Poor Algebra Preparation Once Again
Dom
http://digital.ipcprintservices.com/article/Letter_To_The_Editor/276965/0/article.html
Letter To The Editor
Poor Algebra Preparation Once Again
I can empathize with the many letters in the October/November MAA
FOCUS bemoaning the poor algebra skills of many of our students,
including those who supposedly had a calculus course in high school.
As mathematicians, we are supposed to be adept at identifying
problems, and then finding solutions. It is my contention that we have
identified a symptom, but not the actual problem.
I went to university in Britain in 1975. At that time, every student
bound for higher education, regardless of intended major, was required
to pass O(rdinary)-level mathematics, usually in the sophomore year of
high school. This consisted of a battery of three two-hour
examinations, covering most of the precalculus and typical one-
semester Calculus I course. To stem the tide of "elitism" comments, I
would point out that O-level mathematics was also required of students
going on to business, banking, and even the Merchant Navy.
I believe that the problem is not with students taking calculus "too
early." It is that the American school system passes along students
who have not mastered material. Simply spending more time on algebra
will not help, unless there is an appropriate standard. I would
encourage the MAA to investigate licensure for students in algebra and
precalculus, similar to the AP Calculus tests.
Tim Norfolk, The University of Akron
Rowley
Martin
Dom wrote:
> http://digital.ipcprintservices.com/publication/?i=27730&pre=1
>
> http://digital.ipcprintservices.com/article/Letter_To_The_Editor/276965/0/article.html
>
> Letter To The Editor
>
> Poor Algebra Preparation Once Again
>
> I can empathize with the many letters in the October/November MAA
> FOCUS bemoaning the poor algebra skills of many of our students,
> including those who supposedly had a calculus course in high school.
>
> As mathematicians, we are supposed to be adept at identifying
> problems, and then finding solutions. It is my contention that we have
> identified a symptom, but not the actual problem.
Wow!, it's rare when someone recognizes that identifying symptoms isn't
the same as identifying what is actually causing them...
> I went to university in Britain in 1975. At that time, every student
> bound for higher education, regardless of intended major, was required
> to pass O(rdinary)-level mathematics, usually in the sophomore year of
> high school. This consisted of a battery of three two-hour
> examinations, covering most of the precalculus and typical one-
> semester Calculus I course. To stem the tide of "elitism" comments, I
> would point out that O-level mathematics was also required of students
> going on to business, banking, and even the Merchant Navy.
Not exactly the way things are done here in the US, but I could imagine
that exams like that could be sold on the basis that they were open to
be taken/challenged by anyone...
> I believe that the problem is not with students taking calculus "too
> early." It is that the American school system passes along students
> who have not mastered material.
Which I see more as a symptom than the actual problem...
Martin
Tim Norfolk
> Random thoughts and comments �inline...
>
> Martin
>
>
>
>
>
> Dom wrote:
> >http://digital.ipcprintservices.com/publication/?i=27730&pre=1
>
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
Martin;
Then what is the problem? One that seems obvious to me is that we
'want' more to go to university, even if they are unprepared or
unqualified. I am quite aware of that issue, as I work at an open-
enrollment university.
Herman Rubin
>http://digital.ipcprintservices.com/article/Letter_To_The_Editor/276965/0/article.html
>Letter To The Editor
>Poor Algebra Preparation Once Again
>I can empathize with the many letters in the October/November MAA
>FOCUS bemoaning the poor algebra skills of many of our students,
>including those who supposedly had a calculus course in high school.
>As mathematicians, we are supposed to be adept at identifying
>problems, and then finding solutions. It is my contention that we have
>identified a symptom, but not the actual problem.
On this point, you are correct. But you have missed the
main point; mathematics is not a collection of facts,
theorems, and algorithms, but a way of thinking, which
enables it to be applied even by those who are not adept
at FINDING the above. The concepts are simple, and do
not require leading up to, but use after they are learned
Algebra is not properly taught; the typical algebra course
introduces variables poorly, gives algorithms for the
solution of problems with ONE variable, and then asks
students to solve problems, at least 90% of which should
not be done with one variable.
Here is the content of algebra, and more, in two sentences:
A variable is a temporary name which can be used for
anything at all.
The same operation done on equal entities yields
equal results.
These can be learned in first grade, and then APPLIED.
>I went to university in Britain in 1975. At that time, every student
>bound for higher education, regardless of intended major, was required
>to pass O(rdinary)-level mathematics, usually in the sophomore year of
>high school. This consisted of a battery of three two-hour
>examinations, covering most of the precalculus and typical one-
>semester Calculus I course. To stem the tide of "elitism" comments, I
>would point out that O-level mathematics was also required of students
>going on to business, banking, and even the Merchant Navy.
Before WWII, the college preparatory program in the US was
algebra, Euclid geometry, two years of a foreign language,
three years of science, and three years of English. Good
students also took more algebra and geometry, trigonometry,
and something called "college algebra", which was
non-trivial. Now, most cannot even get a Euclid course,
which was realized back then as the only real mathematics
course taught in high school.
>I believe that the problem is not with students taking calculus "too
>early." It is that the American school system passes along students
>who have not mastered material. Simply spending more time on algebra
>will not help, unless there is an appropriate standard. I would
>encourage the MAA to investigate licensure for students in algebra and
>precalculus, similar to the AP Calculus tests.
About 45 years ago, I brought up in the meeting of a
state chapter of MAA the idea of setting standards.
I did not get a second on the proposal.
>Tim Norfolk, The University of Akron
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
Herman Rubin
Tim Norfolk <tims...@aol.com> wrote:
>On Dec 16, 10:01=EF=BF=BDam, Rowley <industry3dREM...@yahoo.com> wrote:
>> Random thoughts and comments =EF=BF=BDinline...
>> Martin
>> Dom wrote:
................
>Then what is the problem? One that seems obvious to me is that we
>'want' more to go to university, even if they are unprepared or
>unqualified. I am quite aware of that issue, as I work at an open-
>enrollment university.
The problem is the educationist attitude that being
with one's age group is more important than getting
an education appropriate to one's abilities. From
this standpoint, anybody should be able to get a
college education.
Nothing is more false than this, and it is the bright,
and especially the geniuses, who are being mentally
retarded. Also, the ones who have difficulty are not
being helped, and having them repeat the same course
in the same way is not likely to help them, either.
It should be noted that the current educational system
is likely to rate the moderately bright hard worker
above the genius who does not have to work to keep up.
There are recorded cases of students dropping out
because they cannot stand the boredom.
Tim Norfolk
> In article <d663830a-ab83-428d-be72-850b82e03...@x20g2000vbn.googlegroups.com>,
It looks like you and I are on the same side this time, Herman.
Rowley
What? You want someone without a Ph.D. to identify the "problem"?
> One that seems obvious to me is that we
> 'want' more to go to university, even if they are unprepared or
> unqualified.
IMO, I see that as just another symptom...
If I had to put my finger on the "problem", the nearest that I could
probably get to that is - that I think it is that "we" (the public / the
education system) don't clearly have an idea as to what we want to
accomplish. We tell everybody that the goal is to get an education...
what exactly does that mean? Ask a lot of people and you'll probably get
a lot of answers...
I imagine if you asked the students in these classes, "why are you
studying this?" the answers would be something along the lines of "isn't
that what I'm suppose to be doing?"...
Martin
Tim Norfolk
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -
And I have aksed that question, to blank stares. The US system is
particularly confused in this regard.
Marshall
>
> If I had to put my finger on the "problem", the nearest that I could
> probably get to that is - that I think it is that "we" (the public / the
> education system) don't clearly have an idea as to what we want to
> accomplish. We tell everybody that the goal is to get an education...
> what exactly does that mean? Ask a lot of people and you'll probably get
> a lot of answers...
