>"The standards are so ridiculous that every single
>public school in America will be deemed to be a school
>in need of improvement or a failing school by 2013,"
>former Vermont governor Howard Dean said in a
>teleconference yesterday. He said the law, which he has
>pledged to dismantle, was "making education in America
>worse, not better."
This is absolutely true.
The problem involves the way the act is worded. Every school
must demonstrate *adequate yearly progress.* That means
every school must improve by some fixed % even if it is already
high performing. So high performing schools can be deemed
inadequate if they don't *improve* their test scores by a specific
percentage each year. At some point, the law of diminishing
returns sets in.
States must bring *all* students (including mentally disabled
students) up to a proficient level in reading and math by the
2013-2014 school year. Does anyone actually believe that
this is possible for *some* of the mentally disabled special
education students? One of my friends who teaches special
education says that her students must take and pass the algebra
tests. Yet many of them are significantly below the IQ at which
algebra can be understood. The legislation requires that 95%
of all students participate in the mandated assessments.
The new law appropriates about $400 million each year for
the next six years to develop new tests. But, according to
estimates reported in Time magazine, "Full implementation of
the Bush plan, with highquality tests in all 50 states, could cost
up to $7 billion." No wonder an executive of one of the major
testing firms responded to Bush's proposals last year by
declaring, "This almost reads like our business plan."
Educationally, the approach is nothing new and it's simpleminded.
The effects are predictable. Test preparation will dominate the
classrooms especially in struggling schools where children already
are disadvantaged. Curriculum focus will narrow. Already many
schools are de-emphasizing social studies because history is not
on the mandated list to improve.
The bill is also littered with assorted right-wing nuggets, such
as a provision preventing districts from banning the Boy Scouts
from using school facilities because of their anti-gay policies,
and a requirement that districts accepting federal dollars open
their doors to military recruiters
Here's a link to the full text of the law
http://www.ed.gov/policy/elsec/leg/esea02/index.html
--
Dorothy
There is no sound, no cry in all the world
that can be heard unless someone listens ..
The Outer Limits
> "The standards are so ridiculous that every single
> public school in America will be deemed to be a school
> in need of improvement or a failing school by 2013,"
> former Vermont governor Howard Dean
Well no shit. Our Public School system is a failure. We rank among the third
world nations on international test scores. Time we fixed this problem once
and for all. And the only way to do that is to take control of the Public
School system from the socialist left in America.
Note that while some schools are very poor, our best and brightest
still do better than most other nations.
The problem is to bring up the poorer schools to that standard. It
cannot be done without addressing the social problems that the
children bring with them to school.
That is no longer true.
All of our schools have gone down hill.
Heck even the standard tests are getting easier so more students pass. The
teachers have been stuck in a teach the test mode and it is failing our
kids. Our math and science scores are among the 3rd world countries, not the
industrialized countries.
We no longer want to hold a child back if he/she fails a year.
Come on what is up with that.
>
> The problem is to bring up the poorer schools to that standard. It
> cannot be done without addressing the social problems that the
> children bring with them to school.
Yes I can see a good point here. Parents need to be active participants in
their childs education process. Their needs to be effective communication
between the school and the parents about the standing of the child.
>"toto" <scar...@wicked.witch> wrote in message
>news:odvmvv0h4h95m2k19...@4ax.com...
>> On Tue, 6 Jan 2004 18:18:40 -0900, "dpr" <why> wrote:
>>
>> ><red...@suntimesmail.com> wrote in message
>> >news:3FFAC6CA...@suntimesmail.com...
>> >> X-NO-ARCHIVE: YES
>> >
>> >> "The standards are so ridiculous that every single
>> >> public school in America will be deemed to be a school
>> >> in need of improvement or a failing school by 2013,"
>> >> former Vermont governor Howard Dean
>> >
>> >Well no shit. Our Public School system is a failure. We rank among the
>third
>> >world nations on international test scores. Time we fixed this problem
>once
>> >and for all. And the only way to do that is to take control of the Public
>> >School system from the socialist left in America.
>> >
>> Note that while some schools are very poor, our best and brightest
>> still do better than most other nations.
>
>That is no longer true.
>All of our schools have gone down hill.
Wrong again.
The school my kids went to turns out many fine math and science
students today. So do most of the suburban schools on the North
Shore. So do many good schools. The school my kids went
to was not a magnet school. Some kids there do not do well, but
the top kids are getting the best education in the world.
>Heck even the standard tests are getting easier so more students pass. The
>teachers have been stuck in a teach the test mode and it is failing our
>kids. Our math and science scores are among the 3rd world countries, not the
>industrialized countries.
You are comparing apples and oranges though. If we talk about the
TIMSS test, most of the students in other countries who take the test
have taken advanced math courses. Most of the kids from the US
who take the course do not take the courses. The kids who have
taken them do just fine. Many of them beat out the International
competition.
My son's highschool produces Westinghouse Science winners and
International Math competition winners and finalists.
>We no longer want to hold a child back if he/she fails a year.
>Come on what is up with that.
Holding a child back has not been shown to be effective in doing much.
Even so social promotion has actually been stopped in most
schools as high stakes testing has taken it's place.
>>
>> The problem is to bring up the poorer schools to that standard. It
>> cannot be done without addressing the social problems that the
>> children bring with them to school.
>
>Yes I can see a good point here. Parents need to be active participants in
>their childs education process. Their needs to be effective communication
>between the school and the parents about the standing of the child.
>
That's only a part of the social problem that needs to be addressed.
If the community (neighborhood) a child lives in is unsafe, then even
the best parent will have trouble helping the child learn.
I taught in an inner city high school. We had many very good parents
who wanted their kids to do well, but the neighborhood was unsafe
for the kids to walk through. These kids could not go to the library
and do research because they could not get their after dark. Other
kids were the translators for parents who spoke little English. When
a younger sibling had a doctor's appointment, our teen had to take
off school to help mom translate. Many of the parents worked two
and three jobs to make ends meet and still didn't have enough food
for the family. Many had no phone so communicating with them
was problematic in terms of getting to them. Some spoke so little
English that if you wanted to communicate, you had to talk to the
child and have them translate for you. We did have people who
spoke the language at school, but they were not always available
to help translate when a teacher did want to talk to a parent.
And do we give up on the kid who has no parent who cares?
What of the girl I had who came to school in thin cotton pjs one
day because her dad threw her out of the house (this during
a cold Chicago winter)? Do we throw her out of school too?
Do we try to teach her when she has come to school half-frozen?
Which is why they have to take remedial classes in college for math and
science.
Hello they just graduated from high school, and they need remedial math and
science in college.
> >>
> >> The problem is to bring up the poorer schools to that standard. It
> >> cannot be done without addressing the social problems that the
> >> children bring with them to school.
> >
> >Yes I can see a good point here. Parents need to be active participants
in
> >their childs education process. Their needs to be effective communication
> >between the school and the parents about the standing of the child.
> >
>
> That's only a part of the social problem that needs to be addressed.
> If the community (neighborhood) a child lives in is unsafe, then even
> the best parent will have trouble helping the child learn.
>
> I taught in an inner city high school. We had many very good parents
> who wanted their kids to do well, but the neighborhood was unsafe
> for the kids to walk through. These kids could not go to the library
> and do research because they could not get their after dark. Other
> kids were the translators for parents who spoke little English. When
> a younger sibling had a doctor's appointment, our teen had to take
> off school to help mom translate. Many of the parents worked two
> and three jobs to make ends meet and still didn't have enough food
> for the family. Many had no phone so communicating with them
> was problematic in terms of getting to them. Some spoke so little
> English that if you wanted to communicate, you had to talk to the
> child and have them translate for you. We did have people who
> spoke the language at school, but they were not always available
> to help translate when a teacher did want to talk to a parent.
I will agree here. America has been failing her students in foreign
languages. It is about time we start teaching our kids Spanish and at least
French or German or another language before they graduate from high school.
>
> And do we give up on the kid who has no parent who cares?
> What of the girl I had who came to school in thin cotton pjs one
> day because her dad threw her out of the house (this during
> a cold Chicago winter)? Do we throw her out of school too?
> Do we try to teach her when she has come to school half-frozen?
The last one here you are correct. While I myself have never had kids, nor
wanted any, this is what really burns my goat. Parents like this need to be
punished for such irresponsible behavior, and the children need to be
relocated as quickly as possible to other caring family members or foster
parents, so the child at least has a chance.
Cite please. And I won't hold my breath, but just cite you:
>Still waiting liar, where is your proof.
>Oh that's right, you do not have any proof as you are a liar.
>Our math and science scores are among the 3rd world countries, not the
>industrialized countries.
The tests are based on a different curriculum than our society (and
populace) has ever considered necessary.
>We no longer want to hold a child back if he/she fails a year.
I know of several kids that were held back a year upon failure.
>Come on what is up with that.
Your imagination.
>> The problem is to bring up the poorer schools to that standard. It
>> cannot be done without addressing the social problems that the
>> children bring with them to school.
>
>Yes I can see a good point here. Parents need to be active participants in
>their childs education process. Their needs to be effective communication
>between the school and the parents about the standing of the child.
A rarity. Dprshit says something correct.
lojbab
--
lojbab loj...@lojban.org
Bob LeChevalier, Founder, The Logical Language Group
(Opinions are my own; I do not speak for the organization.)
Artificial language Loglan/Lojban: http://www.lojban.org
>> Holding a child back has not been shown to be effective in doing much.
>
>Which is why they have to take remedial classes in college for math
>and science. Hello they just graduated from high school, and they
>need remedial math and science in college.
In general, this happens because kids don't take the advanced math
courses and are admitted to college without them. Even when I went
to school, many colleges required only two years of math - this meant
Algebra I and Geometry and if you took those in 9th and 10th grade,
you might forget plenty by the time you applied to college.
Note here, that the only thing that has happened is that colleges in
the higher tiers have lowered admission standards and thus have
more kids who need remediation. It's nothing new in the middle and
lower tier colleges. They had remediation classes when I went to
college.
toto wrote:
>
> On Tue, 6 Jan 2004 19:40:58 -0900, "dpr" <why> wrote:
>
> >"toto" <scar...@wicked.witch> wrote in message
> >news:odvmvv0h4h95m2k19...@4ax.com...
> >> On Tue, 6 Jan 2004 18:18:40 -0900, "dpr" <why> wrote:
> >>
> >> ><red...@suntimesmail.com> wrote in message
> >> >news:3FFAC6CA...@suntimesmail.com...
> >> >> X-NO-ARCHIVE: YES
> >> >
> >> >> "The standards are so ridiculous that every single
> >> >> public school in America will be deemed to be a school
> >> >> in need of improvement or a failing school by 2013,"
> >> >> former Vermont governor Howard Dean
> >> >
> >> >Well no shit. Our Public School system is a failure. We rank among the
> >third
> >> >world nations on international test scores. Time we fixed this problem
> >once
> >> >and for all. And the only way to do that is to take control of the Public
> >> >School system from the socialist left in America.
