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Herman Rubin
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 Posted: Wed Jul 16, 2008 6:39 pm Post subject: Re: Don't Call It "Algebra"; Call It Something Warm And Fuzz |
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In article <S7KdnaLb2Jyk3eDV4p2dnAA@comporium.net>,
Larry Hewitt <larryhewi@comporium.net> wrote:
| Quote: |
"toto" <scarecrow@wicked.witch> wrote in message
news:vm9q7458hu8s1mc50ecv6kl07pri6c0k9e@4ax.com...
On Tue, 15 Jul 2008 12:53:54 -0400, "Larry Hewitt"
larryhewi@comporium.net> wrote:
And that, as you note, geometry is the "formal" math class, requiring more
rigor in answering questions?
Except that in many schools in order to get kids to pass geometry, the
schools are using *informal geometry* without rigorous proofs.
See:
http://hsfs2.ortn.edu/MYSCHOOL/WJONES/infgeom.htm
Informal Geometry is a standards-based, Euclidean geometry course
which meets the criteria for the state's geometry curriculum. The
major difference between Informal Geometry and Geometry AB is the
amount of formal proofs that are written in this curriculum. There
are more hands-on activities and more real-life geometry problems
versus abstract problem solving.
Having taught this course in a Chicago Public High School, I can tell
you that it is not a college prep course and that while some of the
concepts are taught, much of the course is dumbed down. There were no
formal proofs with statements and reasons in our course. There were
some informal proofs in paragraph form which in many ways was harder
for the students to understand. My dd called this course *geometry
for stones* and she called Conceptual Physics (physics without math)
*physics for trees.*
|
| Quote: |
I know of no distrcit where geometry is intended to be a college prep
course.
|
The main value of the geometry course is to give an understanding
of proofs. The rest is of much less value than one would think.
In a sense, it was a key college prep course before the dumbing down.
| Quote: |
In my district it is the second of 3 reuried course, between the algebras.
|
Which makes it essentially meaningless, with the idea that
all should pass.
| Quote: |
I'll admit calling it rigorous is an overstatement. But it is the first
class where rigor is required, at tleast tothe point of listing _all_ steps
and explaining why you did what you did.
|
This belongs in FIRST grade. One cannot build up to mathematical rigor.
1
| Quote: |
The first college prep class is trig, a far more rigourous course.
|
Trigonometry is a few definitions, a little geometry, and algebra.
There is no way in which it is a rigorous course in the sense
of mathematical rigor.
| Quote: |
But even most college bound kids do not take it, witing until they reach
college to take a :college algebra" course to cover the basic conspts.
|
The current college algebra courses at the universities are
not of much value. The problem is that they are given with
the idea that the students could not get it the first time,
rather than the attitude that they had not seen anything of
even fair value. We can do a reasonable job for those of
ability who are ignorant if we take that approach, but only
if we do not put them in with those who can no longer understand,
or treat them as such.
One cannot build up to rigor, and no non-rigorous mathematics
should be taught. One does not need completeness, which means
all steps presented, but full rigor. The teachers should be
REQUIRED to be able to fill in the steps, and I do not believe
that most of the high school teachers of mathematics can even
learn it.
| Quote: |
At my Alma Mater mor than 90% of incoming freshmen took it, just about
everyone but he math and hard science majors and about half the comp sci
majors.
|
And they came out knowing facts but no understanding.
If one does not understand induction, one does not
understand what makes the integers the integers.
--
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
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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Herman Rubin
Guest
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| Posted: Wed Jul 16, 2008 7:13 pm Post subject: Re: Don't Call It "Algebra"; Call It Something Warm And Fuzz |
|
|
In article <AdKdnQc1u-gl3uDV4p2dnAA@comporium.net>,
Larry Hewitt <larryhewi@comporium.net> wrote:
| Quote: |
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:g5j9cu$6iqa@odds.stat.purdue.edu...
In article <GJWdnXmZ_tO-S-HV4p2dnAA@comporium.net>,
Larry Hewitt <larryhewi@comporium.net> wrote:
|
[References deleted.]