That's just another symptom, not the actual problem.
> I imagine if you asked the students in these classes, "why are you
> studying this?" the answers would be something along the lines of "isn't
> that what I'm suppose to be doing?"...
Symptom again.
Marshall
William Elliot
> On this point, you are correct. But you have missed the
> main point; mathematics is not a collection of facts,
> theorems, and algorithms, but a way of thinking, which
> enables it to be applied even by those who are not adept
> at FINDING the above. The concepts are simple, and do
> not require leading up to, but use after they are learned
>
> Algebra is not properly taught; the typical algebra course
> introduces variables poorly, gives algorithms for the
> solution of problems with ONE variable, and then asks
> students to solve problems, at least 90% of which should
> not be done with one variable.
>
> Here is the content of algebra, and more, in two sentences:
>
> A variable is a temporary name which can be used for
> anything at all.
>
I'd explain them as being like pronouns, except in these days, can a
person expect students to know grammar? Do they even teach grammar any
more?
> The same operation done on equal entities yields
> equal results.
>
Then all those fancy rules, such as when change the sign of a term when
moving a it from one side of an equation to the other, are easily
remember, recreated.
> These can be learned in first grade, and then APPLIED.
>
> Before WWII, the college preparatory program in the US was
> algebra, Euclid geometry, two years of a foreign language,
> three years of science, and three years of English. Good
> students also took more algebra and geometry, trigonometry,
> and something called "college algebra", which was
> non-trivial. Now, most cannot even get a Euclid course,
> which was realized back then as the only real mathematics
> course taught in high school.
>
Now students don't even know how to write. Instead of expressing
themselves, clearly stating a problem for example, they expect you to read
their mind; for you to know what they're talking about as divined from
phrases and fragments of sentences. In extreme some only use "..." to
punctuate long word sequences into a gestalt of artistic word galosh from
which one is to glean some sense and substance.
As for quantification, they not the foggiest, again expecting the reader
to fill in the quantifiers. For example, "prove \/_j Uj = Uj" when what's
meant is "prove there's some j with \/_j Uj = Uj" or it could be "prove
for j, that \/_j Uj = Uj" or even, "prove for all j, \/_j Uj = Uj". Then
when it comes to the difference between continuity and uniformity
continuity or between pointwise convergence of a sequence of functions and
uniform convergence, disregard for qualifiers is asking for confusion.
Tossing out indexes is another fad, using \/ Uj instead of \/_j Uj for
example, is bound to reap confusion. For example the sequence { a_ij }
instead of { a_ij }_j or { a_ij }_i. Even worse is writing a_n for a
sequence. Is a_(n+1) another sequence or is it just a number like a_n?
> About 45 years ago, I brought up in the meeting of a
> state chapter of MAA the idea of setting standards.
> I did not get a second on the proposal.
What do you think of the modern, highly touted,
multiple choice test, standards?
Life is not a multiple choice test.
It expects you to create the choices to choose.
----
Rowley
Well, there you go... if we can't identity the real problem then how is
anyone going to come up with real solution?
Martin
Tim Norfolk
>
> - Show quoted text -
I do not believe that either Herman or I suggested multiple-choice
testing.
Ronald Benedik
news:hgb8lo$3i...@odds.stat.purdue.edu...
> These can be learned in first grade, and then APPLIED.
> Before WWII, the college preparatory program in the US was
> algebra, Euclid geometry, two years of a foreign language,
> three years of science, and three years of English. Good
> students also took more algebra and geometry, trigonometry,
> and something called "college algebra", which was
> non-trivial. Now, most cannot even get a Euclid course,
> which was realized back then as the only real mathematics
> course taught in high school.
A well done Eurclid geometry course is an interesting
qualification, although 3d analytic geometry is a better
preparation for more relevant physics.
I have little expirience teaching math, (I prefered
research) but high school students here in Austria master
basic concepts like division and simple proofs:
"sqrt(3) is not a rational number".
The obvious decline in math was also seen in countries
like Germany which is now transforming their high
schools from 13 to 12 years of schooling and more rigid
final exams, compulsory in german, math and a foreign
languague.
As Bill Gates stated: "The American High School is obsolete".
Pubkeybreaker
The underlying problem???
Apathy. Despite all the rhetoric about improving schools,
noone is really willing to do what it takes.
No one wants to enforce and noone wants to submit to rigorous
academic discipline. The idea of requiring academic excellence
has vanished from our culture. (did we ever have it?)
People are simply academically lazy and don't want to put forth an
effort. One can not teach people who have no interest in learning.
Too many people simply want to MAKE MONEY FAST.
We do not see strong education as having value or as a goal.
This is a cultural problem.
Tim Norfolk
>
> - Show quoted text -
But those of us trying to fix things are doing our best.
Herman Rubin
>> On this point, you are correct. But you have missed the
>> main point; mathematics is not a collection of facts,
>> theorems, and algorithms, but a way of thinking, which
>> enables it to be applied even by those who are not adept
>> at FINDING the above. The concepts are simple, and do
>> not require leading up to, but use after they are learned
>> Algebra is not properly taught; the typical algebra course
>> introduces variables poorly, gives algorithms for the
>> solution of problems with ONE variable, and then asks
>> students to solve problems, at least 90% of which should
>> not be done with one variable.
>> Here is the content of algebra, and more, in two sentences:
>> A variable is a temporary name which can be used for
>> anything at all.
>I'd explain them as being like pronouns, except in these days, can a
>person expect students to know grammar? Do they even teach grammar any
>more?
Sometimes; it is rarely emphasized, even in foreign languages,
where it can make a big difference.
>> The same operation done on equal entities yields
>> equal results.
>Then all those fancy rules, such as when change the sign of a term when
>moving a it from one side of an equation to the other, are easily
>remember, recreated.
I recall seeing a web page as part of a book which gave
50 such rules.
>> These can be learned in first grade, and then APPLIED.
>> Before WWII, the college preparatory program in the US was
>> algebra, Euclid geometry, two years of a foreign language,
>> three years of science, and three years of English. Good
>> students also took more algebra and geometry, trigonometry,
>> and something called "college algebra", which was
>> non-trivial. Now, most cannot even get a Euclid course,
>> which was realized back then as the only real mathematics
>> course taught in high school.
>Now students don't even know how to write. Instead of expressing
>themselves, clearly stating a problem for example, they expect you to read
>their mind; for you to know what they're talking about as divined from
>phrases and fragments of sentences. In extreme some only use "..." to
>punctuate long word sequences into a gestalt of artistic word galosh from
>which one is to glean some sense and substance.
This is part of the educationist view. They are urged
to be creative in their writing, not to be logical and
precise, to put down their impressions, not to make
things clear. The educationists themselves are unable
to consider that one can start out to learn the logical
structure of mathematics without a great deal of building
up and generalizing, because they cannot see its simplicity.
>As for quantification, they not the foggiest, again expecting the reader
>to fill in the quantifiers. For example, "prove \/_j Uj = Uj" when what's
>meant is "prove there's some j with \/_j Uj = Uj" or it could be "prove
>for j, that \/_j Uj = Uj" or even, "prove for all j, \/_j Uj = Uj". Then
>when it comes to the difference between continuity and uniformity
>continuity or between pointwise convergence of a sequence of functions and
>uniform convergence, disregard for qualifiers is asking for confusion.
One must think precisely. The Euclid geometry course taught
formal proofs, and required this precision.
>Tossing out indexes is another fad, using \/ Uj instead of \/_j Uj for
>example, is bound to reap confusion. For example the sequence { a_ij }
>instead of { a_ij }_j or { a_ij }_i. Even worse is writing a_n for a
>sequence. Is a_(n+1) another sequence or is it just a number like a_n?