> >> >
> >> Note that while some schools are very poor, our best and brightest
> >> still do better than most other nations.
> >
> >That is no longer true.
> >All of our schools have gone down hill.
About 35 years ago, the Institute for Child Studies at
the University of Toronto published the results of a 30
year study. One of the salient points made, was that
children who are exposed to books from the time they
can grasp one, do better in every field, physical or intellectual.
Kids today, mostly watch television and the exceptions
prove the rule. TV Nanny is a real menace, and the
schools have few weapons against that.
The one thing that could help, is to open kindergarten
to 3 year olds and do real teaching there using real
books.
My mother sent me to a private kindergarten in a home
across the street from our house (sept 1930). When I
got to public school (G1) three years later, I was in
trouble, because I was reading and writing at a level
beyond what was taught in the 4 grades in that school.
So I was punished for boredom (:-) and that continued
all through public school. One thing that helped,
though, I had unlimited access to the local Carnegie
library courtesy of the librarian, a next door neighbour.
--
--
As Orwell pointed out long ago, pacifism in the face of
armed evil is equivalent to a blind worship of force.
It would be disastrous to entrust our children's fate
to the hands of these sad and complicitous pacifists.
Bob LeChevalier wrote:
>
> Bob LeChevalier, Founder, The Logical Language Group
> (Opinions are my own; I do not speak for the organization.)
That is good because you disgrace the organization.
> Artificial language Loglan/Lojban: http://www.lojban.org
--
>><red...@suntimesmail.com> wrote in message
>>news:3FFAC6CA...@suntimesmail.com...
>>> X-NO-ARCHIVE: YES
>>> "The standards are so ridiculous that every single
>>> public school in America will be deemed to be a school
>>> in need of improvement or a failing school by 2013,"
>>> former Vermont governor Howard Dean
>>Well no shit. Our Public School system is a failure. We rank among the third
>>world nations on international test scores. Time we fixed this problem once
>>and for all. And the only way to do that is to take control of the Public
>>School system from the socialist left in America.
>Note that while some schools are very poor, our best and brightest
>still do better than most other nations.
>The problem is to bring up the poorer schools to that standard. It
>cannot be done without addressing the social problems that the
>children bring with them to school.
Our best and brightest do not do better than many nations,
mainly because we do not let them. Until we make it too
expensive for individuals in the school system to reduce
the level of learning, years are lost, and even the ability
to understand concepts, much stronger in young children than
in most teachers, gets weakened or destroyed. Many of these
end up being dropouts.
One does not achieve understanding by the memorization and
rote encouraged by our schools. The bright, and especially
the gifted, do not need repetition and are turned off by it.
A poorly performing school could be doing an excellent job
with the students available, and a highly performing school
can be doing essentially nothing for the education of those
who attend it, and even doing harm.
Children have different abilities, and for the schools to
even ATTEMPT to teach them the same should be considered
gross child abuse and mentally destructive. Unfortunately,
we cannot replace the teachers who cannot teach conceptually,
and the problems in the colleges with students who have not
learned to think are massive.
--
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
>> >"toto" <scar...@wicked.witch> wrote in message
>> >news:odvmvv0h4h95m2k19...@4ax.com...
>> >> On Tue, 6 Jan 2004 18:18:40 -0900, "dpr" <why> wrote:
>> >> ><red...@suntimesmail.com> wrote in message
>> >> >news:3FFAC6CA...@suntimesmail.com...
>> >> >> X-NO-ARCHIVE: YES
..................
>> Holding a child back has not been shown to be effective in doing much.
>Which is why they have to take remedial classes in college for math and
>science.
>Hello they just graduated from high school, and they need remedial math and
>science in college.
This is NOT why they need remedial courses in college; it
is not that they did not learn what was presented, but that
the "right stuff" was not even presented. Most have not
seen anything but facts and computation, and that is not
what is needed for further development.
This continues; we get graduate students who have had a
course labeled "advanced calculus" or "foundations of real
analysis" who have not seen the material supposed to be in
those courses.
>toto wrote:
>> On Tue, 6 Jan 2004 19:40:58 -0900, "dpr" <why> wrote:
>> >"toto" <scar...@wicked.witch> wrote in message
>> >news:odvmvv0h4h95m2k19...@4ax.com...
>> >> On Tue, 6 Jan 2004 18:18:40 -0900, "dpr" <why> wrote:
>> >> ><red...@suntimesmail.com> wrote in message
>> >> >news:3FFAC6CA...@suntimesmail.com...
>> >> >> X-NO-ARCHIVE: YES
...................
>About 35 years ago, the Institute for Child Studies at
>the University of Toronto published the results of a 30
>year study. One of the salient points made, was that
>children who are exposed to books from the time they
>can grasp one, do better in every field, physical or intellectual.
This may well be true. However, while I learned to read
very early (age 3), there were few books at home, and this
was well before TV was invented.
However, my siblings came out ordinary, and attempts
to get them to read early failed.
>Kids today, mostly watch television and the exceptions
>prove the rule. TV Nanny is a real menace, and the
>schools have few weapons against that.
>The one thing that could help, is to open kindergarten
>to 3 year olds and do real teaching there using real
>books.
>My mother sent me to a private kindergarten in a home
>across the street from our house (sept 1930). When I
>got to public school (G1) three years later, I was in
>trouble, because I was reading and writing at a level
>beyond what was taught in the 4 grades in that school.
>So I was punished for boredom (:-) and that continued
>all through public school. One thing that helped,
>though, I had unlimited access to the local Carnegie
>library courtesy of the librarian, a next door neighbour.
Much still depends on the ability of the individual.
My first-born was reading well at age 4, and enjoyed
the _Britannica_ (NOT the version for children) by
age 5, and progressed accordingly. The later one
did not do this, even with what we had learned from
the first one, not reading fully until 6.
I see that there is someone else who knows the boredom
of the public schools.
So here is the problem. It is the establishment as a whole. They just are
not teaching the required math needed for college.
The kids need to be able to handle a first course in Calculus when they
graduate from high school. Well that should be the goal.
2 years of math is not enough.
>
> Note here, that the only thing that has happened is that colleges in
> the higher tiers have lowered admission standards and thus have
> more kids who need remediation. It's nothing new in the middle and
> lower tier colleges. They had remediation classes when I went to
> college.
Why should they be lowering their standards, why can't the public schools
teach the subjects needed, instead of getting involved with the cultural war
and the attack on Christians.
Thank you Herman. You have expressed what I was thinking.
As red points out, it is not just the public school system, but parents and
society as a whole that needs to address our education system.
Exactly. Our entire education system needs to be reviewed. Our children are
not being taught the needed math and science they need to continue on in
college. A lot of schools only teach the test, just enough material is
taught to have the child pass the standards test.
>"toto" <scar...@wicked.witch> wrote in message
>news:m91ovv8pvr86vphod...@4ax.com...
>> On Tue, 6 Jan 2004 21:55:45 -0900, "dpr" <why> wrote:
>>
>> >> Holding a child back has not been shown to be effective in doing much.
>> >
>> >Which is why they have to take remedial classes in college for math
>> >and science. Hello they just graduated from high school, and they
>> >need remedial math and science in college.
>>
>> In general, this happens because kids don't take the advanced math
>> courses and are admitted to college without them. Even when I went
>> to school, many colleges required only two years of math - this meant
>> Algebra I and Geometry and if you took those in 9th and 10th grade,
>> you might forget plenty by the time you applied to college.
>
>So here is the problem. It is the establishment as a whole. They just are
>not teaching the required math needed for college.
>The kids need to be able to handle a first course in Calculus when they
>graduate from high school. Well that should be the goal.
>2 years of math is not enough.
>
Wow, something we agree on, if we believe that all college freshman
need calculus that is. There are courses of study that require
college level courses which do not require college level mathematics
though. It might be good to have separate schools that gave these
classes.
>
>
>>
>> Note here, that the only thing that has happened is that colleges in
>> the higher tiers have lowered admission standards and thus have
>> more kids who need remediation. It's nothing new in the middle and
>> lower tier colleges. They had remediation classes when I went to
>> college.
>
>Why should they be lowering their standards, why can't the public
>schools teach the subjects needed, instead of getting involved
>with the cultural war and the attack on Christians.
>
The public schools *do* teach these classes. Not every student takes
them, however. My children both had calculus in high school. My son
had two years of it (which meant he had Calc I and II and diffeq
covered), my daughter had just the first semester of Calc. The both
took first year college courses other than these in high school as
well (different classes - my son had AP bio, chem and physic, my
daughter had AP English and American History). The courses are
there, but many kids will not take them because they are seen as
hard and they are not necessary for entrance to most colleges. Why
should the kids take them if the parents don't think they are
necessary and the colleges accept kids without them?
As for the cultural war, none of the public schools I taught in or
that my children went to were involved in any attack on Christians.
They simply did not allow kids to bully each other over religion
at all. So, they didn't allow kids to preach to each other or to
proselytize, that isn't what the schools are for anyway.
>This continues; we get graduate students who have had a
>course labeled "advanced calculus" or "foundations of real
>analysis" who have not seen the material supposed to be in
>those courses.
And that is not the public schools fault now is it, Herman?
If you can't teach the graduate students, then it isn't the fault
of the high schools, but of the colleges who admitted the kids
in the first place if they were not qualified and who dumbed
down their own standards to make sure these students
graduated.
Why is your graduate school admitting unqualified students?
>The one thing that could help, is to open kindergarten
>to 3 year olds and do real teaching there using real
>books.
Kids in preschool are taugh using *real books.*
Three year olds don't need *kindergarten.* They need
real world experience and oral language as well as
being read to, btw.
If you want kids to do well, you fill their whole world with
experiences that allow them to explore the world. They
need to go to the zoo, to go to parks, to go to farms, to
go to stores. They need adults to talk to them and to
listen to them. They need to be read to, but that is only
a part of what they need.
>I see that there is someone else who knows the boredom
>of the public schools.
Herman, I read *during* classes in the public schools. I always
had a book that I could hide under my work when I was done
with what was boring and what I already knew. I managed to
hide it well, mostly, since the only teacher who caught it was
my 6th grade teacher and her only comment was that it was
rude. (that came home in deportment on a report card).
Aside from that a little boredom is not a bad thing. It spurs
imagination and creativity.
Maybe not all College Freshman need that, but the kids coming out of public
school should be prepared to take a college Calculus class their freshman
year in college.
And we also should raise the level of what we expect the kids to know of
physics and biology,etc.
And these kids should be able to speak two other languages besides English.
Spanish due to our huge population of that sub group, and another language,
even Latin.
There are courses of study that require
> college level courses which do not require college level mathematics
> though. It might be good to have separate schools that gave these
> classes.
No, the public schools should all be geared to providing a firm technical
education, Math Science, Language, being of prime importance. At the College
level they can go off and specialize, but while in High School they should
all be taught how to do basic Calculus.
>
> >
> >
> >>
> >> Note here, that the only thing that has happened is that colleges in
> >> the higher tiers have lowered admission standards and thus have
> >> more kids who need remediation. It's nothing new in the middle and
> >> lower tier colleges. They had remediation classes when I went to
> >> college.