..............
| Quote: |
Herman doesn't consider "basic high school-level algebra" to include
the "basic mathematical concepts" that he is talking about, which
are
theoretical and abstract. He thinks that "basic high school-level
algebra" is mostly plug and chug recipes for solving problems, and
rote memorization of terminology, and he considers neither of these
to
be real "mathematics".
|
| Quote: |
The following includes essentially all of algebra, except
for technical terms not used at the high school level:
A variable is a temporary name for something,
which must maintain its meaning in a given context.
The same operation performed on equal entities
yields equal results.
I respectfully disagree. For whatever reason, the term *algebra*
has
taken on some mythical status as something extremely difficult and
fear-inducing.
The reason, as I learned from raising two kids who got that
attitude,
is that *algebra* IS extremely difficult and fear-inducing.
It is, because of the atrocious way it is taught.
The problems set for one variable require the student
to mentally make lots of substitutions. NO word
problem should limit the number of variables used.
|
| Quote: |
No, it is becaue of scoietal attitudes created in large part from attempts
to make intor math rigorous.
|
And why did that approach, which is the hard one but looks
simple, fail? It was because the teachers COULD NOT understand
the simple concepts, but could only do memorization and drill.
We need teachers who have been taught concepts, not trained in
managing the type of class which should not even exist.
The societal attitudes of grade a year, all at the same pace,
were easy for the Dewey socialists to brainwash during the
Depression, and we cannot have good schools except as this
attitude is utterly DESTROYED.
| Quote: |
I had parents in PTOassemblies talk about how hard math was, how boring it
was, and how a reward for meeting fund raising goasl was a pass to ditch
math.
|
They do not have any better an understanding of mathematics
than the most ignorant tribesman. They may be able to do
some arithmetic operations trained into them, but they do
not know what it means. It IS that bad.
| Quote: |
In college I had fellow students in other disciplies ooh and ahh about me
being a math major --- it was just "so hard".
|
If they were given some understanding instead of poor
training, they might not think of it that way.
| Quote: |
I had parents debate the need for math with me when I called them in becauee
theur kid slept through first period.
|
....................
| Quote: |
They may or may not be available. It is not unusual for even
good students not to take the proof geometry course. The
more usual course is terminology, and how to compute perimeters
and areas, and maybe a little more. This was the result of the
educationists in NSF around 1960, who did not accept the
excellent book produced by the committee.
|
| Quote: |
Not around here.
The proof aren;t as riorous as the grad level geometry course. but they are
proofs.
|
They aren't? There are a few axioms which Euclid assumed, and
the high school book not adopted had those included, but the
level of rigor was the same. There are no levels of rigor;
there are of completeness.
| Quote: |
An they learn far more than simple area and perimiter ccalcs for tri- and
quadrilaterals.
About half the course is proofs of the angle theorems and extensions of
these theorems into the larger multilaterals.
|
Gee whiz.
| Quote: |
Even this is betyond many students --- ther eis a high failure rate. A dirty
little secret is thattwo failures puts you into a "math for dummies" section
open to seniors on;y who ar ein jeopardy of mot graduating if they don;t
pass geometry and algebra ii/.
|
The assumption of the educationists that anyone can learn
anything anyone else can is just that, and is false.
Those willing and able to learn should not be held back.
Anyone holding a student back, even in ONE subject, should
be financially responsible for trying to undo it, and
pay substantial damages. Only this will scare the teachers
into doing something remotely intelligent.
You can lead a child to educational opportunities, but
you cannot make him learn.
| Quote: |
Did you know that also in every district I am aware of --- 4 entire
states --- that 2 algebra and 1 geometry course, in different orders, are
all more than 80% of students are required to take to graduate? Public
and
private.Some require even less, especially private schools.
And that, as you note, geometry is the "formal" math class, requiring more
rigor in answering questions?
I do not trust the contents of ANY of these courses, except
possibly at the best high schools. Most come out not knowing
what a proof is, or even that there is such a thing as a theorem.
|
My colleagues have seen the output.
| Quote: |
Truth is, there are very few texts in circulation, most texts are very
simialr, and courses tend to look alike.
|
Yes; the educationist fraternity sees to that.
When subject matter scholars object, they are not even
cursorily listened to.
| Quote: |
In every one of those states geometry is taught in the 10th grade or later
for these 80% (god, I hate block scheduling), who take algebra i in the
9th
grade.
