Don't Call It "Algebra"; Call It Something Warm And Fuzzy

(Herman Rubin) wrote:
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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

A journalist does not need topology.

Agreed. But algebra, and an understanding of
mathematical rigor, is needed.

Not really.

A registered dietician doe snot need a linear algebra course.

Wrong. How else can one balance a diet.

By guess and by golly.

A lawyer deos not need differential equations.

No, but he might well need to know what a differential equation is;

Why?

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.

Won't happen. Half their student bodies will flunk out.

At this time, they should.

Not acceptable.

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.

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.

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
Lojban language www.lojban.org

In article ,
Larry Hewitt wrote:

"Herman Rubin" wrote in message
...
In article ,
Larry Hewitt wrote:

"toto" wrote in message
...
On Tue, 15 Jul 2008 12:53:54 -0400, "Larry Hewitt"
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.

Knowing teachers and students, the amount of formal proofs goes
down to almost nothing, and the amount of it learned by students
is likely to be absolute zero even if it is there.


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.*

And I must strongly accuse the college admissions offices,
in their rush to get more students, being willing to accept
geometry for stones and physics for trees. These students,
if the term can be used for such, lower the standards of the
college courses, as good student evaluations are now needed
for tenure, and often even for promotion of a tenured associate
professor to full professor.


I know of no distrcit where geometry is intended to be a college prep
course.

It was before WWII, and it should be now. This includes for
those not going into mathematical subjects; it is unfortunate
that our politicians and judges have no idea what a formal
proof is, and what an inductive proof (NOT a proof by induction)
is; the latter is what is used in decisions where the facts are
in dispute.


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.

This does not occur by giving names and formulas.

Look, this will go nowhere.

Here's achallenge for you.

Got into a 9th grade calssroom.

Teach the kids.

If they understand English, it might still be possible.

Try to get the averaage 15 yr old to understadn and comply with the rules
of formal proofs.

Average, average, average. Students of different ability
MUST be taught differently; not accepting this is denying
the well-established fact that people are different.

Try to get a 16 yr old to understand number theory.

This might be much easier.

Or, if you'ld rather, pick a lower grade and start them off "right".

I have posted here, many times, that the time to teach about
variables is when they can read a little and make symbols.
It is part of language; restricted to mathematics, it loses
its simplicity.

Let us know how it went.

Do you think the educationists would let me try?

--
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
Phone: (765)494-6054 FAX: (765)494-0558

"Herman Rubin" wrote in message
...
In article ,
Larry Hewitt wrote:

"Herman Rubin" wrote in message
...
In article ,
Larry Hewitt wrote:

"toto" wrote in message
m...
On Tue, 15 Jul 2008 12:53:54 -0400, "Larry Hewitt"
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.

Knowing teachers and students, the amount of formal proofs goes
down to almost nothing, and the amount of it learned by students
is likely to be absolute zero even if it is there.


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.*

And I must strongly accuse the college admissions offices,
in their rush to get more students, being willing to accept
geometry for stones and physics for trees. These students,
if the term can be used for such, lower the standards of the
college courses, as good student evaluations are now needed
for tenure, and often even for promotion of a tenured associate
professor to full professor.


I know of no distrcit where geometry is intended to be a college prep
course.

It was before WWII, and it should be now. This includes for
those not going into mathematical subjects; it is unfortunate
that our politicians and judges have no idea what a formal
proof is, and what an inductive proof (NOT a proof by induction)
is; the latter is what is used in decisions where the facts are
in dispute.


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.

This does not occur by giving names and formulas.

Look, this will go nowhere.

Here's achallenge for you.

Got into a 9th grade calssroom.

Teach the kids.

If they understand English, it might still be possible.

Try to get the averaage 15 yr old to understadn and comply with the rules
of formal proofs.

Average, average, average. Students of different ability
MUST be taught differently; not accepting this is denying
the well-established fact that people are different.

Try to get a 16 yr old to understand number theory.

This might be much easier.

Or, if you'ld rather, pick a lower grade and start them off "right".

I have posted here, many times, that the time to teach about
variables is when they can read a little and make symbols.
It is part of language; restricted to mathematics, it loses
its simplicity.