> >
> >Why should they be lowering their standards, why can't the public
> >schools teach the subjects needed, instead of getting involved
> >with the cultural war and the attack on Christians.
> >
> The public schools *do* teach these classes. Not every student takes
> them, however. My children both had calculus in high school. My son
> had two years of it (which meant he had Calc I and II and diffeq
> covered), my daughter had just the first semester of Calc. The both
> took first year college courses other than these in high school as
> well (different classes - my son had AP bio, chem and physic, my
> daughter had AP English and American History). The courses are
> there, but many kids will not take them because they are seen as
> hard and they are not necessary for entrance to most colleges.
See that is my point. Society, families and the schools need to change to
accept those classes you listed above as the requirements for graduating
from high school. That should be the end result.
Why
> should the kids take them if the parents don't think they are
> necessary and the colleges accept kids without them?
Because we as the older generation know they need those skills.
If the classes your kids took were made requirements for graduation instead
of as elective programs, you lift the entire boat instead of just a few.
Let the specialization occur in college, the public schools should be geared
towards teaching the technical subjects we have today.
Calculus is becoming almost a basic math as technology explodes around us,
and we are not prepairing our children to meet the challenges.
>
> As for the cultural war, none of the public schools I taught in or
> that my children went to were involved in any attack on Christians.
If the NEA is there, or if any leftist is there, there is an attack on the
Christian belief in our public schools.
The Schools should not be involved with the teachings of Morals and
religious beliefs to begin with. All the Schools should be teaching is the
actual subjects like Math , Science, Language, History, etc. The different
religions in the world can be taught during the history classes, so the kids
know that there are many different beliefs, but that is as far as the school
should go.
The school should not be involved in promoting homosexuality or any other
cultural moral issue, that is left to society and the parents outside of the
schoolhouse.
Why are the high schools lowering their standards and teaching less.
It is wasteful in the school environment
>>"toto" <scar...@wicked.witch> wrote in message
>>news:m91ovv8pvr86vphod...@4ax.com...
>>> On Tue, 6 Jan 2004 21:55:45 -0900, "dpr" <why> wrote:
.....................
>>Why should they be lowering their standards, why can't the public
>>schools teach the subjects needed, instead of getting involved
>>with the cultural war and the attack on Christians.
>The public schools *do* teach these classes.
Some do, and some do not.
Not every student takes
>them, however. My children both had calculus in high school.
Most calculus courses in high school are more of the same
junk. A huge proportion of those who have had AP calculus,
and the same in other subjects, have to repeat them in
college. If a student cannot test out of it in college,
the course is not good.
The problem is not with the presence or absence of calculus,
or of trigonometry, or any specific amount of material. It
is that mathematics is taught as a collection of facts and
formulas. The old "Euclid", modernized, should be mandatory
for college preparation, as it was for all good colleges
before WWII. As for algebra, students need to know how to
use it to set up problems in all fields, from economics and
ecology to agriculture and astronomy. This latter is the
mathematical equivalent of writing declarative sentences in
English, and is more important than any calculation.
>>This continues; we get graduate students who have had a
>>course labeled "advanced calculus" or "foundations of real
>>analysis" who have not seen the material supposed to be in
>>those courses.
>And that is not the public schools fault now is it, Herman?
>If you can't teach the graduate students, then it isn't the fault
>of the high schools, but of the colleges who admitted the kids
>in the first place if they were not qualified and who dumbed
>down their own standards to make sure these students
>graduated.
How are the colleges to know if they have the qualifications?
>Why is your graduate school admitting unqualified students?
How is our graduate school to know if they are qualified?
We can see transcripts, and letters of recommendation, but
none of this tells us what was covered in the courses, even
if the texts are given, or how they were graded. We can
see GRE scores, but they do not tell us too much, and if
a student has had weak courses, the GRE subject score will
be low. The other scores rarely tell us much.
We are willing to admit American students with ability and
place them in remedial courses, but how do we find this out?
Short of giving our own exams, we are stuck. Likewise, short
of giving admission exams to applicants, the colleges have
no way of real evaluation. The SAT, having moved away from
a pure aptitude test, is less than good, and grades are of
little value.
>>I see that there is someone else who knows the boredom
>>of the public schools.
>Herman, I read *during* classes in the public schools. I always
>had a book that I could hide under my work when I was done
>with what was boring and what I already knew. I managed to
>hide it well, mostly, since the only teacher who caught it was
>my 6th grade teacher and her only comment was that it was
>rude. (that came home in deportment on a report card).
>Aside from that a little boredom is not a bad thing. It spurs
>imagination and creativity.
A LOT of boredom is, as is having to do a lot of busy
work problems. You should be advancing in subject
matter, not reading novels or other works which do not
do this advancing.
There are a few teachers now who believe in ignoring age
and advancing children as fast as they can. There are
others willing to teach the same way, and most of these
will not consider taking courses in "education". The
job cannot be done fully now, as there are nowhere near
enough competent teachers, but keeping bright children
back only makes the problem worse. Only financial threats
can do anything about it.
>Most calculus courses in high school are more of the same
>junk. A huge proportion of those who have had AP calculus,
>and the same in other subjects, have to repeat them in
>college. If a student cannot test out of it in college,
>the course is not good.
Many of the students who take AP calculus do test out of it.
My son and most of his classmates did.
>> As for the cultural war, none of the public schools I taught in or
>> that my children went to were involved in any attack on Christians.
>
>If the NEA is there, or if any leftist is there, there is an attack on the
>Christian belief in our public schools.\
Pure BS.
The schools my kids went had unionized teachers. NEA membership
was certainly involved.
>The Schools should not be involved with the teachings of Morals and
>religious beliefs to begin with.
They don't. But, they do have to keep *all* students safe. Thus they
must teach tolerance. And, because society and parents have basically
abrogated their duty to teach any kind of character including honesty
and respect for others, schools must teach that largely through
example and through not tolerating behavior that harms other children
who are in the same classroom.
>All the Schools should be teaching is the actual subjects like Math ,
>Science, Language, History, etc.
Art, Music, Physical Education are also important.
>The different religions in the world can be taught during the history
>classes, so the kids know that there are many different beliefs, but
>that is as far as the school should go.
I would like to see more comparative religion in Humanities classes
My children had these in high school. This is not appropriate in
elementary school, but by high school, kids can handle learning
*about* religions if the course is well-taught.
>The school should not be involved in promoting homosexuality or
>any other cultural moral issue, that is left to society and the parents
>outside of the schoolhouse.
The schools don't *promote* homosexuality. But, as we now have
more gay parents and we also have students in the high schools who
have come out of the closet, we must assure that these students and
parents are not harrassed in any way, including being told they are
sinners by the Christian parents and students. I don't care what the
parents and students *think* about it, but they cannot call the other
students names and they cannot harrass them physically or verbally.
>We are willing to admit American students with ability and
>place them in remedial courses, but how do we find this out?
>Short of giving our own exams, we are stuck. Likewise, short
>of giving admission exams to applicants, the colleges have
>no way of real evaluation. The SAT, having moved away from
>a pure aptitude test, is less than good, and grades are of
>little value.
Then get yourselves together and give your own entrance exams.
And if you can't don't blame those below you who have to follow
what the politicians say is important.
But they are teaching it - to those who want to take it. They are not
requiring that the courses taken by some be taken by all. Meanwhile,
teaching it doesn't mean that people retain it. 2 years of not using
algebra, and kids forget the details.
Meanwhile, you can pass a high school math class with a D (minimum of
somewhere between 60% and 70%), but colleges need a higher level of
skill than a D-level in math.
That is why some of us non-right-wing education reformers favor moving
to a mastery-type education system, where a minimum grade is not
considered "good enough".
>The kids need to be able to handle a first course in Calculus when they
>graduate from high school. Well that should be the goal.
>2 years of math is not enough.
Then government would have to increase the requirements for high
school graduation in all 50 states. (The Federal government cannot do
this, since education is controlled at the state level.)
Meanwhile, there are many people who question the need for people not
planning on going to college taking any more than algebra.
Virginia split the difference - it has a college prep diploma and a
regular diploma.
>> Note here, that the only thing that has happened is that colleges in
>> the higher tiers have lowered admission standards and thus have
>> more kids who need remediation. It's nothing new in the middle and
>> lower tier colleges. They had remediation classes when I went to
>> college.
>
>Why should they be lowering their standards,
Maybe they "shouldn't", but in this country, market forces rule.
College is big business, and they want more customers. They may SAY
that they want better-qualified students, but they don't really. They
make shitloads of profits off those remedial courses, which can be
taught by cheap grad students but costs full tuition. They then use
that tuition money to pay for the upper division and graduate level
courses which are less profitable.
> why can't the public schools teach the subjects needed,
They can and do, but not all kids take the classes. You can lead a
horse to water ...
>instead of getting involved with the cultural war
Schools can't help that, since adults bring the culture war to the
schools.
>and the attack on Christians.
There is no attack on Christians.
lojbab
--
lojbab loj...@lojban.org
Bob LeChevalier, Founder, The Logical Language Group
(Opinions are my own; I do not speak for the organization.)
Nope pure reality
>
> >The Schools should not be involved with the teachings of Morals and
> >religious beliefs to begin with.
> >All the Schools should be teaching is the actual subjects like Math ,
> >Science, Language, History, etc.
> >The different religions in the world can be taught during the history
> >classes, so the kids know that there are many different beliefs, but
> >that is as far as the school should go.
> >The school should not be involved in promoting homosexuality or
> >any other cultural moral issue, that is left to society and the parents
> >outside of the schoolhouse.
>
> The schools don't *promote* homosexuality.
They sure as hell are.
No they are not.
> >The kids need to be able to handle a first course in Calculus when they
> >graduate from high school. Well that should be the goal.
> >2 years of math is not enough.
>
> Then government would have to increase the requirements for high
> school graduation in all 50 states.
That is what I said. I have maintained that the entire system is broke in
regards to education, from the students, parents, teachers, administrators,
and politicians.
> Meanwhile, there are many people who question the need for people not
> planning on going to college taking any more than algebra.
The only people who want that, are the people who want slaves.
You people here are not giving the kids the proper needed education. All
students should be able to do Basic operations in calculus leaving High
School. And their Physics and Biology knowledge should be more advanced than
where it is today.
And it should not matter if the student is not going on to college, in fact
it is more important for those who will not go on to college to have those
skills. This makes the person easily trained outside of school.
> >> Note here, that the only thing that has happened is that colleges in
> >> the higher tiers have lowered admission standards and thus have
> >> more kids who need remediation. It's nothing new in the middle and
> >> lower tier colleges. They had remediation classes when I went to
> >> college.
> >
> >Why should they be lowering their standards,
> > why can't the public schools teach the subjects needed,
That is a left-wing approach. The right-wing doesn't want increased
government regulation, which is what higher requirements would entail.