Does it matter if the course is low?
|
| Quote: |
I do not understand.
|
A poor course can be worse than no course at all. With no
course at all, the colleges will not assume that there is
knowledge of the subject.
| Quote: |
This is what society has deigned to be the standard for education. I
agree,
it is probably not enough. But even this much is more than much of society
wants. And this even includes colleges.
|
The inmates running the asylum.
| Quote: |
Most colleges require no more than 2 high school credits in math for
admission. But some require only 1.
And the college courses have mostly sunk. A good student
might not get any of the "standard" upper division mathematics
course, and will not have any way of knowing it.
|
| Quote: |
Thye willnot take it because they do not need it.
|
That is not what I meant. They will take courses with
that title, but not the content.
| Quote: |
A journalist does not need topology.
|
Agreed. But algebra, and an understanding of
mathematical rigor, is needed.
| Quote: |
A registered dietician doe snot need a linear algebra course.
|
Wrong. How else can one balance a diet.
| Quote: |
A lawyer deos not need differential equations.
|
No, but he might well need to know what a differential
equation is; anyone with a calculus course which stresses
the concepts already knows this. And this should be
required for the FIRST physics course.
| Quote: |
You must understand the resistance teachers and HS administrators get when
advising college bound students to take more math courses than admission
to
the college of their choice requires, risking their precious gpa and
possibly even admission.
|
Some of the private colleges already discard these. And many
Indiana high schools, including West Lafayette, will no longer
provide the GPA or class rank, arguing that it hurts their
students who are capable of going to good schools.
You might find this surprising, but I believe that an "A"
in a course should mean the course was too easy.
| Quote: |
If you want to change high school math education stop blaming high
schools,
blame colleges, get them to change. Get them to require trig for
admission.
Get them to require calc II for graduation.
It will not matter. Cookbook calculus is still bad.
So ther eis no hoep.
All you want to do is complain?
|
No; I want to start getting good education. Those with
attitudes like you are not likely to be a part of
providing it. Nor, alas, are most of the current
teachers or teacher candidates.
| Quote: |
Won't happen. Half their student bodies will flunk out.
At this time, they should. How else is Joe Sixpack going
to understand how poor the education is? I do not consider
more than 1/3 of the college students prepared for college,
and I am not sure what portion of the college graduates are
so prepared. There is great pressure not to fail too many.
|
| Quote: |
That is your whine.
|
Is it not justified?
| Quote: |
But hte people paying the bills are satsdisfied.
|
Most of the bills are not paid by the students or
their families.
| Quote: |
AS I said vefore, who am I to tell others how to think?
|
As a libertarian, I do not want the government to tell
anyone how to think. I believe in providing opportunities
to those who can take advantage of them, and not yelling
discrimination by those who cannot.
--
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
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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Larry Hewitt
Guest
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| Posted: Wed Jul 16, 2008 9:33 pm Post subject: Re: Don't Call It "Algebra"; Call It Something Warm And Fuzz |
|
|
"Herman Rubin" <hrubin@odds.stat.purdue.edu> wrote in message
news:g5ktm1$ff6@odds.stat.purdue.edu...
| Quote: |
In article <S7KdnaLb2Jyk3eDV4p2dnAA@comporium.net>,
Larry Hewitt <larryhewi@comporium.net> wrote:
"toto" <scarecrow@wicked.witch> wrote in message
news:vm9q7458hu8s1mc50ecv6kl07pri6c0k9e@4ax.com...
On Tue, 15 Jul 2008 12:53:54 -0400, "Larry Hewitt"
larryhewi@comporium.net> wrote:
And that, as you note, geometry is the "formal" math class, requiring
more
rigor in answering questions?
Except that in many schools in order to get kids to pass geometry, the
schools are using *informal geometry* without rigorous proofs.
See:
http://hsfs2.ortn.edu/MYSCHOOL/WJONES/infgeom.htm
Informal Geometry is a standards-based, Euclidean geometry course
which meets the criteria for the state's geometry curriculum. The
major difference between Informal Geometry and Geometry AB is the
amount of formal proofs that are written in this curriculum. There
are more hands-on activities and more real-life geometry problems
versus abstract problem solving.
Having taught this course in a Chicago Public High School, I can tell
you that it is not a college prep course and that while some of the
concepts are taught, much of the course is dumbed down. There were no
formal proofs with statements and reasons in our course. There were
some informal proofs in paragraph form which in many ways was harder
for the students to understand. My dd called this course *geometry
for stones* and she called Conceptual Physics (physics without math)
*physics for trees.*
I know of no distrcit where geometry is intended to be a college prep
course.
