Only 45% of the students were prepared for math
Dom
CSU Freshmen Face Challenges; Only 45% of the students were prepared
for math and English studies at college level, report says
Author(s): Cynthia H. Cho
Document URL:
http://proquest.umi.com/pqdweb?did=1003262501&Fmt=3&clientId=16778&RQT=309&VName=PQD
CORRECTION: SEE CORRECTION APPENDED; Remedial classes -- An article
Wednesday in California about the California State University system
described the number of students who benefited from English and math
remedial classes. The article said, "Of the freshmen who enrolled in
the fall of 2004 and needed remediation, 84% -- 22,004 out of 38,859 --
became proficient in both subjects before their second year of
college." The article should have said that 84% of the 22,004 freshmen
who took remedial classes became proficient in English and math. The
total number of freshmen is 38,859.
Less than half of the freshmen currently in the California State
University system were ready for college-level math and English courses
upon enrollment -- a figure significantly below the goal established by
the system's trustees a decade ago -- a new report said.
University officials told the Board of Trustees on Tuesday that 45% of
students who entered the Cal State system in the fall were prepared for
college-level work, a mere 2% increase from the previous year. In 1996,
the Board of Trustees said it wanted 90% of students starting college
in the fall of 2007 to be proficient in mathematics and English.
"Obviously, these figures are lower than what we would hope to be in
this particular year if we are to achieve the goals set for 2007," said
Gary Reichard, executive vice chancellor and chief academic officer.
"We don't pretend otherwise," he said.
But administrators for the 23-campus system also said they anticipated
noticeable gains over the next two years, as they began to see results
from a new assessment test for high school juniors that was first
administered last spring.
When 11th-grade students take the mandatory California Standards Tests,
they may now add a voluntary exam that includes 15 additional math
questions, 15 additional English questions and an essay that make up
the Early Assessment Program. The voluntary test helps them find out
whether they are ready for college-level courses.
Last spring, 119,000 juniors took the voluntary math exam and 185,000
students took the English exam, Cal State officials said.
Cal State faculty and high school teachers are working together to
create 12th-grade courses for students whose performance on the
voluntary tests indicate that they are not prepared for college- level
instruction.
"We have trained more than 700 teachers and are in the process of
training thousands more," said Trustee Roberta Achtenberg.
But William G. Tierney, director of the Center for Higher Education
Policy Analysis at USC, said educators can't just rely on high schools
to prepare students for higher education. He said that colleges should
assume some of the responsibility and try to serve high school students
in creative ways -- after school, on weekends and during summers.
"The community colleges, colleges and universities need to be more
involved -- not simply assessing the quality of students but working
with them to prepare them for college," Tierney said.
Of the 43,005 current freshmen, 36% needed to take remedial classes in
math, down 1% from a year ago, and 45% needed remedial English classes,
down 2%.
Since 1998, when Cal State began tracking student performance, math
proficiency has increased 18 percentage points. English proficiency has
increased only 2 percentage points, "unsatisfactory from any point of
view," Achtenberg said.
Pointing to current sophomores, Cal State officials touted the success
of their remedial instruction programs. Of the freshmen who enrolled in
the fall of 2004 and needed remediation, 84% -- 22,004 out of 38,859 --
became proficient in both subjects before their second year of college.
Of those who needed remediation, 10% did not complete their courses and
were not allowed to re-enroll.
Guess who
>CSU Freshmen Face Challenges; Only 45% of the students were prepared
>for math and English studies at college level, report says
Not surprising. Even statistics of percentages of freshmen/women who
graduate won't be comparable from times past. Back then not everybody
and their pet cat went to university in order to say in their resume
that they'd been there. Not everyone back then made it through 1st
year either; it was common to lose at least 1/3 in their first year.
Perhaps some "more traditional" methods of teaching might work to give
better results? ...and perhaps the computer/hand-held calculator are
not the magic pill as stated?
toto
<notreal...@here.com> wrote:
>Perhaps some "more traditional" methods of teaching might work to give
>better results? ...and perhaps the computer/hand-held calculator are
>not the magic pill as stated?
Or perhaps not everyone is suited for college in the first place?
--
Dorothy
There is no sound, no cry in all the world
that can be heard unless someone listens ..
The Outer Limits
Brian VanPelt
>On Wed, 22 Mar 2006 18:00:16 -0500, Guess who
><notreal...@here.com> wrote:
>
>>Perhaps some "more traditional" methods of teaching might work to give
>>better results? ...and perhaps the computer/hand-held calculator are
>>not the magic pill as stated?
>
>Or perhaps not everyone is suited for college in the first place?
That might be so. However, everyone can enroll in a community
college, pay a fraction of the price, and then get the skills needed
to enroll in a traditional college.
This is becoming more popular. Especially for people whose high
schools have let them down (which is a continuously growing
catastrophe) and those who are in situations where education just has
not happened (those who have had to drop out, or try to go to school
as single parents).
I am a community college instructor and we take people who may have no
better than a 5th grade math aptitude (yep, you are reading that
correctly). They can then go through several math courses before
actually taking a college level math class.
They can get up to linear algebra by the time they have finished their
community college experience (which is usually up to the sophomore
level), and then transfer to a traditional college. Most of the
community college math classes transfer anywhere - as long as they are
college level courses.
For example, every year I have people from every conceivable college
attend my classes, and the credits transfer EVERY time. This applies
even to Ivey League schools.
Brian
Guess who
wrote:
>That might be so. However, everyone can enroll in a community
>college, pay a fraction of the price, and then get the skills needed
>to enroll in a traditional college.
>
>This is becoming more popular. Especially for people whose high
>schools have let them down (which is a continuously growing
>catastrophe)
Or they might have matured a little in the meantime, and decided to
pay attention to what they were being taught. Education has always
been a personal matter in the long run, between you and it. When you
mature [attitude, not age] it comes more readily for some reason or
another.
Herman Rubin
It is not the computer/hand-held calculator which is
causing the problem, and giving it up would not make
that much difference. It is the emphasis on teaching
facts and methods which is the problem, rather than
teaching concepts and structure.
The educationists cannot understand the importance of
concepts and structure, and consider these taught by
definitions again. Grammar is highly deemphasized in
English classes in favor of "free expression", and
the emphasis is mathematics classes in computing
answers, rather than being able to ask question,
understanding that things have to be proved, and also
understanding integers and real numbers. The remedial
courses really do not do an adequate job of remediation;
almost none of the concepts get across.
Concepts and structure need to come EARLY, so the students
can know why, and not just how. This also means that the
emphasis on relevance needs to go out; education is for
the distant future, not the current present.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
Herman Rubin
toto <scar...@wicked.witch> wrote:
>On Wed, 22 Mar 2006 18:00:16 -0500, Guess who
><notreal...@here.com> wrote:
>>Perhaps some "more traditional" methods of teaching might work to give
>>better results? ...and perhaps the computer/hand-held calculator are
>>not the magic pill as stated?
>Or perhaps not everyone is suited for college in the first place?
Not everyone is even suited for a decent high school
program. Instead of teaching by age, teach by
knowledge and ability.
Herman Rubin
Brian VanPelt <bvan...@neo.rr.com> wrote:
>On Thu, 23 Mar 2006 02:06:54 GMT, toto <scar...@wicked.witch> wrote:
>>On Wed, 22 Mar 2006 18:00:16 -0500, Guess who
>><notreal...@here.com> wrote:
>>>Perhaps some "more traditional" methods of teaching might work to give
>>>better results? ...and perhaps the computer/hand-held calculator are
>>>not the magic pill as stated?
>>Or perhaps not everyone is suited for college in the first place?
>That might be so. However, everyone can enroll in a community
>college, pay a fraction of the price, and then get the skills needed
>to enroll in a traditional college.
They can get credits so they will be accepted. This does
not mean that they are suited for college. The colleges
have also reduced their quality, and even the graduate
schools.
>This is becoming more popular. Especially for people whose high
>schools have let them down (which is a continuously growing
>catastrophe) and those who are in situations where education just has
>not happened (those who have had to drop out, or try to go to school
>as single parents).
The public schools at all levels are a catastrophe, and
are no longer remediable.
>I am a community college instructor and we take people who may have no
>better than a 5th grade math aptitude (yep, you are reading that
>correctly).
If they do not have better than that APTITUDE, there is
no hope. If they do not have the KNOWLEDGE, there is.
They can then go through several math courses before
>actually taking a college level math class.
>They can get up to linear algebra by the time they have finished their
>community college experience (which is usually up to the sophomore
>level), and then transfer to a traditional college.
This is so low as to be pitiful.
Most of the
>community college math classes transfer anywhere - as long as they are
>college level courses.
>For example, every year I have people from every conceivable college
>attend my classes, and the credits transfer EVERY time. This applies
>even to Ivey League schools.
They should not transfer without an exam. This emphasis
on credits and grades suppresses knowledge, as the methods
used are typically based on not only trivia, but on what
can be easily forgotten.
Guess who
Rubin) wrote:
>Concepts and structure need to come EARLY, so the students
>can know why, and not just how.
Not so; certainly not necessarily so, and far too sweeping a
generalisation. You lose almost everyone if you pontificate. The
young are generally not ready for theory simply due to the fact that
they are very young, but might grasp it later when they have more
detail to put to that theory.
I know and taught both fact and theory, depending on the age and the
level. It's part and parcel of what you do. The order is important
for reasons other than you suggest. You might read up on the general
learning capabilities and capacity of different age groups[ as in
Piaget's principles].
With those clearly showing exceptional talent, they can be prepared
for competition level mathematics. Check out the olympiad
competitions and others for that level of required competence.
Others, by far the majority, need hands-on, "show me how to do it then
leave me to do it." Others in between can have it one way or another;
first practice then theory or vise versa. Some simply do not have the
ability to assimilate both theory and practice, having sufficient
problem handling simple examples one after another.
Guess who
Rubin) wrote:
>>Or perhaps not everyone is suited for college in the first place?
>
>
>Not everyone is even suited for a decent high school
>program. Instead of teaching by age, teach by
>knowledge and ability.
That simply means presenting several programs. However people may be
slotted and allotted, there will always be differences, and the public
system can not afford to tutor each individually. So, you will always
have some who don't quite fit. I'm talking at the college level about
those who should already have a fairly clear image of their
capabilities, but if you've watched American Idol, you'll have seen
the side of human nature that denies that.
Guess who
Rubin) wrote:
>They should not transfer without an exam. This emphasis
>on credits and grades suppresses knowledge, as the methods
>used are typically based on not only trivia, but on what
>can be easily forgotten.
This I'd agree with. In fact, there might be pre-requisite entrance
exams for all, aside from individual school qualifications.
Sumbuny
"Brian VanPelt" <bvan...@neo.rr.com> wrote in message
news:hra42217dg9vrakfn...@4ax.com...
<nodding> Community colleges are one of the more popular choices in my
area...and since it is standard in Florida that *every* Florida state
institution will accept credits from other Florida state institutions for
degree seeking students, it is rather common for students to begin their
university careers in the community colleges...i.e., they will get their
first two years of education in the colleges, and then transfer to the
university system, knowing that their credits will follow them, because all
of the credits have the same numbering system across the board...
What absolutely floors me is that the high schools in our area are not
teaching the students how to do research papers....that's right, even the
"honors" English classes are not teaching their students how to do research
papers...I thought it was just my sons' high school, but no--I work with our
local Boy Scout troop, and we have a couple of Scouts from another high
school in our district, and they are not doing research papers either. When
I was with my older son at college (at *his* request <g>) for moral support
while he was registering for a term, I commented about this to the guidance
counselor, who was, shall I say, rather surprised. I suggested that she
talk to some of the staff at the local high schools to get a feel for the
kids that were coming their way--and she said she would...
--
Buny
" Nobody realizes that some people expend tremendous energy merely to be
normal."