>> About 45 years ago, I brought up in the meeting of a
>> state chapter of MAA the idea of setting standards.
>> I did not get a second on the proposal.
>What do you think of the modern, highly touted,
>multiple choice test, standards?
A multiple choice test can only test for things like
memorization and routine, except wrong ones. They can
test if someone can recognize a formulation of a word
problem, but not if one can produce one.
You can quote me on this:
I object to the objectives of objective tests.
>Life is not a multiple choice test.
>It expects you to create the choices to choose.
>----
Herman Rubin
Ronald Benedik <rben...@fsmat.htu.tuwien.ac.at> wrote:
>"Herman Rubin" <hru...@odds.stat.purdue.edu> schrieb im Newsbeitrag
>news:hgb8lo$3i...@odds.stat.purdue.edu...
>> These can be learned in first grade, and then APPLIED.
>> Before WWII, the college preparatory program in the US was
>> algebra, Euclid geometry, two years of a foreign language,
>> three years of science, and three years of English. Good
>> students also took more algebra and geometry, trigonometry,
>> and something called "college algebra", which was
>> non-trivial. Now, most cannot even get a Euclid course,
>> which was realized back then as the only real mathematics
>> course taught in high school.
>A well done Eurclid geometry course is an interesting
>qualification, although 3d analytic geometry is a better
>preparation for more relevant physics.
Unless you go into the properties of conics and quadric
surfaces, not much. It is not basic.
>I have little expirience teaching math, (I prefered
>research) but high school students here in Austria master
>basic concepts like division and simple proofs:
>"sqrt(3) is not a rational number".
>The obvious decline in math was also seen in countries
>like Germany which is now transforming their high
>schools from 13 to 12 years of schooling and more rigid
>final exams, compulsory in german, math and a foreign
>languague.
They are trying to emulate the US. In my opinion,
a student with the ability to handle a good college
program should be able to do in with six to eight
years of preparation.
Herman Rubin
Pubkeybreaker <pubkey...@aol.com> wrote:
>On Dec 17, 1:45=A0am, Marshall <marshall.spi...@gmail.com> wrote:
>> On Dec 16, 1:40=A0pm, Rowley <industry3dREM...@yahoo.com> wrote:
>> > If I had to put my finger on the "problem", the nearest that I could
>> > probably get to that is - that I think it is that "we" (the public / th=
>e
>> > education system) don't clearly have an idea as to what we want to
>> > accomplish. We tell everybody that the goal is to get an education...
>> > what exactly does that mean? Ask a lot of people and you'll probably ge=
>t
>> > a lot of answers...
>> That's just another symptom, not the actual problem.
>> > I imagine if you asked the students in these classes, "why are you
>> > studying this?" the answers would be something along the lines of "isn'=
>t
>> > that what I'm suppose to be doing?"...
>> Symptom again.
>The underlying problem???
>Apathy. Despite all the rhetoric about improving schools,
>noone is really willing to do what it takes.
Alas, no. The public school situation was radically
changed in the Depression by a school of educationists, who
did not even care how much was learned, and emphasized
social adjustment, which meant rigid age grouping. The
dumbing down was a consequence of this.
Of course, they promised that everyone would learn more
and better. It is easy to promise.
Now, there are few who do not in some sense subscribe to
that. No Child Left Behind implies No Child Gets Ahead.
>No one wants to enforce and noone wants to submit to rigorous
>academic discipline. The idea of requiring academic excellence
>has vanished from our culture. (did we ever have it?)
We did have it in our schools to a fair extent before
the Depression. I was able to observe the chang firsthand.
The high schools did not suffer much until after WWII.
>People are simply academically lazy and don't want to put forth an
>effort. One can not teach people who have no interest in learning.
Of the students I have taught in undergraduate courses,
the worst were engineering students who did not think
they should have had to take the course, and those going
into high school mathematics teaching. Also, since they
have been taught rote and routine, they seem unable to do
any logical thinking.
>Too many people simply want to MAKE MONEY FAST.
>We do not see strong education as having value or as a goal.
>This is a cultural problem.
It is, and its worst effects are on those in the disadvantaged
minority groups who have managed to resist it. But the one who
wants to learn instead of goof off is considered a nerd in most
places.
Tim Norfolk
> In article <365842b4-122b-4e8c-9c96-a84fc7d3b...@x20g2000vbn.googlegroups.com>,
>
> - Show quoted text -
Herman - how much do you blame John Dewey?
Frederick Williams
>
> [...]
>
> Here is the content of algebra, and more, in two sentences:
>
> A variable is a temporary name which can be used for
> anything at all.
I've almost certainly misunderstood, but can a variable be used as a
name for addition or for one of the logical constants?
> The same operation done on equal entities yields
> equal results.
>
> These can be learned in first grade, and then APPLIED.
[...]
--
Pigeons were widely suspected of secret intercourse with the
enemy; counter-measures included the use of British birds of
prey to intercept suspicious pigeons in mid-air.
Christopher Andrew, 'Defence of the Realm', Allen Lane
Ronald Benedik
>>A well done Eurclid geometry course is an interesting
>>qualification, although 3d analytic geometry is a better
>>preparation for more relevant physics.
>
> Unless you go into the properties of conics and quadric
> surfaces, not much. It is not basic.
Of course not, but I refrererd to the cross product like the
Lorentz force F=q(E+vxB) and problems like calculating
distance between point and a plane or the minimal distance
of two lines, and last but not least 3x3 determinants.
> They are trying to emulate the US. In my opinion,
> a student with the ability to handle a good college
> program should be able to do in with six to eight
> years of preparation.
Russia prepares students in six years of schooling,
western europe does it in 8-9 years with students
learning a second (foreign) language. In my case it was
latin.
Herman Rubin
Tim Norfolk <tims...@aol.com> wrote:
>On Dec 17, 8:35=EF=BF=BDpm, hru...@odds.stat.purdue.edu (Herman Rubin) wrot=
>e:
>> In article <365842b4-122b-4e8c-9c96-a84fc7d3b...@x20g2000vbn.googlegroups=
>.com>,
>> Pubkeybreaker =EF=BF=BD<pubkeybrea...@aol.com> wrote:
>> >On Dec 17, 1:45=3DA0am, Marshall <marshall.spi...@gmail.com> wrote:
>> >> On Dec 16, 1:40=3DA0pm, Rowley <industry3dREM...@yahoo.com> wrote:
>> >> > If I had to put my finger on the "problem", the nearest that I could
>> >> > probably get to that is - that I think it is that "we" (the public /=
> th=3D
>> >e
>> >> > education system) don't clearly have an idea as to what we want to
>> >> > accomplish. We tell everybody that the goal is to get an education..=
>.
>> >> > what exactly does that mean? Ask a lot of people and you'll probably=
> ge=3D
>> >t
>> >> > a lot of answers...
>> >> That's just another symptom, not the actual problem.
>> >> > I imagine if you asked the students in these classes, "why are you
>> >> > studying this?" the answers would be something along the lines of "i=
>sn'=3D
>> >t
>> >> > that what I'm suppose to be doing?"...
>> >> Symptom again.
>> >The underlying problem???
>> >Apathy. =EF=BF=BDDespite all the rhetoric about improving schools,
>> >noone is really willing to do what it takes.
>> Alas, no. =EF=BF=BDThe public school situation was radically
>> changed in the Depression by a school of educationists, who
>> did not even care how much was learned, and emphasized
>> social adjustment, which meant rigid age grouping. =EF=BF=BDThe
>> dumbing down was a consequence of this.
>> Of course, they promised that everyone would learn more
>> and better. =EF=BF=BDIt is easy to promise.
<> Now, there are few who do not in some sense subscribe to
<> that. =EF=BF=BDNo Child Left Behind implies No Child Gets Ahead.