The main value of the geometry course is to give an understanding
of proofs. The rest is of much less value than one would think.
|
Nope.
The main value of secondary geometry is to get students to hink spacially.
Look, this will go nowhere.
Here's achallenge for you.
Got into a 9th grade calssroom.
Teach the kids.
Try to get the averaage 15 yr old to understadn and comply with the rules
of formal proofs.
Try to get a 16 yr old to understand number theory.
Or, if you'ld rather, pick a lower grade and start them off "right".
Let us know how it went.
Larry
| Quote: |
In a sense, it was a key college prep course before the dumbing down.
In my district it is the second of 3 reuried course, between the algebras.
Which makes it essentially meaningless, with the idea that
all should pass.
I'll admit calling it rigorous is an overstatement. But it is the first
class where rigor is required, at tleast tothe point of listing _all_
steps
and explaining why you did what you did.
This belongs in FIRST grade. One cannot build up to mathematical rigor.
1
The first college prep class is trig, a far more rigourous course.
Trigonometry is a few definitions, a little geometry, and algebra.
There is no way in which it is a rigorous course in the sense
of mathematical rigor.
But even most college bound kids do not take it, witing until they reach
college to take a :college algebra" course to cover the basic conspts.
The current college algebra courses at the universities are
not of much value. The problem is that they are given with
the idea that the students could not get it the first time,
rather than the attitude that they had not seen anything of
even fair value. We can do a reasonable job for those of
ability who are ignorant if we take that approach, but only
if we do not put them in with those who can no longer understand,
or treat them as such.
One cannot build up to rigor, and no non-rigorous mathematics
should be taught. One does not need completeness, which means
all steps presented, but full rigor. The teachers should be
REQUIRED to be able to fill in the steps, and I do not believe
that most of the high school teachers of mathematics can even
learn it.
At my Alma Mater mor than 90% of incoming freshmen took it, just about
everyone but he math and hard science majors and about half the comp sci
majors.
And they came out knowing facts but no understanding.
If one does not understand induction, one does not
understand what makes the integers the integers.
--
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
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 |
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Bob LeChevalier
Guest
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| Posted: Wed Jul 16, 2008 10:55 pm Post subject: Re: Don't Call It "Algebra"; Call It Something Warm And Fuzz |
|
|
hrubin@odds.stat.purdue.edu (Herman Rubin) wrote:
| Quote: |
It is, because of the atrocious way it is taught.
The problems set for one variable require the student
to mentally make lots of substitutions. NO word
problem should limit the number of variables used.
No, it is becaue of scoietal attitudes created in large part from attempts
to make intor math rigorous.
And why did that approach, which is the hard one but looks
simple, fail?
|
Because the public had no interest in that approach, and indeed didn't
consider that stuff to be the sort of mathematics that they wanted
their non-mathematician kids to be taught. They wanted practical
skills and not useless theory.
| Quote: |
It was because the teachers COULD NOT understand
the simple concepts, but could only do memorization and drill.
|
Whether they could understand or not, there was no political will to
support the teaching of mathematical theory at early ages at the
expense of arithmetical mastery.
| Quote: |
We need teachers who have been taught concepts, not trained in
managing the type of class which should not even exist.
|
That type of class DOES exist, and will continue to exist, and one of
the major skills that a teacher needs is to be able to manage it, or
they won't last a single year in the classroom.
| Quote: |
I had parents in PTOassemblies talk about how hard math was, how boring it
was, and how a reward for meeting fund raising goasl was a pass to ditch
math.
They do not have any better an understanding of mathematics
than the most ignorant tribesman.
|
But "we the people" run the country, whether ignorant or not, and "we
the people" decide what will be the focus of the schools that we pay
for.
| Quote: |
They may be able to do
some arithmetic operations trained into them, but they do
not know what it means.
|
It means that they get the right answer in everyday applications, and
that is all that 90% care about.
| Quote: |
Even this is betyond many students --- ther eis a high failure rate. A dirty
little secret is thattwo failures puts you into a "math for dummies" section
open to seniors on;y who ar ein jeopardy of mot graduating if they don;t
pass geometry and algebra ii/.
