An Interview with James Stewart
Dom
http://www.maa.org/news/061809stewart.html
(A shorter article, "James Stewart and the House That Calculus Built,"
is at:
http://www.maa.org/pubs/augsept09pgs4-6.pdf )
I was particularly intrigued by the following: First, by Stewart's
comments about one of his new books.
"The other new book I am writing is a very interesting one. It's a
reform college algebra book, which I think is more reform than
anything else out there. This is my take on the reform algebra
movement. It’s very much data driven.
"I was actually approached by four instructors from Mercer County
Community College in New Jersey, who requested such a book. A lot of
schools have some math requirement, so you have these kids who are
never going to take another math course, and yet they have to take a
college algebra course. I'm not sure that's a sensible policy, but
given that it is a widespread policy, let’s make it more interesting
for those kids to really try to draw them into it. That's not an easy
task. So I wrote a prolog, "Algebra and Alcohol," for that book, which
is now in production. No matter what your attitude is to alcohol, I
thought this would get their attention."
I wonder why these four instructors are not able to write their own
materials for this "reform college algebra book"?
Second, it seems to me that Stewart appears to be completely clueless
about the bloated junk books of today.
"Compared with the textbooks that I had as a student, textbooks are so
much better now. I don’t know how kids learned from these old books.
There was no motivation. It was very austere. You can go too far in
the other direction, but the state of the exposition of mathematics is
just so much better than it was three decades ago."
As far as calculus texts go, I still like the Third Edition of Thomas,
which I used for four semesters in 1966-68. The derivative was defined
in page 29. In most calculus books today, including Stewart's, it is
defined around page 150.
Most disgraceful are the series of Elementary Algebra, Intermediate
Algebra, College Algebra, Algebra and Trigonometry, and Precalculus
books that are being written for college students. Three years ago, I
received two unsolicited desk copies of
"Precalculus: Concepts Through Functions"
A Unit Circle Approach To Trigonometry
(Pearson Prentice Hall, 2007)
by Michael Sullivan, Chicago State University, and Michael Sullivan,
III, Joliet Junior College.
One version was "A Unit Circle Approach To Trigonometry," the second
version was "A Right Triangle Approach To Trigonometry." Each doorstop
weighed about 5.5 pounds and has more than 1,100 pages. As is the case
with similar doorstops, the first 260 pages are little more than a
review of Algebra I and II. Exponential and Logarithmic functions
start around page 260, and Trigonometric functions around page 360.
Bob LeChevalier
>An Interview with James Stewart, by Ivars Peterson is posted at:
>
>http://www.maa.org/news/061809stewart.html
>"I was actually approached by four instructors from Mercer County
>Community College in New Jersey, who requested such a book. A lot of
>schools have some math requirement, so you have these kids who are
>never going to take another math course, and yet they have to take a
>college algebra course. I'm not sure that's a sensible policy, but
>given that it is a widespread policy, let�s make it more interesting
>for those kids to really try to draw them into it. That's not an easy
>task. So I wrote a prolog, "Algebra and Alcohol," for that book, which
>is now in production. No matter what your attitude is to alcohol, I
>thought this would get their attention."
>
>I wonder why these four instructors are not able to write their own
>materials for this "reform college algebra book"?
Writing a book isn't the easiest thing in the world. Writing a *good*
book is very difficult. Writing a book that is sufficiently
profitable to pay for the time spent by the author is much more rare,
especially in the realm of textbooks that are not backed in advance by
a major textbook publisher.
>Second, it seems to me that Stewart appears to be completely clueless
>about the bloated junk books of today.
Actually, your response to him shows that it is you who are clueless.
>"Compared with the textbooks that I had as a student, textbooks are so
>much better now. I don�t know how kids learned from these old books.
>There was no motivation. It was very austere. You can go too far in
>the other direction, but the state of the exposition of mathematics is
>just so much better than it was three decades ago."
>
>As far as calculus texts go, I still like the Third Edition of Thomas,
>which I used for four semesters in 1966-68. The derivative was defined
>in page 29. In most calculus books today, including Stewart's, it is
>defined around page 150.
Which is entirely nonresponsive to his statement. "I don�t know how
kids learned from these old books. There was no motivation. It was
very austere." Defining the derivative has NOTHING to do with
"motivation". You are dealing with a subject wherein most of the
students are taking the class because someone requires it, not because
they have any specific interest in the material being learned. As
your subject said (and you ignored):
>"A lot of
>schools have some math requirement, so you have these kids who are
>never going to take another math course, and yet they have to take a
>college algebra course. I'm not sure that's a sensible policy, but
>given that it is a widespread policy, let�s make it more interesting
>for those kids to really try to draw them into it. That's not an easy
>task."
You are also dealing with students in the class that have a large
variation in preparation for the course. A textbook that waits 100
more pages to define the derivative is apparently providing 100 pages
of something else instead. If that something else makes them more
prepared to understand the definition when it is defined, then it is
probably useful. If it makes them CARE what the definition is (which
probably 99% of all students do NOT care), then it is even more
useful.
>Most disgraceful are the series of Elementary Algebra, Intermediate
>Algebra, College Algebra, Algebra and Trigonometry, and Precalculus
>books that are being written for college students.
Which of course is entirely irrelevant to Stewart's article.
>One version was "A Unit Circle Approach To Trigonometry," the second
>version was "A Right Triangle Approach To Trigonometry." Each doorstop
>weighed about 5.5 pounds and has more than 1,100 pages. As is the case
>with similar doorstops, the first 260 pages are little more than a
>review of Algebra I and II.
Which is useful when 95% of the students have forgotten significant
chunks of Algebra I and II because they simply don't CARE to remember
what seems irrelevant (or because they weren't taught it well enough
in the first place - after all, the object is to pass the class, which
in many cases means as little as 65% AVERAGE which can mean a lot
lower percentage for whatever is important as a prerequisite for
college calculus.
>Exponential and Logarithmic functions
>start around page 260, and Trigonometric functions around page 360.
So? You don't like doorstops. People who actually teach the classes
apparently do, or they wouldn't sell.
If you think you can do so much better, write your own textbook. Let
us know how well it sells, and how superior the students using the
text are when they complete the class.
lojbab
---
Bob LeChevalier - artificial linguist; genealogist
loj...@lojban.org Lojban language www.lojban.org
William Elliot
> "The other new book I am writing is a very interesting one. It's a
> reform college algebra book, which I think is more reform than
> anything else out there. This is my take on the reform algebra
> movement. It�s very much data driven.
>
What does "data driven" mean. Is that like cook booked?
Give a data driven derivation of the solution for a general
quadratic equation,
p(x) = ax^2 + bx + c = 0, a /= 0
namely
x = (-b +- sqr(b^2 - 4ac)/2a.
Show by data driven methods how the discriminate
d = b^2 - 4ac
determines if the equation has two real roots, one real root
or two complex roots.
Now compile lots of data to show that a quadratic equation
cannot have one root real and the other complex. Is there
an easier way to show that without data mining?
> "I was actually approached by four instructors from Mercer County
> Community College in New Jersey, who requested such a book. A lot of
> schools have some math requirement, so you have these kids who are
> never going to take another math course, and yet they have to take a
> college algebra course. I'm not sure that's a sensible policy
It isn't. It's the dummying of America, reducing education to
entertainment in the manner that news has been reduced to entertainment.
-- the Dummy Down Dunce Dance
Forlorn am I to scorn
the land wherein I'm born
whence creativity is shorn
to fit some standard norm
----
Dom
> Dom <DR...@teikyopost.edu> wrote:
> >An Interview with James Stewart, by Ivars Peterson is posted at:
>
> >http://www.maa.org/news/061809stewart.html
> >Second, it seems to me that Stewart appears to be completely clueless
> >about the bloated junk books of today.