Let us know how it went.

Do you think the educationists would let me try?

Set up a lab program in the math department, say on Saturday mornings, for
interested parents to enroll their child in. Such programs are common in
Schools of Music (and in other fine arts areas). Music teachers aren't
trained by education departments, but by music departments, so such programs
serve multiple purposes. They provide hands-on experience to college
professors, who then are teaching actual children, as opposed to just
hypothesizing about how things will work with children. They provide a
research laboratory to test and try out new programs, which then become
common, and they provide observation and practicum experiences for students
who are going through music training, before they ever begin any significant
training in pedagogy. (Music pedagogy is typically a 5th or even 6th year
program, completed after the music requirements are satisfied. Specialist
training in Orff, Kodaly, or Dalcroze isn't even availble until after a
teacher has a baccalaureate degree in music). My university was the first
to begin Orff-Schelwerk in the USA, in a lab program between the university
and the local schools. Other similar programs have done the same with
Kodaly and Dalcroze, and Edwin Gordon has taken his research as well. The
result is that all of these tested methodologies have found their place in
the elementary school music curriculum, and, in areas where elementary
school music is actually taught by trained music specialists, the quality of
music instruction K-12 is much, much higher than it was 30+ years ago
(finances have eliminated or cut back music from so many districts that
unfortunately it is relatively rare for a child to get regular classes in
the elementary years-and then, such districts wonder why the secondary music
programs fall apart). Even when there is no trained music teacher, if a
district actually purchases and uses a music textbook series, which are
designed for classroom teachers, many of the principles which have been
shown to be effective will be applied, and the students will STILL get a
higher quality music education than was available in most schools 30+ years
ago.


There is absolutely no reason why other academic departments couldn't do
likewise. If you want to teach children, train teachers, and change
education, the first step is doing it yourself, locally, in a situation
under your control. Prove what you do works, and eventually, what works will
be adopted. Given that over half my preschool music students this year were
enrolled in Kumon math (which is simply drill and memorization, at a very
high price tag), I don't think you'd have any trouble getting students.

"Herman Rubin" wrote in message
...
In article ,
Larry Hewitt wrote:

"Herman Rubin" wrote in message
...
In article ,
Larry Hewitt wrote:

"toto" wrote in message
m...
On Tue, 15 Jul 2008 12:53:54 -0400, "Larry Hewitt"
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.

Knowing teachers and students, the amount of formal proofs goes
down to almost nothing, and the amount of it learned by students
is likely to be absolute zero even if it is there.


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.*

And I must strongly accuse the college admissions offices,
in their rush to get more students, being willing to accept
geometry for stones and physics for trees. These students,
if the term can be used for such, lower the standards of the
college courses, as good student evaluations are now needed
for tenure, and often even for promotion of a tenured associate
professor to full professor.


I know of no distrcit where geometry is intended to be a college prep
course.

It was before WWII, and it should be now. This includes for
those not going into mathematical subjects; it is unfortunate
that our politicians and judges have no idea what a formal
proof is, and what an inductive proof (NOT a proof by induction)
is; the latter is what is used in decisions where the facts are
in dispute.


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.

This does not occur by giving names and formulas.

Look, this will go nowhere.

Here's achallenge for you.

Got into a 9th grade calssroom.

Teach the kids.

If they understand English, it might still be possible.

Try to get the averaage 15 yr old to understadn and comply with the rules
of formal proofs.

Average, average, average. Students of different ability
MUST be taught differently; not accepting this is denying
the well-established fact that people are different.

Try to get a 16 yr old to understand number theory.

This might be much easier.

Or, if you'ld rather, pick a lower grade and start them off "right".

I have posted here, many times, that the time to teach about
variables is when they can read a little and make symbols.
It is part of language; restricted to mathematics, it loses
its simplicity.

Let us know how it went.

Do you think the educationists would let me try?


Absolutely. No question.

YOu have impeccable credentials, and there are enough experimental programs,
charter schools, private schools, and the like _begging_ for teachers you
would be snapped up in a heartbeat.

Larry

--
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
Phone: (765)494-6054 FAX: (765)494-0558