You mentioned biology, for example. Right wing private schools that
have problems with Darwin aren't capable of teaching modern biology.
>Why
>> should the kids take them if the parents don't think they are
>> necessary and the colleges accept kids without them?
>
>Because we as the older generation know they need those skills.
We as the older generation don't agree whether they need those skills.
In particular, older generation people without college degrees don't
see a need for such courses (and guess which part of the political
spectrum such people are commonly associated with).
>> As for the cultural war, none of the public schools I taught in or
>> that my children went to were involved in any attack on Christians.
>
>If the NEA is there, or if any leftist is there, there is an attack on the
>Christian belief in our public schools.
Well, since some students are leftists, then as you define things, it
is impossible to remove the culture wars from the school.
>The Schools should not be involved with the teachings of Morals and
>religious beliefs to begin with.
Agreed. It is the right wing that wants to teach morals and religious
beliefs in the schools.
>The school should not be involved in promoting homosexuality or any other
>cultural moral issue, that is left to society and the parents outside of the
>schoolhouse.
The school doesn't have to promote it. The homosexual kids in the
schools will do what they do. The schools have to make sure that the
homophobes don't mistreat the homosexual kids.
And whose fault is that? (Hint: his initials are GWB, and the program
is NCLB)
The problem is that many parents dump their kids in the cheapest day
care that they can find, often one that provides minimal such
experiences. Poor and single parents are more likely to be forced to
do this for financial reasons.
lojbab
>"dpr" <why> wrote:
>>Exactly. Our entire education system needs to be reviewed. Our children are
>>not being taught the needed math and science they need to continue on in
>>college. A lot of schools only teach the test, just enough material is
>>taught to have the child pass the standards test.
>
>And whose fault is that? (Hint: his initials are GWB, and the program
>is NCLB)
And guess what - the rebellion may start with Vermont.
See article below:
http://www.calcare.org/reading/current/2002.04.20.html
>No, the public schools should all be geared to providing a firm technical
>education, Math Science, Language, being of prime importance. At the College
>level they can go off and specialize, but while in High School they should
>all be taught how to do basic Calculus.
Calculus was a college course when I went to college. It can still be
a college course. And I meant different colleges, not different high
schools. Colleges for liberal arts majors may not require them to
learn calculus.
>If the NEA is there, or if any leftist is there, there is an attack on the
>Christian belief in our public schools.
Wrong
>"toto" <scar...@wicked.witch> wrote in message
>news:h8tovvcf5gatmdgl1...@4ax.com...
>> On 7 Jan 2004 11:12:50 -0500, hru...@odds.stat.purdue.edu (Herman
>> Rubin) wrote:
>>
>> >This continues; we get graduate students who have had a
>> >course labeled "advanced calculus" or "foundations of real
>> >analysis" who have not seen the material supposed to be in
>> >those courses.
>>
>> And that is not the public schools fault now is it, Herman?
>>
>> If you can't teach the graduate students, then it isn't the fault
>> of the high schools, but of the colleges who admitted the kids
>> in the first place if they were not qualified and who dumbed
>> down their own standards to make sure these students
>> graduated.
>>
>> Why is your graduate school admitting unqualified students?
>
>Why are the high schools lowering their standards and teaching less.
Ask Bush and the others who have this mania for high stakes testing
that doesn't test anything.
We are not talking about regulation. We are talking about changing the view
society takes on education
> which is what higher requirements would entail.
And here you are wrong. What needs to change is how society looks at
education.
> You mentioned biology, for example. Right wing private schools that
> have problems with Darwin aren't capable of teaching modern biology.
That is pure hogwash. And purely your misguided opinion, as you can not back
that allegation up with any facts.
>
> >Why
> >> should the kids take them if the parents don't think they are
> >> necessary and the colleges accept kids without them?
> >
> >Because we as the older generation know they need those skills.
>
> We as the older generation don't agree whether they need those skills.
> In particular, older generation people without college degrees don't
> see a need for such courses (and guess which part of the political
> spectrum such people are commonly associated with).
And again you have no idea of what you are saying.
It is people like you who do not want to educate the children. It is people
like you who are holding the kids back from achieving their full potential.
>
> >> As for the cultural war, none of the public schools I taught in or
> >> that my children went to were involved in any attack on Christians.
> >
> >If the NEA is there, or if any leftist is there, there is an attack on
the
> >Christian belief in our public schools.
> >The Schools should not be involved with the teachings of Morals and
> >religious beliefs to begin with.
> >The school should not be involved in promoting homosexuality or any other
The NEA and the American left.
Calculus is needed before arriving at college, hence the public high schools
should be teaching the kids calculus.
Nope, reality.
No, we are asking the people responsible for lowering the standards being
taught in public education, and that is the teachers and administrators and
the damn NEA.
Teachers and the NEA have no control over the curriculum taught.
Teachers teach what the politicians tell them to teach. And Bush
managed to dumb us down more than we were before with his
test mania.
What is required by schools is set forth in law. If society changes
its views and does not set forth those changes in law, there will be
no change in the schools.
>> We as the older generation don't agree whether they need those skills.
>> In particular, older generation people without college degrees don't
>> see a need for such courses (and guess which part of the political
>> spectrum such people are commonly associated with).
>
>And again you have no idea of what you are saying.
>It is people like you who do not want to educate the children. It is people
>like you who are holding the kids back from achieving their full potential.
Just as an example:
http://www.sltrib.com/2003/Apr/04212003/utah/49816.asp
> Granite School Board members recently sent a letter to the state
> Board of Education outlining their fears that increasing graduation
> requirements in core subjects and limiting electives could alienate
> students and "will likely increase the high school dropout rate."
The elected school board members of a district in the conservative
state of Utah oppose increasing graduation requirements.
Note their reasons include increased dropout rates. Requiring more
math and science would indeed increase dropout rates.
Probability and statistics is far more useful in life than calculus.
And the ability to make reasonable rough estimates based on crude
data is more valuable yet. Sadly, I don't know that this is
taught anywhere.
-- cary
That is where probability and statistics come in handy. You don't have to
go through life calculating exacts probabilities, but knowing how to do that
makes dealing with rough estimates much easier and more reliable.
True. But I'm talking about even simpler things, like "about how
many tanks of gas to New Orleans?", or "Is it reasonable that I can
get these 400 letters out in the two days I have left?"
-- cary
Real understanding of probability and statistics requires calculus.
Perhaps, same for trigonometry, but you can do a whole bunch of very useful
stuff without understanding the calculus.
One can also make horrendous mistakes without understanding.
OK, using probability and statistics with out through knowledge of calculus
can be dangerous.
OK, this is worth a question or two. When I think of probability,
I think of discrete applications -- how many ways are there
to arrange any number of up to six letters, or how many
possible full houses are there in a poker deck. I've never
had a statistics course, but I find this sort of thing
fairly easy to reason out from first principles.
So: where does calculus enter in? Would this be more in the
realm of statistics, as opposed to probability, and involve
things like deriving the Gaussian distribution?
-- cary
Calculus is not the only mathmatic background necessary for
understanding of probability and statistics. Some of this background
is often introduced in Calculus classes (e.g. summing infinite
series). Others like linear algebra are sometimes taught separately.
> So: where does calculus enter in? Would this be more in the
> realm of statistics, as opposed to probability, and involve
> things like deriving the Gaussian distribution?
>
Understanding the derivations of continuous probability functions
is one aspect of the need for calculus.
Calculus is necessary for understanding why the Gaussian
distributions are assumed in much of statistics, and the sources of
error in using such an assumption.
>>We are willing to admit American students with ability and
>>place them in remedial courses, but how do we find this out?
>>Short of giving our own exams, we are stuck. Likewise, short
>>of giving admission exams to applicants, the colleges have
>>no way of real evaluation. The SAT, having moved away from
>>a pure aptitude test, is less than good, and grades are of
>>little value.
>Then get yourselves together and give your own entrance exams.
>And if you can't don't blame those below you who have to follow
>what the politicians say is important.
It would have to be almost unanimous to work, and this
is unlikely to happen. What is needed here is not two
2-hour exams, but at least 20 hours. Furthermore, a
large proportion, if not most, of the good schools are
state schools. I cannot see any state legislature
accepting that high school valedictorians are not
college material. Some time ago, on the gifted mailing
list, an admissions officer at a large college wrote
that the lowest SAT total (two parts) she had seen for a
valedictorian was 600. I would expect better than this
from good elementary school graduates.
It might be done for graduate application, but again, it
would have to be almost unanimous. The Purdue statistics
department has around 200 applicants a year, and many
departments have far more.
--
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
>>So here is the problem. It is the establishment as a whole. They just are
>>not teaching the required math needed for college.
>But they are teaching it - to those who want to take it. They are not
>requiring that the courses taken by some be taken by all. Meanwhile,
>teaching it doesn't mean that people retain it. 2 years of not using
>algebra, and kids forget the details.
They are NOT teaching it in many places. They are teaching
the DETAILS, as you say, and these are QUICKLY forgotten.
The concepts are not taught, as most of the teachers, and
almonst none of those in the schools of education, seem to
be able to understand concepts. Concepts are not facilitated
by starting with lots of details; those of us who have taught
prospective teachers, who know lots of details, have seen this,
and our colleagues are in agreement on this subject.
>Meanwhile, you can pass a high school math class with a D (minimum of
>somewhere between 60% and 70%), but colleges need a higher level of
>skill than a D-level in math.
I do not care how good one can manipulate; it is the concepts
which are important, and they are not easily forgotten. If one
gives good problem exams, 70% should be an "A".
>That is why some of us non-right-wing education reformers favor moving
>to a mastery-type education system, where a minimum grade is not
>considered "good enough".
Mastery of computational processes? Memorize the formulas in
the present high school geometry courses and calculate numerical
answers? Useless.
>>The kids need to be able to handle a first course in Calculus when they
>>graduate from high school. Well that should be the goal.
>>2 years of math is not enough.
Two years would be enough if it was a year of conceptual
algebra, and a year of "Euclid" geometry. It would be
better to add an old-fashioned college algebra course,
which emphasized the concept, including induction, which
really belongs in primary school, and a couple of weeks
of trigonometry. Teach them to solve problems using
trigonometry, and it does no good.
>Then government would have to increase the requirements for high
>school graduation in all 50 states. (The Federal government cannot do
>this, since education is controlled at the state level.)
>Meanwhile, there are many people who question the need for people not
>planning on going to college taking any more than algebra.
>Virginia split the difference - it has a college prep diploma and a
>regular diploma.
>>> Note here, that the only thing that has happened is that colleges in
>>> the higher tiers have lowered admission standards and thus have
>>> more kids who need remediation. It's nothing new in the middle and
>>> lower tier colleges. They had remediation classes when I went to
>>> college.
>>Why should they be lowering their standards,
>Maybe they "shouldn't", but in this country, market forces rule.
>College is big business, and they want more customers. They may SAY
>that they want better-qualified students, but they don't really. They
>make shitloads of profits off those remedial courses, which can be
>taught by cheap grad students but costs full tuition. They then use
>that tuition money to pay for the upper division and graduate level
>courses which are less profitable.