>
> Actually, your response to him shows that it is you who are clueless.
>
> >"Compared with the textbooks that I had as a student, textbooks are so
> >much better now. I don’t know how kids learned from these old books.
> >There was no motivation. It was very austere. You can go too far in
> >the other direction, but the state of the exposition of mathematics is
> >just so much better than it was three decades ago."
>
> >As far as calculus texts go, I still like the Third Edition of Thomas,
> >which I used for four semesters in 1966-68. The derivative was defined
> >in page 29. In most calculus books today, including Stewart's, it is
> >defined around page 150.
>
> Which is entirely nonresponsive to his statement. "I don’t know how
> kids learned from these old books. There was no motivation. It was
> very austere."
Actually, you are the one who also appears to be clueless. When
compared with the pseudo-educated students of today, students learned
quite well from the old, pre-new-math textbooks. These old books had
very little review material, because previous material, which had been
taught and mastered quite well, was recalled quite readily.
Bob LeChevalier
That is not in evidence. Remember that we had a panic in this country
about math and science education at the time of Sputnik, precisely
because students were not learning those subjects very well - and that
was when the percentage attending college was perhaps half of what it
is now.
Of course, I have some of those pre-new-math textbooks from the k/12
level, and most were far less ambitious in what they covered. Algebra
I consisted of simple linear equations, with a dabbling of quadratics
in the last chapter. No functional notation, no sets, no logic or
proofs. Formulaic word problems that were described in a manner that
allowed trivial formulation.
There wasn't much review, but neither was there much content.
Go further back, around the turn of the century, and there were skinny
algebra books that consisted of a lot of definitions, theorems, and
lemmas. No review material. But then these also were college books,
and were used by the less than 5% of the populace that went to
college, and many of them took no math courses.
>These old books had
>very little review material, because previous material, which had been
>taught and mastered quite well, was recalled quite readily.
No it wasn't, as evidenced by the Sputnik "crisis", and you apparently
haven't looked at many of those books.
Dom
The high school math curriculum, which was extremely sound, was used
as a convenient scapegoat for the launching of Sputnik. The real
problem was with those in charge of our rocket program.
> Of course, I have some of those pre-new-math textbooks from the k/12
> level, and most were far less ambitious in what they covered. Algebra
> I consisted of simple linear equations, with a dabbling of quadratics
> in the last chapter. No functional notation, no sets, no logic or
> proofs. Formulaic word problems that were described in a manner that
> allowed trivial formulation.
My Algebra I book did indeed end with quadratic equations and their
graphs. Functions (mosly trig functions), vectors, matrices, etc. were
covered in Algebra II. More general functional notation was covered in
Advanced Mathematics, a description of which is at:
http://mathforum.org/kb/message.jspa?messageID=1466613&tstart=0
> >These old books had
> >very little review material, because previous material, which had been
> >taught and mastered quite well, was recalled quite readily.
>
> No it wasn't, as evidenced by the Sputnik "crisis", and you apparently
> haven't looked at many of those books.
As I said above, the Sputnik "crisis" had absolutely nothing to do
with the math curriculum. I am surprised that you are still promoting
this major canard. The material in each course was covered thoroughly--
and in a logical sequence--as opposed to being "a mile wide and an
inch deep" and turning out so many pseudo-educated students today.
Nick
> Actually, you are the one who also appears to be clueless. When
> compared with the pseudo-educated students of today, students learned
> quite well from the old, pre-new-math textbooks. These old books had
> very little review material, because previous material, which had been
> taught and mastered quite well, was recalled quite readily.
I'm a bit confused. I'm in England and did my high school math 30 years
ago. My son is starting his A levels, 16-18 year age group exams.
I looked at his math course and text book and it looks pretty much the
same as I did.
Is this because; I did new math, my son is amongst the few students
doing proper math or becuase new math hasn't hit the England.
Tim Norfolk
>
> - Show quoted text -
My wife and I had our 13-year-old work some algebra this Summer. The
book we found is one given to train Ford technicians in nthe 1940's,
and is quite extensive. Given what I see our college freshmen doing,
most of them couldn't handle this stuff.
Dave L. Renfro
> My wife and I had our 13-year-old work some algebra
> this Summer. The book we found is one given to train
> Ford technicians in nthe 1940's, and is quite extensive.
> Given what I see our college freshmen doing, most of
> them couldn't handle this stuff.
For those interested, there are several fairly sophisticated
"school algebra" treatises published in the second half
of the 1800s that are freely available on the internet,
such as the following:
George Chrystal
"Algebra" (2 volumes)
http://books.google.com/books?id=ZhoPAAAAIAAJ
http://books.google.com/books?id=d-MYAAAAYAAJ
Henry Sinclair Hall and Samuel Ratcliffe Knight
"Higher Algebra"
http://books.google.com/books?id=oB4PAAAAIAAJ
Elias Loomis
"A Treatise on Algebra"
http://books.google.com/books?id=meREAAAAIAAJ
Charles Smith
"A Treatise on Algebra"
http://books.google.com/books?id=BagXAAAAIAAJ
Isaac Todhunter
"Algebra"
http://books.google.com/books?id=5FADAAAAQAAJ
Also, a few months earlier this year I was researching
several things that led me to check out and carefully
examine a lot of pre-1930 algebra texts (about 150 texts
in all) from the Univ. of Iowa library. For what it's
worth, the BEST elementary algebra text I saw was:
Charles Smith, "Elementary Algebra", MacMillan and Company,
1890, viii + 403 pages.
http://books.google.com/books?id=cB8ZAAAAYAAJ
Although the 5 books I listed further above are much more
advanced and complete, if someone is looking for a true
high school level algebra text that is light years better
than anything that's been on the market for the past 100 years,
Charles Smith's "Elementary Algebra" is the book you want.
Dave L. Renfro
wwilson
and unavailable ten years earlier.
To give you some idea of the high school curriculum before sputnic.
Freshman: Algebra I (no one took algebra earlier than 9th grade)
Sophomore: Plane Geometry (the textbook was a minor rework of Euclid's
original "Elements")
Junior: Algebra II
Senior: Half year of Trig and half year of solid geometry.
Three comments:
1. Euclid's Elements was still a textbook over 2000 years after it was
written.
2. I once read the math curriculum at U. of Virginia in the year 1800.
At that time college students took the same four years of math as that
described above. So over a one hundred and fifty year period, college
courses drifted down to high school.
3. At that time all college freshman took a course similar to the one
described in the Math Forum. Calculus was taken as a Soph.
It is hard to realize how much the math curriculum has changed over the
years. The current one makes more demands on the student than the one of
60 years ago. Its no surprise that students have more troubles than they
did before the changes. They have to absorb the same amount of material
in less time and when they are less mature.
LEW
--
Using Opera's revolutionary e-mail client: http://www.opera.com/mail/
Tim Norfolk
>
> - Show quoted text -
Except that some studies indicate that students learn some of this
material easier at an early age. In an army school (non-selective)
under the British curriculum, I took algebra in 6/7th grades,
basically precalc in 8th grade, and then went on to grammar school
(selective), where we started calculus in 9th grade - to take an exam
in 10th grade that was required if you wanted to go to college in any
subject.
Bob LeChevalier
>> >> Which is entirely nonresponsive to his statement. �"I don�t know how
>> >> kids learned from these old books. There was no motivation. It was
>> >> very austere."
>>
>> >Actually, you are the one who also appears to be clueless. When
>> >compared with the pseudo-educated students of today, students learned
>> >quite well from the old, pre-new-math textbooks.