<> >No one wants to enforce and noone wants to submit to rigorous
<> >academic discipline. =EF=BF=BDThe idea of requiring academic excellence
<> >has vanished from our culture. =EF=BF=BD(did we ever have it?)
<> We did have it in our schools to a fair extent before
<> the Depression. =EF=BF=BDI was able to observe the chang firsthand.
<> The high schools did not suffer much until after WWII.
<> >People are simply academically lazy and don't want to put forth an
<> >effort. =EF=BF=BDOne can not teach people who have no interest in learni=
>ng.
<> Of the students I have taught in undergraduate courses,
<> the worst were engineering students who did not think
<> they should have had to take the course, and those going
<> into high school mathematics teaching. =EF=BF=BDAlso, since they
<> have been taught rote and routine, they seem unable to do
<> any logical thinking.
<> >Too many people simply want to MAKE MONEY FAST.
<> >We do not see strong education as having value or as a goal.
<> >This is a cultural problem.
<> It is, and its worst effects are on those in the disadvantaged
<> minority groups who have managed to resist it. =EF=BF=BDBut the one who
<> wants to learn instead of goof off is considered a nerd in most
<> places.
<> - Show quoted text -
>Herman - how much do you blame John Dewey?
He and his group are the ones responsible.
I will not go into everything I learned about his
philosophy, but it was explicitly stated in courses
that the idea was to have children adjusted to their
peer group, and that the schools train them to work
in the "rust belt" industries.
Herman Rubin
[...]
>> Here is the content of algebra, and more, in two sentences:
>> A variable is a temporary name which can be used for
>> anything at all.
>I've almost certainly misunderstood, but can a variable be used as a
>name for addition or for one of the logical constants?
Not for addition, but it can be used for the addition
function, and it can be used for logical constants.
There are times when it is not DELIBERATELY used for
them, but it can be. To prove the positive and negative
integers are an abelian group, this would be essentially
a part of the argument.
>> The same operation done on equal entities yields
>> equal results.
>> These can be learned in first grade, and then APPLIED.
[...]
--
Herman Rubin
Ronald Benedik <rben...@fsmat.htu.tuwien.ac.at> wrote:
>"Herman Rubin" <hru...@odds.stat.purdue.edu> schrieb im Newsbeitrag
>news:hgelmj$38...@odds.stat.purdue.edu...
>>>A well done Eurclid geometry course is an interesting
>>>qualification, although 3d analytic geometry is a better
>>>preparation for more relevant physics.
>> Unless you go into the properties of conics and quadric
>> surfaces, not much. It is not basic.
>Of course not, but I refrererd to the cross product like the
>Lorentz force F=q(E+vxB) and problems like calculating
>distance between point and a plane or the minimal distance
>of two lines, and last but not least 3x3 determinants.
Why do this in three dimensions? It is only in three
dimensions that the usual cross product exists, but
in higher dimensions, it becomes a skew symmetric matrix,
the derivative of an orthogonal transformation.
The other aspects can also be done in any number of
dimensions, and is no more difficult.
>> They are trying to emulate the US. In my opinion,
>> a student with the ability to handle a good college
>> program should be able to do in with six to eight
>> years of preparation.
>Russia prepares students in six years of schooling,
>western europe does it in 8-9 years with students
>learning a second (foreign) language. In my case it was
>latin.
--
Ronald Benedik
>>Of course not, but I refrererd to the cross product like the
>>Lorentz force F=q(E+vxB) and problems like calculating
>>distance between point and a plane or the minimal distance
>>of two lines, and last but not least 3x3 determinants.
>
> Why do this in three dimensions? It is only in three
> dimensions that the usual cross product exists, but
> in higher dimensions, it becomes a skew symmetric matrix,
> the derivative of an orthogonal transformation.
Because it is also applied to the torque in physics.
The length of the product also gives the are spanned by the
two vectors. We don't talk about college math but High
School curriculum.
> The other aspects can also be done in any number of
> dimensions, and is no more difficult.
Its true for the mathematican, but not for the common
High School student.
Rowley
> In article <10065fe5-6147-40a5...@y24g2000yqb.googlegroups.com>,
> Tim Norfolk <tims...@aol.com> wrote:
>
<snippage>
>>Herman - how much do you blame John Dewey?
>
>
> He and his group are the ones responsible.
>
> I will not go into everything I learned about his
> philosophy, but it was explicitly stated in courses
> that the idea was to have children adjusted to their
> peer group, and that the schools train them to work
> in the "rust belt" industries.
At the time was that a "bad" thing to do? I don't think that purpose was
some sort of hidden agenda - I think everybody in society at that time
understood what school was for. Especially the students who wanted one
of those jobs in those industries...
Martin
Herman Rubin
Ronald Benedik <rben...@fsmat.htu.tuwien.ac.at> wrote:
>"Herman Rubin" <hru...@odds.stat.purdue.edu> schrieb im Newsbeitrag
>news:hggec4$3v...@odds.stat.purdue.edu...
>>>Of course not, but I refrererd to the cross product like the
>>>Lorentz force F=q(E+vxB) and problems like calculating
>>>distance between point and a plane or the minimal distance
>>>of two lines, and last but not least 3x3 determinants.
>> Why do this in three dimensions? It is only in three
>> dimensions that the usual cross product exists, but
>> in higher dimensions, it becomes a skew symmetric matrix,
>> the derivative of an orthogonal transformation.
>Because it is also applied to the torque in physics.
>The length of the product also gives the are spanned by the
>two vectors. We don't talk about college math but High
>School curriculum.
One can change the physics texts without losing anything.
It then becomes easier to understand; the cross product
is actually a confusing three dimensional artifice.
The application to torque is a rotation in the plane of
the two vectors, and can be so discussed without using
the artifice of setting it up a a vector orthogonal to
those two.
>> The other aspects can also be done in any number of
>> dimensions, and is no more difficult.
>Its true for the mathematican, but not for the common
>High School student.
It is my opinion that doing special cases before, let
alone instead, of the general concept eventually leads
to considerable problems. Physics can change from
using the vector product to using the representation
as rotation without adding to the confusion.
Herman Rubin
<snippage>
That was NOT so. People expected the schools to teach
according to what the children could learn; there were
college preparatory programs, "general" programs, and
vocational programs. These programs only differed at
the high school level; different progress at the lower
grades was done mainly by skipping and retention.
It was not learned until WWII that putting people who
could think in routine type operations for more than
a short time was a major mistake. They do not have
to be very bright for this to show up.
Now I agree that retention was a poor procedure, but
what the "progressive educators" did was little, if
anything, better. Also, I agree that skipping was
not optimal, but it is unclear that anything better
could be done at the time. The educationists did not
get in their licks on the high school curriculum until
after WWII. They have now crippled the erstwhile good
college preparatory program, so that those now going
to college are so much weaker mathematically that
there is essentially no comparison.
To any but the educationists, I was a candidate for
college before I started first grade, as was my son.
Many could be tapped in the primary grades, but not
by the current educationists, who cannot distinguish
between ability and diligent overperformance. The
bright, and especially the gifted, are turned off by
the trivial homework and great amounts of busy work,
which leads away from understanding.
Juan M
a and b were walking down the street when they were accosted by x......
(sorry)
"Herman Rubin" <hru...@odds.stat.purdue.edu> wrote in message
news:hgj9n8$2r...@odds.stat.purdue.edu...
Bob LeChevalier
>In article <hgil4...@news2.newsguy.com>,
>Rowley <industry...@yahoo.com> wrote:
>>Herman Rubin wrote:
>>> In article <10065fe5-6147-40a5...@y24g2000yqb.googlegroups.com>,
>>> Tim Norfolk <tims...@aol.com> wrote:
><snippage>
>
>>>>Herman - how much do you blame John Dewey?