~ Albert Camus
Sumbuny
"Guess who" <notreal...@here.com> wrote in message
news:fq5522pbi7au6iatt...@4ax.com...
...and sometimes "life gets in the way" <BG> It took me about 18 years
between the time I graduated high school and the time I started
college...During that time, I got married, had children while my husband
(who was in the military) and I got to "see the world"...and after my
children were older and more settled in their own scholastic careers (middle
and high school, when they no longer needed as much supervision and
help-let's face it, elementary school tends to ask for a LOT more
volunteerism from parents <G>), and my husband's career in the military
started to allow me more of my own time, then I was able to look at going
back to school...
"Maturity and attitude" are not always the only factors...they can be
important ones, true, but they are not the only ones...Entering college at
28 was a little nerve-wracking--but I was not the only "over 30" student
there...and I was not the oldest by a long shot! <BG> Most of those my age
I spoke with had similar stories about why they put off going to
college....if it wasn't similar to mine, it was the "Serving my country"
one...then again, I *am* in a military community, so that would make sense
<g>
Herman Rubin
Guess who <notreal...@here.com> wrote:
>On 23 Mar 2006 11:33:53 -0500, hru...@odds.stat.purdue.edu (Herman
>Rubin) wrote:
>>Concepts and structure need to come EARLY, so the students
>>can know why, and not just how.
>Not so; certainly not necessarily so, and far too sweeping a
>generalisation. You lose almost everyone if you pontificate. The
>young are generally not ready for theory simply due to the fact that
>they are very young, but might grasp it later when they have more
>detail to put to that theory.
Do you mean you cannot teach grammatical structure to
someone who has not learned a language? Nonsense.
You do not understand concepts. They are NOT the same as
theory; one can learn the theory and have no understanding
of the concepts, and vice versa. A concept is not understood
by going through the motions; it is only understood when it
can be used. Also, a general concept is often misunderstood
when it is given as a generalization of a special concept.
A former student told me that the biggest problem he had with
general topology was that he had learned metric topology,
which is a specialization of it, but that the details of the
specialization hid the general concept.
Note that there was no explicit conceptualization of the
integers before the late 19th century or theory, and the
first axiomatization was somewhat later. One of the problems
here is that there are two totally distinct concepts, which
happen to coincide in operational practice. In my opinion,
and it was my opinion then, they chose the apparently easier
one, which actually is harder. They both should be taught
somewhat together, and it is not necessary to give all the
proofs to teach the concepts. A few should be given to
teach what a proof is.
Also, the concept of variable is often misunderstood. For
one thing, it is taught for numbers only initially, instead
of being used for anything, and not just as a noun or pronoun.
For another, the presentation attempts to do things with one
variable, which further causes confusion. Variables are a
part of "mathematical linguistics", and belong with beginning
reading. One does not have to build up to it.
There was a science fiction story in which there were the
slogans, "The Wistik dufels the Moraddy.", and "The
Moraddy dufels the Wistik." At the end of the story, the
protagonist only knows that Wistik and Moraddy are proper
nouns, and dufels represents a third person singular verb.
This is really a use of variables as far as he knew.
>I know and taught both fact and theory, depending on the age and the
>level. It's part and parcel of what you do. The order is important
>for reasons other than you suggest. You might read up on the general
>learning capabilities and capacity of different age groups[ as in
>Piaget's principles].
Piaget never got to the point of understanding concepts.
>With those clearly showing exceptional talent, they can be prepared
>for competition level mathematics. Check out the olympiad
>competitions and others for that level of required competence.
That is the use of theory and ingenuity, not concepts.
>Others, by far the majority, need hands-on, "show me how to do it then
>leave me to do it."
When these get to college, they are almost mentally dead.
One can sometimes teach them theory, but not concepts.
I have the regrettably too rare ability to recognize that
I may know how to prove the theorems, and use the material
for computation and representation, and NOT know what is
really going on. The schools are deliberately attempting
to destroy this.
Others in between can have it one way or another;
>first practice then theory or vise versa. Some simply do not have the
>ability to assimilate both theory and practice, having sufficient
>problem handling simple examples one after another.
I have found in my decades as a professor that the one who
learns practice and then theory is usually unable to apply
the theory to the practice, because both teach HOW. The
concepts teach why, and need to be extremely general to be
understood. A typical "methods" course can be taught in
10% of the time to someone who understands the concepts,
often if much of the theory is not known.
Herman Rubin
Even at the elementary school level, there are ways around
the problem. One can get the advantage of classes, and
even a fair amount of interaction, if the classes are
arranged electronically, which is not overly costly.
A lot can also be done by individual reading, which can
start quite early.
How can the typical American college student have any idea
of his or her capabilities? The elementary and high school
curricula are designed not to give the appropriate positive
or negative feedbacks.
Herman Rubin
Not aside from, but instead of. My confidence in course
grades, recommendations by teachers, etc., is very low.
It is difficult to interpret the chicken tracks even if
one knows which chicken made them.
Dave Rusin
Herman Rubin <hru...@odds.stat.purdue.edu> wrote:
>There was a science fiction story in which there were the
>slogans, "The Wistik dufels the Moraddy.",
Actually "The Gostak distimms the Doshes".
Herman Rubin
The World Wide Wade
hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
> A former student told me that the biggest problem he had with
> general topology was that he had learned metric topology,
> which is a specialization of it, but that the details of the
> specialization hid the general concept.
That's hardly believable, as the transition from metric spaces to
general topology is quite natural. And if you haven't seen metric
spaces, the axioms for point-set topology will appear like some
arbitrary abstract nonsense from another planet. You keep
repeating this little story as if it implied something for
pedagogy; it doesn't.
Guess who
Rubin) wrote:
>In article <m4p522tsf03cd3aq8...@4ax.com>,
>Guess who <notreal...@here.com> wrote:
>>On 23 Mar 2006 11:33:53 -0500, hru...@odds.stat.purdue.edu (Herman
>>Rubin) wrote:
>
>>>Concepts and structure need to come EARLY, so the students
>>>can know why, and not just how.
>
>>Not so; certainly not necessarily so, and far too sweeping a
>>generalisation. You lose almost everyone if you pontificate. The
>>young are generally not ready for theory simply due to the fact that
>>they are very young, but might grasp it later when they have more
>>detail to put to that theory.
>
>Do you mean you cannot teach grammatical structure to
>someone who has not learned a language? Nonsense.
In what language to you teach it then?
>You do not understand concepts. They are NOT the same as
>theory; one can learn the theory and have no understanding
>of the concepts, and vice versa.
Don't be speculative about what I do or do not know. I *taught*
concepts. I *argued* that is was lack of knowledge and understanding
of concepts that made the difference, being not surprised even when my
own daughter showed a decided lack of that knowledge in her studies in
physics.
James Dolan
the world wide wade <wadera...@comcast.remove13.net> wrote:
|In article <e016cc$1r...@odds.stat.purdue.edu>,
| hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
|
|> A former student told me that the biggest problem he had with
|> general topology was that he had learned metric topology, which is
|> a specialization of it, but that the details of the specialization
|> hid the general concept.
|
|That's hardly believable, as the transition from metric spaces to
|general topology is quite natural.
it's entirely believable. if you hadn't already demonstrated your
limitations in other discussions it would seem amazing that you don't
know that _some_ (not all) people, including an especially high
proportion of strongly creative mathematicians, experience a revulsion
towards anything that smacks of the baroque complication of "classical
analysis", and are pleasantly surprised to discover in contrast the
austere simplicity of its topological underpinnings.
|And if you haven't seen metric
|spaces, the axioms for point-set topology will appear like some
|arbitrary abstract nonsense from another planet.
grossly false; again you might have managed a true statement if you'd
confined yourself to describing the experiences and preferences of
those who share your own limitations.
|You keep repeating
|this little story as if it implied something for pedagogy; it
|doesn't.
agreed, but the details of the specialization hides the general
concept that herman keeps repeating all of his little stories as if
they implied something; they don't.
--
[e-mail address jdo...@math.ucr.edu]
Guess who
Rubin) wrote:
>The elementary and high school
>curricula are designed not to give the appropriate positive
>or negative feedbacks.
You are being purely argumentative. That is pure rubbish.
Virgil
Guess who <notreal...@here.com> wrote:
Rubin's statement is a bit ambiguous. While those curricula may not have
bee designed with that intent, the design may still have produced that
outcome. It is not clear which Rubin meant 'intent' or merely 'outcome'.
I would certainly argree with the 'outcome' inerpretation of his
comment, but not necessarily with the 'intent' interpretation.
Herman Rubin
The transition is not natural; the use of the metric is
what is actually confusing. Also, sequences are confusing;
the extension to nets requires getting rid of the idea that
a subsequence can be obtained from a sequence by striking
out terms. The classic example of a compact Hausdorff space
which is not sequentially compact shows where the problem
is, as well as many other points.
I myself did not really understand the topology of probability
distributions and random variables until these were extended
to non-metric spaces, where even the standard definition is
unclear, and has different versions.
As for "arbitrary abstract nonsense", this is what it takes
to understand mathematics, and even to be able to apply it
to "concrete" situations. Abstract ideas are NOT abstractions
of more concrete ones, but have a real meaning otherwise.
The process of generalization is difficult, requiring unlearning.
Specialization does not require anything of the sort.
Herman Rubin
Guess who <notreal...@here.com> wrote:
>On 24 Mar 2006 11:22:36 -0500, hru...@odds.stat.purdue.edu (Herman
>Rubin) wrote:
>>In article <m4p522tsf03cd3aq8...@4ax.com>,
>>Guess who <notreal...@here.com> wrote:
>>>On 23 Mar 2006 11:33:53 -0500, hru...@odds.stat.purdue.edu (Herman
>>>Rubin) wrote:
>>>>Concepts and structure need to come EARLY, so the students
>>>>can know why, and not just how.
>>>Not so; certainly not necessarily so, and far too sweeping a
>>>generalisation. You lose almost everyone if you pontificate. The
>>>young are generally not ready for theory simply due to the fact that
>>>they are very young, but might grasp it later when they have more
>>>detail to put to that theory.
>>Do you mean you cannot teach grammatical structure to
>>someone who has not learned a language? Nonsense.
>In what language to you teach it then?
One needs very little of a language. Scientists have
demonstrated that little vocabulary is learned before
the idea of grammatical structure is managed; there
has been an argument, with data to back it, that
children earlier than one year, with zero vocabulary,
can comprehend grammatical ideas.
Once one has an adequate amount to use to communicate,
entirely foreign grammar can be taught.
>>You do not understand concepts. They are NOT the same as
>>theory; one can learn the theory and have no understanding
>>of the concepts, and vice versa.
>Don't be speculative about what I do or do not know. I *taught*
>concepts. I *argued* that is was lack of knowledge and understanding
>of concepts that made the difference, being not surprised even when my
>own daughter showed a decided lack of that knowledge in her studies in
>physics.
What are the unrelated concepts of the integers, which
I have been mentioning? They do need to be tied together,
but they are totally distinct concepts. There are other
conceptual extensions, but these are very basic.
Also, the classical Euclidean geometry used intuition
only for the axioms (including some unstated ones), and
then was completely formal. This does not mean that SOME
"geometric intuition" may not be helpful; however, I saw
early that it was a mistake to rely on this, despite the
standard pedagogical saw about the importance. This is
the case even in many "geometric" situations.
Herman Rubin
The appropriate positive feedbacks are about understanding
and learning; this is completely opposed to trying to get
good grades. Learning is for the distant future, not the
present, and it is necessary to get the sometimes distasteful
basics before the applications.