The assumption of the educationists that anyone can learn
anything anyone else can is just that, and is false.
|
That is the assumption of, and the REQUIREMENT of both the state and
national legislatures. It was not "educationists" that adopted "No
Child Left Behind" which quite clear evinces that assumption.
| Quote: |
You can lead a child to educational opportunities, but
you cannot make him learn.
|
Correct. But the legislatures are quite willing to punish the
teachers for failure to make him learn anyway, so that is what the
teachers have to focus on.
| Quote: |
Truth is, there are very few texts in circulation, most texts are very
simialr, and courses tend to look alike.
Yes; the educationist fraternity sees to that.
|
The economics of textbook publishing, and the existence of state
standards in Texas and California which select and purchase textbooks
at the state level, sees to that.
| Quote: |
When subject matter scholars object, they are not even
cursorily listened to.
|
College professors are quite willing to choose a textbook that no one
else uses, because they can, and because the enormous cost of the
textbooks comes out of their students' pockets and not out of their
department budgets. If your department had to pay for the textbooks
and materials that your students used, there might be more pressure on
YOU to standardize your choice of textbook.
| Quote: |
In every one of those states geometry is taught in the 10th grade or later
for these 80% (god, I hate block scheduling), who take algebra i in the
9th
grade.
Does it matter if the course is low?
I do not understand.
A poor course can be worse than no course at all. With no
course at all, the colleges will not assume that there is
knowledge of the subject.
|
The colleges know what the textbooks are, and therefore should assume
that the knowledge corresponds to what the textbook covers.
| Quote: |
This is what society has deigned to be the standard for education. I
agree,
it is probably not enough. But even this much is more than much of society
wants. And this even includes colleges.
The inmates running the asylum.
|
That is the nature of free markets.
| Quote: |
A journalist does not need topology.
Agreed. But algebra, and an understanding of
mathematical rigor, is needed.
|
Not really.
| Quote: |
A registered dietician doe snot need a linear algebra course.
Wrong. How else can one balance a diet.
|
By guess and by golly.
| Quote: |
A lawyer deos not need differential equations.
No, but he might well need to know what a differential equation is;
|
Why?
| Quote: |
anyone with a calculus course which stresses
the concepts already knows this. And this should be
required for the FIRST physics course.
|
A lawyer doesn't need to know calculus-based physics, either.
| Quote: |
Won't happen. Half their student bodies will flunk out.
At this time, they should.
|
Not acceptable.
| Quote: |
How else is Joe Sixpack going
to understand how poor the education is? I do not consider
more than 1/3 of the college students prepared for college,
and I am not sure what portion of the college graduates are
so prepared. There is great pressure not to fail too many.
That is your whine.
Is it not justified?
|
If it is justified at the university level, where you have nominal
academic freedom, then it is at least as justified at the K/12 level,
where there is little academic freedom, and much higher political
pressure to not fail ANYONE.
| Quote: |
But hte people paying the bills are satsdisfied.
Most of the bills are not paid by the students or
their families.
|
The taxpayers are satisfied by such things as NCLB. They would NOT be
satisfied by courses that flunked half the students.
| Quote: |
AS I said vefore, who am I to tell others how to think?
As a libertarian, I do not want the government to tell
anyone how to think.
|
Then pay for it yourself.
What government pays for, government controls, which means "we the
people" determine the goals.
lojbab
Bob LeChevalier - artificial linguist; genealogist
lojbab@lojban.org Lojban language www.lojban.org |
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Sarah Vaughan
Guest
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| Posted: Fri Jul 18, 2008 10:34 am Post subject: Re: Don't Call It "Algebra"; Call It Something Warm And Fuzz |
|
|
lenona321@yahoo.com wrote:
| Quote: |
Reminds me of when, years ago, Miss Manners wrote a column about how,
in her opinion, mandatory charity work at school is good for kids
because "no doubt they do as little as possible and vow never to
return, but isn't that also true of many other subjects they have to
study?
|
To go off on a complete and potentially controversial tangent, this is
why I never understand the "If they learn about it at school, they'll
want to try it at home!" argument that has often been advanced against
sex education classes.
All the best,
Sarah
--
http://www.goodenoughmummy.typepad.com
"That which can be destroyed by the truth, should be" - P. C. Hodgell |
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