>> why can't the public schools teach the subjects needed,
>They can and do, but not all kids take the classes. You can lead a
>horse to water ...
This has to start in kindergarten. Putting a child who
knows how to read with one just recognizing letters should
bankrupt those doing it.
>>instead of getting involved with the cultural war
>Schools can't help that, since adults bring the culture war to the
>schools.
>>and the attack on Christians.
>There is no attack on Christians.
There never has been. The "attack" is on preaching
the various aspects of Christianity.
This started with the educationists, who decided that all
of a given age should be in the same classroom. Even in
the social sciences, there used to be separate geography
and history, and the students were expected to use their
geography in history. As most of them had not memorized
the details, the educationists said they could not look
them up when the need occurred, but they had to be taught
them together.
There is much more of that. But it is memorization and
routine, which is what they can understand and know how
to test with multiple choice.
I disagree. Mathematical concepts are needed.
Calculus manipulations are highly overrated, and even
detract from understanding the concepts involved. The
removal of conceptual mathematics from the high school
courses, and the demands of engineering and physics to
teach calculus manipulations, plus the objections of the
students from all these years of learning essentially
only computations, has made it impossible for college
mathematics departments to teach concepts, as the low
student ratings would keep their faculty from being
promoted.
Teaching facts and manipulations at least makes it harder
for those who are not really bright to have a chance to
understand concepts. Maybe it can be done if we are given
years to do it, but we are not.
>>.
>>"toto" <scar...@wicked.witch> wrote in message
>>news:8mnpvvg1ksptma299...@4ax.com...
>>> On Wed, 7 Jan 2004 13:03:21 -0900, "dpr" <why> wrote:
>>> >"toto" <scar...@wicked.witch> wrote in message
>>> >news:h8tovvcf5gatmdgl1...@4ax.com...
>>> >> On 7 Jan 2004 11:12:50 -0500, hru...@odds.stat.purdue.edu (Herman
>>> >> Rubin) wrote:
........................
>>> Ask Bush and the others who have this mania for high stakes testing
>>> that doesn't test anything.
>>No, we are asking the people responsible for lowering the standards being
>>taught in public education, and that is the teachers and administrators and
>>the damn NEA.
>Teachers and the NEA have no control over the curriculum taught.
>Teachers teach what the politicians tell them to teach. And Bush
>managed to dumb us down more than we were before with his
>test mania.
Other than issues of "morality", the politicians who
are involved in the decision making are those who are
in the state Departments of Education; these are all
educationists. It is not the NEA per se, but the
educationist indoctrination all of them have had, and
most of them have fallen for.
LEGALLY, this is not the case. But the unpaid school
boards do not have the time, and the efforts of
university subject matter faculty, not at least jointly
in the school of education, to volunteer to upgrade the
curriculum are ignored or even rebuffed. "We know HOW
to teach" comes from the educationists, who do not know
anything about the subject. So they can teach how to
solve problems, and definitions, but not the concepts,
which are inconceivable to them.
"Herman Rubin" <hru...@odds.stat.purdue.edu> wrote in message
news:btmiv9$2g...@odds.stat.purdue.edu...
>>That is no longer true. All of our schools have gone down hill.
>Not here in NH. About 50% of the students go to 4 year colleges,
>another 25% go to 2-year colleges.
>You call that a failure ? I don't.
It is a failure if those who graduate college know less
than those who graduated high school knew a half century
ago. They may know a few more facts, which can be easily
looked up, but that is all.
>>Calculus is needed before arriving at college, hence the public high schools
>>should be teaching the kids calculus.
>Calculus is not needed before college. At college, it's needed by hard
>science subjects such as physics, chemistry or engineering, but not to
>many others. And with the computer revolution, we're seeing the
>increased need to teach discrete math instead of calculus.
Calculus is needed for economics and psychology, agriculture,
biology, and if any non-trivial statistics is to be used,
in any discipline which uses it.
To understand probability, one needs to understand algebra,
set algebra, measure, and integration, which can be done at
a high school level, but usually is not. One quickly gets
into a need for the concepts, but not the manipulations, of
calculus, and unfortunately these are almost totally skipped
in the usual calculus courses. Combinatorics should be
looked upon as a means to calculate probabilities in some
simple cases, and not any more.
Statistics requires all of this, and even a little more.
Cookbook statistics courses, usually ignoring the above,
cause people to improperly use statistics as religion.
>In article <3ffe5ea...@news.mv.net>,
>Alberto Moreira <junk...@moreira.mv.com> wrote:
>>Said "dpr" <why> :
>
>
>>>That is no longer true. All of our schools have gone down hill.
>
>>Not here in NH. About 50% of the students go to 4 year colleges,
>>another 25% go to 2-year colleges.
>
>>You call that a failure ? I don't.
>
>
>It is a failure if those who graduate college know less
>than those who graduated high school knew a half century
>ago. They may know a few more facts, which can be easily
>looked up, but that is all.
This is the effect of the secular trend on the population of the U.
S. I invite you to read "Arkansas Benchmark Exams: An Explanation of Education
Decline in America?" about half way down the page:
www.anthropogeny.com/research.html .
James Michael Howard
Even more important is the understanding that apparently
simple problems are not, and that such rough estimates can
be way off, with what looks like a big increase even being
a fair-sized decrease. This has happened in many areas.
><Dan Listermann wrote:
><> "Robert N. Newshutz" <news...@nospam.com> wrote in message
><> news:vvrhasj...@corp.supernews.com...
><>>Dan Listermann wrote:
><>>>"Alberto Moreira" <junk...@moreira.mv.com> wrote in message
><>>>news:3fff5f2...@news.mv.net...
><One can also make horrendous mistakes without understanding.
>OK, this is worth a question or two. When I think of probability,
>I think of discrete applications -- how many ways are there
>to arrange any number of up to six letters, or how many
>possible full houses are there in a poker deck.
These are trivial, and of little importance except in
playing games and such. Most real problems are much
harder, and computation often must be left to computers,
with estimates and crude approximations requiring the
use of calculus.
I've never
>had a statistics course, but I find this sort of thing
>fairly easy to reason out from first principles.
See the above.
>So: where does calculus enter in? Would this be more in the
>realm of statistics, as opposed to probability, and involve
>things like deriving the Gaussian distribution?
The normal distribution was derived by de Moivre 47 years
before Gauss was born, as an approximation to the binomial
distribution. One CAN use it without calculus, but then
one needs to know how to use tables, not taught much today.
>>Real understanding of probability and statistics requires calculus.
>I don't think so, much modern statistics is discrete, not continuous.
>However, real understanding of probability and statistics requires
>modern math: set theory and stuff.
Even the discrete stuff is likely to require calculus to
compute. Also, the parameter space is not discrete; the
probability that the experiment will succeed can be any
real number. Even if not, large discrete is more difficult
than continuous; nobody attempts to evaluate the behavior
of a gas by looking at the discrete set of molecules.
The underlying assumed probability distribution is often continuous.
> However, real understanding of probability and statistics requires
> modern math: set theory and stuff.
>
I only claim that calculus is necessary for understanding, not
sufficient. Discrete math and algebra are also necessary.
Set theory and stuff are required for understanding it all.
The bulk of the posts currently on misc.edu demonstrate the dangers
of misunderstanding statistics.
>It might be done for graduate application, but again, it
>would have to be almost unanimous. The Purdue statistics
>department has around 200 applicants a year, and many
>departments have far more.
I see no reason why it has to be unanimous. If you want *your
school* to exceed the standards then set up a test for admission
to your school.
That's the way it is done in private prep schools. Not every private
school gives tests, but those that do are highly desirable and take
the cream of the crop.
--
Dorothy
There is no sound, no cry in all the world
that can be heard unless someone listens ..
The Outer Limits
That, BTW, is the proper answer to Cary, who is scientifically
trained. Thermodynamics is pretty much pure probability, and it
pretty much requires calculus. I'm not sure that I've seen any
definition of entropy that did not use an integral. Thermodynamics is
rather important to understanding a lot of everyday phenomena.
lojbab
--
lojbab loj...@lojban.org
Bob LeChevalier, Founder, The Logical Language Group
(Opinions are my own; I do not speak for the organization.)
Artificial language Loglan/Lojban: http://www.lojban.org
<snip>
>One does not achieve understanding by the memorization and
>rote encouraged by our schools. The bright, and especially
>the gifted, do not need repetition and are turned off by it.
I do not entirely agree with this. There are a class of things that
are best learned by repetition. One example is arithmetic: higher
level concepts fall into place much more easily if sums, averages,
ratios, and products can be pulled from the available data by one's
hindbrain. A correlary can be observed in Marital Arts training
wherein one is engrained with certain basic motions and combinations,
allowing those to be recalled and employed automatically. Explicit
thinking about the basic concepts greatly slows the analysis and
reaction processes.
I believe you will find that the "gifted" have mastered these basic
repetitive actions by the 4th grade or earlier, and that the schools
do not recognize this. Sometimes the teachers at that level have
themselves not mastered the curriculum, and so project this deficiency
into their estimation of students' progress and needs.
<snip>
>Children have different abilities, and for the schools to
>even ATTEMPT to teach them the same should be considered
>gross child abuse and mentally destructive. Unfortunately,
>we cannot replace the teachers who cannot teach conceptually,
>and the problems in the colleges with students who have not
>learned to think are massive.
For your point, I agree, but your defeatest conclusion is misguided.
The reason we cannot replace those individuals is that they cannot be
identified, because there is no quantitative information collected on
the performance of teachers, because school administration pits one
principal against 40 or 50 teachers. Besides, in most cases it is
inefficient to replace those individuals: it would be better to
proactively monitor and guide their teaching behavior; most are
probably willing to accept criticism and guidance if it is timely,
presented diplomatically and in managable pieces. Simply sacking
sub-par teachers does nothing to recycle "lessons learned" back into
the system. In other words, once we have paid for a mistake, it would
do no good to eliminate the persons who most likely learned from that
mistake. The key is to catch mistakes while they are still small, low
cost and easily corrected.
The one-teacher-fits-all model of elementary education is
anachronistic, and should be eliminated. Instead, schools should be
encouraged to separate the teaching, reinforcement, and social
processes, and assign them to individuals specializing in those
activities. Not only would this affect each teacher's focus and
workload, but the children would benefit by seeing a number of
teachers interacting through professional teamwork, and the student
would have alternatives when a student-teacher pairing is failing.
Also, a student's mistakes during reinforcement would be separated
from his or her grade-giver, reducing the performance pressure that
even elementary school children experience as they try to "please the
teacher" and learn without errors (an impossible task sometimes
adopted by the student).
Kevin
<snip>
>"The more people know about this particular law, the
>less they like it," NEA spokeswoman Kathleen Lyons
>said. She called a key requirement -- that all
>elementary and middle-school children in public schools
>be proficient in math and English by 2014 -- unworkable
>and absurd.
<snip>
Educators, beware! The NEA thinks that teaching children is
unworkable and absurd!