>
>
>>> He and his group are the ones responsible.
>
>>> I will not go into everything I learned about his
>>> philosophy, but it was explicitly stated in courses
>>> that the idea was to have children adjusted to their
>>> peer group, and that the schools train them to work
>>> in the "rust belt" industries.
>
>>At the time was that a "bad" thing to do? I don't think that purpose was
>>some sort of hidden agenda - I think everybody in society at that time
>>understood what school was for. Especially the students who wanted one
>>of those jobs in those industries...
>
>That was NOT so. People expected the schools to teach
>according to what the children could learn; there were
>college preparatory programs, "general" programs, and
>vocational programs.
Bull. Before Dewey, in much of the country, there were one-room
schoolhouses, and exactly ONE program for all kids, taught by a
teacher who was usually no more than a high school graduate herself,
not necessarily any older than the oldest students, and often with no
training at all in pedagogy. The textbooks were rudimentary and aimed
at farm kids who would grow up to be farmers, because that is what
half the country did.
>These programs only differed at
>the high school level; different progress at the lower
>grades was done mainly by skipping and retention.
When only 5% of the population attended high school, programs that
differed only at the high school level were in fact all the same
program for 95% of the population.
When society decided that they wanted more than 5% to attend high
school, then naturally high school programs were made more uniform.
When mobility of families increased so that a significant percentage
of the people in a given class weren't in the school a few years ago,
programs had to be standard in order to accept kids from anywhere in
the country, arriving at any time of the school year.
>It was not learned until WWII that putting people who
>could think in routine type operations for more than
>a short time was a major mistake.
That statement applies to the pre-Dewey period as well as the post-.
>They have now crippled the erstwhile good
>college preparatory program, so that
more than 3% of the population can handle it, since society expects a
helluva lot more than 3% to go to college.
>those now going
>to college are so much weaker mathematically that
>there is essentially no comparison.
Actually, I suspect that the 3% who could handle your "good college
preparatory program" probably still get at least as strong a
preparation as ever. But your perceptions are skewed by the 97% that
never would have taken such a program (but who still go to college
today, and are accepted because someone has to pay the tuition to
cover the salaries of all you college professors)
>To any but the educationists, I was a candidate for
>college before I started first grade, as was my son.
Nonsense.
>The bright, and especially the gifted, are turned off by
>the trivial homework and great amounts of busy work,
Tough. Most people in the world learn that you have to put up with a
goodly amount of shit to get what you want, especially if others are
paying the bills.
lojbab
---
Bob LeChevalier - artificial linguist; genealogist
loj...@lojban.org Lojban language www.lojban.org
Rowley
> In article <hgil4...@news2.newsguy.com>,
> Rowley <industry...@yahoo.com> wrote:
>
>>Herman Rubin wrote:
>>
>>>In article <10065fe5-6147-40a5...@y24g2000yqb.googlegroups.com>,
>>>Tim Norfolk <tims...@aol.com> wrote:
>
>
>
> <snippage>
>
>>>>Herman - how much do you blame John Dewey?
>
>
>
>>>He and his group are the ones responsible.
>
>
>>>I will not go into everything I learned about his
>>>philosophy, but it was explicitly stated in courses
>>>that the idea was to have children adjusted to their
>>>peer group, and that the schools train them to work
>>>in the "rust belt" industries.
>
>
>>At the time was that a "bad" thing to do? I don't think that purpose was
>>some sort of hidden agenda - I think everybody in society at that time
>>understood what school was for. Especially the students who wanted one
>>of those jobs in those industries...
>
Hmm... maybe the problem is the term you used "Rust Belt"... I assumed
that you were talking about the time at the beginning of industrial
build up (say end of 1800's to the beginning of the 1900's)
But now looking on Wikipedia I see that the time of the "Rust Belt"
actually starts in the mid-1970's and continuing on to today...
http://en.wikipedia.org/wiki/Rust_Belt
Martin
Herman Rubin
How does a one-room schoolhouse even indicate ONE program
for all? I have met many who had the pleasure of going
to one-room schoolhouses, and they were certainly educated
better than many.
With few children in a given grade, individualization was
de rigeur, and much had to be done by individual reading,
not listening to the teacher. As for training in pedagogy,
not having it is an advantage for the students; the teacher
can think instead of using a program created by someone who
does not understand the subject. That is much better than
the memorize and regurgitate, also called, "drill and kill",
that is going on now.
That 19th century Kansas exam certainly did not look at all
rudimentary.
The urban, suburban, and semiurban communities did have
teachers teaching single subjects in moderate to large
classes. My elementary school had sixteen half-grades,
as did most of the fair-sized cities then. Alas, this
has gone by the wayside.
>>These programs only differed at
>>the high school level; different progress at the lower
>>grades was done mainly by skipping and retention.
>When only 5% of the population attended high school, programs that
>differed only at the high school level were in fact all the same
>program for 95% of the population.
I believe that Illinois had a fair number of high school
graduates in the first half of the 20th century. Otherwise,
how could they have managed different high school programs
for the various types of students?
>When society decided that they wanted more than 5% to attend high
>school, then naturally high school programs were made more uniform.
>When mobility of families increased so that a significant percentage
>of the people in a given class weren't in the school a few years ago,
>programs had to be standard in order to accept kids from anywhere in
>the country, arriving at any time of the school year.
WHY should more going to school call for more uniform
programs? It should call for more variety. It was
the educationists who could not understand that people
differ greatly in ability that called for uniformity.
>>It was not learned until WWII that putting people who
>>could think in routine type operations for more than
>>a short time was a major mistake.
>That statement applies to the pre-Dewey period as well as the post-.
>>They have now crippled the erstwhile good
>>college preparatory program, so that
>more than 3% of the population can handle it, since society expects a
>helluva lot more than 3% to go to college.
Most now going to college do NOT have an education
when they graduate, even with the dumbing down.
>>those now going
>>to college are so much weaker mathematically that
>>there is essentially no comparison.
>Actually, I suspect that the 3% who could handle your "good college
>preparatory program" probably still get at least as strong a
>preparation as ever.
False. It may not even be available. And the
proportion who could handle a good college preparatory
program was more like 20% or even higher; the foreign
language classes, even Latin, were not that unpopulated,
and quite possibly 50% took the high school algebra
class then, much stronger than now.
But your perceptions are skewed by the 97% that
>never would have taken such a program (but who still go to college
>today, and are accepted because someone has to pay the tuition to
>cover the salaries of all you college professors)
>>To any but the educationists, I was a candidate for
>>college before I started first grade, as was my son.
>Nonsense.
Here you are wrong. People then looked for ability,
not conformity.
>>The bright, and especially the gifted, are turned off by
>>the trivial homework and great amounts of busy work,
>Tough. Most people in the world learn that you have to put up with a
>goodly amount of shit to get what you want, especially if others are
>paying the bills.
So you would kill off this asset to society in the name
of giving every child a "college education". You can't
make a silk purse out of a sow's ear, but by treating
the silk as sow's ears you can ruin a lot of silk.
Herman Rubin
Rowley <industry...@yahoo.com> wrote:
>Herman Rubin wrote:
>> In article <hgil4...@news2.newsguy.com>,
>> Rowley <industry...@yahoo.com> wrote:
>>>Herman Rubin wrote:
>>>>In article <10065fe5-6147-40a5...@y24g2000yqb.googlegroups.com>,
>>>>Tim Norfolk <tims...@aol.com> wrote:
<snippage>
>>>>>Herman - how much do you blame John Dewey?
>>>>He and his group are the ones responsible.