>>
>> That is not in evidence. �Remember that we had a panic in this country
>> about math and science education at the time of Sputnik, precisely
>> because students were not learning those subjects very well - and that
>> was when the percentage attending college was perhaps half of what it
>> is now.
>
>The high school math curriculum, which was extremely sound,
The people in charge disagreed with you.
>> Of course, I have some of those pre-new-math textbooks from the k/12
>> level, and most were far less ambitious in what they covered. �Algebra
>> I consisted of simple linear equations, with a dabbling of quadratics
>> in the last chapter. �No functional notation, no sets, no logic or
>> proofs. Formulaic word problems that were described in a manner that
>> allowed trivial formulation.
>
>My Algebra I book did indeed end with quadratic equations and their
>graphs. Functions (mosly trig functions), vectors, matrices, etc. were
>covered in Algebra II.
Except that almost no one took Algebra II in high school.
>> No it wasn't, as evidenced by the Sputnik "crisis", and you apparently
>> haven't looked at many of those books.
>
>As I said above, the Sputnik "crisis" had absolutely nothing to do
>with the math curriculum. I am surprised that you are still promoting
>this major canard. The material in each course was covered thoroughly
You know this because you were present in every high school math
classroom in the country, right?
I never knew a single class, in any subject I took, that made it to
the last chapter of the textbook (i.e. the one with quadratics in your
algebra I class). My algebra I class managed to complete only about 8
or 9 of the 12 chapters.
>and in a logical sequence
There was so little content that there was no "sequence", much less a
logical one.
Bob LeChevalier
>Tim Norfolk wrote:
>
>> My wife and I had our 13-year-old work some algebra
>> this Summer. The book we found is one given to train
>> Ford technicians in nthe 1940's, and is quite extensive.
>> Given what I see our college freshmen doing, most of
>> them couldn't handle this stuff.
>
>For those interested, there are several fairly sophisticated
>"school algebra" treatises published in the second half
>of the 1800s that are freely available on the internet,
>such as the following:
>
>George Chrystal
>"Algebra" (2 volumes)
>http://books.google.com/books?id=ZhoPAAAAIAAJ
specifically says in the preface (p vii/viii) that, while it starts at
the beginning of the subject, it is NOT a book for beginners. It
states that it has prerequisite knowledge of trig functions, and the
FIRST part is intended to be used in the higher classes of secondary
school and the lower classes of college.
>http://books.google.com/books?id=d-MYAAAAYAAJ
The subtitle of this book echoes the preface of the first book - the
book is intended for higher secondary and college
>
>Henry Sinclair Hall and Samuel Ratcliffe Knight
>"Higher Algebra"
>http://books.google.com/books?id=oB4PAAAAIAAJ
is a college textbook for British universities, and indeed the preface
says that it is a sequel to another book of similar name, and this
book contains "theorems and examples which are unsuited for a first
course of reading" The concept of "reading" a course is itself
contrary to American education below the graduate level, as I
understand it.
>Elias Loomis
>"A Treatise on Algebra"
>http://books.google.com/books?id=meREAAAAIAAJ
college level: "preparation for the SUBSEQUENT branches of a COLLEGE
course in mathematics.
>Charles Smith
>"A Treatise on Algebra"
>http://books.google.com/books?id=BagXAAAAIAAJ
"for the use of the higher classes of schools and junior classes of
universities"
>
>Isaac Todhunter
>"Algebra"
>http://books.google.com/books?id=5FADAAAAQAAJ
subtitle "for the use of colleges and schools"
>Also, a few months earlier this year I was researching
>several things that led me to check out and carefully
>examine a lot of pre-1930 algebra texts (about 150 texts
>in all) from the Univ. of Iowa library. For what it's
>worth, the BEST elementary algebra text I saw was:
>
>Charles Smith, "Elementary Algebra", MacMillan and Company,
>1890, viii + 403 pages.
>http://books.google.com/books?id=cB8ZAAAAYAAJ
Doesn't give the level, but it is clearly of the same level of the
others listed above and thus intended for college students.
I note that the authors of all of these were masters of subjects at
the major English universities. I suspect that these were the
textbooks for their beginning classes as taught in those universities.
>Although the 5 books I listed further above are much more
>advanced and complete, if someone is looking for a true
>high school level algebra text that is light years better
>than anything that's been on the market for the past 100 years,
>Charles Smith's "Elementary Algebra" is the book you want.
Except of course that it almost certainly WASN'T written as a high
school level text.
Dave L. Renfro
> For those interested, there are several fairly sophisticated
> "school algebra" treatises published in the second half
> of the 1800s that are freely available on the internet,
> such as the following:
>
> George Chrystal
> "Algebra" (2 volumes)
> http://books.google.com/books?id=ZhoPAAAAIAAJ
> http://books.google.com/books?id=d-MYAAAAYAAJ
>
> Henry Sinclair Hall and Samuel Ratcliffe Knight
> "Higher Algebra"
> http://books.google.com/books?id=oB4PAAAAIAAJ
>
> Elias Loomis
> "A Treatise on Algebra"
> http://books.google.com/books?id=meREAAAAIAAJ
>
> Charles Smith
> "A Treatise on Algebra"
> http://books.google.com/books?id=BagXAAAAIAAJ
>
> Isaac Todhunter
> "Algebra"
> http://books.google.com/books?id=5FADAAAAQAAJ
I didn't intend to compile a complete list of advanced
"school algebra" texts, but here's another one that I
happened to notice (by accident) on my shelves at home [1],
so I may as well archive it in a sci.math post with the
other titles for those interested in Chrystal-like texts
from 100+ years ago.
Aldis William Steadman, "A Text Book of Algebra"
http://books.google.com/books?id=cV4-AAAAIAAJ
[1] I have an original bound version and/or a reprint version
of each of these books, except for Todhunter's book.
Given what at least one poster has said, it seems I need to
be more explicit than I already have by saying what I'm not
saying, since apparently not saying something doesn't seem
to be enough.
I am not recommending these books for current high school
or even for current undergraduate math students. These are
for the large number of math-enthusiasts who read sci.math
(many of whom only lurk) that may be looking for interesting
and accessible (in the sense of not requiring being currently
"up on" graduate level pure mathematics) books or topics to
possibly pursue recreationally. These books are somewhat like
Spivak's or Apostol's or Courant/John's calculus books as
compared to typical calculus texts, although the gap between
them and current college algebra level texts is quite a bit
higher than the gap between these three calculus texts and
typical calculus texts.
These books were written back when the term "elementary algebra"
included all of what we would now call elementary, intermediate,
and college algebra, along with much of precalculus, sequences
and series, elements of differential calculus, combinatorics
(more than just binomial coefficients and elementary probability,
but also generating functions), number theory, etc. Also, back
then, the term "higher algebra" was often (but not always)
reserved for topics that would now be called abstract algebra
(the 1800s analog of our abstract algebra, that is).
The Davis "Elementary Algebra" book I recommended, on the
other hand, is something I think very good and motivated
high school students (and many teachers) would find quite
useful. While it too is fairly advanced by today's standards,
it is definitely well below the level of the other books
I cited.
Dave L. Renfro
Dom
I am not familiar with how the new math impacted England, but in the
U. S. it completely wiped out the traditional college preparatory
mathematics curriculum. The New Math strand developed by E.G. Begle's
School Mathematics Study Group (SMSG) had become completely
institutionalized by 1970. This was accomplished through the Houghton
Mifflin series of books, which were copied by other publishers, co-
authored by Mary P. Dolciani. A priceless article describing how this
occurred at the public school system from which I had graduated in
1966 is posted at:
http://mathforum.org/kb/thread.jspa?forumID=206&threadID=483954
and was reprinted as a filler item in The American Mathematical
Monthly, January 2002, page 12.
