methods that you favour?
I'm part of it.
I grade homework papers at the graduate level.
And I do it well, because I take my time, trace through the
students' work, find their mistakes, point them out, and grade on
that basis. Not simply on the basis of 'correct' or 'incorrect.'
I may not get their papers back to them by the next class
session, but generally within 10 days, and always in time for an
exam. (People like to study from their homework for this class.)
DB Simpson
don't like any subject is because of the teachers. The number of education
classes one has to take to teach varies inversely with the grade level. You
basically have to have a M.S. in education to teach pre-k, and you just have
to be good at math to teach graduate level math. University profs, for the
most part, don't have the slightest idea how to convey information.
A personal anecdote will illustrate my point. I wanted to improve my score
on the analytical portion of the GRE, so I could get a fellowship at this
really good school. I asked all kinds of people for stratigies on how to
attack those problems. Note, I do not mean the quantitative (math) portion,
I mean the other hard part. Anyway, I asked university profs who did
well on it. I asked fellow students who did well on it. I asked everybody.
The typical answer from these people was a confused look and a statement like
"well, you just do it, I don't know how to explain it." Obviously not.
Then I asked a second grade teacher. She informed me of some stratigies
she heard about in one of her education classes. I borrowed her book that
had the info in it, read it, cleared up my questions with her, and took a
practice test. The total time between first speaking with her and taking
the practice test was about 30 minutes.
I improved my score 130 points. In the real test (the one for the record)
I went up 110 points. It wasn't that she was some brilliant analytical
thinker who showed me some magical trick that only she knew. She just showed
me a simple strategy that every education major on the planet knows.
Obviously some of the people who do well on it know this trick, or the
education majors would have a higher average. The difference was, she was
informed of the method formally, and was able to convey it to me in perfect
clarity in a matter of minutes. BTW, I beat her own score on that part by
over 200 points, so it wasn't like she was some raving genious. She simply
had some training in how to convey information effectively, and it helped
me immensely. Every teacher at every level should be required to have a
B.S. in education, at the very minimum.
Bruce Helenb
>In article <CFtFy...@newcastle.ac.uk>, Craig....@newcastle.ac.uk (Craig Graham) writes:
>|>
>|> And like an instrument, maths & such are Talents. If you are great at them,
>|> you will love them and find them easy. Few do. But people can be shown how to
>|> appreciate them all the same, without having to slog it out. I love music,
>|> but I don't pretend I could ever do it myself - this doesn't lessen my
>|> appreciation of it. My talent for Maths is on a par with this - but I despise
>|> maths as it has been forced on me at a level I could not comprehend.
>|>
>|> Teaching people to appreciate, does not mean forcing them to hate a subject
>|> ^^^^^^^^^^
>|> that they have no talent for, which is something which many lecturers & teachers
>|> should bare in mind if they want more sympathy from Joe Public.
>|>
>Oh come on!
>There's no such thing as talent.
>Believe me, I know. I met a lot of supposedly talented people and they're dumb
>as posts for the most part.
>I was also called talented at math/physics at one point in my short life, but
>I could remember the hours I spent at the physics library trying to understand
>a concept I could just rattle off in class, and I got a lot humbler. I remember
>when I was a kid, I didn't know _anything_, I had to learn it all, damn it, and
>I didn't do it any faster then anyone else (I just seemed to 'cause I spent my
>entire waking life learning physics)
>There is no math talent, there is no physics talent. There is interest in math
>or physics, or art for that matter, and there is luck.
>But you will never find the "math genes"
Except in those that invent transistors.
>Ron Maimon
Stan Friesen
|> In article <mcdonald.1...@aries.scs.uiuc.edu>
|> mcdo...@aries.scs.uiuc.edu (J. D. McDonald) writes:
|> >
|> > I enjoyed math VERY much in college ..... especially the proofs.
|> > Many of them are very beautiful.
Ah, a mathemetician.
|>
|> In my opinion, the biggest service that one can do for someone who is
|> encountering proofs for the first time is to explain that what the books and
|> (most) teachers show in the way of proofs has very little to do with the way
|> that you actually do proofs, rather what is shown is just a quasi-standard
|> final form used for presentation only (a fact that I suspect most of the
|> primary and secondary school teachers I had were unaware of).
Well, that would help in *doing* the proofs, for those few courses
where doing proofs is required.
However, for those of us who are taking math to learn a set of *tools*
to use in doing other things, the proofs seem to be *irrelevent*.
I mean, in *applying* a mathematical technique, I generally do not
do proofs, or even use published proofs. At the most, I directly
apply the stated theorems, but more likely I just use a method
that produces the proper result.
Furthermore, in most of the math courses I took, even the tests did
*not* require doing proofs, just the working out of problems [for
instance: compute the integral of some hairy formula]. In such
courses spending hours listening to the prof. do proofs on the board
seems sort of silly.
So the queastion is: what is the significance of the proofs presented
in such classes? Why are they there at all?
|> The second biggest service you can perform is to introduce the person to
|> formal logic, and thereby ...
|> and math professors just assume that
|> everyone else has seen it somewhere as well. However, most of the
|> non-math majors (i.e. most of the students) haven't even heard of formal logic,
|> and therefore are (quite properly) totally confused.
Well, that wasn't my problem, I got the formal logic quite well.
I just didn't see any *point* to the proofs, at least as a non-math
major. [I can see that it might be different for math majors].
--
sar...@teradata.com (formerly tdatirv!sarima)
or
Stanley...@ElSegundoCA.ncr.com
The peace of God be with you.
Stan Friesen
|>
|> I doubt many thought that. The question is whether the prof _cares_ about
|> "anything useful to do test problems." The failure of the system is that
|> the test problems don't tell us anything useful about whether or not you
|> understand proofs, the essence of math (and science).
I must disagree here. Proofs (especially mathematical ones) have
*nothing* to do with the essence of science, only the essence of
math.
Of course, if what is desired is that the student understand the
meaning of proofs, then *that* is what should be taught. *Doing*
proofs does *not* teach what they are *for* - the *why* of proofs.
[I can, or at least could once, do proofs - but I have never managed
to really understand why I should *want* to do them, unless I were
a mathematician trying to prove some new theorem].
What is needed is at least a short course in the philosophy of proofs,
and in what they are supposed to accomplish.
|> >They are very beautiful when you understand what is going on. However
|> >IMHO when a student is trying to keep up with the material, do
|> >problems, and keep up with their other courses, then most of the
|> >students will see anything that is not directly helping their grade as
|> >a pain and they will ignore it. I think that we need to recognize this
|>
|> I agree completely. We need to recognize it and rethink the way we
|> assign grades (or the very fact that we do so). And also the kinds (and
|> quantity) of problems we assign.
Well, then there is also the fact that a truly mathematics based
calculus course (of the sort you seem to want) would be rather
useless for somebody trying to learn how to *apply* the calculus.
I think what is needed is a seperation between the math course
for math majors, and the math course for non-majors. Most physics
departments do quite well in making such a distinction, for instance,
but I find few math departments really provide much in the way of
applied math courses for non-majors.
Stan Friesen
|>
|> This is EXACTLY right! I wouldn't touch the subject as to why high school
|> students (on average) seem dumber these days, but it seems to me that those
|> that decide to go to college should, by definition, understand their
|> responsibility as students. I've seen more college teachers with inadequate
|> teaching skills than college students with learning disabilities. My first
|> calculus professor couldn't teach a dog to bark. HE made math ugly. Luckily I
|> found another teacher worthy of the title.
|>
I was lucky, I took my first two semesters of calculus in High School,
from the chairman of the math department, and one of the best teachers
in the school. (One of two or three that consistantly got the "Best
Teacher" award).
When I took multivariate calculus in college, I found it very hard
to stay with it, despite my intelligence and background - the teacher
was *lousy*, and managed to make the subject boring.
john baez
>However, for those of us who are taking math to learn a set of *tools*
>to use in doing other things, the proofs seem to be *irrelevent*.
>I mean, in *applying* a mathematical technique, I generally do not
>do proofs, or even use published proofs. At the most, I directly
>apply the stated theorems, but more likely I just use a method
>that produces the proper result.
>Furthermore, in most of the math courses I took, even the tests did
>*not* require doing proofs, just the working out of problems [for
>instance: compute the integral of some hairy formula]. In such
>courses spending hours listening to the proof. Do proofs on the board
>seems sort of silly.
>So the question is: what is the significance of the proofs presented
>in such classes? Why are they there at all?
Part of what's going on is as follows. In many places math majors take
the same elementary courses as the non-majors. Heck, when you're
taking freshman calculus, how are you supposed to know what you'll major
in? Anyone who majors in math needs to know how to do proofs. Right
now I'm teaching advanced calculus, which is where the folks here
finally start doing PROOFS as homework instead of calculations. All of
a sudden they are being expected to do proofs! If they hadn't seen
proofs before they would be dead in the water. Even as it is some of
them are having plenty of trouble.
Plus, even among non-majors, not everyone is like you. Some people want
to understand WHY something is true, not just use it as a tool.
I don't know what the answer is, but you have to realize that every
course in every department has two audiences: the "outsiders," who will
never study the subject very deeply, and the "insiders," meaning the
professor and those students who are really in tune to the material and
may go on to study it more deeply.
Ron Maimon
|>
|> I, personally, have a small amount of mathematical talent. I'm
|> no god, especially not by professional levels, but of my
|> classmates as an undergrad, I picked up the pure math concepts
|> more quickly than most other people. I also spent far less time
|> on the homework, and I got better grades.