As for the negative feedback, those who do not have the
ability to understand need to learn it earlier. Mental
abilities vary greatly, and are not as linear as the
educationists try to get people to believe. I have seen
students who seem good apparently run into complete
obstacles. And those who learn how to compute seem to
have great problems in ever understanding. It is often
like teaching a fanatical alchemist that the foundations
are wrong, and that chemistry has to be started anew.
Dave Rusin
James Dolan <jdo...@math-cl-n03.math.ucr.edu> wrote:
>in article <waderameyxiii-E2E...@comcast.dca.giganews.com>,
>the world wide wade <wadera...@comcast.remove13.net> wrote:
>|And if you haven't seen metric
>|spaces, the axioms for point-set topology will appear like some
>|arbitrary abstract nonsense from another planet.
>
>grossly false;
OK, I have a bright student uncorrupted by point-set topology before me.
I present the definition of a topology; the collection of open sets
is closed under _finite_ intersections but _arbitrary_ unions. The
student asks why on earth one would take such an asymmetrical set of
axioms. Your answer?
A bit later we have to decide what the morphisms of the category are.
I hope you don't consider it a corrupting previous specialization that
the student has already encountered homomorphisms of groups and rings.
So now we have topological spaces: sets and preferred subsets. We
define the topological maps to be: functions between the sets that, um,
do what?! you define the appropriate morphisms so that the INVERSE images
of the preferred sets in Y are preferred sets in X? Why on earth would
you do that? Your answer?
I'm all about not dwelling on minutiae that hide rather than highlight
What's Really Going On. That's cool. On the other hand, I can't imagine
hiding the origins of the definitions, the conjectures that prompted the
theorems, etc. I don't know about you but I'm not interested in preparing
desert-island mathematicians who have discovered all the consequences of
a set of axioms that no one cares about in the least. My students all
want to be part of a larger culture -- at least a mathematical one --
and they want to know why the goofy axioms I present might possibly
be connected to anything else at all. So I always spend some time on
historically-important special cases.
Guess I'm just doing it wrong then.
dave
James Dolan
dave rusin <ru...@vesuvius.math.niu.edu> wrote:
i have to question your reading comprehension if you think that your
questions here are somehow responsive to something i wrote. however
if we disregard the issue of what inspired your questions and just
consider them as dropped out of thin air for no particular reason then
i don't mind spending a minute or two answering a couple of them.
first consider what happens if you omit the cardinality restriction in
the definition of topology. namely, there's an elegant lemma (with
proof probably shorter than the statement of the lemma) that such
topologies on a set are precisely equivalent to pre-orders (which are
structures of a lower level of complexity, more directly accessible to
the intuition), and that a map is pre-order-preserving precisely in
case the inverse images of open sets are open.
it's then obvious that topologies in general are ideal refinements of
pre-orders, and that continuous maps in general are ideal refinements
of pre-order-preserving maps, and this provides the appropriate
geometric intuition for understanding topological spaces and
continuous maps as tools for studying "cohesion" in a context where
pre-orders are refined more and more finely without limit.
there's a lot more that can be said to help students understand the
details as well as the broad currents of ideas here and anyone who'd
like to pay me to say more of it is welcome to make an offer.
--
[e-mail address jdo...@math.ucr.edu]
toto
Rubin) wrote:
>One needs very little of a language. Scientists have
>demonstrated that little vocabulary is learned before
>the idea of grammatical structure is managed; there
>has been an argument, with data to back it, that
>children earlier than one year, with zero vocabulary,
>can comprehend grammatical ideas.
Herman, you do this constantly. What scientists? How many
studies? Have these studies been replicated? Where is this
data? For heaven's sake, what parents have even allowed
their children of less than a year old to be involved in this kind
of foolishness?
--
Dorothy
There is no sound, no cry in all the world
that can be heard unless someone listens ..
The Outer Limits
Herman Rubin
Dave Rusin <ru...@vesuvius.math.niu.edu> wrote:
>In article <e01oge$4u9$1...@glue.ucr.edu>,
>James Dolan <jdo...@math-cl-n03.math.ucr.edu> wrote:
>>in article <waderameyxiii-E2E...@comcast.dca.giganews.com>,
>>the world wide wade <wadera...@comcast.remove13.net> wrote:
>>|And if you haven't seen metric
>>|spaces, the axioms for point-set topology will appear like some
>>|arbitrary abstract nonsense from another planet.
>>grossly false;
>OK, I have a bright student uncorrupted by point-set topology before me.
>I present the definition of a topology; the collection of open sets
>is closed under _finite_ intersections but _arbitrary_ unions. The
>student asks why on earth one would take such an asymmetrical set of
>axioms. Your answer?
Give examples. In fact, give many of the other characterizations
of topological spaces; I do not call any of the definitions, since
they are equivalent.
If you are going to do one-dimensional topology first, do
it with intervals rather than a metric. The difference is
a great improvement in understanding, and a total lack of
reliance on the irrelevant arithmetic properties of the
real numbers. Unless algebraic properties are used, the
precise metric is an irrelevancy.
>A bit later we have to decide what the morphisms of the category are.
Morphisms in category theory are not the same as morphisms
dealing with object and sets. Isomorphism is a general
principle, and does not even depend on which system is used;
a bijection preserving all the properties being considered.
And a topological isomorphism (homeomorphism) between metric
spaces need not be an isometry, and usually is not.
>I hope you don't consider it a corrupting previous specialization that
>the student has already encountered homomorphisms of groups and rings.
Not every student who does analysis has done abstract algebra.
It is not a prerequisite.
>So now we have topological spaces: sets and preferred subsets. We
>define the topological maps to be: functions between the sets that, um,
>do what?! you define the appropriate morphisms so that the INVERSE images
>of the preferred sets in Y are preferred sets in X? Why on earth would
>you do that? Your answer?
There is more than one; one possibility is in using limits
of nets. A similar situation occurs in analysis, where
measure has the same property. Also, few examples will
show why one gets too much by using "open" rather than
"continuous".
>I'm all about not dwelling on minutiae that hide rather than highlight
>What's Really Going On. That's cool. On the other hand, I can't imagine
>hiding the origins of the definitions, the conjectures that prompted the
>theorems, etc. I don't know about you but I'm not interested in preparing
>desert-island mathematicians who have discovered all the consequences of
>a set of axioms that no one cares about in the least. My students all
>want to be part of a larger culture -- at least a mathematical one --
>and they want to know why the goofy axioms I present might possibly
>be connected to anything else at all. So I always spend some time on
>historically-important special cases.
None of this is left out. The historically important special
case may be pedagogically confusing. This is the case with
measure and integration, where the key spaces are discrete
spaces and what results from them by the limit process. The
first integration was computing a merchant's bill, and the
ancient Greek method of approaching area was using this idea
plus the idea of limit.
>Guess I'm just doing it wrong then.
One can have rigor without hiding the essential ideas.
However, the historical approach often makes things very
difficult, by introducing irrelevancies.
>dave
Herman Rubin
toto <scar...@wicked.witch> wrote:
>On 24 Mar 2006 21:10:22 -0500, hru...@odds.stat.purdue.edu (Herman
>Rubin) wrote:
>>One needs very little of a language. Scientists have
>>demonstrated that little vocabulary is learned before
>>the idea of grammatical structure is managed; there
>>has been an argument, with data to back it, that
>>children earlier than one year, with zero vocabulary,
>>can comprehend grammatical ideas.
>Herman, you do this constantly. What scientists? How many
>studies? Have these studies been replicated? Where is this
>data? For heaven's sake, what parents have even allowed
>their children of less than a year old to be involved in this kind
>of foolishness?
I do not recall the specific articles in _Science_.
The experiments are described, and I can easily
see that parents might be willing for their children
to engage in such.
Bob LeChevalier
>On 24 Mar 2006 21:10:22 -0500, hru...@odds.stat.purdue.edu (Herman
>Rubin) wrote:
>
>>One needs very little of a language. Scientists have
>>demonstrated that little vocabulary is learned before
>>the idea of grammatical structure is managed; there
>>has been an argument, with data to back it, that
>>children earlier than one year, with zero vocabulary,
>>can comprehend grammatical ideas.
>
>Herman, you do this constantly. What scientists? How many
>studies? Have these studies been replicated? Where is this
>data? For heaven's sake, what parents have even allowed
>their children of less than a year old to be involved in this kind
>of foolishness?
He seems to be arguing that because children who are a year old learn
correct grammar by absorption without explanation, that they could
similarly learn mathematical thinking by absorption without
explanation.
The flaw is that a two year old does not in fact "understand" any of
the rules that he follows; he just follows them, very concretely
(though the result looks like an abstraction to those who are thinking
abstractly). Mathematicians expect to understand the rules that they
follow, and learning the understanding is NOT something that young
kids tend to be able to do very easily. Young kids "understand"
grammatical structure in the same way that computers "understand" the
programs that they execute; young kids subconsciously "program
themselves" in the same way that programs running in computers can be
written to adapt to stimuli.
lojbab
James Dolan
james dolan <jdo...@math-rs-n03.math.ucr.edu> wrote:
to amplify a bit:
a nice space is triangulable. associated to a triangulation is the
pre-order "p belongs to the smallest simplex that q belongs to". the
topology is the ideal coarsest common refinement of the sequence of
pre-orders associated to a sequence of triangulations which are
subdivided more and more finely without limit. no metric is involved
and introducing one into the conceptual development would be worse
than useless for most sensible purposes. continuous maps have
simplicial approximations, which can be interpreted as
pre-order-preserving maps. the seemingly weird asymmetry between
unions and intersections is explained by the fact that the simplest
way of repairing the asymmetry in fact yields the simpler and more
useful and more beautiful concept of "pre-order", of which the concept
of "topology" is a deliberate generalization meant to include examples
arising as ideal coarsest common refinements of sequences of
increasingly fine pre-orders which naively have only the trivial
pre-order as their coarsest common refinement. the possibility of
repairing the asymmetry between unions and intersections in a less
beautiful way can be explored by anyone with the motivation to study
the resulting more general objects.
metric spaces are actually somewhat interesting objects, interpreted
as enriched categories of a sort, but they don't have much to do with
topology since the natural kinds of morphisms between them are pretty
different in character from the continuous maps.
students with different preferences can try different approaches to
topology. i was not promoting any one-size-fits-all approach; rather
i was pointing out how silly it was for wade ramey to doubt the
existence of _some_ students who are quite happy grasping the point of
topology without bothering with a detour through the red herring of
metric spaces. historical studies can be interesting and useful to
mathematicians but mostly with a good dose of -as-it-should-have-been
and metric spaces could arguably stand considerable de-emphasis.
--
[e-mail address jdo...@math.ucr.edu]
The World Wide Wade
jdo...@math-cl-n03.math.ucr.edu (James Dolan) wrote:
> in article <waderameyxiii-E2E...@comcast.dca.giganews.com>,
> the world wide wade <wadera...@comcast.remove13.net> wrote:
>
> |In article <e016cc$1r...@odds.stat.purdue.edu>,
> | hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
> |
> |> A former student told me that the biggest problem he had with
> |> general topology was that he had learned metric topology, which is
> |> a specialization of it, but that the details of the specialization
> |> hid the general concept.
> |
> |That's hardly believable, as the transition from metric spaces to
> |general topology is quite natural.
>
> it's entirely believable. if you hadn't already demonstrated your
> limitations in other discussions
LOL, I see you're still smarting over being called a
"preposterous gasbag". You need to get over that.
> it would seem amazing that you don't
> know that _some_ (not all) people, including an especially high
> proportion of strongly creative mathematicians,
> experience a revulsion
> towards anything that smacks of the baroque complication of "classical
> analysis", and are pleasantly surprised to discover in contrast the
> austere simplicity of its topological underpinnings.
Even if a huge proportion of strongly creative mathematicians are
"revulsed" by classical analysis in your imaginary world, they
should, by virtue of their big brains, be able to skate from
metric spaces to topological spaces with ease.