Dom
of Advanced Mathematics," The American Book Company, New York (1959)
519p. [Note: the second edition (1965) is identical to the original,
with the exception of Chapter Review Tests that were added after page
500] is a classic example of a pre-Sputnik textbook, even though it
was first published two years after the launching of Sputnik. The
corresponding post-Sputnik book, which incorporated the SMSG new math,
is: Mary P. Dolciani et al., "Modern Introductory Analysis," Houghton
Mifflin (1964) 651p.
Mr. Robert Millett, my superb Advanced Mathematics teacher, retired in
1969, at age 62, when the Dolciani book replaced the former. My guess
is that it would have been sheer torture for him, as it was for the
students, to make the switch.
On Aug 21, 4:41 pm, wwilson <leon.wins...@notes.udayton.edu> wrote:
Dom
> Dom <DR...@teikyopost.edu> wrote:
> >> >> Which is entirely nonresponsive to his statement. "I don’t know how
> >> >> kids learned from these old books. There was no motivation. It was
> >> >> very austere."
>
> >> >Actually, you are the one who also appears to be clueless. When
> >> >compared with the pseudo-educated students of today, students learned
> >> >quite well from the old, pre-new-math textbooks.
>
> >> That is not in evidence. Remember that we had a panic in this country
> >> about math and science education at the time of Sputnik, precisely
> >> because students were not learning those subjects very well - and that
> >> was when the percentage attending college was perhaps half of what it
> >> is now.
>
> >The high school math curriculum, which was extremely sound,
>
> The people in charge disagreed with you.
Unfortunately, the people in charge were not the teachers but the NSF
and other organizations that funded E.G. Begle's
School Mathematics Study Group (SMSG)--a disaster from which the U.S.
has yet to recover.
> >> Of course, I have some of those pre-new-math textbooks from the k/12
> >> level, and most were far less ambitious in what they covered. Algebra
> >> I consisted of simple linear equations, with a dabbling of quadratics
> >> in the last chapter. No functional notation, no sets, no logic or
> >> proofs. Formulaic word problems that were described in a manner that
> >> allowed trivial formulation.
>
> >My Algebra I book did indeed end with quadratic equations and their
> >graphs. Functions (mosly trig functions), vectors, matrices, etc. were
> >covered in Algebra II.
>
> Except that almost no one took Algebra II in high school.
According to the "Student Guidebook" from my High School (1962-66):
1. Students who plan to apply to a College of Liberal Arts or
Engineering must take Algebra I, Euclidean Geometry, Algebra II and
Advanced Mathematics.
2. Students who plan to apply to a College of Business Administration
must take a minimum of Algebra I and Algebra II.
Bob LeChevalier
>On Aug 22, 12:22�am, Bob LeChevalier <loj...@lojban.org> wrote:
>> Dom <DR...@teikyopost.edu> wrote:
>> >> >> Which is entirely nonresponsive to his statement. �"I don�t know how
>> >> >> kids learned from these old books. There was no motivation. It was
>> >> >> very austere."
>>
>> >> >Actually, you are the one who also appears to be clueless. When
>> >> >compared with the pseudo-educated students of today, students learned
>> >> >quite well from the old, pre-new-math textbooks.
>>
>> >> That is not in evidence. �Remember that we had a panic in this country
>> >> about math and science education at the time of Sputnik, precisely
>> >> because students were not learning those subjects very well - and that
>> >> was when the percentage attending college was perhaps half of what it
>> >> is now.
>>
>> >The high school math curriculum, which was extremely sound,
>>
>> The people in charge disagreed with you.
>
>Unfortunately, the people in charge were not the teachers but the NSF
>and other organizations that funded E.G. Begle's
>School Mathematics Study Group (SMSG)--a disaster from which the U.S.
>has yet to recover.
No. The people in charge were the school boards and state textbook
agencies.
>> >My Algebra I book did indeed end with quadratic equations and their
>> >graphs. Functions (mosly trig functions), vectors, matrices, etc. were
>> >covered in Algebra II.
>>
>> Except that almost no one took Algebra II in high school.
>
>According to the "Student Guidebook" from my High School (1962-66):
post Sputnik. And that was your state - other states had lower
requirements. Even so, only around 20% of the population even
attended college back then, and only 10% completed a 4 year degree.
In 1965, 28.5% of high school students took algebra - that's algebra
I. 13.9% took Geometry. 2.0% took trig. 76.3% of the 17 year old
populace graduated high school.
In 1934, 30.4% of high school students took algebra. 17.1% took
Geometry. 1.3% took trig. Only 39% of the populace graduated high
school.
In 1910, 56.9% of high school students took algebra. 30.9% took
Geometry. 1.9% took trig. Of course, only .2% of 23 year olds
graduated from college that year. Only 8% graduated high school. So
the percentage that actually took an algebra class was far less than
50%
http://www2.census.gov/prod2/statcomp/documents/CT1970p1-01.pdf
chapter H
(If you look at the 1910 statistical abstract, there were only around
900,000 high school students, 60,000 prep school students, and 150,000
college students. There were 17.5 million kids enrolled in public
schools, though only around 2/3 of them showed up on any given day.
http://www.census.gov/prod/www/abs/statab1901-1950.htm
Thus in 1910, the sort of math education you talk of was for a small
percentage of the elite that would attend college. In 1934, it was
for a smaller percentage of the elite that would graduate high school.
In 1965, it was for a smaller still percentage of ALL students.
The dropoff in percentage taking these courses took place long before
"New Math", but rather when high schools became schools for more than
just the elite. But even when they were schools for the elite, most
did not take more than a year or two of math.
zzbu...@netscape.net
> Dom <DR...@teikyopost.edu> wrote:
> >An Interview with James Stewart, by Ivars Peterson is posted at:
>
> >http://www.maa.org/news/061809stewart.html
> >"I was actually approached by four instructors from Mercer County
> >Community College in New Jersey, who requested such a book. A lot of
> >schools have some math requirement, so you have these kids who are
> >never going to take another math course, and yet they have to take a
> >college algebra course. I'm not sure that's a sensible policy, but
> >given that it is a widespread policy, let’s make it more interesting
> >for those kids to really try to draw them into it. That's not an easy
> >task. So I wrote a prolog, "Algebra and Alcohol," for that book, which
> >is now in production. No matter what your attitude is to alcohol, I
> >thought this would get their attention."
>
> >I wonder why these four instructors are not able to write their own
> >materials for this "reform college algebra book"?
>
> Writing a book isn't the easiest thing in the world. Writing a *good*
> book is very difficult. Writing a book that is sufficiently
> profitable to pay for the time spent by the author is much more rare,
> especially in the realm of textbooks that are not backed in advance by
> a major textbook publisher.
Well, that's why the people with post Gutenenburg Brains still
work on Electronic Books, Laser Disks Libraries, Blue Ray, HDTV,
Home Broadband, Desktop Publishing with no num locks, Fiber Optics,
Data Fusion, Atomic Clock Wrsitewatches, and On-Line Publishing.
And just say to hell all of idiot Calculus and Quantum Mechanics.
> loj...@lojban.org Lojban languagewww.lojban.org- Hide quoted text -
Dom
> Dom <DR...@teikyopost.edu> wrote:
> >On Aug 22, 12:22 am, Bob LeChevalier <loj...@lojban.org> wrote:
> >> Dom <DR...@teikyopost.edu> wrote:
> >> >> >> Which is entirely nonresponsive to his statement. "I don’t know how
> >> >> >> kids learned from these old books. There was no motivation. It was
> >> >> >> very austere."