I have found that everytime I do a problem quicker or easier then someone
else, it's because I have seen it, or something similar, before.
I am sure you will find the same thing working in your case too.
In addition, I don't think that the essence of mathematical knowledge is
being able to come up with neat tricks. Neat tricks are just that, neat
tricks. They don't often help you understand fundamental physics any better.
I find them highly distasteful. I don't learn something unless I could have
come up with it myself.
|>
|> But I have no ability for languages, other than English. I can
|> _learn_ other languages. At one point, I spoke German, and could
|> puzzle through written (and slowly spoken) Latin. I even got A's
|> in the classes (this was high school.) But I only learned them
|> by spending twice as much time as anyone else, and I can't
|> remember much of them today. An old acquaintance of mine,
|> however, used to pick up languages like nothing. A true
|> polyglot.
You are aware that there is a "trick" to learning languages.
The reason most adults fail to learn languages quickly is that they think
too much. They have an overwhelming desire to compartmentalize the language
into rules that they can memorise (i after e except after c) and then the
rules multiply and multiply, and exceptions build up, and they find they can't
learn the language well at all.
This is completely wrongheaded. The only way to learn a language is to _feel_
it, like a native speaker. The way to do this is to stop using rules altogether,
and learn to speak ungrammatically like native speakers speak. You then find,
after a while, that you can _feel_ what the right rules and exceptions are, just
by listening to how they sound.
People who know a lot of languages know this, and this makes it easier for them
to learn a third.
I highly doubt talent enters into the picture at all, but even if it did, it
is much less important then the factors above.
|>
|> Anecdotal evidence, but she had a talent for languages.
|> I have a talent for math.
|>
|> [...]
|>
|> >But you will never find the "math genes"
|>
|> I remember hearing a report, about a year and a half ago, which
|> tracked math ability in young students. It seems that
|> mathematical ability (and particularly three-dimensional
|> visualization and conceptualization) was strongly correlated with
|> the child's exposure to particular hormones (testosterone?) in
|> the womb.
|>
|> If someone else remembers hearing the report, or better yet can
|> point me to it, that would be non-anecdotal evidence.
|>
It would be far worse then anecdotal evidence. I would believe anecdotal evidence,
I would never believe a scientific study.
The way these studies are done is that they take a large sample of babies, measure
hormone levels and genes and stuff, and then give them a test a few years later
and look for correlations.
people really want to find something, so this has been a million times.
999,999 have found nothing.
By a statistical fluke, once in a while 1 does find something, and everyone gets
excited. Of course, whatever it is they find, it turns out that men have it more
then women (proving that women are inherently less capable at math) and if it
was done in the 19th century, that whites have more of it then blacks and asians.
This is total nonsense.
I would much prefer that you give anecdotal evidence, because if there was such
a thing as talent, you would expect there to be an _overwhelming_ amount of
evidence of this type.
e.g. I would have met lots of people so much smarter then me, that I couldn't
even begin to understand them.
I havn't met any
Ron Maimon
Andy Boden
> I would much prefer that you give anecdotal evidence, because if there was such
> a thing as talent, you would expect there to be an _overwhelming_ amount of
> evidence of this type.
>
> e.g. I would have met lots of people so much smarter then me, that I couldn't
> even begin to understand them.
>
> I havn't met any
>
> Ron Maimon
This is getting silly.
I suppose it's entirely possible that you're just the smartest person around.
Maybe you should ask yourself if you're ever known anyone who isn't a quick
as you?
Seriously, you're simply the only person I've ever heard espouse the belief
that everyone is given the *same* amount of horsepower in all different areas
(and yes, I've talked to more than one person about this over the years).
The overwhelming evidence that you ask for...
In my own experience, in *any* given nitch there is an entire spectrum of
aptitudes in the general population -- both by objective and subjective
figures of merit. This *is* a counter-example to your argument. Now one
of us could be wrong (take me for sake of discussion), but we can't *all*
be wrong.
Or maybe we *can* all be wrong and you can correct us (or would that
disprove your point...)
- A.B.
Robert Casey
>The only reasonable question left for me to ask at this point is
>the following. Is it possible to construct a test with one or
>two questions which test the ability to synthesize the
>information, one or two difficult, but familiar problems, and the
>rest routine problems?
>
like: do the derritive of: X to the Xth power d/dx
I tried to answer: (X-1)X to the (X-1) power, which turns out to be wrong.
I figured that it would go the same way that something like
3X to the 4th power d/dx = 12X to the 3rd power (did I get that right?
been a long time since I had calculus :-) ). Chain rule, I think it
was called.
Turns out that Xth to the X power d/dx question was a way for the math
prof to see who really knew what was going on, and who just did
memorized procedures.
One difficulty I remember having was getting used to the notation in
calculus class. like
5
3X d/dx
I first thought that I could cancel out the d's in the d/dx, like as
if it was a regular fraction like in algebra class. Duuuuhh..
The calculus prof probably mentioned what d/dx meant ONCE, but eighter
I missed that class, or daydreamed, or something.
And more notation I had to learn was the ' , like f'(x).
Hard to follow the presentation if you don't know what the notation means,
and I felt too shy and didn't want to embarris myself by asking the
stupid question of "What's the d/dx in that equasion for?
But there were some success in these classes, like "You can find the
area under the curve by doing the intergral. Imagine you cut up that area
into narrow rectangular strips, and add up the area of all those strips.
Now make those strips narrower, and do it again. Less error.
You eventually get to infinitestially narrow, etc.
We also spent time on limits, and something called Lopetal's(sp) rule.
Not sure what this did other than generate correct answers on tests.
And something about convergence or divergence.
And we spent a LOT of time doing antiderritives. Like:
(csc(1/(x+1))tan3(x-2))/(x+2) dx
I didn't have a clue....
My college made me take the second semester calc class even though I
bombed the first semester. Guess they figured I might make sense of
it on my own (I suppose some students might just do that).
Took these again in summer school, at the same time. Imagine taking
calc 1 and calc 2 at the same time! calc 1 is a prerequesite of calc 2!
That didn't work, ended taking calc 1 yet again (I must have been a
glutton for punishment!, no, just wanted to do engineering) and got
a prof who did a decent job of teaching it, and then made it thru
calc 2 also finally. I don't think I ever made it thru a calc class
without repeating it at least once :-(
Wonder if anyone in the Math field ever did research and written papers
like "Successfully teaching students who have failed calculus before
and are repeating it, so they actually understand it" Or " Teaching
students (who did well on SAT's and Math Achievement tests and decent
high school math grades) who are getting D's and F's on their calc
tests, so they can get up to speed and understand it".
Maybe doing simple stuff like making the students DO the homework
(collect and grade it) and spending some class time having students
work some problems on the blackboard (like teachers did in high school
algebra) might make a big difference at the lower level calc classes.
Sort of "jump starting" the students, to make them say "Hey, I'm lost
here, what did I miss?" It's too late when you get a bad grade on
the midterm test. At that point, I could never catch up.
Ron Maimon
|> In article <2b403i$a...@scunix2.harvard.edu>
|> rma...@husc9.Harvard.EDU (Ron Maimon) writes:
|> >In article <1993Nov1.2...@hobbes.kzoo.edu>,
|> > k08...@hobbes.kzoo.edu (Josh Vander Berg) writes:
|> >|> rma...@husc9.Harvard.EDU (Ron Maimon) wrote:
|> >|> %There's no such thing as talent.
|> >|>
|> >|> Oh, really?
|> >
|> >really.
|>
|> Do you consider that to be true about physical ability also? If
|> so, do you really believe that you could have been a good a high
|> jumper as Javier Sotomayor? If not, why is mental ability so
|> different?
|>
|> I have no trouble believing that Carl Lewis is just *faster* than
|> me and that Anthony Gatto is a better juggler than I will ever be.
|> Similarly I have no trouble believing that Donald Knuth is smarter
|> than I am.
There is a slight difference. Saying that a person can run a 100m dash in
10 seconds is sort of analogous to saying a person can understand galois
theory in one lecture. This has to do with how fast people learn things,
and I agree that they do learn at different rates.
This doesn't make them more intelligent, however, since if I start walking, I
will get to the end of the track sooner or later. If it takes me 20 lectures,
if I want to, I will understand galois theory. Once I know it, and there is
no way to make me unknow it.
I don't like arguing by analogy. I don't like saying "A is like B, B is X,
therefore A is X". Since if you know _why_ B is X you can sidestep the analogy
altogether, and if you don't know _why_ B is X, maybe it isn't X after all.
So I will argue directly.
People are not born understanding math. They have to learn. In order to learn
it they need motivation, real motivation.
Not " I need an A so I can get a good job"
Not " I want to look smart to impress my friends"
but something along the lines of "gosh, I am really curious as to why it
is that the angles in all these triangles add up to two right angles!"
The problem with math, however, is that people obscure these types of ideas
behind the "canned problem". These are artificial situations set up so that
people can apply formulas. The number of formulas is just small enough to
make a person who wants to get an "A" can more easily memorize them all rather
then figure out their derivation. It's just large enough, that no human being
can memorize all of them for all his or her classes _without_ understanding
their derivation.
Different people have a different level of understanding of where these
relationships come from. This is 100% due to experience. Sometimes acquired
alone by sitting and struggling with a problem, sometimes from a book, sometimes
from a teacher. But no one is born with anything that helps them in this task
of understanding.