>>>>I will not go into everything I learned about his
>>>>philosophy, but it was explicitly stated in courses
>>>>that the idea was to have children adjusted to their
>>>>peer group, and that the schools train them to work
>>>>in the "rust belt" industries.
>>>At the time was that a "bad" thing to do? I don't think that purpose was
>>>some sort of hidden agenda - I think everybody in society at that time
>>>understood what school was for. Especially the students who wanted one
>>>of those jobs in those industries...
>Hmm... maybe the problem is the term you used "Rust Belt"... I assumed
>that you were talking about the time at the beginning of industrial
>build up (say end of 1800's to the beginning of the 1900's)
No; it was commonly used for the large factory operations
during the entire first half of the 1900's and more. The
term was due to the use of large amounts of iron and steel.
>But now looking on Wikipedia I see that the time of the "Rust Belt"
>actually starts in the mid-1970's and continuing on to today...
>http://en.wikipedia.org/wiki/Rust_Belt
This must be new. I definitely recall the use I stated.
>Martin
toto
Rubin) wrote:
>
>That 19th century Kansas exam certainly did not look at all
>rudimentary.
There you go again. It was quite rudimentary. Very few concepts were
emphasized. Mostly, the exam had to do with those *practical*
problems you say you despise.
--
Dorothy
There is no sound, no cry in all the world
that can be heard unless someone listens ..
The Outer Limits
Rowley
That's what I thought too.. but don't really see that referenced anywhere...
>
>>But now looking on Wikipedia I see that the time of the "Rust Belt"
>>actually starts in the mid-1970's and continuing on to today...
>>http://en.wikipedia.org/wiki/Rust_Belt
>
>
> This must be new. I definitely recall the use I stated.
Eh.. it's Wikipedia.. not the Encyclopaedia Britannica... nor the
Encyclopedia Galactica...
Did run across a mention of Frederick Winslow Taylor and been reading
some of the things he did during the period...
Martin
>
>
>>Martin
Bob LeChevalier
>>Bull. Before Dewey, in much of the country, there were one-room
>>schoolhouses, and exactly ONE program for all kids, taught by a
>>teacher who was usually no more than a high school graduate herself,
>>not necessarily any older than the oldest students, and often with no
>>training at all in pedagogy. The textbooks were rudimentary and aimed
>>at farm kids who would grow up to be farmers, because that is what
>>half the country did.
>
>How does a one-room schoolhouse even indicate ONE program
>for all?
Easily. One textbook used for all kids, and one teacher who is barely
more advanced than the end of the textbook. The kids are all be
taught the same thing. The more advanced kids are expected to help
out the less advanced.
>I have met many who had the pleasure of going
>to one-room schoolhouses, and they were certainly educated
>better than many.
That may be so, but all the kids in that one schoolhouse had exactly
the same program (and even one-room schoolhouses undoubtedly changed a
lot between the 1800s and the 1930s or later when most of the people
you know were educated.
>With few children in a given grade, individualization was
>de rigeur, and much had to be done by individual reading,
>not listening to the teacher.
But the one book was the same for all, and the understanding was
limited to that of the teacher.
>As for training in pedagogy,
>not having it is an advantage for the students;
Bull.
>the teacher
>can think instead of using a program created by someone who
>does not understand the subject.
The teacher doesn't understand ANY subject, being minimally educated,
so *whatever* the teacher does is done by someone who doesn't
understand the subject.
>That is much better than
>the memorize and regurgitate, also called, "drill and kill",
That was precisely the only method that was used.
Wikipedia:
<By 1900, 31 states required children to attend school from the ages of
< 8- to 14-years-old. As a result, by 1910 72 percent of American
< children attended school. Half the nation's children attended
< one-room schools. In 1918, every state required students to complete
< elementary school. Lessons consisted of students reading aloud from
< their texts such as the McGuffey Readers, and placed emphasis on rote
< memorization. Teachers often used physical punishment, such as
< hitting students on the knuckles with switches, for incorrect
< answers.
Reading aloud and rote memorization and physical punishment for giving
the wrong answer.
There was a major innovation tried around 1900, and in your state:
<The child was "given, wherever possible, intellectual responsibility
< for selecting the materials and instruments that are most fit, and
< given an opportunity to think out his own model and plan of work, led
< to perceive his own errors, and find how to correct them." Thus the
< work was never "reduced to a mere routine or custom and its educational
< value lost."
That was of course your arch-nemesis John Dewey, and the University of
Chicago lab schools. Before Dewey, the concept of individual
responsibility for education didn't really exist in schools, and that
concept is essential to any sort of self-propelled individualization
of the sort you seem to think existed. (There were of course, people
who self-educated before then, but they weren't especially common, and
the concept was more or less antithetical to "schooling", which
implicitly includes a group acting together doing the same thing in
response to some sort of leadership.)
>that is going on now.
Not in any school I or my kids ever attended.
>That
mythical
>19th century Kansas exam certainly did not look at all rudimentary.
It was almost all simple regurgitation, as I have repeatedly
demonstrated, usually in response to this same nonsense claim by you.
Do I need to do it again?
>>>These programs only differed at
>>>the high school level; different progress at the lower
>>>grades was done mainly by skipping and retention.
>
>>When only 5% of the population attended high school, programs that
>>differed only at the high school level were in fact all the same
>>program for 95% of the population.
>
>I believe that Illinois had a fair number of high school
>graduates in the first half of the 20th century.
A rather large range of time. The schools of 1901 were quite
different from the schools of 1950, as you yourself have repeatedly
noted. In 1901, the average school year was 145 days, and the average
student only attended 98 of them. In 1950, it was 158 out of 178.
In 1900, half of all kids did not reach 9th grade, and only 6.3% of 17
year olds graduated high school; in 1950 57% did.
For every 1000 5th graders in 1924-1925, only 302 graduated high
school in 1932, and only 118 of those went on to start college. The
graduating class of 1950, just 18 years later, was 505 of the 1000 5th
graders, and 205 of those went to college, almost double the rates.
At the beginning of the 20th century, fewer than 1,000 colleges with
160,000 students existed in the United States (out of 76 million
people). (That's an average of only 160 enrolled per college.)
>Otherwise,
>how could they have managed different high school programs
>for the various types of students?
Outside of Chicago, I am rather sure that they did not.
Vocational education started around WWI, and was pretty minimal until
the depression years.
>>When society decided that they wanted more than 5% to attend high
>>school, then naturally high school programs were made more uniform.
>>When mobility of families increased so that a significant percentage
>>of the people in a given class weren't in the school a few years ago,
>>programs had to be standard in order to accept kids from anywhere in
>>the country, arriving at any time of the school year.
>
>WHY should more going to school call for more uniform
>programs?
Money, among other things.
Parental demand, that their kids not receive an education inferior to
other kids, for another. Differences in education pretty much
guarantees inequality, and in this country that hasn't been an
acceptable goal for public endeavors (nor private schools for that
matter - if parents are paying the bills themselves, they certainly
don't accept their kids being taught less than other kids.)
>It should call for more variety.
The people paying the bills have not wanted more variety.
>It was the educationists who could not understand that people
>differ greatly in ability that called for uniformity.
It was the public that demanded uniformity, and continues to demand it
as exemplified in such endeavors as "No Child Left Behind" - which is
precisely a manifestation of the sort of uniformity you abhor, and
which has been rather strongly opposed by the 'educationists" you
blame for it.
>>>They have now crippled the erstwhile good
>>>college preparatory program, so that
>
>>more than 3% of the population can handle it, since society expects a
>>helluva lot more than 3% to go to college.
>
>Most now going to college do NOT have an education
>when they graduate, even with the dumbing down.
Of course they have "an education". Maybe not the sort you would
prefer, but there is a distinct difference between those who go to
college, and those who never attend school at all.