> |And if you haven't seen metric
> |spaces, the axioms for point-set topology will appear like some
> |arbitrary abstract nonsense from another planet.
>
> grossly false; again you might have managed a true statement if you'd
> confined yourself to describing the experiences and preferences of
> those who share your own limitations.
Right, I couldn't possibly understand a genius like yourself.
toto
I agree.
And, young children don't get that there are exceptions to rules
either. They overgeneralize the rules.
>lojbab
The World Wide Wade
jdo...@math-rs-n03.math.ucr.edu (James Dolan) wrote:
> i was pointing out how silly it was for wade ramey to doubt the
> existence of _some_ students who are quite happy grasping the point of
> topology without bothering with a detour through the red herring of
> metric spaces.
Of course I said no such thing. But don't let that get in the way
of your ongoing string of tirades.
Herman Rubin
Bob LeChevalier <loj...@lojban.org> wrote:
>toto <scar...@wicked.witch> wrote:
>>On 24 Mar 2006 21:10:22 -0500, hru...@odds.stat.purdue.edu (Herman
>>Rubin) wrote:
>>>One needs very little of a language. Scientists have
>>>demonstrated that little vocabulary is learned before
>>>the idea of grammatical structure is managed; there
>>>has been an argument, with data to back it, that
>>>children earlier than one year, with zero vocabulary,
>>>can comprehend grammatical ideas.
>>Herman, you do this constantly. What scientists? How many
>>studies? Have these studies been replicated? Where is this
>>data? For heaven's sake, what parents have even allowed
>>their children of less than a year old to be involved in this kind
>>of foolishness?
>He seems to be arguing that because children who are a year old learn
>correct grammar by absorption without explanation, that they could
>similarly learn mathematical thinking by absorption without
>explanation.
This is not what I said, and is not what the article
said. This article is in _Science_, the official
journal of the American Association for the Advancement
of Science. I believe the age was 11 months.
The World Wide Wade
hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
> In article <waderameyxiii-E2E...@comcast.dca.giganews.com>,
> The World Wide Wade <wadera...@comcast.remove13.net> wrote:
> >In article <e016cc$1r...@odds.stat.purdue.edu>,
> > hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
>
> >> A former student told me that the biggest problem he had with
> >> general topology was that he had learned metric topology,
> >> which is a specialization of it, but that the details of the
> >> specialization hid the general concept.
>
> >That's hardly believable, as the transition from metric spaces to
> >general topology is quite natural. And if you haven't seen metric
> >spaces, the axioms for point-set topology will appear like some
> >arbitrary abstract nonsense from another planet. You keep
> >repeating this little story as if it implied something for
> >pedagogy; it doesn't.
>
> The transition is not natural; the use of the metric is
> what is actually confusing.
A metric is a natural abstraction of distance. You study metric
spaces, you learn quickly about open sets and all the wonderful
things they can do for you. The transistion to topological spaces
seems very natural to me.
> Also, sequences are confusing;
They certainly are to calculus students. Let's teach them nets!
> the extension to nets requires getting rid of the idea that
> a subsequence can be obtained from a sequence by striking
> out terms. The classic example of a compact Hausdorff space
> which is not sequentially compact shows where the problem
> is, as well as many other points.
> I myself did not really understand the topology of probability
> distributions and random variables until these were extended
> to non-metric spaces, where even the standard definition is
> unclear, and has different versions.
> As for "arbitrary abstract nonsense", this is what it takes
> to understand mathematics, and even to be able to apply it
> to "concrete" situations.
Abstract, yes. Arbitrary, no.
Herman Rubin
>> in article <waderameyxiii-E2E...@comcast.dca.giganews.com>,
>> the world wide wade <wadera...@comcast.remove13.net> wrote:
>> |In article <e016cc$1r...@odds.stat.purdue.edu>,
>> | hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
>> |> A former student told me that the biggest problem he had with
>> |> general topology was that he had learned metric topology, which is
>> |> a specialization of it, but that the details of the specialization
>> |> hid the general concept.
>> |That's hardly believable, as the transition from metric spaces to
>> |general topology is quite natural.
>> it's entirely believable. if you hadn't already demonstrated your
>> limitations in other discussions
>LOL, I see you're still smarting over being called a
>"preposterous gasbag". You need to get over that.
>> it would seem amazing that you don't
>> know that _some_ (not all) people, including an especially high
>> proportion of strongly creative mathematicians,
>> experience a revulsion
>> towards anything that smacks of the baroque complication of "classical
>> analysis", and are pleasantly surprised to discover in contrast the
>> austere simplicity of its topological underpinnings.
I question whether most people working in classical
analysis, in any of its forms, now even learn general
topology. This was much less the case 30 years ago,
when there was far more emphasis on getting a basic
graduate education; it is almost back to the old prewar
specialization.
>Even if a huge proportion of strongly creative mathematicians are
>"revulsed" by classical analysis in your imaginary world, they
>should, by virtue of their big brains, be able to skate from
>metric spaces to topological spaces with ease.
No, the skating is not with ease, Situations which are
unique in metric spaces become very much not uniques in
general spaces, and can even not be so. On the other
hand, where they are similar, the lack of the metric
tricks make the proof much easier, even in metric spaces.
>> |And if you haven't seen metric
>> |spaces, the axioms for point-set topology will appear like some
>> |arbitrary abstract nonsense from another planet.
Not at all if properly presented. Precision does not
require obfuscation.
>> grossly false; again you might have managed a true statement if you'd
>> confined yourself to describing the experiences and preferences of
>> those who share your own limitations.
>Right, I couldn't possibly understand a genius like yourself.
>> |You keep repeating
>> |this little story as if it implied something for pedagogy; it
>> |doesn't.
>> agreed, but the details of the specialization hides the general
>> concept that herman keeps repeating all of his little stories as if
>> they implied something; they don't.
They don't make understanding easier? Take convergence in
probability on metric spaces; the usual definition, using
the metric, is often quite difficult to use, and does not
seem to generalize even to uniform spaces. On the other
hand, the form X_n -> Y in measure if for any open set U,
m({a: Y(a) \in U and X_n(a) \notin U}) -> 0. which is
equivalent if m is finite, the usual situation, is easier
to work with in the metric case. BTW, uniformities, which
are the extension of metrics, are in my opinion much easier
to understand.
Unless the metric is a "natural" one, such as in a normed
space, that a space is metrizable may be important, but
finding the metric not.
Serial Killfiler
>On Wed, 22 Mar 2006 18:00:16 -0500, Guess who
><notreal...@here.com> wrote:
>
>>Perhaps some "more traditional" methods of teaching might work to give
>>better results? ...and perhaps the computer/hand-held calculator are
>>not the magic pill as stated?
>
>Or perhaps not everyone is suited for college in the first place?
Well, you said it.
TSK
----------------------------------
"May those who damn us be damned."
alhuriy...@NOBOTSyahoo.com
Serial Killfiler
It's not rubbish at all. We mere high school teachers would never be
trusted to grade kids strictly upon what they know. Therefore, their
grades do not really measure their aptitudes as they should.
Guess who
<alXXh...@NOSPAMyahoo.com> wrote:
>On Fri, 24 Mar 2006 16:16:42 -0500, Guess who
><notreal...@here.com> wrote:
>
>>On 24 Mar 2006 12:37:28 -0500, hru...@odds.stat.purdue.edu (Herman
>>Rubin) wrote:
>>
>>>The elementary and high school
>>>curricula are designed not to give the appropriate positive
>>>or negative feedbacks.
>>
>>You are being purely argumentative. That is pure rubbish.
>
>It's not rubbish at all. We mere high school teachers would never be
>trusted to grade kids strictly upon what they know. Therefore, their
>grades do not really measure their aptitudes as they should.
I am a high school teacher retired, and dialogue with students was an
intricate and necessary part of the teaching process. In fact, that
was one of the reasons that parents and students of absentees could
never understand. When a child missed a class, he did not miss just
the material content, but the dialogue surrounding it by both teacher
and students. What IS digusting in general is the feedback required
which is entirely meaningless, such as "eraly warning reports' which
here at least were based upon past material bieng "reviewed",rather
than new, which would be much more descriptive.
Aptitude? That lies in the realm of psychology in general, and why in
industry there are, at least for positions of management, some hefty
psychological testing procedures. However, I am definitely in favour
of the teacher [who has been already tested to death in order to gain
the position in the first place] being able to decide the rightness or
wrongness of student placement within any given course of study.
Reasons for that require lengthy discussion, but basically, anyone who
has worked at anything for a lifetime should have some intuitive idea
of rightness and wrongness that can later be detailed. Mind, some
students make it simple to make such decisions about aptitude
Guess who
>>>The elementary and high school
>>>curricula are designed not to give the appropriate positive
>>>or negative feedbacks.
>>
>>You are being purely argumentative. That is pure rubbish.
>
>It's not rubbish at all. We mere high school teachers would never be
>trusted to grade kids strictly upon what they know. Therefore, their
>grades do not really measure their aptitudes as they should.
We mere high school teachers have our own limitations as well.
Aptitude can be subtle and hidden as well as clear and obvious. Some
who have struggled mightily with other courses in mathematic suddenly
bloom when taking statistics at university. It happens. I've also
seen students who suddenly saw the light of what they were really
studying; an awesome experience that keeps you coming back. However,
I agree that the experienced teacher should in general have much more
say in appropriate placement of students based upon observed apttude.
Pre-testing might prove to be instrumental in making such decisions,
but then here we go again on the roller coaster of standardised
objective testing vs subjective judgement. There will always be
mistakes, no matterwhat. However, respect for input from the teacher
would go a long way towards evening things out.
Herman Rubin
Guess who <notreal...@here.com> wrote:
>On Sun, 26 Mar 2006 08:37:04 -0600, Serial Killfiler
><alXXh...@NOSPAMyahoo.com> wrote:
>>On Fri, 24 Mar 2006 16:16:42 -0500, Guess who
>><notreal...@here.com> wrote:
>>>On 24 Mar 2006 12:37:28 -0500, hru...@odds.stat.purdue.edu (Herman
>>>Rubin) wrote:
>>>>The elementary and high school
>>>>curricula are designed not to give the appropriate positive
>>>>or negative feedbacks.
>>>You are being purely argumentative. That is pure rubbish.
>>It's not rubbish at all. We mere high school teachers would never be
>>trusted to grade kids strictly upon what they know. Therefore, their
>>grades do not really measure their aptitudes as they should.
>I am a high school teacher retired, and dialogue with students was an
>intricate and necessary part of the teaching process.
It can be a useful part, or totally useless. For a student
who quickly understands the material, it is more likely to
be the latter. For someone not that bright, it may well be
even worse than useless.
[Irrelevant comments about attendance deleted.]
>Aptitude? That lies in the realm of psychology in general, and why in
>industry there are, at least for positions of management, some hefty
>psychological testing procedures. However, I am definitely in favour
>of the teacher [who has been already tested to death in order to gain
>the position in the first place] being able to decide the rightness or
>wrongness of student placement within any given course of study.
Teachers may have been moderately tested for understanding
the trivia, keeping order, using multimedia materials,
running projects, and other irrelevant matters. What has
not been tested is understanding of the subject.
>Reasons for that require lengthy discussion, but basically, anyone who
>has worked at anything for a lifetime should have some intuitive idea
>of rightness and wrongness that can later be detailed. Mind, some
>students make it simple to make such decisions about aptitude
This is one of the most stupid statements made. As the golf
saying goes, "Practice makes perfect your errors." As the
important mathematical concepts are often totally omitted in
the curriculum, including now the college curriculum, the
one who has learned how to compute in special cases can do
nothing of the sort. Even faculty members who do not keep up
can fall into that trap; to understand, one must know why the
particular assumptions are made, and what happens without them.