What will you follow? Your belief that you are being productive and
successful as you teach children, or your Union's view that your work
cannot succeed?
The system is truly broken.
Kevin
Lack of reading comprehension.
The NEA thinks that teaching *all* children, which includes such kids
as the severely mentally retarded and those who arrived in the school
system two days before the exam not speaking English or reading or
writing, to be proficient in math and English by 2014 is unworkable
and absurd.
--------------------------------------------------------
<http://www.boston.com/news/politics/president/articles/2004/01/06/democrats_b
roaden_attack_on_school_law/>
[snip]
"The more people know about this particular law, the less they like it," NEA
spokeswoman Kathleen Lyons said. She called a key requirement -- that all
elementary and middle-school children in public schools be proficient in math
and English by 2014 -- unworkable and absurd.
Indeed, there are signs that the growing pains of implementing No Child Left
Behind are spreading beyond school administrators and teachers to Republican
and Democratic legislators, who in some states are balking at the new federal
mandates in the midst of budget crises that have forced them to cut state
funding for education.
Meanwhile, parents are receiving the first reports that their public schools
have failed to make "adequate yearly progress" under the law. Data collected
by the publication Education Week show that more than 23,000 schools did not
reach state proficiency standards in the 2002-03 school year, and 5,200 had
missed the target for two years. Under federal law, those schools, deemed "in
need of improvement," must give students the option to transfer to a
better-performing school. Those on the list for three years also must provide
private tutoring.
"This law is starting to fray because it's starting to hit home," said
William J. Mathis, an education finance professor at the University of
Vermont and school superintendent in Brandon, Vt.
The White House has reason to fear political fallout. In an ABC News/
Washington Post poll last month, Bush's approval rating on education was 47
percent, the first time a majority of Americans did not have a favorable view
of the president's handling of the issue and a stunning drop from 71 percent
approval in January 2002, when Bush signed the No Child Left Behind Act.
"I have long suspected that the day Bush signed the act was the day he would
get the most credit for improving education," said John F. Jennings, director
of the Center on Education Policy, a nonprofit group that advocates for
public schools. "It is very difficult for the federal government to bring
about change in public schooling, where the tradition is for local control."
Determined to end the Democrats' traditional advantage on education,
particularly with female voters in the suburbs, Bush made the improvement of
public schools a campaign theme in 2000. He pledged unprecedented federal
intervention to close the achievement gap between white and minority
students, and tied an increase in federal funds to rigorous requirements for
standardized testing and school accountability.
Polls showed it was a winning issue for Bush. Democrats, led by Senator
Edward M. Kennedy of Massachusetts, saw a way to target more federal money to
public schools in low-income neighborhoods, and voted almost unanimously for
the legislation in late 2001.
Within months, the bipartisan comity collapsed, as Democrats charged that
Bush reneged on at least $6 billion in funds promised to implement the law
and was saddling states with an "unfunded mandate."
[snip]
--------------------------------------------------------
<snip>
>>One does not achieve understanding by the memorization and
>>rote encouraged by our schools. The bright, and especially
>>the gifted, do not need repetition and are turned off by it.
>I do not entirely agree with this. There are a class of things that
>are best learned by repetition. One example is arithmetic: higher
>level concepts fall into place much more easily if sums, averages,
>ratios, and products can be pulled from the available data by one's
>hindbrain.
Arithmetic, and similar skills, are enhanced (not learned)
by appropriate practice. The bright and gifted are, if
anything, likely to do too much practice to achieve this if
they are not given loads of busy work.
But none of this does any good whatever when it comes to
learning concepts. It makes it difficult to realize that
the mechanics have NOTHING to do with understanding. This
is exemplified by the almost total failure of prospective
and actual elementary school teachers to understand
mathematical concepts.
A correlary can be observed in Marital Arts training
>wherein one is engrained with certain basic motions and combinations,
>allowing those to be recalled and employed automatically. Explicit
>thinking about the basic concepts greatly slows the analysis and
>reaction processes.
If you want fast reaction time, you do not want thinking.
>I believe you will find that the "gifted" have mastered these basic
>repetitive actions by the 4th grade or earlier, and that the schools
>do not recognize this.
I suggest you forget the arithmetic prowess. Unless the
person is profoundly gifted, it really makes it hard to
learn the concepts. Lots of first-class mathematicians
are poor at arithmetic. Lots are not.
I can teach statistical concepts at any level from the
understanding of algebra up, but for those who have had
a statistical methods course, it will be at least
difficult, if not impossible. Ingrained habits are
like religion.
Sometimes the teachers at that level have
>themselves not mastered the curriculum, and so project this deficiency
>into their estimation of students' progress and needs.
<snip>
>>Children have different abilities, and for the schools to
>>even ATTEMPT to teach them the same should be considered
>>gross child abuse and mentally destructive. Unfortunately,
>>we cannot replace the teachers who cannot teach conceptually,
>>and the problems in the colleges with students who have not
>>learned to think are massive.
>For your point, I agree, but your defeatest conclusion is misguided.
>The reason we cannot replace those individuals is that they cannot be
>identified, because there is no quantitative information collected on
>the performance of teachers, because school administration pits one
>principal against 40 or 50 teachers.
If the educationists allowed subject matter scholars to
check on it, they could be identified quickly.
Besides, in most cases it is
>inefficient to replace those individuals: it would be better to
>proactively monitor and guide their teaching behavior; most are
>probably willing to accept criticism and guidance if it is timely,
>presented diplomatically and in managable pieces.
That you stated this is evidence that you do not understand
concepts; they are not generalizations, not memorized, and
cannot be broken into manageable pieces.
No, we need teachers who understand concepts, who do not
teach by memorization and routine, and preferably who
have not taken the "education" courses which tell them
supposedly how to teach, but actually make it difficult
or even impossible to teach anything important.
><snip>
>>"The more people know about this particular law, the
>>less they like it," NEA spokeswoman Kathleen Lyons
>>said. She called a key requirement -- that all
>>elementary and middle-school children in public schools
>>be proficient in math and English by 2014 -- unworkable
>>and absurd.
><snip>
>Educators, beware! The NEA thinks that teaching children is
>unworkable and absurd!
What is unworkable and absurd is the idea that all
children are to be taught the same material at the
same rate in the same manner.
>What will you follow? Your belief that you are being productive and
>successful as you teach children, or your Union's view that your work
>cannot succeed?
You cannot make a silk purse from a sow's ear.
>The system is truly broken.
It sure is; the educationists broke it when they
came up with the idea that children of the same
age should be in the same classroom. They broke
it further when they allowed any lowering of the
curriculum, but that was forced by the first.
Some of the current teachers could teach concepts;
most are incapable of learning them, at least
without taking many years to do it.
>>Even the discrete stuff is likely to require calculus to
>>compute. Also, the parameter space is not discrete; the
>>probability that the experiment will succeed can be any
>>real number. Even if not, large discrete is more difficult
>>than continuous; nobody attempts to evaluate the behavior
>>of a gas by looking at the discrete set of molecules.
>The "discrete stuff" means that all the calculus we need to learn
>reduces to one phrase:
>"An integral is a discrete sum of products."
No, a limit of such. Limit is key, and it belongs early.
>Discrete isn't more difficult than continuous, it's just different,
>and it sits on a different set of bases: it's fundamental that we
>learn modern math before we can properly learn discrete stuff.
<snip>
>But none of this does any good whatever when it comes to
>learning concepts. It makes it difficult to realize that
>the mechanics have NOTHING to do with understanding. This
>is exemplified by the almost total failure of prospective
>and actual elementary school teachers to understand
>mathematical concepts.
(See the last paragraph.)
> A correlary can be observed in Marital Arts training
>>wherein one is engrained with certain basic motions and combinations,
>>allowing those to be recalled and employed automatically. Explicit
>>thinking about the basic concepts greatly slows the analysis and
>>reaction processes.
>
>If you want fast reaction time, you do not want thinking.
Fast mechanics are a fundamental part of real-world, real-time problem
solving. It is necessary to formulate theories ("thinking"), and test
them quickly to see if a theory stands. To perform that testing
requires mechanics and zero-time reactions; The gifted spend more time
testing than theorizing, and have simply been able to align the
process of theorize-test-reject-repeat into their routine way of
looking at things, and have accepted the fact that 90% (or more) of
these quick theories are rejected before one opens one's mouth.
<snip
>No, we need teachers who understand concepts, who do not
>teach by memorization and routine, and preferably who
>have not taken the "education" courses which tell them
>supposedly how to teach, but actually make it difficult
>or even impossible to teach anything important.
OK, so what do you do with the teachers you have? You must play the
cards that are dealt, and cannot get new cards through wishful
thinking. It would be better to bring the teachers that you have (who
individually bring many divers skills), to a more uniform level of
what you want. You do this by (1) breaking the herd-of-cats
mentality, and (2) diplomatically guiding improvements. One is
cultural and the other is time consuming. The divergence has occured
slowly, and recovery must be developed, not dictated.
There is no science of teaching. The schools are _way_ behind the
curve, and now suffer with teachers produced in the 80's and 90's,
when education was already in decline: its a closed loop.
Until the schools begin to take quantitative measurements and make
archives of successful concepts and practices, the teacher-schools
will never be able to achieve your goal. In other words, the
"education courses" are insufficient because they have no detailed,
known-working concepts to teach to the teachers, and the schools do
nothing to discover, enumerate, name, or even record those concepts.
Until concepts are named with solid definitions, concepts cannot be
discussed by peers or introduced to new recruits, and until the
concepts are proven effective they should only be discussed by those
with sufficient to maturity.
Kevin
>>No, a limit of such. Limit is key, and it belongs early.
>Herman, one of the characteristics of Discrete Math as it is used in
>Computer Science is, there's basically no such a thing as an infinite
>set.
One can discuss infinite sets with finite strings of
characters. This does not make it "discrete math". Anyone
who does not understand proofs by induction does not
understand the integers, and it is these which point out
the essential infinity, and also the wau to deal with it.
It's all about finiteness, and hence, limit is something that
>ceases to be nearly that importance.
Limit, and error, are of great importance.
So, no, an integral isn't a
>limit, an integral is the sum of products.
It might be, or it might not be. The Beta and Gamma functions
were defined as integrals, but nobody approximates them on the
computer by sums of products. Nor are their logarithms so
approximated, and they are usually computed using these.
It then boils down to how
>many points you want to use to compute it, and that is tied to the
>precision we're working with.
Not if you want good accuracy. This even applies to
indefinite integrals; I have never seen a computer
program in a decent mathematical library attempt to
compute the error function, or the Fresnel functions,
or others of this type which were originally defined
as integrals, by numerical integration procedures.
One uses continuous mathematical theory to come up
with other methods.
>It's no longer pure math, you know !
I know how to carry out good accurate computations.
>Alberto.
<snip>
>>But none of this does any good whatever when it comes to
>>learning concepts. It makes it difficult to realize that
>>the mechanics have NOTHING to do with understanding. This
>>is exemplified by the almost total failure of prospective
>>and actual elementary school teachers to understand
>>mathematical concepts.