>>Actually, I suspect that the 3% who could handle your "good college
>>preparatory program" probably still get at least as strong a
>>preparation as ever.
>
>False. It may not even be available.
At least 3% of the kids in the country are capable of the sort of
self-education that you yourself managed. If they have access to a
library, it is available.
>And the
>proportion who could handle a good college preparatory
>program was more like 20% or even higher; the foreign
>language classes, even Latin, were not that unpopulated,
>and quite possibly 50% took the high school algebra
>class then, much stronger than now.
In 1900, every one in high school pretty much took the same courses.
There were no electives. High school education included Latin and
every kid took it. But when "every kid in high school" is only 10% of
the relevant population, you simply cannot say that 50% took high
school algebra.
And no, high school algebra was NOT "much stronger than now". First
order linear equations, one variable. Maybe quadratics in the last
chapter, but the last chapter in the textbook was only reached in the
ideal. No sets, no functional notation, no proofs. The best that can
be said is that in some books, the rules were stated in more precise
mathematical language (and the kids had to memorize and regurgitate
these theorems and lemmas, not understand them)
>>>To any but the educationists, I was a candidate for
>>>college before I started first grade, as was my son.
>
>>Nonsense.
>
>Here you are wrong. People then looked for ability,
>not conformity.
Nothing to do with ability nor conformity. No one looked at kids
under 5 (or probably any age short of puberty) for college attendance.
Period. Colleges were for young adults.
>>>The bright, and especially the gifted, are turned off by
>>>the trivial homework and great amounts of busy work,
>
>>Tough. Most people in the world learn that you have to put up with a
>>goodly amount of shit to get what you want, especially if others are
>>paying the bills.
>
>So you would kill off this asset to society in the name
>of giving every child a "college education".
What >I< would do is irrelevant. What society will do is what
matters. Society these days wants everyone to have the *opportunity*
for a college education, which means including all necessary elements
in the curriculum, and lowering the standards of college entrance so
as to make passing all the classes in the prerequisites is sufficient
for admission.
Those who want more than society chooses to offer for free will have
to pay for it themselves (or find a scholarship). If not enough want
more, then the free market won't rise to the occasion, and
self-education will be necessary. So far, this seems to be sufficient
- indeed there are shortages of people willing even to seek the
highest education levels that the public *IS* willing to pay for.
Most kids would rather spend their time playing Wii, texting their
friends, and pursuing the opposite sex to maximizing their education.
>You can't make a silk purse out of a sow's ear,
The people who pay the bills don't find your elitism acceptable as a
basis for the school systems they pay for.
>but by treating the silk as sow's ears you can ruin a lot of silk.
In this country, we are by definition all silk, or all sow's ears.
"all men are created equal" and all that.
Herman Rubin
Bob LeChevalier <loj...@lojban.org> wrote:
>hru...@odds.stat.purdue.edu (Herman Rubin) wrote:
>>>Bull. Before Dewey, in much of the country, there were one-room
>>>schoolhouses, and exactly ONE program for all kids, taught by a
>>>teacher who was usually no more than a high school graduate herself,
>>>not necessarily any older than the oldest students, and often with no
>>>training at all in pedagogy. The textbooks were rudimentary and aimed
>>>at farm kids who would grow up to be farmers, because that is what
>>>half the country did.
>>How does a one-room schoolhouse even indicate ONE program
>>for all?
>Easily. One textbook used for all kids, and one teacher who is barely
>more advanced than the end of the textbook. The kids are all be
>taught the same thing. The more advanced kids are expected to help
>out the less advanced.
The children in a one-room schoolhouse are at different
levels. Nobody uses the same textbook for a first grader
and a fifth grader. It is having a large class learning
the same material which calls for a single textbook.
>>I have met many who had the pleasure of going
>>to one-room schoolhouses, and they were certainly educated
>>better than many.
>That may be so, but all the kids in that one schoolhouse had exactly
>the same program (and even one-room schoolhouses undoubtedly changed a
>lot between the 1800s and the 1930s or later when most of the people
>you know were educated.
>>With few children in a given grade, individualization was
>>de rigeur, and much had to be done by individual reading,
>>not listening to the teacher.
>But the one book was the same for all, and the understanding was
>limited to that of the teacher.
You mean children cannot read and learn? That is to some
extent the view of the educationists, who claim that they
can only learn from the teacher.
You are accusing the teachers at the time of the one-room
schoolhouse to have been making the mistakes of the current
practices of the educationists.
>>As for training in pedagogy,
>>not having it is an advantage for the students;
>Bull.
YOU have not seen the lack of thinking ability on the part
of those "educated" by the current teachers. One time when
my son was home for winter vacation, he gave two examples of
lack of thinking on a late-term (in the second year) calculus
examination. One of those, my daughter, who had just taken
calculus in high school, got immediately. The other involved
linear algebra, so she could not attempt that problem.
These students were from Cal Tech. The selection of those
students is very strong, and they can do manipulations very
well; so well, that they cannot think instead of blindly
using the "tricks".
>>the teacher
>>can think instead of using a program created by someone who
>>does not understand the subject.
>The teacher doesn't understand ANY subject, being minimally educated,
>so *whatever* the teacher does is done by someone who doesn't
>understand the subject.
The PRESENT teachers go by memorization and routine, which is
not particularly helpful in understanding. It should be done
the other way, teaching concepts and logical structure.
>>That is much better than
>>the memorize and regurgitate, also called, "drill and kill",
>That was precisely the only method that was used.
It was used too much, but not as much as now.
>Wikipedia:
><By 1900, 31 states required children to attend school from the ages of
>< 8- to 14-years-old. As a result, by 1910 72 percent of American
>< children attended school. Half the nation's children attended
>< one-room schools. In 1918, every state required students to complete
>< elementary school. Lessons consisted of students reading aloud from
>< their texts such as the McGuffey Readers, and placed emphasis on rote
>< memorization. Teachers often used physical punishment, such as
>< hitting students on the knuckles with switches, for incorrect
>< answers.
>Reading aloud and rote memorization and physical punishment for giving
>the wrong answer.
Reading aloud is not rote memorization. Multiple choice tests
were not used back then.
>There was a major innovation tried around 1900, and in your state:
><The child was "given, wherever possible, intellectual responsibility
>< for selecting the materials and instruments that are most fit, and
>< given an opportunity to think out his own model and plan of work, led
>< to perceive his own errors, and find how to correct them." Thus the
>< work was never "reduced to a mere routine or custom and its educational
>< value lost."
>That was of course your arch-nemesis John Dewey, and the University of
>Chicago lab schools. Before Dewey, the concept of individual
>responsibility for education didn't really exist in schools, and that
>concept is essential to any sort of self-propelled individualization
>of the sort you seem to think existed. (There were of course, people
>who self-educated before then, but they weren't especially common, and
>the concept was more or less antithetical to "schooling", which
>implicitly includes a group acting together doing the same thing in
>response to some sort of leadership.)
Individualization does not mean ignoring concepts and
structure. The only places where the individualization
took place was in the humanities and social sciences, not
in mathematics and good science.
They introduced individualization in writing, which meant
that sloppily expressing ideas, with poor spelling and
worse grammar, was highly encouraged, which the bright
child who knew that he or she was doing a poor job of
expression found it difficult to write. This is a major
problem of those who can think logically.
>>that is going on now.
>Not in any school I or my kids ever attended.
>>That
>mythical
>>19th century Kansas exam certainly did not look at all rudimentary.
>It was almost all simple regurgitation, as I have repeatedly
>demonstrated, usually in response to this same nonsense claim by you.
>Do I need to do it again?
Some of it was, but even that was more than children
learn now. Grammar was taught in grammar school then;
I doubt if the present teachers know grammar.