Serial Killfiler
<notreal...@here.com> wrote:
>On Sun, 26 Mar 2006 08:37:04 -0600, Serial Killfiler
><alXXh...@NOSPAMyahoo.com> wrote:
>
>>On Fri, 24 Mar 2006 16:16:42 -0500, Guess who
>><notreal...@here.com> wrote:
>>
>>>On 24 Mar 2006 12:37:28 -0500, hru...@odds.stat.purdue.edu (Herman
>>>Rubin) wrote:
>>>
>>>>The elementary and high school
>>>>curricula are designed not to give the appropriate positive
>>>>or negative feedbacks.
>>>
>>>You are being purely argumentative. That is pure rubbish.
>>
>>It's not rubbish at all. We mere high school teachers would never be
>>trusted to grade kids strictly upon what they know. Therefore, their
>>grades do not really measure their aptitudes as they should.
>
>I am a high school teacher retired, and dialogue with students was an
>intricate and necessary part of the teaching process. In fact, that
>was one of the reasons that parents and students of absentees could
>never understand. When a child missed a class, he did not miss just
>the material content, but the dialogue surrounding it by both teacher
>and students.
I have been teaching French for years, so you aren't telling me
anything I don't know. It's hard to make some parents understand
that mountains of worksheets simply cannot substitute for my
instruction. They seem to think I say it out of conceit.
>What IS digusting in general is the feedback required
>which is entirely meaningless, such as "eraly warning reports' which
>here at least were based upon past material bieng "reviewed",rather
>than new, which would be much more descriptive.
The best feedback I can give is in composition and oral proficiency
tests. These will really tell you how efficiently you are
communicating and, with oral interviews, if you tape them you can get
as specific as judging them on the sounds and intonation patterns that
most clearly distinguish French French from Atlanta French. However
these are the grades I am constantly pressured to inflate... because
Mary "tried" and Bill was "absent" and Mark had baseball practice and
Lucy broke up with her boyfriend, etc. etc.
>Aptitude? That lies in the realm of psychology in general, and why in
>industry there are, at least for positions of management, some hefty
>psychological testing procedures. However, I am definitely in favour
>of the teacher [who has been already tested to death in order to gain
>the position in the first place] being able to decide the rightness or
>wrongness of student placement within any given course of study.
>Reasons for that require lengthy discussion, but basically, anyone who
>has worked at anything for a lifetime should have some intuitive idea
>of rightness and wrongness that can later be detailed. Mind, some
>students make it simple to make such decisions about aptitude
Aptitude, like intelligence, is plastic. Whatever you work at
produces mental growth, draws upon and expands your existing
aptitudes. Growth will happen-- only the rate and subjective ease
will vary. But because grades are worth money, you are in for trouble
if you use them to measure actual achievement. You are expected to
provide customer service, not an assessment.
TSK
----------------------------------
"May those who damn us be damned."
alhuriy...@NOBOTSyahoo.com
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fishfry
Serial Killfiler <alXXh...@NOSPAMyahoo.com> wrote:
Every time I see this endless thread, I think, "... and the other 65%
have no clue!"
Reef Fish
fishfry wrote:
Your name was the only thing that attracted me to read what you had
to say about what "Serial Killfiler" had to say. ;-)
Are you suggesting that 65 + 45 = 100?
While others wondered why: Only 45% of the students were prepared for
math
Killfiler seemed to have something much more interesting and
substantial
than you had to say.
>>What IS digusting in general is the feedback required
>>which is entirely meaningless, such as "eraly warning reports' which
>>here at least were based upon past material bieng "reviewed",rather
>>than new, which would be much more descriptive.
KF " The best feedback I can give is in composition and oral
proficiency
tests. These will really tell you how efficiently you are
communicating and, with oral interviews, if you tape them you can get
as specific as judging them on the sounds and intonation patterns that
most clearly distinguish French French from Atlanta French. However
these are the grades I am constantly pressured to inflate... because
Mary "tried" and Bill was "absent" and Mark had baseball practice and
Lucy broke up with her boyfriend, etc. etc. "
Bah!!
The best feedback I gave my college students is in what they scored
on a well-thought out, comprehensive 1-hr exam (open book and
open notes -- nothing to memorize). It took me about 30 hours to
make up one such test.
I actually had students who score less than ZERO on such a test
(in which the expected value of guessing ALL T/F and Multiple
Choice questions is actually POSITIVE; and there were problems
involving setup and verbal explanations in which partial credits
were given).
A NEGATIVE Total Score (or any other score for that matter) were
excellent feedbacks to the students.
KF: "Aptitude, like intelligence, is plastic. "
A bewildering metaphor!
KF> But because grades are worth money,
Since when? Grades are worthless in schools and classes in which
everyone gets the obligatory "A"s.
KF> you are in for trouble if you use them to measure actual
achievement.
KF> You are expected to provide customer service, not an assessment.
That's almost unversally true now, in what's euphemistically called
"institutes of higher education". It's only worse in lower education.
:-)
-- Bob.
PATRICIA BURNS
> fishfry wrote:
> > Every time I see this endless thread, I think, "... and the other 65%
> > have no clue!"
> Reef Fish wrote:
> Are you suggesting that 65 + 45 = 100?
>
> While others wondered why: Only 45% of the students were prepared for
> math
>
> Killfiler seemed to have something much more interesting and
> substantial
> than you had to say.
I found fishfry's tidbit very amusing. Correcting his/her math only
spoils the joke.
--
Patricia Burns
(Just one s)
Reef Fish
Sorry about missing your k.12.chat mentality of a joke. I've seen it
too
many times where it was no joke. Since I don't know fishfry from
fish 'n chips, I naturally assumed that s/he was one of the k.12 or
pre-kintergarden teachers who have difficulty with double digit
arithmetic.
I have enough trouble with the college students and teachers making
the same 'rithmetic errors. :) They are the "graduates" of the
kind
of classes killfiler and I talked about -- everyone expects, and most
get
A's for paying the tuition -- even attendance is not required, as in
k.12.
I don't find anything amusing about finding "tree stumps" in class
disguised as "college students".
-- Bob.
Reef Fish
Bob LeChevalier wrote:
> toto <scar...@wicked.witch> wrote:
> >On 24 Mar 2006 21:10:22 -0500, hru...@odds.stat.purdue.edu (Herman
> >Rubin) wrote:
> >
> >>One needs very little of a language. Scientists have
> >>demonstrated that little vocabulary is learned before
> >>the idea of grammatical structure is managed; there
> >>has been an argument, with data to back it, that
> >>children earlier than one year, with zero vocabulary,
> >>can comprehend grammatical ideas.
> >
> >Herman, you do this constantly. What scientists? How many
> >studies? Have these studies been replicated? Where is this
> >data? For heaven's sake, what parents have even allowed
> >their children of less than a year old to be involved in this kind
> >of foolishness?
>
> He seems to be arguing that because children who are a year old learn
> correct grammar by absorption without explanation, that they could
> similarly learn mathematical thinking by absorption without
> explanation.
>
> The flaw is that a two year old does not in fact "understand" any of
> the rules that he follows; he just follows them, very concretely
> (though the result looks like an abstraction to those who are thinking
> abstractly).
First of all, Herman seems excessively gullible about one article of
which he couldn't quite recall.
The idea of young children understand grammatical ideas before
vocabulary has to have come from someone who is linguistically
challenged. The grammatical structure of Romance languages
(French, Spanish) and Germanic languages (German) and their
derivatives from Latin, such as English, are vastly different.
Children
who are less than 6 years old should have no difficulty being multi
lingual in English, French, Spanish, German, and even Chinese.
The older one gets, the more difficult it is to learn.
I was told by a Berlitz teacher that I tried to THINK too much about
the grammar of Spanish (when I already learned those in French,
German, and English). I was no match for any 6 year old.
In fact, when I was 6 years old, I was multi-lingual in four dialects
of Chinese -- each of which is as different as German, French,
and English.
Young children have a completely different way of learning a
language, by "imitation of rules" rather than abstraction of rules.
Vocabulary certainly precedes grammar.
At Yale, there is a tall science building called the Kline Tower.
The mother of a German kid mused when her son couldn't
understand why the tower was "Klein" when the word means
"small" in German. :-) The kid had no trouble speaking
English and German fluently. I had the hardest time learning
why every inanimate object is male, female, or neuter in German,
and how to look for the separable prefixes and suffixes that may
be a page or two away. Kids NEVER had that kind of problem
in learning German.
Scientist are often blinded by their own prejudices and ignorance
in conjecturing and testing the untestible, as in less than 1-yr olds.
But often they get GRANTS to do the silliness, if they can BS
enough pages in application for the grant.
-- Bob.
Bob LeChevalier
There have been multiple articles, but they simply did not say what
Herman thinks it said. It said that the infants had shown that they
had learned grammatical rules by some sort of pattern identification,
not that the could "comprehend grammatical ideas" which suggests that
they consciously could think about those rules.
Here is probably the article Herman meant, since it was in Science
http://www.psych.nyu.edu/gary/marcusArticles/marcus%20et%20al%201999%20science.pdf
and here are some of the multitude of commentaries on the
interpretation of the results.
http://lcnl.wisc.edu/people/marks/courses/lang&mind/6marcusLetters.html
http://cnl.psych.cornell.edu/abstracts/transfer-learning.html
and a related article by the original author
http://www.psych.nyu.edu/gary/marcusArticles/marcus%202000%20cdps.pdf
Here is another reporting on experiments with somewhat older infants.
http://www.associatedcontent.com/article/23681/artificial_grammar_learning_by_1yearolds.html
>The idea of young children understand grammatical ideas before
>vocabulary has to have come from someone who is linguistically
>challenged.
They can *recognize* simple grammatical rules at a time fairly close
to when they start to *recognize* that particular words have meaning.
The issue is whether pattern recognition is "understanding". I didn't
even know what a differential equation was, when I "tutored" a kid who
was reading a textbook section on solving 2nd order linear
differential equations - I recognized the pattern of the quadratic
formula in the method of solution. That doesn't mean that I had any
clue as to why the quadratic formula could be used, or even what
"solution" meant other than getting the right answer to the problem,
but having recognized the pattern that the other kid had missed, HE
was able to better understand.
Thus clearly pattern recognition is a useful tool in abstraction, but
I don't think it constitutes "understanding".
>Young children have a completely different way of learning a
>language, by "imitation of rules" rather than abstraction of rules.
Tough call because Herman uses a vague definition of "abstraction".
Clearly They must DO some kind of abstract pattern recognition in
order to be able to imitate rules, since that seems to be how kids
learn which rules to imitate.
>Vocabulary certainly precedes grammar.
>
>At Yale, there is a tall science building called the Kline Tower.
>The mother of a German kid mused when her son couldn't
>understand why the tower was "Klein" when the word means
>"small" in German. :-)
And yet he understood that Klein was modifying Tower and not vice
versa (there are languages where the adjective comes after the noun).
>Scientist are often blinded by their own prejudices and ignorance
>in conjecturing and testing the untestible, as in less than 1-yr olds.
>
>But often they get GRANTS to do the silliness, if they can BS
>enough pages in application for the grant.
But the research wasn't silly - it just wasn't testing what Herman
seems to think it was testing.
lojbab
Pubkeybreaker
Dom wrote:
> Los Angeles Times Mar 15, 2006 Page B9
>
> CSU Freshmen Face Challenges; Only 45% of the students were prepared
> for math and English studies at college level, report says
> Author(s): Cynthia H. Cho
>
> Document URL:
> http://proquest.umi.com/pqdweb?did=1003262501&Fmt=3&clientId=16778&RQT=309&VName=PQD
>
> CORRECTION: SEE CORRECTION APPENDED; Remedial classes -- An article
> Wednesday in California about the California State University system
> described the number of students who benefited from English and math
> remedial classes. The article said, "Of the freshmen who enrolled in
> the fall of 2004 and needed remediation,
<snip>
Those needing remedial courses should be required to take them at
a community college, and NOT at a state university that is supported
by tax money.