People place too much of an emphasis on being able to "rotate objects in your
mind". I am very good at math and physics, and I can't do that. Whenever they
have those "matching" problems which most people do by rotating things in their
heads, I do by using an appropriate "right hand rule".
Some people would say that that makes me more intelligent, because I am solving
the problem quicker then the people who mentally rotate the blocks. I say that
that makes me dumber, just that I compensate for it.
I think there is no limit to the dumbness I can compensate for. No matter how
dumb I get, there is a way of thinking about things that will let me understand
a given peice of knowledge.
|>
|> >|> Really? I have met people like that also. I have also met people whose
|> >|> ability to grasp complex concepts FAR exceeded my own, and not through any
|> >|> hard work on their part.
|> >
|> >well, I guess youve been hanging around all these exceptional people, because
|> >I have never met anyone whose ability to grasp complex concepts exceeded my
|> >own by even one iota.
|> >
|> >and, believe me, this has nothing to do with me.
|>
|> Maybe it has to do with the people you hang out with. I count myself as
|> a pretty bright guy all around and I have certainly met people who can
|> run little tiny mental circles around me. Not many, but they certainly exist.
I havn't met any.
I hang out with a lot of the physics department at harvard too.
I admit that they know a lot more physics then I do, but this doesn't mean that
I can't know what they know. As a matter of fact, I am well on my way to doing
this.
|>
|> >Well, I know that it is the case that anybody who is born with a normal brain
|> >can know physics as well as Glashow, Witten, Hawking, or any other physicist.
|>
|> How do you *know* this? I haven't heard any final word from the
|> psychologist over the nature vs. nurture battle. Maybe you should
|> pop over to sci.psychology and inform them you have the answer.
I am not saying that nature has nothing to do with mathematical ability, its
just that you will find that even the ones least "gifted" count themselves
among the greatest mathematicians.
|>
|> >They just have better things to do with their time, and I can respect that.
|>
|> I tutored someone in high school. She was really earnest and wanted
|> to do well because she was very close to not graduating because she
|> couldn't pass math. She (and I) spent several hours a day for the
|> last few weeks of the year going over algebra. You will no doubt
|> find this hard to believe but SHE JUST DIDN'T GET IT. It wasn't that she
|> wasn't interested or didn't want to spend the time on it, she just
|> didn't understand it. She finally passed with a C- and was overjoyed
|> to get that. I'm sure she would be happy to hear she could have been
|> the next Godel if she had just had the inclination.
I have tutored dozens of people, some with zero math background and zero
interest, and I found that all of them could understand everything that I
taught them as well as I could. I have never met anyone without a serious
defect who was any dumber then me.
Even if it took 10 times as long as I thought it would, they will get it in the
end.
|>
|> >|> And then there are people who just seem to "understand" math, who grasp
|> >|> concepts intuitively. I have met people like this. They were not arrogant
|> >|> asses trying to pass off their secret hard work as natural talent, they were
|> >|> TRULY gifted.
|> >
|> >I have _never_ met anyone like that. I have never seen anyone "intuit" math
|> >through some oracle.
|>
|> I presume you have heard of Ramanujan? Most mathematicians that I have
|> met consider him a "natural" mathematician. The people who he worked
|> with thought that of him. He certainly could "intuit" math and I don't
|> believe that just anyone can demonstrate that ability. Even if (by
|> some miracle) that was possible, I still think that Ramanujan would
|> become a Ramanujan^2 under those circumstances.
Ramanujan is a much too often cited example of mathematical genius.
Ramanujan spent his entire life reading math!
His favorite part of mathematics was continued fractions, a very obscure branch
of mathematics which is nearly all advanced trickery.
Of course he could impress everyone with his knowledge!
I am not detracting from his contribution to mathematics, but remember, he was
just a normal human being, and did mathematics just like everyone else. He wasn't
"gifted", he wasn't "superhuman", he was a good mathematician, who worked
in isolation and reinvented a lot of mathematics for himself.
If you consider mathematics as an art, then IMO, his was pretty bad. It was way
too tricky for my taste, and far to limited in its applicability.
But that doesn't make his results any less true.
|>
|> >|> %But you will never find the "math genes"
|> >|>
|> >|> And I suppose genetics have absolutely nothing to do with intellectual
|> >|> ability...
|> >
|> >I certainly don't think so.
|>
|> You don't think genes have *anything* to do with intellectual ability?
|> I am prepared to believe that nurture plays a major role, but that nature
|> plays *none*?
Yup.
You can convince me when I meet someone whose understanding of math and physics
surpasses my own by such an overwhelming amount that I could never hope to know
what they know.
Alternatively, show me a normal, interested person who I cannot teach the entire
body of modern physics to, and I'll believe you.
until then...
Ron Maimon
Ron Maimon
|> In <2b403i$a...@scunix2.harvard.edu> rma...@husc9.Harvard.EDU (Ron Maimon) writes:
|>
|> >|> %Believe me, I know. I met a lot of supposedly talented people and they're dumb
|> >|> %as posts for the most part.
|>
|> >|> Really? I have met people like that also. I have also met people whose
|> >|> ability to grasp complex concepts FAR exceeded my own, and not through any
|> >|> hard work on their part.
|>
|> >well, I guess youve been hanging around all these exceptional people, because
|> >I have never met anyone whose ability to grasp complex concepts exceeded my
|> >own by even one iota.
|>
|> Personally, I think you're crocked.
|> While IQ tests are by no means a perfectly accurate or
|> precise measurement tool, they do have some weight.
|>
|> Saying that no one has any greater or lesser ability to learn is
|> tantamount to saying that everyone has an IQ of 100.
no, it is tatamount to saying that with a little practice anyone can learn how
to get a 200 on their IQ test.
|>
|> >|> So everyone does it at exactly the same speed? There is no one on this
|> >|> earth who is any faster at comprehending complex subject material than
|> >|> anyone else? Hmmm... I KNOW that such is not the case.
|>
|> >Well, I know that it is the case that anybody who is born with a normal brain
|> >can know physics as well as Glashow, Witten, Hawking, or any other physicist.
|> >They just have better things to do with their time, and I can respect that.
|>
|> And how, exactly, do you know this?
|> And, do you also 'know' that people can learn physics as quickly
|> Hawking?
|>
|> I'd also like to see an operating definition of a 'normal' brain.
|> Whose is the standard?
Well, a person can't learn physics as _quickly_ as Hawking, but, who cares? I
just said anyone could know all the physics Hawking knows. It might take more
time then they are willing to put in, though.
Some people have congenital brain defects that don't even allow them to talk!
I mean that anyone who can understand high school algebra can understand quantum
field theory, is this better?
|>
|> >I have _never_ met anyone like that. I have never seen anyone "intuit" math
|> >through some oracle. At times, of course, I see someone solve a problem through
|> >an ingenious trick, but this is not so impressive, since its usually a trick they
|> >have seen someplace before, and the same result can almost always be gotten by
|> >a more brute force approach, which is the way I solve things.
|>
|> I suspect that you're simply unobservant in this respect.
|>
oh no.
Ron Maimon
cy...@msc.cornell.edu
>
> e.g. I would have met lots of people so much smarter then me, that I couldn't
> even begin to understand them.
>
> I havn't met any
>
> Ron Maimon
Ron,
You must not have met many people. I have lived in 3 countries on
3 different continents. I have met enough people who are so much smarter
than me in physics that it makes me look like a moron. People (who are not
physicists) would think I am above average, however, in the company of other
physicists, I'm just a normal nerd, i.e. not too smart. One other thing, I
work as hard as any other physics grad student here at Cornell. However
hard work is not all there is. There are two grad students here, both doing
QFT. One of them is 16 and the other is 18. Both got their first degrees
at the tender age of 14. Tell me, do you think you could have gone off
to college at 12, get first class honours and continue on to grad school?
There ARE people who are more talented.
Cheng-Yang Tan
Ron Maimon
|>
|> I think you confuse talent & intelligence - the two do not necessarily go hand
|> in hand.
|>
Excuse me.
There is no such thing as intelligence.
Or, at least, if there is, I'm the smartest guy in the world.
Ron Maimon
SCOTT I CHASE
I have been watching this newsgroup long enough to be sure that, given the
choice, there must be no such thing as intelligence. :-)
-Scott
-------------------- i hate you, you hate me
Scott I. Chase let's all go and kill barney
SIC...@CSA2.LBL.GOV and a shot rang out and barney hit the floor,
no more purple dinosaur.
Herman Rubin
............................
>The only reasonable question left for me to ask at this point is
>the following. Is it possible to construct a test with one or
>two questions which test the ability to synthesize the
>information, one or two difficult, but familiar problems, and the
>rest routine problems?
My typical hour tests for low-level service courses are three or four
multi-part problems, with the routine parts interspersed; they are not
displayed as such, and the student has to find them. Crib sheets are
allowed, so that memorization is clearly not of importance. Much credit
is given if the student can understand what the problem is. Calculators
are allowed and their use encouraged; it is much easier to figure out
if they understand something if I do not have to figure out what
procedure known only to God was used to get that number.
Herman Rubin
>|> I doubt many thought that. The question is whether the prof _cares_ about
>|> "anything useful to do test problems." The failure of the system is that
>|> the test problems don't tell us anything useful about whether or not you
>|> understand proofs, the essence of math (and science).