>
> >> >> >Actually, you are the one who also appears to be clueless. When
> >> >> >compared with the pseudo-educated students of today, students learned
> >> >> >quite well from the old, pre-new-math textbooks.
>
> >> >> That is not in evidence. Remember that we had a panic in this country
> >> >> about math and science education at the time of Sputnik, precisely
> >> >> because students were not learning those subjects very well - and that
> >> >> was when the percentage attending college was perhaps half of what it
> >> >> is now.
>
> >> >The high school math curriculum, which was extremely sound,
>
> >> The people in charge disagreed with you.
>
> >Unfortunately, the people in charge were not the teachers but the NSF
> >and other organizations that funded E.G. Begle's
> >School Mathematics Study Group (SMSG)--a disaster from which the U.S.
> >has yet to recover.
>
> No. The people in charge were the school boards and state textbook
> agencies.
May I suggest that you read the article posted at:
http://mathforum.org/kb/thread.jspa?forumID=206&threadID=483954
Herman Rubin
Dom <DR...@teikyopost.edu> wrote:
>On Aug 21, 11:12=A0am, Nick <N...@spam.com> wrote:
>> Dom wrote:
>> > Actually, you are the one who also appears to be clueless. When
>> > compared with the pseudo-educated students of today, students learned
>> > quite well from the old, pre-new-math textbooks. These old books had
>> > very little review material, because previous material, which had been
>> > taught and mastered quite well, was recalled quite readily.
>> I'm a bit confused. I'm in England and did my high school math 30 years
>> ago. My son is starting his A levels, 16-18 year age group exams.
>> I looked at his math course and text book and it looks pretty much the
>> same as I did.
>> Is this because; I did new math, my son is amongst the few students
>> doing proper math or becuase new math hasn't hit the England.
>I am not familiar with how the new math impacted England, but in the
>U. S. it completely wiped out the traditional college preparatory
>mathematics curriculum. The New Math strand developed by E.G. Begle's
>School Mathematics Study Group (SMSG) had become completely
>institutionalized by 1970.
The Begle group put out some good stuff. However, the
educationists in charge of the project had them water
it down considerably. You can consider this to be a
second or third hand report; I spoke to someone who
knew what was going on in 1960.
--
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
wwilson
wrote:
Bob
You keep introducing facts into this argument and they will throw you
out! Opeinions are so much more fun than dull facts. Keep trying
though. You might convince a somebody.
LEW
Dom
> In article <a9ce9ad6-b309-42b0-9a59-d27a56fc4...@s15g2000yqs.googlegroups.com>,
>
>
>
>
>
> Dom <DR...@teikyopost.edu> wrote:
> >On Aug 21, 11:12=A0am, Nick <N...@spam.com> wrote:
> >> Dom wrote:
> >> > Actually, you are the one who also appears to be clueless. When
> >> > compared with the pseudo-educated students of today, students learned
> >> > quite well from the old, pre-new-math textbooks. These old books had
> >> > very little review material, because previous material, which had been
> >> > taught and mastered quite well, was recalled quite readily.
> >> I'm a bit confused. I'm in England and did my high school math 30 years
> >> ago. My son is starting his A levels, 16-18 year age group exams.
> >> I looked at his math course and text book and it looks pretty much the
> >> same as I did.
> >> Is this because; I did new math, my son is amongst the few students
> >> doing proper math or becuase new math hasn't hit the England.
> >I am not familiar with how the new math impacted England, but in the
> >U. S. it completely wiped out the traditional college preparatory
> >mathematics curriculum. The New Math strand developed by E.G. Begle's
> >School Mathematics Study Group (SMSG) had become completely
> >institutionalized by 1970.
>
> The Begle group put out some good stuff. However, the
> educationists in charge of the project had them water
> it down considerably. You can consider this to be a
> second or third hand report; I spoke to someone who
> knew what was going on in 1960.
Although the Dolciani series was distinct from the typed, paperbound
SMSG monographs, nevertheless this series is clearly an outgrowth of
the SMSG juggernaut. Begle's name is not listed, but the following is
listed under ABOUT THE AUTHORS in Algebra 1 (1967), Geometry (1963),
or Modern Introductory Analysis (1964):
Mary P. Dolciani ... has been a member of ...(SMSG) and a director and
teacher in numerous National Science Foundation and New York State
Education Department institutes for mathematics teachers.
William Wooton ... has been a member of the SMSG writing team and a
team member of the [NCTM] summer writing projects.
Edwin F. Beckenbach ... is co-author of ... one of the SMSG
monographs ..., and has been a team member of the [NCTM] summer
writing projects.
Ray C. Jurgensen ... has been a member of the SMSG writing team on
geometry and a lecturer at [NSF] institutes for mathematics teachers.
Alfred J Donnelly is the only co-author without SMSG affiliation.
Editorial Advisers
Andrew M. Gleason ... was Chairman of the Advisory Board of SMSG as
well as co-chairman of the Cambridge Conference which wrote the
influential report, Goals for School Mathematics.
Albert E. Meder, JR. ... was Executive Director of the Commission on
Mathematics of the College Entrance Examination Board and has been an
advisory member of SMSG.
I have been unable to find an original edition of Algebra 2. The 1986
edition makes no mention of the SMSG affiliations of Dolciani,
Sorgenfrey, Brown, and Kane. Does anyone know what the 1960s edition
says?
By the way, the Gleason above is the same one who spearheaded the
Harvard Calculus Reform Project. I met him at a special session of the
Oct. 1995 American Mathematical Society meeting in Boston, MA. My
presentation was titled, "A brief survey of mathematics pseudo-
education in the United States." When the Dolciani books came up,
Gleason indicated that some of his advice had not been followed.
Herman Rubin
wwilson <leon.w...@notes.udayton.edu> wrote:
>On Tue, 25 Aug 2009 09:10:50 -0400, Bob LeChevalier <loj...@lojban.org>
>wrote:
>> Dom <DR...@teikyopost.edu> wrote:
>>> On Aug 22, 12:22am, Bob LeChevalier <loj...@lojban.org> wrote:
>>>> Dom <DR...@teikyopost.edu> wrote:
...............
>>>> >My Algebra I book did indeed end with quadratic equations and their
>>>> >graphs. Functions (mosly trig functions), vectors, matrices, etc. were
>>>> >covered in Algebra II.
I do not recall this being covered around 1940. Algebra 1.5
was a weak course, but College Algebra covered exponents,
logarithms, induction, polynomials, etc. Vectors and matrices
seem to be covered poorly in any non-abstract course, and
trig functions were relegated to trigonometry.
>>>> Except that almost no one took Algebra II in high school.
>>> According to the "Student Guidebook" from my High School (1962-66):
>> post Sputnik. And that was your state - other states had lower
>> requirements. Even so, only around 20% of the population even
>> attended college back then, and only 10% completed a 4 year degree.
>> In 1965, 28.5% of high school students took algebra - that's algebra
>> I. 13.9% took Geometry. 2.0% took trig. 76.3% of the 17 year old
>> populace graduated high school.
Many did not graduate until 18, or sometimes 19.
Also, why should this matter?
>> In 1934, 30.4% of high school students took algebra. 17.1% took
>> Geometry. 1.3% took trig. Only 39% of the populace graduated high
>> school.
This was not the situation in Chicago, and I do not
believe in Illinois. Also, the college preparatory
program required algebra and geometry; to those of
us who understand mathematics, geometry was the only
"real mathematics" course; there was some in College
Algebra, but the rest was cookbook. I do not know
the proportions in Chicago at that time, but I do know
that there were, besides college preparatory, "regular"
programs and "technical" programs for the weak.
When students who had not been able to afford college
went to school on the GI Bill, these courses, even as
remedial, were not lowered at all. It was only after
the educationists got their hyperegalitarian program
in the high schools that there was lowering.