These students should not have been accepted in the first place.
And I doubt that the problem is restricted to just math and English.
I strongly suspect that most of these students simply lacked the
dedication and intellectual maturity required at any college in any
subject.
Too many students go to college just to party and have a good time.
Maybe if they had to pay for their own education, rather than just
partying at mommy's and daddy's expense, they would actually dedicate
themselves to LEARNING.
Michael Stemper
In article <e02vhb$q1a$1...@news.math.niu.edu>, Dave Rusin writes:
>In article <e01oge$4u9$1...@glue.ucr.edu>, James Dolan <jdo...@math-cl-n03.math.ucr.edu> wrote:
>>in article <waderameyxiii-E2E...@comcast.dca.giganews.com>, the world wide wade <wadera...@comcast.remove13.net> wrote:
>>|And if you haven't seen metric
>>|spaces, the axioms for point-set topology will appear like some
>>|arbitrary abstract nonsense from another planet.
>>
>>grossly false;
>
>OK, I have a bright student uncorrupted by point-set topology before me.
>I present the definition of a topology; the collection of open sets
>is closed under _finite_ intersections but _arbitrary_ unions. The
>student asks why on earth one would take such an asymmetrical set of
>axioms.
Yup, that'd be me.
I'd gone through chapter 3 of my topology book, which covered metric
spaces, and was just fine. I could prove things about metric spaces,
and mappings from one to another. Felt fairly confident.
I got to chapter 4, which introduced topologies. Unlike the previous
chapter, there was no motivational material -- just the definition
of a "topology". I did, indeed, ask myself the question of "why
arbitrary unions, but only finite intersections?" The first thought
to come to my mind was that it was to keep the empty set from cropping
up its ugly head. But, no, the empty set was explicity included. Then,
the set itself was explicitly included, as well. Where'd that come
from? No way to tell, at least from the text.
After puzzling it over for a few weeks (my Usenet access was gone at
the time), I finally set aside the topology book and bought a book
on algebra, instead.
--
Michael F. Stemper
#include <Standard_Disclaimer>
A preposition is something that you should never end a sentence with.
A N Niel
Stemper <mste...@siemens-emis.com> wrote:
>
> After puzzling it over for a few weeks (my Usenet access was gone at
> the time), I finally set aside the topology book and bought a book
> on algebra, instead.
So I hope that algebra book did not start out: A group is a set with a
binary operation satisfying these axioms...
Michael Stemper
<g> No, it started out with a few examples of groups and abstracted the
properties from them. *Then* it gave the formal definition.
--
Michael F. Stemper
#include <Standard_Disclaimer>
COFFEE.SYS not found. Abort, Retry, Fail?
A N Niel
Stemper <mste...@siemens-emis.com> wrote:
> >So I hope that algebra book did not start out: A group is a set with a
> >binary operation satisfying these axioms...
>
> <g> No, it started out with a few examples of groups and abstracted the
> properties from them. *Then* it gave the formal definition.
And you can find topology texts that start out with examples of
topologies and abstract the properties (arbitrary unions but only
finite intersections) from them.
I wonder if Herman Rubin is reading this...He always says that the best
technique for instruction is to begin with the abstract, then
specialize...
Dave L. Renfro
> I'd gone through chapter 3 of my topology book, which covered
> metric spaces, and was just fine. I could prove things about
> metric spaces, and mappings from one to another. Felt fairly
> confident.
>
>
> I got to chapter 4, which introduced topologies. Unlike the
> previous chapter, there was no motivational material -- just
> the definition of a "topology". I did, indeed, ask myself
> the question of "why arbitrary unions, but only finite
> intersections?"
The following book is excellent for someone who wants to go
from the specific to the general:
Robert Herman Kasriel, "Undergraduate Topology", Krieger
Publishing Company, 1971, xiv + 285 pages.
There's an extensive chapter on topological ideas in R^n:
Euclidean distance properties, open and closed sets,
limit points, continuous functions (and equivalence of
epsilon/delta, sequence, and open set formulations of
continuity), several types of connectedness, compactness
(including limit point compactness, finite open covering
kind, and others), and much more.
Then there's a lengthy chapter that goes through essentially
the same topics for metric spaces, in which some (but not all)
of the earlier equivalences are no longer equivalences.
There's also a lot of motivation for why one would want
to consider the generalization to a metric space, including
applications to existence theorems using fixed points of
contraction operators on certain function spaces.
Finally, at least halfway through the book if not more,
topological spaces are introduced. Again, for the third
time now, essentially the same topics as above are covered,
in which even more of the earlier equivalences wind up
no longer being equivalences.
I think this is an excellent text for someone to read on
their own, especially if they haven't had an advanced
calculus course where much of the R^n material is often
covered. In fact, I read through about the first 85% of
this book as an independent study reading course from
a topologist at a nearby college when I was in high
school. It's probably a bit too repetitious for someone
with a fairly strong background, but for me at the time
and for you (given what you said), I think this book
was/would-be a very good fit.
Dave L. Renfro
Herman Rubin
Reef Fish <Large_Nass...@Yahoo.com> wrote:
>Bob LeChevalier wrote:
>> toto <scar...@wicked.witch> wrote:
>> >On 24 Mar 2006 21:10:22 -0500, hru...@odds.stat.purdue.edu (Herman
>> >Rubin) wrote:
>> >>One needs very little of a language. Scientists have
>> >>demonstrated that little vocabulary is learned before
>> >>the idea of grammatical structure is managed; there
>> >>has been an argument, with data to back it, that
>> >>children earlier than one year, with zero vocabulary,
>> >>can comprehend grammatical ideas.
.................
>First of all, Herman seems excessively gullible about one article of
>which he couldn't quite recall.
I can recall the article; I cannot recall the issue of
_Science_ in which it occurred. It was also referred
to in _U S News and World Report_.
>The idea of young children understand grammatical ideas before
>vocabulary has to have come from someone who is linguistically
>challenged. The grammatical structure of Romance languages
>(French, Spanish) and Germanic languages (German) and their
>derivatives from Latin, such as English, are vastly different.
Vastly? Not at all. The way in which the parts of speech
are put together does differ in detail, but not much in
concept, in the Indo-European family. I am not that much
of a linguist, but I am familiar with the grammatical
structures of all the languages listed above (I can read
all of them), and somewhat with that of Russian and other
IE languages. I can also compare them to the different
structures, but still similar ideas, of the Semitic
languages, and the differences are not such as to cause as
great problems as idiomatic expressions do.
>Children
>who are less than 6 years old should have no difficulty being multi
>lingual in English, French, Spanish, German, and even Chinese.
>The older one gets, the more difficult it is to learn.
They have just as much problem with detail confusion.
In reading or listening to a language, grammatical details
are not that much of a problem; in writing or speaking,
they definitely are. I have read mathematical papers in
Latin, Italian, Portuguese, and Romanian, never having
taken any of those languages.
>I was told by a Berlitz teacher that I tried to THINK too much about
>the grammar of Spanish (when I already learned those in French,
>German, and English). I was no match for any 6 year old.
In speaking or reading? My one-year French course gave me
a reading vocabulary larger than the speaking vocabulary of
a 6 year old native speaker. I did carry on discussions in
which the other person spoke French and I spoke English.
BTW, that course did all the grammar in less than 1/2
academic year.
>In fact, when I was 6 years old, I was multi-lingual in four dialects
>of Chinese -- each of which is as different as German, French,
>and English.
>Young children have a completely different way of learning a
>language, by "imitation of rules" rather than abstraction of rules.
>Vocabulary certainly precedes grammar.
I suggest you read articles by scientists. Children learn
regular rules, and then the irregularities; that is why
phonics is far better at teaching reading than the whole
word method.
>At Yale, there is a tall science building called the Kline Tower.
>The mother of a German kid mused when her son couldn't
>understand why the tower was "Klein" when the word means
>"small" in German. :-)
One can easily have a 6-footer named "Small" or a 5-footer
named "Gross". This happens in any language.
The kid had no trouble speaking
>English and German fluently. I had the hardest time learning
>why every inanimate object is male, female, or neuter in German,
>and how to look for the separable prefixes and suffixes that may
>be a page or two away. Kids NEVER had that kind of problem
>in learning German.
Are you so sure? I had no problem with learning about
grammatical gender, and there are more kinds than that.
Many languages have only "masculine" and "feminine",
and their speakers are quite aware that gender is not
the same as biological sex. There may be some changes
to drop some endings, but speakers of those languages
do not object to "hurricane" because its first syllable
is pronounced the same as "her".
>Scientist are often blinded by their own prejudices and ignorance
>in conjecturing and testing the untestible, as in less than 1-yr olds.
I suggest you read the paper before jumping to conclusions.
>But often they get GRANTS to do the silliness, if they can BS
>enough pages in application for the grant.
>-- Bob.
--
Reef Fish
Here, we are obviously not speaking of the same meanings of the
terms "detail", "concept", and "structure", linguistically speaking!
The fact that Germanic and Romance languages are vastly
different in those respect are well-known.
> >Children
> >who are less than 6 years old should have no difficulty being multi
> >lingual in English, French, Spanish, German, and even Chinese.
> >The older one gets, the more difficult it is to learn.
>
> They have just as much problem with detail confusion.
> In reading or listening to a language, grammatical details
> are not that much of a problem; in writing or speaking,
> they definitely are.
I was speaking of their SPEAKING ability in those languages. Not
many children read or write well at or below that age.
> I have read mathematical papers in
> Latin, Italian, Portuguese, and Romanian, never having
> taken any of those languages.
That's because it's the TYPE of mathematical papers you read,
especially if the mathematical content is something with which you
are already familiar. In some mathematical journals, you can throw
away ALL the words and leave only the symbols and equations,
you can probably read it. In that case, naming the languages is
not even necessary. I can probably read a few of those papers
in Outer Mongolian too. ;)
L.J.Savage has written four papers in Italian, totalling over 100
pages,
on Bayesian statistics. The number of equations and mathematical
symbols in those 100+ pages total less than half a page, if that much.
I challenge you to make a coherent translation/paraphrase/summary
of any one of thoe 100+ pages!
> >I was told by a Berlitz teacher that I tried to THINK too much about
> >the grammar of Spanish (when I already learned those in French,
> >German, and English). I was no match for any 6 year old.
>
> In speaking or reading?
In speaking of course. Berlitz is the "total immersion" method in
which
both teacher and students speak ONLY in the language in which the
students knew absolutely NOTHING to begin with, and reach some
proficiency after a short course of limited number of hours. Just
like
kids learn how to speak a foreign language. Thus,"reading" in Berlitz
is an oxymoron. In practice, unfortunately, the instructors cheat and
sneak in some English in class as well as Berlitz books -- which is
contradictory to the founding philosophy of Maximilien Berlitz.
> My one-year French course gave me
> a reading vocabulary larger than the speaking vocabulary of
> a 6 year old native speaker.
Sure. No 6 year old would start his speaking with "this is a blue
pen".
That's why most of the traditional courses in foreign languages are
worthless, for ordinary or scientific use.
> >In fact, when I was 6 years old, I was multi-lingual in four dialects
> >of Chinese -- each of which is as different as German, French,
> >and English.
>
> >Young children have a completely different way of learning a
> >language, by "imitation of rules" rather than abstraction of rules.
> >Vocabulary certainly precedes grammar.
>
> I suggest you read articles by scientists.
Unfortunately, I read too many of them. Now everyone calls themselves
a scientist and an engineer. A garbage pick up man is a "sanitation
engineer", and the garbage department is full of "sanitation disposal
scientists"! :-) But the behavioral scientists produce MUCH MORE
garbage than all the sanitation engineers in the world put together.