The prof should care about how well you can understand the material years down
the line. The typical test problems are of little use here; learning how to
calculate answers can lead to understanding only in those with mathematical
research ability, and need not even then.
>I must disagree here. Proofs (especially mathematical ones) have
>*nothing* to do with the essence of science, only the essence of
>math.
Proofs, as such, also are not always the way to get understanding.
They are more likely to lead to it than computation. There are,
however, cases in which the only understanding available is that of
the proofs. I have proved such myself, and I also know of a very
important theorem, for which I know at least a half-dozen essentially
unrelated proofs, and only partial understanding. The most commonly
used of those proofs conveys no understanding whatever.
>Of course, if what is desired is that the student understand the
>meaning of proofs, then *that* is what should be taught. *Doing*
>proofs does *not* teach what they are *for* - the *why* of proofs.
Agreed. And constructing proofs is pure artistry, not teachable.
It is as much of an art form as composition, and constrained by
the fact that it must be within rigid rules.
>What is needed is at least a short course in the philosophy of proofs,
>and in what they are supposed to accomplish.
Look at any good book on logic. Everything known in mathematics, or in
any theoretical science, are assumptions and conclusions obtained from
proofs. Observational properties decide what assumptions are made.
............................
>Well, then there is also the fact that a truly mathematics based
>calculus course (of the sort you seem to want) would be rather
>useless for somebody trying to learn how to *apply* the calculus.
A purely proof-based course would not be good for anyone. For those
who will apply it, the first thing they need is to know the concepts
so that they can formulate problems. FORMULATE, not solve. Especially
in the case of calculus, present-day computer programs can do all of
the manipulations in calculus, and can usually even decide if there are
such which can be applied. Unless the student gets to be able to do
them quickly, not much is gained for the non-mathematician by learning
how to calculate the results.
>I think what is needed is a seperation between the math course
>for math majors, and the math course for non-majors. Most physics
>departments do quite well in making such a distinction, for instance,
>but I find few math departments really provide much in the way of
>applied math courses for non-majors.
It is rather that they do not provide much in the way of mathematics
courses for mathematicians.
Gregory Hamlin
most people were smarter than they were...
Greg Hamlin
ham...@ral.rpi.edu
David D Auerbach
>In article <CFrow...@dartvax.dartmouth.edu> Benjamin...@dartmouth.edu (Benjamin J. Tilly) writes:
>>In article <CFqpw...@mentor.cc.purdue.edu>
>>hru...@snap.stat.purdue.edu (Herman Rubin) writes:
>>
>>> In article <1993Oct30.1...@sarah.albany.edu> km9...@phoebe.albany.edu (MADIGAN KEVIN M) writes:
>>> >In article <2as3ie$m...@galaxy.ucr.edu> ba...@guitar.ucr.edu (john baez) writes:
> ..........................
>> Personally I think that we should test ideas as well as
>>math. Here is a _radical_ suggestion, why not have a test or homework
>>question which was to explain the underlying heuristic idea behind some
>>theorem, or one case of a theorem. That is part of the material in the
>>sense that they will not be able to understand how and why that
>>material is applied, or what motivates it, until they can try to answer
>>questions like that. So why *not* test them on that. Perhaps they would
>>learn it because we told them that it was on the test! That might make
>>them integrate the material more, which would help them understand it,
>>apply it, and would make the subject make sense.
>>
>While I most definitely agree that we should test ideas, the only good
>way to test them that I know is to ask the students to use them, preferably
>in situations they have not seen. But I have made the mistake of asking
>students to explain ideas on a test; they either have the definitions
>memorized, or they provide some words without meaning.
Here's a question that I use in logic class that a) is useful and b) I
think generalizes: In the Henkin style completeness proof why use
equivalence classes of terms rather than the terms themselves as the basic
elements of the model?
The idea here is rather than ask them to regurgitate the proof to ask them
to motivate some key moves in the proof.
Scott Brown
^^^^^^^^^^^^^^
Is this for real (the address, not the post)?
>This isn't going to be very popular, but
>the biggest reason people in college
>don't like any subject is because of the teachers.
I think blaming anyone but oneself for poor progress
in a subject is a very popular pasttime. Sometimes
it's appropriate, but more often it's just an attempt
to excuse oneself from responsibility.
In my experience, a lot of students come into their
math classes woefully unprepared. Regardless of whose
fault this is, no one else is going to solve this for
them now; in this sense, it's up to them. I'm sorry if
that sounds callous. I am more than willing to help
students who are poorly prepared find the areas they
need improvement in, and don't mind covering material
that should be prerequisite briefly in class and in
more detail in office hours, but it seems like a lot
of students either don't have or won't spend the time
to fill the gaps in their background. Many of these
students just aren't able to follow the details of
a complicated or lengthy calculation, and seem to
get exasperated when a problem takes more than two
or three steps to solve or requires drawing out
some new combination of ideas from what they have
learned.
I think they've been taking too many standardized,
multiple-choice tests.
>The number of education
>classes one has to take to teach varies
>inversely with the grade level. You
>basically have to have a M.S. in education
>to teach pre-k, and you just have
>to be good at math to teach graduate level
>math.
Well, there's a whole lot more to taking care of the needs
of 6 year olds for several hours a day than to helping adults
(and near-adults in some cases) learn a single subject.
By the time students get to college they really ought to
have a pretty good idea of how to study and how to learn.
>University profs, for the
>most part, don't have the slightest
>idea how to convey information.
Hmm....in my experience that's just not true. There
are some genuinely bad teachers but some are excellent
and most are adequate.
>A personal anecdote will illustrate my point.
>I wanted to improve my score
>on the analytical portion of the GRE, so
>I could get a fellowship at this
>really good school.
[anecdote details deleted]
DB, this is very interesting. Your measure of "good teaching"
is that the elementary school teacher showed you some kind
of "tricks" or techniques (you aren't very clear about what
these were) to improve your score on a multiple choice exam.
This really doesn't have a lot to do with teaching the
substance of any course.
>I improved my score 130 points.
Hmmm....so, you think you know more about the subjects the
test was over because you learned some techniques to improve
your score on a multiple-choice test?
>Every teacher at every level should be required to have a
>B.S. in education, at the very minimum.
While I don't dispute the fact that there are some bad
teachers out there (at every level, many with a BS in
education), I think the problems at the high-school
level and below are probably more due to too much focus
on education requirements and not enough on the material
the teachers will be teaching.
But then, my degrees are in math so I speak from only
one perspective.
Scott Brown
--
Benjamin J. Tilly
sbr...@symcom.math.uiuc.edu (Scott Brown) writes:
> >I agree. However does the level of the class
> >really vary from year to year?
>
> The average level is probably about the same, but each
> student comes in with a different set of strengths and
> weaknesses. Some are weak in algebra, others can't see
> the connection between pictures and formulas, and some
> do fine but are always worried they are doing worse
> than they are (and of course some come in well-prepared)!
>
Agreed.
> It is in trying to help with these individual weaknesses
> that I run out of time. It takes a while to get an idea
> of where each student is coming from. In the meantime, a
> lot of them are using the "I'm not good at math" excuse
> to place the blame for their difficulties on something
> out of their control, and their problems compound. *sigh*.
>
If only I had a penny for every person who does this with math...
> >> What I would give for a class of third-semester calculus
> >> students, all of whom could define "limit", "derivative"
> >> and "continuous"! For some reason, although I don't show
> >> it, it really pisses me off to ask a bunch of students in
> >> vector calc "Ok, now how do we find the equation of this
> >> tangent line", and get 33 blank stares.
>
> >I would care less at that point about any of those
> >definitions than I would care that they understood what
> >a tangent line is and why it is important!
>
> I agree, and my point is that once they have the
> intuitive notion clear they will be able to answer
> the question about the equation for the line. When
> I say, for instance, define "continuous", I'd like
> to have them able to explain that a function is
> continuous if the graph has no "holes" (f(a) not
> defined), no "jumps" (limit not defined at a)
> and no "hops" (for want of a better term) (limit
> at a not equal to f(a)), then the part in parentheses
> is easy to remember. If they understood that the
> tangent line and the instantaneous slope are essentially
> equivalent, and the derivative is the instantaneous
> rate of change giving the best linear approximation,
> they'd have no trouble finding its equation.
Agreed. And in addition if they got the intuitive idea down they would
find it a lot easier to remember than the formulas. That was the entire
point of my criticisms of how math is taught.
Ben Tilly
Keith Ramsay
|This doesn't make them more intelligent, however, since if I start
|walking, I will get to the end of the track sooner or later. If it
|takes me 20 lectures, if I want to, I will understand galois theory.
So perhaps instead of taking seven years to write Wiles' proof, you'd
have been able to do it in seventy or seven hundred. Too late. If it
takes one too much longer to do something, one won't finish.
Keith Ramsay
ram...@unixg.ubc.ca
MADIGAN KEVIN M
>|> If someone else remembers hearing the report, or better yet can
>|> point me to it, that would be non-anecdotal evidence.
>|>
>
>It would be far worse then anecdotal evidence. I would believe anecdotal evidence,
>I would never believe a scientific study.
>
>The way these studies are done is that they take a large sample of babies, measure
>hormone levels and genes and stuff, and then give them a test a few years later
>and look for correlations.
>
>people really want to find something, so this has been a million times.
>
>999,999 have found nothing.