>(See the last paragraph.)
>> A correlary can be observed in Marital Arts training
>>>wherein one is engrained with certain basic motions and combinations,
>>>allowing those to be recalled and employed automatically. Explicit
>>>thinking about the basic concepts greatly slows the analysis and
>>>reaction processes.
>>If you want fast reaction time, you do not want thinking.
>Fast mechanics are a fundamental part of real-world, real-time problem
>solving.
Not so.
It is necessary to formulate theories ("thinking"), and test
>them quickly to see if a theory stands.
You cannot test them quickly; you need lots of observations,
and the calculations have to be performed on computers.
If fact, 60 years ago Trygve Haavelmo suggested that
economists spend the next 15-20 years to produce all
the "crackpot" theories they could, so they could
tell the governments what data to collect to make
reasonable decisions after a century or so. This
has not changed.
To perform that testing
>requires mechanics and zero-time reactions; The gifted spend more time
>testing than theorizing, and have simply been able to align the
>process of theorize-test-reject-repeat into their routine way of
>looking at things, and have accepted the fact that 90% (or more) of
>these quick theories are rejected before one opens one's mouth.
I have been involved in research in mathematics and
statistics for almost 60 years. Any such thinking does not
involve computational mechanics, and none of my strong
research colleagues use that either.
><snip
>>No, we need teachers who understand concepts, who do not
>>teach by memorization and routine, and preferably who
>>have not taken the "education" courses which tell them
>>supposedly how to teach, but actually make it difficult
>>or even impossible to teach anything important.
>OK, so what do you do with the teachers you have? You must play the
>cards that are dealt, and cannot get new cards through wishful
>thinking. It would be better to bring the teachers that you have (who
>individually bring many divers skills), to a more uniform level of
>what you want.
This was attempted for the "new math". It did not work.
It will not work for most of the present teachers or
teacher candidates, at least without going through a
long period of UNlearning. It cannot be done gradually.
Also, the schools of education are against it, and will
not give up their ideas that one learns concepts by
memorizing facts and routine in abundance first; this
is what is deadly.
Some of the teachers have managed to overcome this, but
not many. We can get teachers who have not been through
the educationist wringer, and put them in good positions,
but the unions, educationists, and politicians will
scream bloody murder. It will take decades to get a
decent educational setup AFTER we realize that the present
one is not fixable as it stands.
You do this by (1) breaking the herd-of-cats
>mentality, and (2) diplomatically guiding improvements. One is
>cultural and the other is time consuming. The divergence has occured
>slowly, and recovery must be developed, not dictated.
It can be done slowly only by providing a very affordable
alternative to the present offal. We can recover some of
those now in the system by making it financially ruinous
to keep those willing and able to learn many times more
from doing so; age-grouping MUST be eradicated.
>There is no science of teaching. The schools are _way_ behind the
>curve, and now suffer with teachers produced in the 80's and 90's,
>when education was already in decline: its a closed loop.
>Until the schools begin to take quantitative measurements and make
>archives of successful concepts and practices, the teacher-schools
>will never be able to achieve your goal.
The present ones, never. If we keep children from being
brainwashed, and allow affordable education which has NO
connection to the present public schools, and which also
is free from government control, we can build up. There
is much art in education, but those who cannot recognize
concepts are only useful for teaching the unimportant
material. We can get children to recognize concepts, but
only if we keep them AWAY from the present schools.
In other words, the
>"education courses" are insufficient because they have no detailed,
>known-working concepts to teach to the teachers, and the schools do
>nothing to discover, enumerate, name, or even record those concepts.
I suggest you study abstract mathematics and theoretical
science. There you will see concepts, but these concepts
are not taught as you state. Knowing how to prove theorems
does not give a command of concepts.
>Until concepts are named with solid definitions, concepts cannot be
>discussed by peers or introduced to new recruits, and until the
>concepts are proven effective they should only be discussed by those
>with sufficient to maturity.
We did a fair to middling job of getting concepts across
before those like you, with their insistence on breaking
concepts into small pieces, or even ignoring the matter,
got into the act. Those who would attempt that detailed
approach you advocate are not capable of teaching concepts.
We need to start by having the subject matter scholars
take over, and throw out those who claim to know how to
teach what they do not understand.
On 12 Jan 2004 17:10:35 -0500, hru...@odds.stat.purdue.edu (Herman
Rubin) wrote:
>In article <pl4500lmec2vp166f...@4ax.com>,
>Kevin Kilzer <kkilzer.r...@mindspring.com> wrote:
>>Fast mechanics are a fundamental part of real-world, real-time problem
>>solving.
>
>Not so.
<snip>
>I have been involved in research in mathematics and
>statistics for almost 60 years. Any such thinking does not
>involve computational mechanics, and none of my strong
>research colleagues use that either.
It was not my intention to belittle your experience, but in 25 years
of engineering I have spent many hours deciding if an approach is
practical. Fortunately, most of my problems could be solved (or at
least estimated), in less than a few hours, and I have the opportunity
to try many different approaches for most problems. In engineering,
quick mechanics lends itself to faster estimations.
<snip>
> In other words, the
>>"education courses" are insufficient because they have no detailed,
>>known-working concepts to teach to the teachers, and the schools do
>>nothing to discover, enumerate, name, or even record those concepts.
>
>I suggest you study abstract mathematics and theoretical
>science. There you will see concepts, but these concepts
>are not taught as you state. Knowing how to prove theorems
>does not give a command of concepts.
It is here that I believe we had a misunderstanding. I was not
talking about concepts that would eventually be taught to the
children, but about concepts of teaching: concepts to be taught to the
teachers. If I may compare the art of teaching to the art of
mathematics, I hope you would agree that until you had named theorems
and forms, communication that built upon those theorems was difficult
if not impossible. Likewise, until teachers can name theorems and
forms in their art, systematic building cannot take place because
communication will not be efficient. Teaching has no Euclid or Newton
or Euler to bring the art to the level of science.
For example, you could use the phrase "gradient of the curl", and
reasonably expect your colleagues to reconstruct what that shorthand
implies. Teachers, to the contrary, have no nouns and verbs that
encapsulate what they do or how they do it. In fact, I believe that
many teachers would shun a technical decomposition of teaching in the
same way that mathematics has been formalized, but until that happens
I cannot foresee the realization of systematic improvements.
Our understanding of the problem may not be as far apart as you
imagine. It is clear to me that the present system does not lend
itself to being corrected.
Kevin
P.S. My last foray into theoretical mathematics was when I helped a
local 5th grade teacher with a class in group theory, so she could
achieve her state certification. As with most of the other times that
I have tutored teachers, I came away amazed and stunned that anybody
learns anything from the public schools.
>On 12 Jan 2004 17:10:35 -0500, hru...@odds.stat.purdue.edu (Herman
>Rubin) wrote:
>>In article <pl4500lmec2vp166f...@4ax.com>,
>>Kevin Kilzer <kkilzer.r...@mindspring.com> wrote:
>>>Fast mechanics are a fundamental part of real-world, real-time problem
>>>solving.
>>Not so.
><snip>
>>I have been involved in research in mathematics and
>>statistics for almost 60 years. Any such thinking does not
>>involve computational mechanics, and none of my strong
>>research colleagues use that either.
>It was not my intention to belittle your experience, but in 25 years
>of engineering I have spent many hours deciding if an approach is
>practical. Fortunately, most of my problems could be solved (or at
>least estimated), in less than a few hours, and I have the opportunity
>to try many different approaches for most problems. In engineering,
>quick mechanics lends itself to faster estimations.
On some practical problems, this is the case, and as I am
one of those with strong mental computational abilities, I
do it when it is appropriate and convenient. But often I
will invoke a calculator or computer to do this. I do not
object to doing computation to investigate even a theoretical
problem, but I see no reason to demand this be done by hand.
If anything, in some cases it takes me longer because of this.
The biggest problem with the use of statistics, besides the
amount of computation being too great to do by hand, even
before computers (I know about using the now obsolete desk
calculators, slide rules, books of tables, trick formulas,
and other such devices), is that the person with the real
problem has learned to compute answers by computer, and does
not know enough to identify his problem. Even worse, there
is the tendency to force the problem into a mold where it
does not belong. The engineer who forces the problem into
an inappropriate differential equation for which he knows
the closed form solution may well have the edifice collapse.
Computers are able to do all the calculus computations which
the typical engineer can do.
><snip>
>> In other words, the
>>>"education courses" are insufficient because they have no detailed,
>>>known-working concepts to teach to the teachers, and the schools do
>>>nothing to discover, enumerate, name, or even record those concepts.
>>I suggest you study abstract mathematics and theoretical
>>science. There you will see concepts, but these concepts
>>are not taught as you state. Knowing how to prove theorems
>>does not give a command of concepts.
>It is here that I believe we had a misunderstanding. I was not
>talking about concepts that would eventually be taught to the
>children, but about concepts of teaching: concepts to be taught to the
>teachers.
As the teachers do not know the concepts which the children
should be learning, they cannot teach them to the children.
Teaching concepts is NOT done by memorization and rote, and
is NOT done gradually; we have empirical evidence for that.
It is also the case that related concepts can interfere; in
a study for which I saw a technical report, the figures
showed this clearly, as well as going from special to general
being the most time-consuming manner.
If I may compare the art of teaching to the art of
>mathematics, I hope you would agree that until you had named theorems
>and forms, communication that built upon those theorems was difficult
>if not impossible.
The first thing to learn in mathematics is what a theorem
is, and what a proof is. Having a good language to do it
in is very helpful; the use of variables belongs with the
first steps in reading, and is purely grammatical. But
grammar is not in favor now.
One can get by without variables in principle, but it is
almost impossible to read the statements, let alone the
proofs, and even the manipulations. The present use of
variables is at best late 19th century, and the "modern"
development of mathematics started with Viete, using
many variables for numbers, in the late 16th century.
Many believe that Archimedes would have developed calculus
if he had variables.
As far as being able to NAME theorems. this is rarely of
importance until an advanced stage. Landau's book gives
a good development of the positive integers and positive
rational numbers first; the named theorems are the laws
of addition and multiplication. Induction is widely
used, but is not a theorem; it is an axiom. The axioms
are about counting.
One does not memorize names, except of such theorems
which are so widely used that their names do not need
to be memorized.
Likewise, until teachers can name theorems and
>forms in their art, systematic building cannot take place because
>communication will not be efficient. Teaching has no Euclid or Newton
>or Euler to bring the art to the level of science.
One can teach facts and manipulations without understanding
them, but not concepts. Before teaching concepts, one
must understand what a concept it. It is the case that
students can learn a concept even if the teacher does not
understand it provided the teacher does not dumb down the
material, but the text material must then be carefully
provided by the scholars. This was the case with "Euclid"
in the old days, when this was the standard geometry course.