What were you saying, Herman, about scientists? ;-/
> >At Yale, there is a tall science building called the Kline Tower.
> >The mother of a German kid mused when her son couldn't
> >understand why the tower was "Klein" when the word means
> >"small" in German. :-)
>
> One can easily have a 6-footer named "Small" or a 5-footer
> named "Gross". This happens in any language.
You missed tht point that Kline was a proper name in Kline Tower,
and the kid, in his spoken language knowledge naturally took
Kline to be an adjective, qualifying the noun Tower, hence small
tower, without having to understand any grammatical structure of
what is a noun and what is an adjective. But the word KLEIN
means "small" in whatever form of speech to the kid. Hence
vocabulary over grammatical structure.
Your example does not even FIT that analogy. If a kid hears
"Herman Small is a basketball player", he probably would understood
immediately that the speaker wasn't talking about the SIZE of Herman!
>
> The kid had no trouble speaking
> >English and German fluently. I had the hardest time learning
> >why every inanimate object is male, female, or neuter in German,
> >and how to look for the separable prefixes and suffixes that may
> >be a page or two away. Kids NEVER had that kind of problem
> >in learning German.
>
> Are you so sure?
Sure in the sense that if a kid took 1/10 as long as I needed to learn
the conjugation of ordinary verbs and the dem-die-das matrix
associated with objects, they would not have learned to speak
a word before they are 10.
> I had no problem with learning about
> grammatical gender, and there are more kinds than that.
> Many languages have only "masculine" and "feminine",
> and their speakers are quite aware that gender is not
> the same as biological sex. There may be some changes
> to drop some endings, but speakers of those languages
> do not object to "hurricane" because its first syllable
> is pronounced the same as "her".
Confusion of a different kind..
>
> >Scientist are often blinded by their own prejudices and ignorance
> >in conjecturing and testing the untestible, as in less than 1-yr olds.
>
> I suggest you read the paper before jumping to conclusions.
I would agree with you if it's about 6 year olds, because by that
age, I was already in the 3rd grade, having passed a written
entrance exam.
But LESS than 1-yr olds? The only ones the scientists fooled are
themselves and the gullible!
Herman Rubin
In article <1143567470....@i40g2000cwc.googlegroups.com>,
Pubkeybreaker <Robert_s...@raytheon.com> wrote:
>Dom wrote:
>> Los Angeles Times Mar 15, 2006 Page B9
>> CSU Freshmen Face Challenges; Only 45% of the students were prepared
>> for math and English studies at college level, report says
>> Author(s): Cynthia H. Cho
>> Document URL:
>> http://proquest.umi.com/pqdweb?did=1003262501&Fmt=3&clientId=16778&RQT=309&VName=PQD
......................
>Those needing remedial courses should be required to take them at
>a community college, and NOT at a state university that is supported
>by tax money.
They should be required to take them at a place which gives
quality remedial courses, not dumbed down.
>These students should not have been accepted in the first place.
True, but there is no way the colleges can know that they are
needed. Reading transcripts, there is no way to tell what
material was covered in a course at any level.
>And I doubt that the problem is restricted to just math and English.
>I strongly suspect that most of these students simply lacked the
>dedication and intellectual maturity required at any college in any
>subject.
Much of it is due to the fact that the material needed was not
presented to the student. One of my colleagues told me he was
mentoring a minority student having difficulties, often with
easy problems. He was; nobody had told him that he could use
symbols to formulate problems.
The problem is that most remedial courses are taught on the
assumption that the student was not good enough to get it
the first time, and therefore it should be at a weak pace.
The results are what you would expect.
>Too many students go to college just to party and have a good time.
The solution for that is clear; the colleges need to maintain
standards. They do not; they continue the elhi strategy of
teaching what they thing the weak students in the class can
manage.
>Maybe if they had to pay for their own education, rather than just
>partying at mommy's and daddy's expense, they would actually dedicate
>themselves to LEARNING.
It probably is too late. They learned in elhi that socialization
comes before learning.
Herman Rubin
In article <1143586499.4...@i40g2000cwc.googlegroups.com>,
Reef Fish <Large_Nass...@Yahoo.com> wrote:
.................
I had no problems with the passage from the Romance languages
to German. English grammar comes mainly from German, not Latin,
and the vocabulary is common words from German, uncommon from
Latin, mainly through Norman French.
So German puts all of the parts of the verb except the
inflected part at the end of the clause, and in dependent
clauses even that, and in opposite order. This gave me
no problems at all.
>> >Children
>> >who are less than 6 years old should have no difficulty being multi
>> >lingual in English, French, Spanish, German, and even Chinese.
>> >The older one gets, the more difficult it is to learn.
>> They have just as much problem with detail confusion.
>> In reading or listening to a language, grammatical details
>> are not that much of a problem; in writing or speaking,
>> they definitely are.
>I was speaking of their SPEAKING ability in those languages. Not
>many children read or write well at or below that age.
The bright ones should at least read well before that age.
Speaking, not as a native, can be picked up in a few months
of immersion after the structure of the language is known.
>> I have read mathematical papers in
>> Latin, Italian, Portuguese, and Romanian, never having
>> taken any of those languages.
>That's because it's the TYPE of mathematical papers you read,
>especially if the mathematical content is something with which you
>are already familiar.
It probably is easier, knowing what the subject matter
is and the concepts.
1
In some mathematical journals, you can throw
>away ALL the words and leave only the symbols and equations,
>you can probably read it.
Definitely NOT. I know a very small amount of Russian,
and I can pick out the international words fairly easily.
But I cannot read a Russian paper in probability, which
is easier than statistics.
In that case, naming the languages is
>not even necessary. I can probably read a few of those papers
>in Outer Mongolian too. ;)
Try it; you will find it harder than you think.
>L.J.Savage has written four papers in Italian, totalling over 100
>pages,
>on Bayesian statistics. The number of equations and mathematical
>symbols in those 100+ pages total less than half a page, if that much.
>I challenge you to make a coherent translation/paraphrase/summary
>of any one of thoe 100+ pages!
When I reviewed papers for _Mathematical Reviews_, I got a
few in Italian. One was in mathematical economics, and a
couple of the economic terms gave me some difficulty.
>> >I was told by a Berlitz teacher that I tried to THINK too much about
>> >the grammar of Spanish (when I already learned those in French,
>> >German, and English). I was no match for any 6 year old.
>> In speaking or reading?
>In speaking of course. Berlitz is the "total immersion" method in
>which
>both teacher and students speak ONLY in the language in which the
>students knew absolutely NOTHING to begin with, and reach some
>proficiency after a short course of limited number of hours. Just
>like
>kids learn how to speak a foreign language.
Kids learn how to speak a language that way because they
cannot do it any other way. A literate person can use
reading and direct structure to speed up the acquisition
of much at once using the grammatical structure.
Also, one does not have to think of the proper grammatical
structure in reading, just as one does not have to go back
to the axioms every time a problem is being discussed. I
do not often do word-for-word translating in any foreign
language; one can try to think in the language. This is
not as difficult as one thinks if the process does not
proceed by memorization.
Thus,"reading" in Berlitz
>is an oxymoron. In practice, unfortunately, the instructors cheat and
>sneak in some English in class as well as Berlitz books -- which is
>contradictory to the founding philosophy of Maximilien Berlitz.
>> My one-year French course gave me
>> a reading vocabulary larger than the speaking vocabulary of
>> a 6 year old native speaker.
>Sure. No 6 year old would start his speaking with "this is a blue
>pen".
Neither did the French course I took. It was intended for
capable college students, who could use their knowledge of
English to quickly learn the structure, pronunciation, and
some of the idiosyncracies of French.
>That's why most of the traditional courses in foreign languages are
>worthless, for ordinary or scientific use.
Those which crawl are worthless. There used to be courses
for graduate students, typically one basic term in a language,
and one term either in science or art. Most students needed
only the first term to pass the reading exam, which generally
consisted of the introductions of a couple of articles in the
field. This was the case of my exam in German, and it was as
expected, with essentially no formulas, and maybe 5% technical
terms. My French exam was a 600 word philosophical comparison
of the relative merits of analysis and synthesis in proof,
no mathematics whatever.
>> >In fact, when I was 6 years old, I was multi-lingual in four dialects
>> >of Chinese -- each of which is as different as German, French,
>> >and English.
>> >Young children have a completely different way of learning a
>> >language, by "imitation of rules" rather than abstraction of rules.
>> >Vocabulary certainly precedes grammar.
>> I suggest you read articles by scientists.
>Unfortunately, I read too many of them. Now everyone calls themselves
>a scientist and an engineer. A garbage pick up man is a "sanitation
>engineer", and the garbage department is full of "sanitation disposal
>scientists"! :-) But the behavioral scientists produce MUCH MORE
>garbage than all the sanitation engineers in the world put together.
>What were you saying, Herman, about scientists? ;-/
Are behavioral scientists scientists? The articles I am
discussing are not written by behavioral or "social"
scientists, but by those trying to understand how the
brain works. Their results are almost entirely the
opposite of social or "educational" pundits.
>> >At Yale, there is a tall science building called the Kline Tower.
>> >The mother of a German kid mused when her son couldn't
>> >understand why the tower was "Klein" when the word means
>> >"small" in German. :-)
>> One can easily have a 6-footer named "Small" or a 5-footer
>> named "Gross". This happens in any language.
>You missed tht point that Kline was a proper name in Kline Tower,
>and the kid, in his spoken language knowledge naturally took
>Kline to be an adjective, qualifying the noun Tower, hence small
>tower, without having to understand any grammatical structure of
>what is a noun and what is an adjective. But the word KLEIN
>means "small" in whatever form of speech to the kid. Hence
>vocabulary over grammatical structure.
The child would not have been misled about the Sears Tower,
and the name IS used as an adjective. It is just that it
does not describe the size of the tower. I suspect that an
American of that age would make the same mistake about the
Short Building. BTW, Klein is not that uncommon a German
name.
>> Are you so sure?
Not as much as social scientists, who insist on their prejudices.
The educationists do not think that children can learn abstract
concepts except by abstracting form concrete models, often from
only one type.
>> I suggest you read the paper before jumping to conclusions.
>I would agree with you if it's about 6 year olds, because by that
>age, I was already in the 3rd grade, having passed a written
>entrance exam.
The educational researchers are opposed to 6 year olds being
in anything other than first grade.
>But LESS than 1-yr olds? The only ones the scientists fooled are
>themselves and the gullible!
>> >But often they get GRANTS to do the silliness, if they can BS
>> >enough pages in application for the grant.
>-- Bob.
--
Serial Killfiler
<Large_Nass...@Yahoo.com> wrote:
>First of all, Herman seems excessively gullible about one article of
>which he couldn't quite recall.
>
>The idea of young children understand grammatical ideas before
>vocabulary has to have come from someone who is linguistically
>challenged. The grammatical structure of Romance languages
>(French, Spanish) and Germanic languages (German) and their
>derivatives from Latin, such as English, are vastly different.
>Children
>who are less than 6 years old should have no difficulty being multi
>lingual in English, French, Spanish, German, and even Chinese.
>The older one gets, the more difficult it is to learn.
>
Comprehension of grammar is innate in the human mind. We are born
primed to use language, and we learn the particular sound systems,
syntatical patterns, vocabulary, idioms and exceptions inherent in our
maternal language. The fundamentals of grammar are wired in. That
has been demonstrated by top researchers in linguistics and cognitive
psychology.
>I was told by a Berlitz teacher that I tried to THINK too much about
>the grammar of Spanish (when I already learned those in French,
>German, and English). I was no match for any 6 year old.
>
>In fact, when I was 6 years old, I was multi-lingual in four dialects
>of Chinese -- each of which is as different as German, French,
>and English.