>
>By a statistical fluke, once in a while 1 does find something, and everyone gets
>excited. Of course, whatever it is they find, it turns out that men have it more
>then women (proving that women are inherently less capable at math) and if it
>was done in the 19th century, that whites have more of it then blacks and asians.
>
>This is total nonsense.
>
>I would much prefer that you give anecdotal evidence, because if there was such
>a thing as talent, you would expect there to be an _overwhelming_ amount of
>evidence of this type.
>
>e.g. I would have met lots of people so much smarter then me, that I couldn't
>even begin to understand them.
>
>I havn't met any
>
>Ron Maimon
You are one of the most arrogant people I have ever encountered on usenet.
Or you are pulling our chain.
I will give you one anectode, then i will put you in my kill file.
One day this summer, I was helping my Linear Algebra students. Outside my
office was an 18 year old acquaintance of mine (who had never seen Linear
Algebra before), listening to what I was saying. After my students left,
this 18 year old walked in and said, "Kevin, is that Linear Algebra? That
stuff is easy." Based on hearing 10 or 20 minutes of my explanation, he
started explaining the subject to me. I suppose you will tell me that he
learned it elsewhere but forgot. The point is, some (few) people out there
"see" Mathematics, they don't have to try to figure it out until they get
to the really hard stuff. These people exist. Many of us have met them.
Some of them occassionally are on usenet.
You are making the naive mistake of assuming that your experiences are the
only ones. This is silly.
I wish I had the strength at this late hour to flame you appropriately. You
really deserve it.
Kevin Madigan
John Novak
>I have found that everytime I do a problem quicker or easier then someone
>else, it's because I have seen it, or something similar, before.
>I am sure you will find the same thing working in your case too.
I am sure that you overgeneralize.
Sometimes, this is the reason. Sometimes, it is not.
>In addition, I don't think that the essence of mathematical knowledge is
>being able to come up with neat tricks. Neat tricks are just that, neat
>tricks. They don't often help you understand fundamental physics any better.
>I find them highly distasteful. I don't learn something unless I could have
>come up with it myself.
I don't remember mentioning anything about neat tricks. I don't
remember saying anything about physics. I do not trust my
intuition on physics.
>You are aware that there is a "trick" to learning languages.
[...]
>People who know a lot of languages know this, and this makes it easier for them
>to learn a third.
>I highly doubt talent enters into the picture at all, but even if it did, it
>is much less important then the factors above.
How do you know these things?
How many examples to the contrary will be needed to disqualify
your sweeping overgeneralization? (The answer is 'one' which I
have more than provided.)
>It would be far worse then anecdotal evidence. I would believe anecdotal evidence,
I have given it. You persist in your arguments.
>I would never believe a scientific study.
Ah. Then I suspect we have little more to discuss.
>The way these studies are done is that they take a large sample of babies, measure
>hormone levels and genes and stuff, and then give them a test a few years later
>and look for correlations.
>people really want to find something, so this has been a million times.
>999,999 have found nothing.
Oh? Justify that.
>By a statistical fluke, once in a while 1 does find something, and everyone gets
>excited. Of course, whatever it is they find, it turns out that men have it more
>then women (proving that women are inherently less capable at math) and if it
>was done in the 19th century, that whites have more of it then blacks and asians.
>This is total nonsense.
So, you're saying that because you believe that everyone has
exactly the same abilities, it must be so. Do you let your
personal beliefs dictate the results of all your investiations?
>I would much prefer that you give anecdotal evidence, because if there was such
>a thing as talent, you would expect there to be an _overwhelming_ amount of
>evidence of this type.
>e.g. I would have met lots of people so much smarter then me, that I couldn't
>even begin to understand them.
Do the stats-- if you have an IQ of 145 (after which conventional
IQ scores become less than helpful indicators) then a reasonably
small percentage of the population will be 'smarter' than you.
John Novak
>Excuse me.
>There is no such thing as intelligence.
>Or, at least, if there is, I'm the smartest guy in the world.
You expect anyone to buy this?
"There is no such thing as intelligence" indeed.
I'm intelligent. My dog is not.
John Novak
>no, it is tatamount to saying that with a little practice anyone can learn how
>to get a 200 on their IQ test.
Out of curiosity, have you done any reading on the measurement of
intelligence quotients?
>|> And how, exactly, do you know this?
>|> And, do you also 'know' that people can learn physics as quickly
>|> Hawking?
>|> I'd also like to see an operating definition of a 'normal' brain.
>|> Whose is the standard?
>Well, a person can't learn physics as _quickly_ as Hawking, but, who cares? I
>just said anyone could know all the physics Hawking knows. It might take more
>time then they are willing to put in, though.
Sounds like an admission of the 'talent' concept.
>Some people have congenital brain defects that don't even allow them to talk!
Is it such a stretch to leap from "normal brain" and
"congenitally defective" to a set which also includes
"congenitally brilliant?"
And from that set of three to a full spectrum of brains, some of
which fall so far outside the norms that they are noticeably more
or less efficient and successful at certain tasks?
I don't think so.
But apparently, a brain is either normal, or broken.
>I mean that anyone who can understand high school algebra can understand quantum
>field theory, is this better?
This may or may not be true. I am not enough of an expert on
physics to judge whether QFT is understandable by a typical high
school graduate. Namely, because I don't know QFT.
John Novak
>My typical hour tests for low-level service courses are three or four
>multi-part problems, with the routine parts interspersed; they are not
>displayed as such, and the student has to find them. Crib sheets are
>allowed, so that memorization is clearly not of importance. Much credit
>is given if the student can understand what the problem is. Calculators
>are allowed and their use encouraged; it is much easier to figure out
>if they understand something if I do not have to figure out what
>procedure known only to God was used to get that number.
In other words, even though they may not be able to do the
manipulation needed, you'll give credit for a proper set-up and
an attempt on the right track? (Ie, "The answer is obviously the
definite integration of this curve (drawn) from this to that
point (marked) expressed like this. It is this integral, because
the quantity relates tp the area under this curve. However, I
can't remember the form...")
Or, from my undergrad days, "I need to do this and this and this,
combine the answers this way, but I', outta time!"
I couldn't ask for more.
Shimpei Yamashita
flurry of flames.... I have met, in my <20 years of life, lots of
people whose brain capacity simply exceeded mine. Not like they "had more math"
than I did (I've also met people who took really advanced courses who were
"dumb as posts" in your words), but their minds came up with ideas that took me
long, long time even to comprehend. Heck, some of them actually attend Harvard.
If you can keep up with their math talks, you ARE smarter than, say, me. Trust
me, I think I know my limits to a good extent. On the other hand, if you can't,
maybe some people are more talented than others. And don't tell me you can come
up with these ideas, too, if you had time or the right education...the point is
that they don't even have to think about what's going on before understanding
it. Could you have come up with enough materials to have a whole theory named
after you before getting killed at age 21 (I think it was 21), like Galois?
Or even comparable achievements in some other field besides math? Could you
have written a sonata at age 6, like Mozart? At age 21, for that matter?
--
Shimpei Yamashita, Stanford University email:shi...@leland.stanford.edu
"When declaring your major, remember this simple equation: MBA=BMW."
Stanford is getting paid $25,000 a year not to censor my mail.
Daniel P Heyman
>
>In freshman level classes I never collect homework (too easy to cheat,
>pain to grade), but I always begin class with the same phrase:
>"Any questions?" Few students have any questions, because they don't do the
>homework. I tell them repeatedly that they must do the homework in a timely
>fashion. It is not my responsibility to make sure they do. If they are
>legally old enough to vote, get married and join the military, then they
>don't need a babysitter.
>
>I know many people think this attitude is callous, but I don't care.
>I make it clear to the students what thier responsibilities are, and I
>am always availiable for help. It is up to them to do the work.
>
>By the way - many students seem upset that I don't collect homework.
>They seem incapable of doing it unless it will be collected - very strange.
>I got my BS in 1986, and RARELY had to turn in homework until I took my
>senior real analysis course.
>
>-
>
I took Calculus I and II in 1956-57 with a profoessor who used the
same method. He announced that he doesn't assign homework because if
he assigned 10 problems, those who mastered the material after 5 problems
would waste their time on the last 5 problems, while those who didn't
master the material after 10 problems wouldn't do any more. It was up
to us to do as many problems as we needed. We used Thomas' book, which
had a zillion problems at the end of each section, and another zillion at
the back of the book. It also had answers, so we could check ourselves.
I thought this was a terrific course, and I think I learned a lot.
I've used this method, with a slight twist, in an upper division probability
course. I chose a book with lots of problems, and suggested several to the
class. Students could turn in homework if they wanted to, and a TA would
read it and explain errors, if any. The TA also recorded who turned in
homework. I told the class that when it came time to assign a grade for
the course, if a student was on the borderline between 2 grades, doing
homework would earn the higher grade. This gave them a small incentive
to do problems regularly.
BTW, all my exams were open book. I think I devised problems where the
book wasn't any help unless you had already absorbed the concepts. The
open book meant that if you needed a fact, such as the variance of a gamma
distribution, you didn't have to panic if it didn't come to mind right
away. For graduate courses I always assigned one-week takehome exams
consisting of problems that were long on formulation and short on
computation if you knew how do them.
That was the way I liked to examined, and I think it was effective.
--
Dan Heyman d...@bellcore.com
Monisha Ghosh
Ron Maimon writes:
> Well, a person can't learn physics as _quickly_ as Hawking, but, who cares? I
>just said anyone could know all the physics Hawking knows. It might take more
>time then they are willing to put in, though.