BTW, I was told that others called the students on the
GI Bill "DAR", "damned average raisers". These students,
who were not in the class of those who could go to college
on scholarships before WWII, did not receive any dumbing
down to their supposed abilities.
>> In 1910, 56.9% of high school students took algebra. 30.9% took
>> Geometry. 1.9% took trig. Of course, only .2% of 23 year olds
>> graduated from college that year. Only 8% graduated high school. So
>> the percentage that actually took an algebra class was far less than
>> 50%
So what? The content of a course should not depend on
who is taking it, but upon the subject matter.
>> http://www2.census.gov/prod2/statcomp/documents/CT1970p1-01.pdf
>> chapter H
>> (If you look at the 1910 statistical abstract, there were only around
>> 900,000 high school students, 60,000 prep school students, and 150,000
>> college students. There were 17.5 million kids enrolled in public
>> schools, though only around 2/3 of them showed up on any given day.
>> http://www.census.gov/prod/www/abs/statab1901-1950.htm
>> Thus in 1910, the sort of math education you talk of was for a small
>> percentage of the elite that would attend college. In 1934, it was
>> for a smaller percentage of the elite that would graduate high school.
>> In 1965, it was for a smaller still percentage of ALL students.
As I stated above, the content of a course should depend
on the subject matter. Not everybody has the ability to
take decent subject matter, and the course should not
accommodate those who show up.
>> The dropoff in percentage taking these courses took place long before
>> "New Math", but rather when high schools became schools for more than
>> just the elite. But even when they were schools for the elite, most
>> did not take more than a year or two of math.
>Bob
>You keep introducing facts into this argument and they will throw you
>out! Opeinions are so much more fun than dull facts. Keep trying
>though. You might convince a somebody.
>LEW
I have inserted facts, from personal knowledge.
Dave L. Renfro
> The dropoff in percentage taking these courses took place
> long before "New Math", but rather when high schools became
> schools for more than just the elite. But even when they
> were schools for the elite, most did not take more than
> a year or two of math.
Over the past couple of decades, while looking through
old journal volumes and old books for things relating
to my various mathematical interests, I've come across
and read (or skimmed, in many cases) thousands of comments
about the problems of teaching mathematics. These comments
were in book reviews, in educational commentary articles,
in prefaces of old textbooks, and in other places. I've
posted some of these, and a collection of URLs for these
posts is at:
http://mathforum.org/kb/message.jspa?messageID=6738335
One of the things that most stands out to me is the
cyclical nature of what the problems are and what the
solutions are (e.g. concepts vs. back to basics). This
becomes especially transparent if you pick a specific
journal, such as "Mathematics Teacher" or "American
Mathematical Monthly" or "Mathematical Gazette", and
spend two or three weeks flipping through the pages
of every volume from volume 1 to the present volume,
something I've done with each of the journals I listed
and several others as well.
I wrote the following comments about this observation
in a post on 25 March 2008:
---------------------------------------------------
I find it very interesting how each generation seems
to have its "traditionalists vs. reformists" battles.
The same arguments are made each time, with little
awareness (or at least, with virtually no explicit
acknowledgment in print) that the same arguments had
been raised over and over again in previous generations.
Moreover, it often seems to me that each side invokes
what I strongly suspect previous generations would
regard as straw men.
---------------------------------------------------
For the remainder of this post, I've copied an abstract
of a talk given on 13 November 1926, published in American
Mathematical Monthly 34 (1927), pp. 2-3. This is a good
example of the many things I've encountered, whether
written in 1875, 1900, 1920, 1935, 1950, 1965, 1980, etc.
---------------------------------------------------
10th annual meeting of the Missouri Section of the Mathematical
Association of America, 13 November 1926.
(1) "Causes of the present popular attitude toward mathematics"
by R. A. Wells, Park College.
Abstract of Wells' talk:
A study of the attitude of college students and of the educational
public reveals the existence of much indifference and considerable
antagonism to the study of mathematics. One frequently hears such
expressions as, "I cannot learn mathematics," and "I do not care
for mathematics." Attempts are continually being made to give it
a less important place in the scheme of education. Professor Wells
stated that the causes of this condition seem to be:
(a) Ignorance of the real nature of the subject matter of
mathematics, caused usually by the ignorance or carelessness
of teachers of elementary mathematics,
(b) The persistent agitation carried on by persons, willing to
be known as educational experts, who have the public ear
and who are continually trying to convince the public that
there is no use in studying mathematics beyond the simple
processes of arithmetic,
(c) Carelessness on the part of writers of text books on
elementary mathematics shown in the use of inaccurate
English and in the lack of regard for the technical use
of mathematical terms.
The remedy seems to be for those who are interested in the
subject of mathematics and who know what it really means to
seize every opportunity to go before the educational public
and give them some real information as to what mathematics
is and why it should have a place in the scheme of education.
Mathematics does not deserve a place in the curriculum because
of its training in the use of formal logic or in symbolic
thinking, although these are all important reasons for studying
it. But it does deserve a place in the scheme of education because
of what it is. Mathematics is an important science with a
perfectly definite subject matter and that subject matter is
of vital interest to every human being. That is the reason why
mathematics should have a place in the course of study. Teachers
of mathematics should keep this idea before the public and they
should do it as persistently and insistently as the other group
have worked in trying to discredit the study of mathematics.
---------------------------------------------------
Dave L. Renfro
Tim Norfolk
Thanks for this. Some things never change.
Dave L. Renfro
>> Over the past couple of decades, while looking through
>> old journal volumes and old books for things relating
>> to my various mathematical interests, I've come across
>> and read (or skimmed, in many cases) thousands of comments
>> about the problems of teaching mathematics. These comments
>> were in book reviews, in educational commentary articles,
>> in prefaces of old textbooks, and in other places.
[snip]
>> For the remainder of this post, I've copied an abstract
>> of a talk given on 13 November 1926, published in American
>> Mathematical Monthly 34 (1927), pp. 2-3. This is a good
>> example of the many things I've encountered, whether
>> written in 1875, 1900, 1920, 1935, 1950, 1965, 1980, etc.
Tim Norfolk wrote:
> Thanks for this. Some things never change.
Here are three more excerpts, all from Volume 35 (1928)
of AMM. After these excerpts I give a few general personal
comments.
***********************************************************
***********************************************************
The 12th Annual Meeting of the Mathematical Association
of America (29-30 December 1927), Nashville, Tenn.
AMM 35 #3 (March 1928), p. 106
3. "The reorganization of secondary mathematics in theory
and practice" by Vice-principal William Betz, East High
School, Rochester, New York.
ABSTRACT: After a brief analysis of the present educational
situation, Mr. Betz showed that a crisis has resulted from
the conflicting views of specialists and educational theorists.
It is of paramount importance, in his opinion, that these
opposing groups should work in greater harmony toward a tangible
goal. The speaker offered a critical review of the progress made
in reorganizing secondary mathematics during the past quarter of
a century. He pointed out that neither the hopes of the reformers
of twenty-five years ago nor the demands of the general educator
had been fully realized. The compartment system is still in full
vogue, and the "unification of pure and applied mathematics" is
still a dream. The curriculum expert is complaining of the purely
"academic" character of mathematical instruction and of the total
disregard of many necessary readjustments. Mr. Betz insisted that
more attention must be given to the human significance of mathematics,
to scientific classroom procedures, and to improved professional
resources for the training of teachers. In conclusion, the speaker
offered a tentative six-year curriculum. He also submitted to the
Association a memorandum on behalf of the curriculum committees
appointed by the New York State Department of Education, asking
for cooperation in the preparation of new syllabi for New York State.