>
>Young children have a completely different way of learning a
>language, by "imitation of rules" rather than abstraction of rules.
>Vocabulary certainly precedes grammar.
Young children understand the rules in the same effortless way you can
tell cars from motorcycles and dogs from cats. They are born with an
innate grasp of language structure because of its essential survival
value.
>I had the hardest time learning
>why every inanimate object is male, female, or neuter in German,
You don't understand gender, then. It is a linguistic property of the
word itself and has nothing to do with the object. The only exception
are "natural" gender nouns like man, woman, lion, cow, etc. which must
necessarily match in sexual and grammatical gender. However
grammatical gender sometimes overrides natural gender.
>and how to look for the separable prefixes and suffixes that may
>be a page or two away. Kids NEVER had that kind of problem
>in learning German.
Even native speakers of German can lose track of prefixes and
infinitives in certain sentence structures, but those structures are
avoided by most speakers. Every language has examples of heavy style
that few people use much.
Colleyville Alan
news:e016cc$1r...@odds.stat.purdue.edu...
> You do not understand concepts. They are NOT the same as
> theory; one can learn the theory and have no understanding
> of the concepts, and vice versa.
People often use the words "theory" and "concepts" interchangeably, but you
are asserting that those terms do not mean the same thing at all. I am
interested in your meanings for those terms. What do you mean by concepts
as opposed to theory? How can somebody understand one but not the other?
p.s. May I email you privately?
Alan
The World Wide Wade
Serial Killfiler <alXXh...@NOSPAMyahoo.com> wrote:
> Comprehension of grammar is innate in the human mind. We are born
> primed to use language, and we learn the particular sound systems,
> syntatical patterns, vocabulary, idioms and exceptions inherent in our
> maternal language. The fundamentals of grammar are wired in. That
> has been demonstrated by top researchers in linguistics and cognitive
> psychology.
This view of grammar, associated above all with Noam Chomsky, is
more controversial than you describe.
Herman Rubin
>In article <e02vhb$q1a$1...@news.math.niu.edu>, Dave Rusin writes:
>>In article <e01oge$4u9$1...@glue.ucr.edu>, James Dolan <jdo...@math-cl-n03.math.ucr.edu> wrote:
>>>in article <waderameyxiii-E2E...@comcast.dca.giganews.com>, the world wide wade <wadera...@comcast.remove13.net> wrote:
>>>|And if you haven't seen metric
>>>|spaces, the axioms for point-set topology will appear like some
>>>|arbitrary abstract nonsense from another planet.
>>>grossly false;
>>OK, I have a bright student uncorrupted by point-set topology before me.
>>I present the definition of a topology; the collection of open sets
>>is closed under _finite_ intersections but _arbitrary_ unions. The
>>student asks why on earth one would take such an asymmetrical set of
>>axioms.
>Yup, that'd be me.
>I'd gone through chapter 3 of my topology book, which covered metric
>spaces, and was just fine. I could prove things about metric spaces,
>and mappings from one to another. Felt fairly confident.
>I got to chapter 4, which introduced topologies. Unlike the previous
>chapter, there was no motivational material -- just the definition
>of a "topology".
There should have been an explanation of why. Moreover, you
expected it to be like metric spaces, where in general the
metric is rather arbitrary form the topological standpoint,
and convergence definitions are ill-suited for extension.
I did, indeed, ask myself the question of "why
>arbitrary unions, but only finite intersections?"
Were you not aware that in a metric space any closed set is
an intersection of a sequence of open sets? Or at least any
closed interval in the real line is such an intersection?
And that the metric definition of open set gets arbitrary
unions, but only finite intersections in general?
Herman Rubin
Begin with the formal, and illustrate. If you start out
with examples of topologies, how is the student going to
realize they are topologies except by fiat?
Also, there are many ways of "defining" a topological
space. If one uses a neighborhood system, where anything
which contains a neighborhood of a point is a neighborhood,
arbitrary unions are trivial. Even if one introduces the
idea of neighborhood without using the formal criteria for
something to be a neighborhood system, this will illustrate
it. I am not sure how many "definitions" I gave the last
time I taught it, but it was well over 10.
Marc Olschok
It seems, that the prior exposure to metric spaces did indeed not
help you when you first encountered topological spaces.
But perhaps, the author of that book viewed chapter 3 as the motivational
material for chapter 4. I do not know the book, so I cannot tell.
The problem is this: metric spaces are an important tool for analysis
and those topologies constructed from metrics are important examples
for topologies, which is why they should certainly be included in an
introductory topology textbook.
But metric spaces do not provide a good motivation for a particular system
of axioms for topology (especially not for the one you mentioned), which
is why they do not need to be introduced before topological spaces.
They should be introduced when they become helpful, which is after
the introduction of topological spaces.
Marc
Michael Stemper
>Michael Stemper wrote (in part):
>> I got to chapter 4, which introduced topologies. Unlike the
>> previous chapter, there was no motivational material -- just
>> the definition of a "topology". I did, indeed, ask myself
>> the question of "why arbitrary unions, but only finite
>> intersections?"
>
>The following book is excellent for someone who wants to go
>from the specific to the general:
>
>Robert Herman Kasriel, "Undergraduate Topology", Krieger
>Publishing Company, 1971, xiv + 285 pages.
[snip]
>I think this is an excellent text for someone to read on
>their own,
Sounds like it.
> especially if they haven't had an advanced
>calculus course
That'd be me.
>with a fairly strong background, but for me at the time
>and for you (given what you said), I think this book
>was/would-be a very good fit.
I've made a note of it. Thanks for the recommendation!
Herman Rubin
This seems to be too often the situation. Understanding the
theory means knowing the axioms, and a sufficient number of
the theorems and proofs, and even possibly being able to
produce new theorems or proofs.
On the other hand, understanding the concepts means having
an "intuitive" understanding of WHY, and being able to use
them to apply mathematics to problems in other areas, or one
part of mathematics to another.
Some examples might help. To understand the theory behind
derivatives and differential equations, one needs to do a
fair amount of working with Euclidean spaces, and to be able
to at least understand proofs of various properties of functions
from one finite dimensional manifold to another. On the other
hand, if one understands the concept of derivative, which
should come before starting to compute them, one can take a
problem in physics or chemistry or economics and formulate an
appropriate calculus or differential equation problem whose
solution should approximate the solution of the practical
problem. The theory might require a small amount of ability
to compute or solve, but not much; that is a bad approach to
both aspects.
Another one is that of the ordinary integers, etc. There
happen to be TWO distinct main concepts here, and this is
one reason why it is harder to teach the understanding.
There is the ordinal version and the cardinal version;
these even have different names in practice, although the
isomorphism between the names is readily apparent. The
ordinal one is self-contained, while the cardinal version
for finite sets involved the ordinal somewhere.
The ordinal concept can be quickly developed as the Peano
Postulates, with either second-order ideas for the
existence of addition and multiplication, or the assumption
that processes with those properties exist. In this, the
integers are what one can get by counting, and addition is
continuing the count, and multiplication repeated addition.
The cardinal approach considers the "size" of the set, with
two sets having the same size if they can be put into
one-to-one correspondence. Addition consists of uniion of
disjoint sets with the appropriate numbers of elements, and
multiplication corresponds to cartesian product.
But what is a finite set? In some form or other, it is a
set which can be counted with the counting terminating at
a finite ordinal; this is the basic connection. One can
use these without understanding any proofs, although it
is likely that some theorems will have to be used.
A similar situation exists with respect to measure and
integration. The usual presentation proves theorems,
but does an excellent job of hiding the concepts.
Instead of starting with the real line, start with
discrete sets. All measures are approximated by
measures on finite sets and their limits, and integrals
by sums of products and their limits. Finite extension
gives Riemann-type integrals, and countable extension
gives Lebesgue-type integrals. The oldest integration
we have is the computation of a merchant's bill; a good
example for students of measure is number of credits,
and of integral number of grade points.
>p.s. May I email you privately?
Yes.
>Alan
Michael Stemper
>In article <200603281743....@walkabout.empros.com>, Michael Stemper <mste...@siemens-emis.com> wrote:
>>I'd gone through chapter 3 of my topology book, which covered metric
>>spaces, and was just fine. I could prove things about metric spaces,
>>and mappings from one to another. Felt fairly confident.
>
>>I got to chapter 4, which introduced topologies. Unlike the previous
>>chapter, there was no motivational material -- just the definition
>>of a "topology".
>
>There should have been an explanation of why.
I quite agree. But, Dover reprints are cheap enough ($10-$15) that I
don't need to learn *too* much from any given book in order to feel
that I've received my money's worth. Understanding what a metric and
a metric space are was probably worth that right there. Certainly
the hours of entertainment (yeah, I should get a life) that I got from
working my way through the first three chapters was incredibly cheap.
> Moreover, you
>expected it to be like metric spaces,
I'm not sure what you mean by this statement. I did expect the introduction
of topologies to be structurally similar (from a pedagogic point of view) to
the introduction of metrics. But, this is presentation and exposition. I did
not have any expectations that topologies themselves would be like or unlike
anything else. That's why I was studying the book. Ever since I was about
ten years old, I've seen various popularizations -- none of which ever got
beyond the "a coffee cup has the same genus as a doughnut" stage. This was
enough to intrigue me (c'mon kid, the first one's free), and make me want
to seek out the meat. I haven't given up.
> I did, indeed, ask myself the question of "why
>>arbitrary unions, but only finite intersections?"
>
>Were you not aware that in a metric space any closed set is
>an intersection of a sequence of open sets?
No. In fact, I'm still not. The book that I was using defined "open sets"
as the elements of a topology, so that's not much help, either. I'm
currently studying real analysis -- hopefully, I'll be better prepared
when I make my next attempt at scaling Mt. Topos.
>And that the metric definition of open set gets arbitrary
The chapter on metrics and metric spaces in this book didn't define,
or even discuss, open sets.
--
Michael F. Stemper
#include <Standard_Disclaimer>
Indians scattered on dawn's highway bleeding;
Ghosts crowd the young child's fragile eggshell mind.
Dave L. Renfro
>> Robert Herman Kasriel, "Undergraduate Topology",
>> Krieger Publishing Company, 1971, xiv + 285 pages.
[snip]
>> I think this is an excellent text for someone to read on
>> their own, especially if they haven't had an advanced
>> calculus course with a fairly strong background, but
>> for me at the time and for you (given what you said),
>> I think this book was/would-be a very good fit.
Michael F. Stemper wrote (in part):
> I've made a note of it. Thanks for the recommendation!
Another book that I think would be excellent for self-study,
maybe even more so than Kasriel's text, is:
"Introduction to Topology and Modern Analysis"
by George F. Simmons
I didn't think about Simmons's book until now, otherwise
I would have mentioned it earlier. Simmons' book is less
of a topology text than Kasriel's book and its coverage
is much broader. There's a lot of verbal exposition
in Simmons' book, also, which is why I think it'd be
great for self-study. Another interesting feature of
Simmons' book that it covers a lot of topics that you
usually find only in texts that are much more advanced,
topics that have a broad genuine interest and a lot
of mathematical substance to them.
Dave L. Renfro
Michael Stemper
>Dave L. Renfro wrote (in part):
>>> Robert Herman Kasriel, "Undergraduate Topology",
>>> Krieger Publishing Company, 1971, xiv + 285 pages.
>[snip]
>Another book that I think would be excellent for self-study,
>maybe even more so than Kasriel's text, is:
>
>"Introduction to Topology and Modern Analysis"
>by George F. Simmons
Fifty-five dollars!? At that, Kasriel makes this look cheap - that
weighs in at $194.37. Well, I'll put it on the list, anyway.
I assume that these prices for topology books are based more on the
"low supply" side of the supply v demand function.
--
Michael F. Stemper
#include <Standard_Disclaimer>
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