Ron, I think you are missing the basic point which is learning or understanding
something _after_ someone else has proven it to be true, versus being the first
person to _conceive_ an idea and prove it to be true. Sure I could know all
the physics Hawking or anyone else knows _now_, but could I (or you) propose
and prove to be true what he has done, before he had done it? That, IMHO,
is what sets apart the averagely intelligent from the 'genius' variety -
the creativity to see something without having to spend years slogging at it.
I _know_ that I don't have the creativity (I prefer that word to intelligence)
of Galois, do you?
The sort of knowledge that you are talking about can be
acquired by sheer diligence and time spent on a subject, be it math, physics
or Latin; creativity and insight are something else which need more than just
time and effort to develop. Integral calculus can be mastered given enough
time, but could you have developed the theory all by yourself?
Monisha
Beth Kevles
become restricted to mathematics and proofs. I've been thinking about
this issue a great deal, and would like to posit the following:
1. At the post-secondary level, science teachers are normally
professors whose own training has been in science, focusing on research,
and who have had little or no training in teaching. In fact in the
sciences, as contrasted to the humanities, little attention is paid (in
the educational process) to improving the quality of communication to
the non-initiate. In other words, scientists are taught to do research
and expected to understand science, and are taught to communicate to
other scientists, but are not trained in communication to the general
audience. That there exist good science teachers is DESPITE this
system, rather than because of it.
2. Science as it is practiced is a reqarding, COLLABORATIVE effort.
Science as it is taught, especially at the secondary and early
undergraduate levels (that of introductory courses) is more of a
competetive, individual effort. That is, those who practice science get
to explore new territory where the answers may be suspected but are
certainly not known, and they are expected to work together as teams.
Students, however, are expected to work by themselves, are expected to
ge the "right" results and are penalized for "wrong" ones, even if the
METHOD they use is valid. Unlike scientific researchers, students
normally only get to run experiments once, and under deadline. The
combination of isolation (as opposed to collaboration) and the high risk
of getting a wronge result, are both counter to gaining a deep knowledge
of science and to enjoying its practice.
I'd be interested in hearing what other people think of the preceding
statements, and whether steps are being taken anywhere to counter these
problems that I perceive.
--Beth Kevles
kev...@nyu.edu (preferred email address)
William Tyler
>In article <42...@tdbunews.teradata.COM> s...@elsegundoca.ncr.com writes:
>
>>However, for those of us who are taking math to learn a set of *tools*
>>to use in doing other things, the proofs seem to be *irrelevent*.
>
[parts omitted]
>
>Plus, even among non-majors, not everyone is like you. Some people want
>to understand WHY something is true, not just use it as a tool.
>
The issue of understanding the tool is extremely important, in my
view. All mathematical (and other) tools have limitations and
strengths. Understanding why a certain theorem is true, by
understanding its proof, is often a very important part of applying it
correctly to a particular problem.
What's more, understanding the structure of proofs and relationships
gives one a much more robust method for retaining information. Instead
of a collection of unrelated theorems, mathematical tricks, etc., one
has a tightly interrelated, meaningful structure in which each part
reinforces the others.
Bill
--
Bill Tyler wty...@adobe.com
Herman Rubin
>In article <1993Nov1.1...@sarah.albany.edu>,
>MADIGAN KEVIN M <km9...@phoebe.albany.edu> wrote:
>>By the way - many students seem upset that I don't collect homework.
>>They seem incapable of doing it unless it will be collected - very strange.
>Some of them may also figure that the homework will help pull up their
>final grade. Last year, as an experiment, our instructors in first
>semester General Physics collected and graded homework. For _some_
>students, the homework grade made a big enough difference in the final
>average to raise their letter grade from, say, a C to a B. These were
>students who were conscientious about doing all the homework, of course.
I believe that this does a lot to continue the demeaning of grades.
The only legitimate meaning of a grade for me is the assessment of the
knowledge and ability of the student, preferably well after the end of
the course, but there are limitations.
Do you really think that the student who handed in 100 more problems and
got the same grades on the exams knew the material any better?
DB Simpson
> >University profs, for the
> >most part, don't have the slightest
> >idea how to convey information.
>
> Hmm....in my experience that's just not true. There
> are some genuinely bad teachers but some are excellent
> and most are adequate.
>
Hmm ... in my experience that is true. Of course though, I had an elementary
school teacher teach me a strategy, not a trick, in 30 minutes. As I said before,
none of the college teacher I asked about it, and none of the people I knew who
did really well on that part, could explain in the least little bit. I later
questioned people about whether or not they knew the technique she showed me,
and they said of course they did. It was the same method. They just couldn't
explain it, which pissed me off to tell you the truth. Why should anyone have
to ask an elementary school teacher for advice about a college exam when they
have already asked a bunch of people that should have been able to help, and who
teach college?
> DB, this is very interesting. Your measure of "good teaching"
> is that the elementary school teacher showed you some kind
> of "tricks" or techniques (you aren't very clear about what
> these were) to improve your score on a multiple choice exam.
> This really doesn't have a lot to do with teaching the
> substance of any course.
If a person knows how to teach, then they should be able to explain anything
they know about easily. The college teachers, and the people I knew who did
really well on the test, could not. They should be able to.
>
> >I improved my score 130 points.
>
> Hmmm....so, you think you know more about the subjects the
> test was over because you learned some techniques to improve
> your score on a multiple-choice test?
You have almost certainly taken the GRE, so you should know that the analytical
portion doesn't test a subject. Read the rest of my post without blood in
your eyes.
>
> >Every teacher at every level should be required to have a
> >B.S. in education, at the very minimum.
>
> While I don't dispute the fact that there are some bad
> teachers out there (at every level, many with a BS in
> education), I think the problems at the high-school
> level and below are probably more due to too much focus
> on education requirements and not enough on the material
> the teachers will be teaching.
Excuse me, but you're changing the subject.
--
Ron Maimon
|> From article <2b6lra$q...@scunix2.harvard.edu>, by rma...@husc9.Harvard.EDU (Ron Maimon):
|>
|> You must not have met many people. I have lived in 3 countries on
|> 3 different continents. I have met enough people who are so much smarter
|> than me in physics that it makes me look like a moron. People (who are not
|> physicists) would think I am above average, however, in the company of other
|> physicists, I'm just a normal nerd, i.e. not too smart. One other thing, I
|> work as hard as any other physics grad student here at Cornell. However
|> hard work is not all there is. There are two grad students here, both doing
|> QFT. One of them is 16 and the other is 18. Both got their first degrees
|> at the tender age of 14. Tell me, do you think you could have gone off
|> to college at 12, get first class honours and continue on to grad school?
Yeah, but why would I want to?
I have better things to do with my time.
|> There ARE people who are more talented.
well, all right.
Just because they know their field theory at 16 and I know it at 20 doesn't
mean that they know more of it, or know it better.
If you want to call "knowing the same thing that people know at age 30, except
at age 16" talent, then fine, they're talented. Big deal.
I just think they should spend more time partying.
Ron Maimon
Ron Maimon
|>
|> >I highly doubt talent enters into the picture at all, but even if it did, it
|> >is much less important then the factors above.
|>
|> How do you know these things?
I don't, but neither does anybody else. And until proven otherwise, I will
continue to assume that I could learn French as well as other adults.
|>
|> So, you're saying that because you believe that everyone has
|> exactly the same abilities, it must be so. Do you let your
|> personal beliefs dictate the results of all your investiations?
No, I am just saying that I believe that the more tests are done, the fewer
the genetic correlations to intelligence that you will find.
For example, it was once believed that intelligence genes correllated with myopia
genes, since so many "smart" people were myopic.
Now, of course, it has been shown that reading leads to both increased "smartness"
and increased incidence of myopia.
|>
|> >e.g. I would have met lots of people so much smarter then me, that I couldn't
|> >even begin to understand them.
|>
|> Do the stats-- if you have an IQ of 145 (after which conventional
|> IQ scores become less than helpful indicators) then a reasonably
|> small percentage of the population will be 'smarter' than you.
|>
I had an IQ of 130 when it was last measured.
and this is misleading, because it was 110 spatial, the verbal brought it up.
I have met people who score way above 145.
they are no smarter then I am, as a matter of fact, they are usually obsessed
with puns and chess (hence their increased verbal and spatial IQ) and not with
anything important.
I never found any bit of physics that they could understand that I can't, because
of their high IQ and my relativly low IQ. Go figure!
Ron Maimon
benjamin j elkins
NOT a textbook question, nor a homework question. It is computer
related and I am in need of solving this sum. Thanks you in advance.
I am in search of a closed form solution for the finite sum:
Sum[ 1, log n ] of ( x / 2^x )
2
I am in search of the infinite sum:
Sum[ 1, infinity ] of ( x / 2^x )
Thank you in advance for your speedy replies.......until.
BeSn
--
Benjamin Joseph Elkins
"living the impossible dream."
Aephraim M. Steinberg
benjamin j elkins <bjel...@mksol.dseg.ti.com> wrote:
> Hello fellow netters. Let me begin by stressing that what follows is
> NOT a textbook question, nor a homework question. It is computer
> related and I am in need of solving this sum. Thanks you in advance.
>
> I am in search of a closed form solution for the finite sum:
>
> Sum[ 1, log n ] of ( x / 2^x )
> 2
I'll assume you mean that x varies from 1 to N (and if N =log_2(n), that's
hunky-dory).