In the discussion of this paper, Professor Slaught said that we offer
no apology for our interest in secondary mathematical education;
that one of our first plans was to form the National Committee,
and that it is perfectly logical that we continue our active
interest in the improving the teaching of mathematics. [...]
***********************************************************
***********************************************************
Review (by J. W. Clawson) of "Modern Plane Geometry" by
J. R. Clark and A. S. Otis (1927), pp. 141-142.
[...] But it is emphatically not just another plane geometry text-
book.
"In this book," the authors claim, "you will find for the first time,
carefully planned and fully prepared, that development of each topic
which psychology teaches and which your experience has shown you to
be essential to the complete understanding of the statement and proof
of a proposition." The authors further assert that tests in some
twenty schools, in which experimental editions of their book were
brought into competition with old style texts giving complete
synthetic proofs, showed their book "significantly superior in
developing _power_" and "slightly superior in developing
_information_."
In the hands of skillful, wise and sympathetic teachers, it seems
probable that this record will be maintained in the larger field
now open.
This greater efficiency has been secured by giving the student a
different attitude than is common towards the work before him. The
authors consistently place the student in the position of a
discoverer,
not only of proofs but of facts. "Do you think that if a triangle
has two equal angles, the sides opposite those angles are equal?"
"Ernest reasoned as follows . . . . . Do you see any error in the
reasoning?" The student is also met throughout by a series of
_challenges_. These usually ask the student to prove a fact whose
truth is suspected without the use of the next section in the book.
If he succeeds he may give himself a grade of A in a table provided
for that purpose at the back of the book. If he fails, he may read
the next section for suggestions; if, with the help of these hints,
he succeeds in devising a proof, he marks himself B. This system of
self-classification is extended also to work with originals. Other
distinctive features are found in this text [...]
The merits of this progressive text are so great, that overstatement
in the preface may be forgiven. For the book, though a pioneer in
modernism, is not entirely without precursors. For example, among
books known to the reviewer, the _Elementary_Geometry_ by the English
authors Godfrey and Siddons, published in 1903 by the Cambridge
University Press, featured a thing, -- "systematic training in the
discovery of geometric facts" -- that Clark and Otis say "has not
appeared in any previous text book;" and E. R. Smith in this
_Plane_Geometry_developed_by_the_Syllabus_Method_, published in
1909 by the American Book Company, taught students to discover
proofs, if not facts, for themselves.
***********************************************************
***********************************************************
Elizabeth B. Cowley, "Solid Geometry and the New Curricula",
35 # 5 (May 1928), 251-253.
(p. 252) [...] Many who really wish to abolish the college requirement
in this subject hold the theory that as knowledge advances it is
inevitable that some subjects, once considered as all-important,
should gradually be shoved aside to make way for other branches.
They recall the disappearance of spherical trigonometry. These
critics would replace college solid geometry by an introduction
to the calculus. There is much to be said in favor of this point
of view. While the calculus is working its way down into the
freshman year in college (and, in a simplified form, into the
high school), there is a natural tendency to place more stress
upon solid geometry in the high school. Why should this subject
be held back till the thirteenth school year? [...]
***********************************************************
***********************************************************
I previously wrote
>> One of the things that most stands out to me is the
>> cyclical nature of what the problems are and what the
>> solutions are (e.g. concepts vs. back to basics). This
>> becomes especially transparent if you pick a specific
>> journal, such as "Mathematics Teacher" or "American
>> Mathematical Monthly" or "Mathematical Gazette", and
>> spend two or three weeks flipping through the pages
>> of every volume from volume 1 to the present volume,
>> something I've done with each of the journals I listed
>> and several others as well.
and
>> I find it very interesting how each generation seems
>> to have its "traditionalists vs. reformists" battles.
>> The same arguments are made each time, with little
>> awareness (or at least, with virtually no explicit
>> acknowledgment in print) that the same arguments had
>> been raised over and over again in previous generations.
>> Moreover, it often seems to me that each side invokes
>> what I strongly suspect previous generations would
>> regard as straw men.
For "fairness" purposes I should at least mention a few
things I think have truly changed over the years. Examples
of this are diversity awareness in textbooks (in word problems,
in text pictures, etc.), the use of teaching evaluations (I don't
know when they began in earnest, but I've read of their use
as far back as 1925 [1]), the introduction of calculators,
the use of fairly universal college entrance exams, and the
increasing percentages of students in each stage of education.
[1] http://mathforum.org/kb/message.jspa?messageID=4923713
However, I often read inflated claims of priority, uniqueness,
and the like in educational writing. It often seems to me that
the suggestions and insights which get heard are akin to which
dog has the loudest bark rather than from a true investigation
of the merits involved. For example, in the past two decades
students are supposed to be "constructing" their own knowledge
and "discovering for themselves" mathematical relationships,
as if no one had ever thought of this before or had ever tried
this before. And this is just one of many examples I could
give, but I suspect most people over a certain age already
know this.
Dave L. Renfro
Bob LeChevalier
>> >Unfortunately, the people in charge were not the teachers but the NSF
>> >and other organizations that funded E.G. Begle's
>> >School Mathematics Study Group (SMSG)--a disaster from which the U.S.
>> >has yet to recover.
>>
>> No. �The people in charge were the school boards and state textbook
>> agencies.
>
>May I suggest that you read the article posted at:
>
>http://mathforum.org/kb/thread.jspa?forumID=206&threadID=483954
"the Mathematics Department approximately six years ago introduced
modern math into its high school program"
"Mr. Edward Bond, Director of the Mathematics Department, consulted
with Superintendent Arigo L. LaTanzi concerning the problems inherent
in the transition from traditional math to the new program"
"In this coming September the Mathematics Department hopes to
introduce the new mathematics course of study to grades 3 to 6."
I see no mention of the NSF or other organizations that funded SMSG.
In this case the decision was made by "the Mathematics Department",
which in most schools would mean the teachers. Context however
suggests that this is a district level math department, and thus was
operating under the authority of the school board, as I said.
Dom
A message posted by Ralph A. Raimi at:
http://mathforum.org/kb/thread.jspa?forumID=206&threadID=478108
contains various references that may provide information about the
extensive role of the NSF in funding and promoting SMSG.
Bob LeChevalier
If I wanted to subscribe to mathforum, I would already have done so.
Likely, if you had convinced them, you wouldn't feel the urge to post
here.
You made a claim, and then your support for that claim turned out to
be your own posting, a posting which said more or less the same thing
that I had said.
That NSF funded and promoted SMSG is of course irrelevant. The
question was who were the people who were in charge of adopting
textbooks and curricula. In pretty much all cases, they were school
boards and textbook agencies. In some cases, teachers and former
teachers were probably consulted (sometimes the textbooks themselves
are written by such teachers).
Herman Rubin
>>> Dom <DR...@teikyopost.edu> wrote:
>>> >> >Unfortunately, the people in charge were not the teachers but the NSF
>>> >> >and other organizations that funded E.G. Begle's
>>> >> >School Mathematics Study Group (SMSG)--a disaster from which the U.S.
>>> >> >has yet to recover.
>>> >> No. The people in charge were the school boards and state textbook
>>> >> agencies.
>>> >May I suggest that you read the article posted at:
>>> >http://mathforum.org/kb/thread.jspa?forumID=206&threadID=483954
>>> "the Mathematics Department approximately six years ago introduced
>>> modern math into its high school program"
Modern math? The teachers do not understand math;
just facts and algorithms.
>>> "Mr. Edward Bond, Director of the Mathematics Department, consulted
>>> with Superintendent Arigo L. LaTanzi concerning the problems inherent
>>> in the transition from traditional math to the new program"
>>> "In this coming September the Mathematics Department hopes to
>>> introduce the new mathematics course of study to grades 3 to 6."