>>>>These programs only differed at
>>>>the high school level; different progress at the lower
>>>>grades was done mainly by skipping and retention.
>>>When only 5% of the population attended high school, programs that
>>>differed only at the high school level were in fact all the same
>>>program for 95% of the population.
>>I believe that Illinois had a fair number of high school
>>graduates in the first half of the 20th century.
>A rather large range of time. The schools of 1901 were quite
>different from the schools of 1950, as you yourself have repeatedly
>noted. In 1901, the average school year was 145 days, and the average
>student only attended 98 of them. In 1950, it was 158 out of 178.
So what? Half of the time in school now is spent on
the Humanist philosophy and not on honest subject matter.
Instead of teaching Egyptian history, they teach the life
of the Egyptian peasant.
>In 1900, half of all kids did not reach 9th grade, and only 6.3% of 17
>year olds graduated high school; in 1950 57% did.
>For every 1000 5th graders in 1924-1925, only 302 graduated high
>school in 1932, and only 118 of those went on to start college. The
>graduating class of 1950, just 18 years later, was 505 of the 1000 5th
>graders, and 205 of those went to college, almost double the rates.
>At the beginning of the 20th century, fewer than 1,000 colleges with
>160,000 students existed in the United States (out of 76 million
>people). (That's an average of only 160 enrolled per college.)
>>Otherwise,
>>how could they have managed different high school programs
>>for the various types of students?
>Outside of Chicago, I am rather sure that they did not.
How about New York, Detroit, Philadelphia, Boston, Cleveland,
St. Louis, Cincinnati, Milwaukee, Pittsburgh?
>Vocational education started around WWI, and was pretty minimal until
>the depression years.
>>>When society decided that they wanted more than 5% to attend high
>>>school, then naturally high school programs were made more uniform.
>>>When mobility of families increased so that a significant percentage
>>>of the people in a given class weren't in the school a few years ago,
>>>programs had to be standard in order to accept kids from anywhere in
>>>the country, arriving at any time of the school year.
>>WHY should more going to school call for more uniform
>>programs?
>Money, among other things.
>Parental demand, that their kids not receive an education inferior to
>other kids, for another. Differences in education pretty much
>guarantees inequality, and in this country that hasn't been an
>acceptable goal for public endeavors (nor private schools for that
>matter - if parents are paying the bills themselves, they certainly
>don't accept their kids being taught less than other kids.)
THIS was generated by the educationists. My late wife told
me that skipping was rather common in New York at the time
it was being eliminated in Chicago. As I said before, the
gifted were recognized. Colleges were set up in the 19th
century in large numbers, and research universities started
in the last quarter of the 19th century, and were numerous
by the beginning of the 20th.
>>It should call for more variety.
>The people paying the bills have not wanted more variety.
>>It was the educationists who could not understand that people
>>differ greatly in ability that called for uniformity.
>It was the public that demanded uniformity, and continues to demand it
>as exemplified in such endeavors as "No Child Left Behind" - which is
>precisely a manifestation of the sort of uniformity you abhor, and
>which has been rather strongly opposed by the 'educationists" you
>blame for it.
I am frankly surprised that Bush thought of it that way.
Anyhow, it is not working, and never could work. The
current exams are at the level of those with IQ in the
low 90's, and this means that 75% can pass. The schools
that fail are those whose students do not have the mental
ability, and until this is realized, we cannot have good
education.
>>>>They have now crippled the erstwhile good
>>>>college preparatory program, so that
>>>more than 3% of the population can handle it, since society expects a
>>>helluva lot more than 3% to go to college.
>>Most now going to college do NOT have an education
>>when they graduate, even with the dumbing down.
>Of course they have "an education". Maybe not the sort you would
>prefer, but there is a distinct difference between those who go to
>college, and those who never attend school at all.
>>>Actually, I suspect that the 3% who could handle your "good college
>>>preparatory program" probably still get at least as strong a
>>>preparation as ever.
>>False. It may not even be available.
>At least 3% of the kids in the country are capable of the sort of
>self-education that you yourself managed. If they have access to a
>library, it is available.
They are capable of self-education, to a good extent.
But even the gifted need some guidance, and occasionally
need clarification. I could have learned the high school
algebra course which I learned very quickly at age 12
many years earlier with little more time spent on it,
and the gradual exposure to elementary school arithmetic
would have been unnecessary. I was doing addition and
multiplication before going to school.
However, I did not know anything more about algebra than
the word, and the library books available to elementary
school students did not contain it. The same applies to
other branches of mathematics; the ideas are very simple,
simpler than the poor introduction by examples.
>>And the
>>proportion who could handle a good college preparatory
>>program was more like 20% or even higher; the foreign
>>language classes, even Latin, were not that unpopulated,
>>and quite possibly 50% took the high school algebra
>>class then, much stronger than now.
>In 1900, every one in high school pretty much took the same courses.
>There were no electives. High school education included Latin and
>every kid took it. But when "every kid in high school" is only 10% of
>the relevant population, you simply cannot say that 50% took high
>school algebra.
>And no, high school algebra was NOT "much stronger than now". First
>order linear equations, one variable. Maybe quadratics in the last
>chapter, but the last chapter in the textbook was only reached in the
>ideal. No sets, no functional notation, no proofs. The best that can
>be said is that in some books, the rules were stated in more precise
>mathematical language (and the kids had to memorize and regurgitate
>these theorems and lemmas, not understand them)
Set algebra is trivial, and not used. I do not recall
any material in the high school algebra books which were
even asked for in memorization. Theorems were introduced
in geometry, and really introduced, and algebra was little
used. This is no real surprise, as algebra was unknown
in Euclid's time.
>>>>To any but the educationists, I was a candidate for
>>>>college before I started first grade, as was my son.
>>>Nonsense.
>>Here you are wrong. People then looked for ability,
>>not conformity.
>Nothing to do with ability nor conformity. No one looked at kids
>under 5 (or probably any age short of puberty) for college attendance.
>Period. Colleges were for young adults.
Not for immediate college attendance, but for the
ability. Early reading, and the ability to form
logical conclusions, can be often recognized.
>>>>The bright, and especially the gifted, are turned off by
>>>>the trivial homework and great amounts of busy work,
>>>Tough. Most people in the world learn that you have to put up with a
>>>goodly amount of shit to get what you want, especially if others are
>>>paying the bills.
>>So you would kill off this asset to society in the name
>>of giving every child a "college education".
>What >I< would do is irrelevant. What society will do is what
>matters. Society these days wants everyone to have the *opportunity*
>for a college education, which means including all necessary elements
>in the curriculum, and lowering the standards of college entrance so
>as to make passing all the classes in the prerequisites is sufficient
>for admission.
And thus destroying the mental abilities of those with them.
>Those who want more than society chooses to offer for free will have
>to pay for it themselves (or find a scholarship). If not enough want
>more, then the free market won't rise to the occasion, and
>self-education will be necessary. So far, this seems to be sufficient
>- indeed there are shortages of people willing even to seek the
>highest education levels that the public *IS* willing to pay for.
College scholarships were not that difficult to get even
during the Depression. However, many of the majority who
took the general program and not the college preparatory
one did so because the believed they would never be able
to afford it.
>Most kids would rather spend their time playing Wii, texting their
>friends, and pursuing the opposite sex to maximizing their education.
>>You can't make a silk purse out of a sow's ear,
>The people who pay the bills don't find your elitism acceptable as a
>basis for the school systems they pay for.
>>but by treating the silk as sow's ears you can ruin a lot of silk.
>In this country, we are by definition all silk, or all sow's ears.
>"all men are created equal" and all that.
The idea that all are created academically even approximately
equal is the stupidity introduced by the educationists. After
more than a half century of that, Joe Sixpack has accepted it.