I prefer arithmetic to math, so let me use ellipses...
1/2 + 2/4 + 3/8 + 4/16 + 5/32 + ...
=
1/2 + 1/4 + 1/8 + 1/16 +...
+ 1/4 + 1/8 + 1/16 + ..
+ 1/8 + 1/16 + ...
+...
=
1
+ 1/2
+ 1/4
+ ...
= 2 for the infinite series. Now let me think about the finite version.
We just chop off the RHS of all those sequences, starting with 2^(-N-1).
So we lose N copies of the linear sequence beginning with N+1, each of
which adds up to 2^(-N). We also lose one pyramid, which looks just
like the whole pyramid I've drawn, but divided by 2^N. Its sum is
of course 2^(1-N). Thus the finite sum should be
2 - (N+2)/2^N if I haven't just counted something wrong. You should be
able to check my work pretty easily, so I'm just going to run off to
work and leave that part to you.
--
Aephraim M. Steinberg | "If the human brain were simple
UCB Physics | enough for us to understand, we
aeph...@physics.berkeley.edu | would be too simple to understand
| it." -- anonymous
Ron Maimon
I agree that there is a huge amount of variability in who comes up with something
first,
but most people, including me, don't care if they come up with something first-
they just want to understand it, and a lot of people, when they find that they
can't understand something, blame their genes instead of their textbook.
I wish they wouldn't.
Ron Maimon
t...@sleepy.cc.utexas.edu
Aephraim M. Steinberg <aephraim@physics3> wrote:
->> I am in search of a closed form solution for the finite sum:
->>
->> Sum[ 1, log n ] of ( x / 2^x )
->> 2
-> 2 - (N+2)/2^N if I haven't just counted something wrong.
Since the original expression is a finite sum, isn't it already in closed
form to begin with -- just by definition?
DB Simpson
Thanks for the post. I think you are completely correct. In fact,
what you said in your first point is much of what I was trying to say with my
example a few posts ago.
DB Simpson
Jonathan Dixon
>
>Oh come on!
>There's no such thing as talent.
>
>Believe me, I know. I met a lot of supposedly talented people and they're dumb
>as posts for the most part.
There is indeed such a thing as talent, with various people given
differing amounts in different areas. Some people (Mozart, for
example) can play piano virtuositically (?) at age 4 (or whatever)
while others won't reach that level if they spent their whole lives
that way; some people can hear a piece of music in their heads,
complete with harmonies, and write it directly to paper - but most
have to struggle through analyzing chord structures.
In the same way, there are people who can add long columns of numbers
on sight, visualize in 3D accurately that which is drawn in 2D,
immdediately grasp complex concepts behind physical (or non-physical
even) problems. Most people cannot do these; but this doesn't mean
that people can't develop some of these skills. With practice, you
can improve your abilities in most of these areas; the talent is just
the base you start at, which is not always the same.
For a specific example, I have talents in math, science, and music,
while my sister has talents in drawing, painting, and selling.
Throughout school, I have had to put in little time in most of my
technical classes to get the A, whereas it is often a struggle for my
sister to do well in, for example, math classes. It isn't that she
can't learn the concepts, it's a matter of the amount of time she has
to spend to understand them is longer than mine. On the other hand,
were I to take a drawing class, I'm sure I would spend a lot more time
for less results than she would have to.
This is the difference talent makes - the amount of effort it takes to
be able to do a certain task as opposed to the amount of effort
required of most other people. This is what is refered to when people
are called "geniuses" in science, music, art, writing - they can do
things with little effort that others would have to spend all their
time to even approach.
Now just because somebody is talented in an area doesn't mean that
they won't be dumb in others. A brilliant teacher who can really
inspire their students may be completely absentminded and devoid of
most areas of common sense. But that doesn't mean they aren't
talented teachers. So talent shouldn't be confused with intelligence
(intelligence may be a manifestation of a type of talent, but is
certainly not the only measure for talent).
Jon Dixon
di...@mimicad.colorado.edu
Craig Graham
In article <2b6q0b$q...@scunix2.harvard.edu>, rma...@husc9.Harvard.EDU (Ron Maimon) writes:
>Well, a person can't learn physics as _quickly_ as Hawking, but, who cares? I
>just said anyone could know all the physics Hawking knows. It might take more
>time then they are willing to put in, though.
>
I think, that our 'freind' here is confused. Knowledge is not a measure of talent
or intelligence (other than in the context that a good memory may be considored a
talent). Intelligence and talent are ability. Not 'I have' but 'I can do' or 'I understand'. To KNOW that something is true is not really to understand it, all it needs is a spot of beleif - but no intelligence.
>Some people have congenital brain defects that don't even allow them to talk!
So we should regard speech as a talent - all be it a widespread one. Some people
talk early, some later, a small minority sadley will never be able to do it.
Craig Graham. /\ E-mail:Craig....@newcastle.ac.uk
BAe Space Systems || Phone : (UK) 091 4883098
Stevenage,England.|| Snail-mail: 2 Sun Street, Suniside, Newcastle, England.
-----------------/__\-----------------------------------------------------------
SPACE the final^^^^frontier. Seen it,done it,read the book,got the T-shirt....
Scott Brown
>school teacher teach me a strategy, not a trick, in 30 minutes.
>As I said before,
>none of the college teacher I asked about it, and none of the people
>I knew who
>did really well on that part, could explain in the least little bit.
>I later
>questioned people about whether or not they knew the technique she
>showed me,
>and they said of course they did. It was the same method. They
>just couldn't
>explain it, which pissed me off to tell you the truth. Why should
>anyone have
>to ask an elementary school teacher for advice about a college exam
>when they
>have already asked a bunch of people that should have been able to
>help, and who
>teach college?
Well, if you'd provide a bit of detail as to just what this
technique you were shown was or what type of problem it was
meant to solve, I might be able to answer that question.
Perhaps I misunderstood your point. It sounded like you
meant the teacher showed you some sort of test-taking strategy.
If you mean she showed you some mathematical techniques, I
doubt that it was her education classes that had anything to
do with her knowing those or being able to explain them more
clearly. I suspect she was just better at explaining ideas
than those "other people" you asked.
Please, can you give some more information about what the
technique you were shown was?
I wrote:
>> DB, this is very interesting. Your measure of "good teaching"
>> is that the elementary school teacher showed you some kind
>> of "tricks" or techniques (you aren't very clear about what
>> these were) to improve your score on a multiple choice exam.
>> This really doesn't have a lot to do with teaching the
>> substance of any course.
>If a person knows how to teach, then they should be able to explain
>anything
>they know about easily. The college teachers, and the people I knew
>who did
>really well on the test, could not. They should be able to.
Hmm...While I agree that one measure of good teaching is being
able to explain things clearly, I'm not sure I'd go quite as far
as above. I have sometimes found that explanations that one person
finds clear and concise can confuse and befuddle another person.
Some things _are_ rather complicated, after all, and don't admit
simple explanations. At such times it is important that the student
be willing to work hard for a while to reach an understanding.
>> Hmmm....so, you think you know more about the subjects the
>> test was over because you learned some techniques to improve
>> your score on a multiple-choice test?
>You have almost certainly taken the GRE, so you should know that the
>analytical
>portion doesn't test a subject. Read the rest of my post without
>blood in
>your eyes.
Please, as I said before, tell me what these techniques you were
shown were! Were they mathematical or methodological? Details!
(disregard what follows if what you were shown was not
merely test-taking techniques)
Learning how to pick better from the guesses on a multiple
choice test doesn't mean you learned more or know more about
any of the material covered on the test, or that you are
any more intelligent. It _is_ good to know such techniques,
but it is _hardly_ the job of your college math teachers to
show you test-taking methods. It was certainly nice that
you found someone to show you such techniques for free,
because otherwise you'd have had to pay one of those
test-preparation services to show you.
(If the techniques you were referring to were not
just about test-taking but rather dealt with more
substantive issues, please let us know what they
were.)
>> >Every teacher at every level should be required to have a
>> >B.S. in education, at the very minimum.
Another piece of paper will not make someone a better
teacher. Most of what is taught in an undergraduate program
in education seems irrelevant to teaching (supposed)
adults in college. Furthermore, are you really seriously
suggesting that an additional 2-3 years on top of other
requirements be added to the demands of those planning on
attending graduate school? Ridiculous.
>> While I don't dispute the fact that there are some bad
>> teachers out there (at every level, many with a BS in
>> education), I think the problems at the high-school
>> level and below are probably more due to too much focus
>> on education requirements and not enough on the material
>> the teachers will be teaching.
>Excuse me, but you're changing the subject.
How is that changing the subject? You complained because
in your opinion the lack of teaching degrees among college
instructors results in poor instructors. I replied that
teaching degrees don't necessarily make better instructors
and that more focus on the material to be taught does.
I have a couple other remarks, but I should wait until
I see more details about these "techniques" you were shown.
Scott Brown
--
Stan Friesen
|> rma...@husc9.Harvard.EDU (Ron Maimon) wrote:
|> %Oh come on!
|> %
|> %There's no such thing as talent.
|>
|> Oh, really?
|>
|> %Believe me, I know. I met a lot of supposedly talented people and they're dumb
|> %as posts for the most part.
|>
|> Really? I have met people like that also. I have also met people whose
|> ability to grasp complex concepts FAR exceeded my own, and not through any
|> hard work on their part.