>For example, you could use the phrase "gradient of the curl", and
>reasonably expect your colleagues to reconstruct what that shorthand
>implies. Teachers, to the contrary, have no nouns and verbs that
>encapsulate what they do or how they do it. In fact, I believe that
>many teachers would shun a technical decomposition of teaching in the
>same way that mathematics has been formalized, but until that happens
>I cannot foresee the realization of systematic improvements.
Mathematics is almost pure grammar. You are concentrating on
specific nouns, and this is almost irrelevant.
>Our understanding of the problem may not be as far apart as you
>imagine. It is clear to me that the present system does not lend
>itself to being corrected.
On this we agree.
>P.S. My last foray into theoretical mathematics was when I helped a
>local 5th grade teacher with a class in group theory, so she could
>achieve her state certification. As with most of the other times that
>I have tutored teachers, I came away amazed and stunned that anybody
>learns anything from the public schools.
They may learn by exposure, but not from the teachers, who are
likely to make things harder.
most Third World nations school test scores do infinitely better than
the US, with about 1/10th to 1/20th the per pupil expediture, AND
40-60 students per classroom. even in Europe, there are routinely
35-50 students per class.
how come no one ever asks the national extortion, er education,
association about these facts?
you're asking the wrong question, peoples.
as for the law: any new federal law takes years, if ever, to work the
kinks out of. Social Security is still a ponzi scheme with OUR
trillions.
No. Most 3rd world nations not only to worse than us, they don't even
educate most of their kids through the high school level. The
(invalid) comparisons that you read about in the press are with other
advanced nations, and in general they spend about the same as us on
K12 education as a percentage of GNP.
>with about 1/10th to 1/20th the per pupil expediture,
Only because the cost of living in 3rd world nations is such that
teachers might get paid a couple hundred bucks a year.
>AND 40-60 students per classroom.
That requires that kids be trained in the herd instinct, something not
possible in a society that promotes individualism like ours does.
> even in Europe, there are routinely 35-50 students per class.
>
>how come no one ever asks the national extortion, er education,
>association about these facts?
Because they aren't facts and they aren't relevant to the problem of
education in this country.
>most Third World nations school test scores do infinitely better than
>the US, with about 1/10th to 1/20th the per pupil expediture, AND
>40-60 students per classroom. even in Europe, there are routinely
>35-50 students per class.
Data that shows this?
None of the test scores I have seen show third world nations doing
infinitely better than the US, not that the word infinitely even makes
sense in this context.
Of the countries that are compared in the touted International
tests, please tell us which ones are *third world* and how
those countries do in relationship to the US on the tests.
Here's the list. The US scores above the international average,
but not by a lot.
Here is a pdf file that has a table of the scores for 1999
on page 32
This report is focused on gender differences so it does
not really get into the comparisons of the countries much.
http://timss.bc.edu/timss1999i/pdf/T99i_Math_1.pdf
What is interesting is comparing that to the measure
of competitiveness in the International Market as
ranked by the World Economic Federation. This is a
complex ranking and the US comes out 2nd among
the same countries who took the TIMSS tests.
The article below goes to that point. It was published in
the Washington Post, but this is a mathed news forum
which includes a bit more data on the rankings.
http://mathforum.org/epigone/mathed-news/kimvomquei
The part of the opinion I found extremely interesting, I
quote here. Note to Herman, I know the correlation
analysis doesn't provide the entire picture, but the interesting
points are in the paragraphs after that. I only include
that part because it shows a bit about how statistical
correlations can be misleading to people who don't
understand the more sophisticated statistical analysis.
>:The Third International
>:Mathematics and Science Study (TIMSS) provides test
>:scores for 41 nations, including the United States. Thirty-
>:eight of those countries are ranked on the World Economic
>:Forum's CCI. It's a simple statistical matter to correlate the
>:test scores with the CCI.
>:
>:There is little correlation. The United States is 29th in
>:mathematics, but second in competitiveness. Korea is
>:third in mathematics, but 27th in competitiveness. And
>:so forth. If the two lists had matched, place for place, that
>:would produce a perfect correlation of +1.0. But because
>:some countries are high on competitiveness and low on
>:test scores (and vice versa), the actual correlation is +.23.
>:In the world of statistics, this is considered quite small.
>:
>:Actually, even that small correlation is misleadingly high:
>:Seven countries are low on both variables, creating what
>:little relationship there is. If these seven nations are removed
>:from the calculation, the correlation between test scores
>:and competitiveness actually becomes negative, meaning
>:that higher test scores are slightly associated with lower
>:competitiveness.
>:
>:The education variables in the index include: the quality of
>:schools; the TIMSS scores; the number of years of education
>:and the proportion of the country's population attending college
>:(these two are variables in which the United States excels);
>:and survey rankings from executives who, theWorld Economic
>:Forum claims, have "international perspectives." The WEF
>:ranked U.S. schools 27th of the 75 nations -- not exactly eye-
>:popping, but given all of the horrible things said about American
>:schools in the past 25 years, perhaps surprisingly high. (The
>:United States looked particularly bad in one WEF category: the
>:difference in quality between rich and poor schools. We finished
>:42nd, lower than any other developed nation. That is shameful
>:in a country as rich as ours.)
>:
>:So, if 26 nations have better schools, how did we earn our
>:No. 2 overall competitiveness ranking? The WEF uses dozens
>:of variables from many sectors, and the United States rates
>:well across the board. One important consideration is the "brain
>:drain" factor. Our scientists and engineers stay here, earning us
>:a top ranking in this category. No other country, not even Finland,
>:came close on this measurement.
>:
>:But what really caught my eye were the top U.S. scores on a
>:set of variables that make up what the WEF calls "National
>:Innovation Capacity." Innovation variables are critical to
>:competitiveness, according to the WEF. Ten years ago, the
>:competitive edge was gained by nations that could lower costs
>:and raise quality. Virtually all developed countries have
>:accomplished this, the WEF report asserts, and thus
>:"competitive advantage must come from the ability to create
>:and then commercialize new products and processes, shifting
>:the technology frontier as fast as rivals can catch up."
>:
>:Innovation is itself a complicated affair, but my guess is that it is
>:not linked to test scores. If anything, too much testing
>:discourages innovative thinking.
>:
This is the author's opinion, but I agree that we do allow a lot
of questioning especially in our best schools.
>:American schools, believe it or not, have developed a culture
>:that encourages innovative thinking. How many other cultures
>:do that? A 2001 op-ed in The Washington Post was titled "At
>:Least Our Kids Ask Questions." In the essay, author Amy
>:Biancolli described her travails in trying to get Scottish students
>:to discuss Shakespeare. She found that they weren't used to
>:being allowed to express their opinions or having them valued.
>:I had the same experience when I taught college students in
>:Hong Kong. Years later, I mentioned this to a professor in
>:Taiwan who said that even today, "professors' questions are
>:often met with stony silence."
>:
>:We take our questioning culture so much for granted that we
>:don't even notice it until we encounter another country that
>:doesn't have it. A 2001 New York Times article discussed,
>:in the words of Japanese scientists, why Americans win so
>:many Nobel prizes while the Japanese win so few. The
>:Japanese scientists provided a number of reasons, but
>:the one they cited as most important was peer review. Before
>:American scientists publish their research, they submit it to
>:the scrutiny -- questioning -- of other researchers. Japanese
>:culture discourages this kind of direct confrontation; one
>:Japanese scientist recalled his days in the United States, when
>:he would watch scholars -- good friends -- engage in furious
>:battles, challenging and testing each other's assumptions and
>:logic. That would never happen in Japan, he told the Times
>:reporter.
>:
>:Japan's culture of cooperation and consensus makes for a
>:more civil society than we find here, but our combative culture
>:leaves us with an edge in creativity. We should think more
>:than twice before we tinker too much with an educational
>:system that encourages questioning. We won't benefit from
>:one that idolizes high test scores.
>:
>:It could put our very competitiveness as a nation at risk.
>>Our understanding of the problem may not be as far apart as you
>>imagine. It is clear to me that the present system does not lend
>>itself to being corrected.
>
>On this we agree.
I also believe it unlikely that I will be around to see the change
completed.
If you consider the revolution for civil rights, it began about 140
years ago with the Civil War. Compared to the time of a generation,
say 30 years, that is about 5:1, and it is not yet fully complete.
The revolution for Detroit automobile manufacturing began in the early
1970's and lasted into the 1990's. Given that the development cycle
of a car model is about 4-5 years, this is again a 5:1 ratio (give or
take).
Taking the product cycle of a public school to be about 16 years
(kindergarten until a new teacher emerges from college), the
revolutionary change that is necessary will therefore take over 80
years, given that it starts at all. There might be some interesting
times ahead.
Kevin
Mmmm...I dunno. If someone thinks that third world kids can
somehow perform "infinitely" better on tests, then we may
indeed be in trouble.
-- cary
>>>Our understanding of the problem may not be as far apart as you
>>>imagine. It is clear to me that the present system does not lend
>>>itself to being corrected.
>>On this we agree.
>I also believe it unlikely that I will be around to see the change
>completed.
Completed, very unlikely. But a good start can be made.
We cannot do it THROUGH the present public school system;
we will have to go around it. We need to set up alternative
systems for learning not tied down to age grouping, not tied
down to teaching all at the same rate, or even in the same
manner, and not tied down to being in the same "grade" for
different subject. And we will have to eliminate holding
a student back because the other students, or the teacher,
cannot keep up. We will have to keep those teachers who do
not understand conepts out of the way, or at least insist
that they do not interfere with the students learning what
they can not.
We might well have to do without physical presence for a
large part of it. We will have to use teachers who can
understand their subjects, but who have not taken the
"education" courses now required; these courses are a
large part of the problem. We will have to find out just
what we can do, in most cases, about teaching concepts
and structure efficiently, although in certain cases, such
as "proof" geometry and grammar, we can go back to the past.
Concepts are not learned in small steps, or by rote or
routine manipulation.
As there are some who will not be able to keep up with the
pace, and possibly with the manner, of the ones who can
learn conceptually. Having them repeat a "grade", as is
the case at present when it is used, is highly inefficient
and also not likely to succeed unless the material was
almost mastered. Clearly, in that case it is not the best
way to do things.
>If you consider the revolution for civil rights, it began about 140
>years ago with the Civil War. Compared to the time of a generation,
>say 30 years, that is about 5:1, and it is not yet fully complete.
>The revolution for Detroit automobile manufacturing began in the early
>1970's and lasted into the 1990's. Given that the development cycle
>of a car model is about 4-5 years, this is again a 5:1 ratio (give or
>take).
>Taking the product cycle of a public school to be about 16 years
>(kindergarten until a new teacher emerges from college), the
>revolutionary change that is necessary will therefore take over 80
>years, given that it starts at all. There might be some interesting
>times ahead.
I do not think the situation is that bad. If the
educationists are not allowed to block it, as was done
with civil rights, and their ideas about academic
progress and methods of teaching are allowed to be
discarded in the huge number of cases where they are
interfering with learning, we can use those who seem
able to think. Many of them are now even dropping out
of school, as having a very high IQ does not by itself
provide the information about how to handle the present
miseducational system.