What I have seen, and frequently, is what I call different *aptitudes*
for various types of material. I am not sure that I like the word
'talent' for these differences, but I do agree, they are *real*.
|> %when I was a kid, I didn't know _anything_, I had to learn it all, damn it, and
|> %I didn't do it any faster then anyone else (I just seemed to 'cause I spent my
|> %entire waking life learning physics)
|>
|> So everyone does it at exactly the same speed? There is no one on this
|> earth who is any faster at comprehending complex subject material than
|> anyone else? Hmmm... I KNOW that such is not the case.
What I have seen is people who take to different classes of material
with different speeds.
I can pick up computer or biology related concepts almost immediately
on contact. I can do formal mathematics only with difficulty (although
I can solve applied mathematics problems easily).
Back, years ago, when I tried to tutor some people in computer science,
I found that some of them did not seem to understand even the basics
after literally *hours* of one-on-one discussion. Yet, given the way
some of these people tried to program the computer, I suspect that many
of them may have been truly brilliant at, say, English composition (or
similar forms of expression).
A friend of mine, who has a real ability to deal with people, and to
help them through hard times, could barely understand symbolic logic.
An this was not through stupidity, but because it required a style of
thought that was foreign to him (I think he finally made that break-
through into the appropriate thought mode, but only after two semesters
of effort).
Or, take my cousin, who's intensely visual approach to understanding
gives her a real advantage in dealing with the visual arts (as compared
to my very verbal mode of understanding).
|> %There is no math talent, there is no physics talent. There is interest in math
|> %or physics, or art for that matter, and there is luck.
|>
|> And then there are people who just seem to "understand" math, who grasp
|> concepts intuitively. I have met people like this. They were not arrogant
|> asses trying to pass off their secret hard work as natural talent, they were
|> TRULY gifted.
Yep, and then there are people like me who have the same inuititive
type of understanding for an entirely different realm of knowledge.
[For a good example of an inutitive mathematician - try Dan Ashlock,
or even better a mutual friend of ours, Arthur Parker]
--
sar...@teradata.com (formerly tdatirv!sarima)
or
Stanley...@ElSegundoCA.ncr.com
The peace of God be with you.
DB Simpson
> DB Simpson writes, in lines that are too long:
I just use the default window size, which everyone using xvnews
gets. Thanks just the same.
>
> Well, if you'd provide a bit of detail as to just what this
> technique you were shown was or what type of problem it was
> meant to solve, I might be able to answer that question.
>
> Perhaps I misunderstood your point. It sounded like you
> meant the teacher showed you some sort of test-taking strategy.
> If you mean she showed you some mathematical techniques, I
> doubt that it was her education classes that had anything to
> do with her knowing those or being able to explain them more
> clearly. I suspect she was just better at explaining ideas
> than those "other people" you asked.
>
> Please, can you give some more information about what the
> technique you were shown was?
What she taught me doesn't really matter, at least not
to the point I'm trying to make. What matters is that
this talented teacher was actually able to verbalize how
to do the problems. The other people I asked just thought
I was asking a dumb question and couldn't or wouldn't
explain how to do the problems better. Apparently I'm
not too dumb because I got in the 95th percentile on
that part, after talking to her. Two of the people I
asked got a perfect score. I know it's hard to believe
I know two of the very few, but I do. I would think they
would be able to give me more of an idea how to do them
than "you just do them." As I mentioned earlier, these
same two people said after it was all said and done that
I did them the same way they did most of the problems.
I can't tell you how many times I've gone to college
teachers with homework problems and received the same
stupid stare, that says to me "you idiot, you should be
able to do that given what I said in class." Well,
obviously I couldn't. Most of the public school teachers
at a point like this would switch to a different method of
instruction. Education classes would at least give college
teachers an awareness that the way they would naturally
do it is not the only way. Contrary to what Ron Maimon
thinks, talent would take over after that to determine
whether they would be able do it effectively. I suspect
that most teachers in college would be very good at
teaching if they had the same basic instructions as
most public school teachers. Most college instructors
ARE very intelligent after all, so I would really expect
them to be better. Of course, a lot are there just to do
research, and the teaching is a requirement rather than
there purpose, like a public school teacher.
>
> >> >Every teacher at every level should be required to have a
> >> >B.S. in education, at the very minimum.
>
> Another piece of paper will not make someone a better
> teacher. Most of what is taught in an undergraduate program
> in education seems irrelevant to teaching (supposed)
> adults in college. Furthermore, are you really seriously
> suggesting that an additional 2-3 years on top of other
> requirements be added to the demands of those planning on
> attending graduate school? Ridiculous.
Yes, of course I am suggesting that. If they want to teach
then they NEED it, and should be willing to take the extra
courses. If they want to do just research ... well that
would just be part of the price.
>
> >> While I don't dispute the fact that there are some bad
> >> teachers out there (at every level, many with a BS in
> >> education), I think the problems at the high-school
> >> level and below are probably more due to too much focus
> >> on education requirements and not enough on the material
> >> the teachers will be teaching.
>
> >Excuse me, but you're changing the subject.
>
> How is that changing the subject? You complained because
> in your opinion the lack of teaching degrees among college
> instructors results in poor instructors. I replied that
> teaching degrees don't necessarily make better instructors
> and that more focus on the material to be taught does.
On average it sure does make better instructors. More focus
on the material makes a difference also. That's why some states
have recently started to require that for someone without
a degree of any kind to be able to teach, they will have to
get a degree in the subject of their specialization (ie a B.S.
in math for a high school math teacher) PLUS an extra two
years of education classes, versus the old 4-year education
degree.
Herb Brown
The infinite series sums to 2.
The finite series sums to
2 - 2*2^(-ln(n)/ln(2)) - 2^(-ln(n)/ln(2))*ln(n)/ln(2)
Herb
--
Herbert I Brown Mathematics Dept, The Univ at Albany, Albany, NY 12222
Director, (518) 442-4640
Computer Assisted Instruction in Mathematics hib...@math.albany.edu
------------------------------------------------------------------------
Benjamin J. Tilly
dark...@cegt201.bradley.edu (John Novak) writes:
> In <2b403i$a...@scunix2.harvard.edu> rma...@husc9.Harvard.EDU (Ron Maimon) writes:
[..]
> >well, I guess youve been hanging around all these exceptional people, because
> >I have never met anyone whose ability to grasp complex concepts exceeded my
> >own by even one iota.
>
> Personally, I think you're crocked.
> While IQ tests are by no means a perfectly accurate or
> precise measurement tool, they do have some weight.
>
Not much in my books. The basically test your ability on tests. I
happen to be very good on timed tests. But there are people who I would
say are more intelligent who do significantly worse than I do on timed
tests. IMO the difference is that they do not have the same sorts of
skills that I have on tests. Something that I find interesting is that
women do significantly worse than men on the SAT's...and significantly
better in college. I would guess that the reason for this is that women
are less likely to take shortcuts. This will slow them down, which
hurts them on the timed test, but it also will make them do a generally
better job, which helps them in college. I find it interesting,
whatever the real reason is, that there is some set of traits than you
tend to find in women that make them *worse* on a test that is supposed
to tell you how good they are at something that they are *better* at.
> Saying that no one has any greater or lesser ability to learn is
> tantamount to saying that everyone has an IQ of 100.
No. Saying that everyone has an IQ of 100 is a statement about how they
do on certain tests. If the tests do what we want them to then the
tests say something about how well they learn, but it is possible that
everyone could be just the same when it comes to learning even though
there is variation on IQ tests. Furthermore I would say that there are
real differences in how people learn, but as far as I can see the
biggest differences are learned, not innate. For example a lot of it is
in the attitude that they have and in the way that they approach
things. For another example, if I was to say what it is that has made
me good at math I would probably include the following.
1) I am obstinate about *understanding* what is going on. Time after
time I find that this makes me do extra work to start with...and it
pays off every time.
2) I used to play role-playing games and I wanted a good table of
probabilities for the sorts of dice rolls that we were doing. This was
in highschool. As a result of this I wound up creating them myself *by
hand*. In the process of doing that I learned that I could really
understand math, and that math was kind of fun. I also learned during
that that simple is not the same as easy. In addition it was the first
of a number of projects that I took on. The math that I learned in
doing these things for myself gave me a headstart that I have been able
to capitalize on.
3) I had an outstanding highschool teacher, Mr. Bradley. He would
encourage me to do things for myself like that last one. Or the time
that he asked me if I could write a program which could come up with
planes that intersected either at a given point, or on a line through
two points. Remember, this is a grade 12 student who has *no* linear
algebra. Figuring out that one was HARD for me w/o matrices. However
doing these sort of exercises builded up my confidence, and made me
bring math down to my level.
4) I understand that simple is not the same as easy. This is
extremely important. It happens all of the time that you hear some math
and think, "That is simple, it will not be a problem." Sorry. It is
extremely easy to *think* that you understand w/o actually
understanding it. Also you will often not get a problem, and then when
someone explains it you will realize that it was really simple all
along. However that does *not* mean that you are stupid to have not
understood the question. We are not wired to do simple things. We are
wired to do certain complex tasks well. For example think about how you
would get a person and a computer to (a) judge someone elses
approximate emotional state, and (b) do 1000 computations...getting the
right answer w/o needing to double-check. Task (b) is a simpler task,
but it certainly is *NOT* easy for the person. But if you think about
getting the computer to do it, the first task (which is easier for the
person) is actually a lot more complex of a task. :-)
Ben Tilly