>>> I see no mention of the NSF or other organizations that funded SMSG.
>>> In this case the decision was made by "the Mathematics Department",
>>> which in most schools would mean the teachers. Context however
>>> suggests that this is a district level math department, and thus was
>>> operating under the authority of the school board, as I said.
Few high school mathematics teachers, and almost no elementary
school teachers, have any understanding of mathematics. Ability
at arithmetic does not help to any extent, if at all.
>>A message posted by Ralph A. Raimi at:
>>http://mathforum.org/kb/thread.jspa?forumID=206&threadID=478108
>>contains various references that may provide information about the
>>extensive role of the NSF in funding and promoting SMSG.
>If I wanted to subscribe to mathforum, I would already have done so.
>Likely, if you had convinced them, you wouldn't feel the urge to post
>here.
>You made a claim, and then your support for that claim turned out to
>be your own posting, a posting which said more or less the same thing
>that I had said.
>That NSF funded and promoted SMSG is of course irrelevant. The
>question was who were the people who were in charge of adopting
>textbooks and curricula. In pretty much all cases, they were school
>boards and textbook agencies. In some cases, teachers and former
>teachers were probably consulted (sometimes the textbooks themselves
>are written by such teachers).
Where are those who understand mathematics involved in these
decisions? They have volunteered, but the schools will have
nothing to do with those without education degrees, who claim
to know how to teach what they have no understanding of.
Larry Hewitt
I have experience with textbook selection in 3 states, most formally
with South Carolina where as a math undergraduate I was part of a team
analyzing textbooks for the state. My graduate advisor was a consultant
for a text publisher, and I worked a little with him on text development
by interviewing officials in 2 other states.
In all 3 states texts are vetted by "experts" in the subject, that is
math professors do math, history history, and so on. No text not written
by an "expert" on the subject --- a phd in the field --- ever made it to
consideration.
The primary consideration for a textbook was whether or not it
accurately addressed the state mandated curriculum requirements for the
subject. (These requirements were defined by experts in the subject, not
bureaucrats or educationists, whatever they are).Secondarily were the
aesthetics of the text --- clearness of writing, examples, readability,
and lastly teachers' aids like overheads.
We undergrads would select many, many random examples and problems from
the text and check them for accuracy and completeness.
Math professors double checked our work and rated the texts on aesthetics.
Three texts were recommended to the state for consideration, and the
final decision was based on costs and, frankly, political
considerations. But *all* recommended texts had been vetted by experts
before any political or cost decisions were made.
Larry
Herman Rubin
>>>>>> http://mathforum.org/kb/thread.jspa?forumID=206&threadID=483954
>>>> http://mathforum.org/kb/thread.jspa?forumID=206&threadID=478108
There are a large number of PhD's who scholars in the
field would not consider knowledgeable, and the standards
keep going down from the levels they reached a half
century ago.
Few PhD's in "mathematical education" would qualify for
a PhD in a good mathematics department.
>The primary consideration for a textbook was whether or not it
>accurately addressed the state mandated curriculum requirements for the
>subject. (These requirements were defined by experts in the subject, not
>bureaucrats or educationists, whatever they are).Secondarily were the
>aesthetics of the text --- clearness of writing, examples, readability,
>and lastly teachers' aids like overheads.
See the above. Reseach mathematicians, the ones who
understand the subject, are NOT consulted.
Forget the esthetics. The texts used in good high schools
in the period before and just after WWII do not really
teach the concepts, but they are at least presented. The
old "Euclid" style geometry books had essentially NO
prerequisites; algebra is not a prerequisite, as the Greeks
did not know algebra.
One topic which USED to be taught in high school is induction;
nobody can understand the integers without it. Euclid did use
a form of induction, although without mathematical notation,
he could not use the modern form. It belongs with the early
understanding of the counting numbers, which are not strings of
decimal digits, although that is one REPRESENTATION of them.
>We undergrads would select many, many random examples and problems from
>the text and check them for accuracy and completeness.
Being able to solve problems by the use of algorithms does
not seem to help in understanding, but hinders. The great
bulk of the problems can be done by machines; they have no
intelligence, but their programs tell them how to grind
through the problems. Intelligence does not require this
knowledge; one can derive the methods.
Also, in grading a problem, and it should be a long problem
with many steps, are the steps graded, or the answer?
>Math professors double checked our work and rated the texts on aesthetics.
So what?
>Three texts were recommended to the state for consideration, and the
>final decision was based on costs and, frankly, political
>considerations. But *all* recommended texts had been vetted by experts
>before any political or cost decisions were made.
As I said before, what experts? How many recognized researchers
in mathematics, NOT "mathematics education", have been consulted?
A head of a high school mathematics department said he used to
ask his candidated for faculty positions to prove that 2+2=4.
Not only could they not prove it, but they could not understand
why such a question could be raised. Anyone who understands
the counting numbers can understand it, and should be able to
come up with a proof; this includes first grade teachers of
arithmetic.
Can they do this? If not, they should learn basic mathematics;
it does not start with doing arithmetic, but with the understanding
of what it means.
Dom
> In article <b0us9514ghh62dare144hhvh7ckfomb...@4ax.com>,
> Bob LeChevalier <loj...@lojban.org> wrote:
>
> >Dom <DR...@teikyopost.edu> wrote:
> >>On Aug 28, 3:41pm, Bob LeChevalier <loj...@lojban.org> wrote:
> >>> Dom <DR...@teikyopost.edu> wrote:
> >>> >> >Unfortunately, the people in charge were not the teachers but the NSF
> >>> >> >and other organizations that funded E.G. Begle's
> >>> >> >School Mathematics Study Group (SMSG)--a disaster from which the U.S.
> >>> >> >has yet to recover.
> >>> >> No. The people in charge were the school boards and state textbook
> >>> >> agencies.
> >>> >May I suggest that you read the article posted at:
> >>> >http://mathforum.org/kb/thread.jspa?forumID=206&threadID=483954
> >>> "the Mathematics Department approximately six years ago introduced
> >>> modern math into its high school program"
>
> Modern math? The teachers do not understand math;
> just facts and algorithms.
"Modern math" referred to the SMSG "new math," as incorporated in the
books co-authored by Mary P. Dolciani, which demolished the
traditional college preparatory mathematics curriculum; just as
"reform math" refers to all the rubbish that has been promoted during
the past 20 years.
Dom
> >A message posted by Ralph A. Raimi at:
>
> >http://mathforum.org/kb/thread.jspa?forumID=206&threadID=478108
>
> >contains various references that may provide information about the
> >extensive role of the NSF in funding and promoting SMSG.
[snip]
> That NSF funded and promoted SMSG is of course irrelevant. The
> question was who were the people who were in charge of adopting
> textbooks and curricula. In pretty much all cases, they were school
> boards and textbook agencies. In some cases, teachers and former
> teachers were probably consulted (sometimes the textbooks themselves
> are written by such teachers).
The NSF-funded promoters played a key role in the demise of the
traditional mathematics curriculum in the U.S. One such promoter made
several visits to our 7th-grade math class in fall 1960. Despite his
pitches about "new math," sets, and subsets, our teacher didn't buy
it. Two years later, our 64-year-old Algebra I teacher refused to
adopt a "new math" book and taught us a traditional course. After she
retired the next year, the Dolciani book was adopted.
Bob LeChevalier
>On Sep 2, 4:52锟絧m, Bob LeChevalier <loj...@lojban.org> wrote:
>> Dom <DR...@teikyopost.edu> wrote:
>[snip]
>
>> >A message posted by Ralph A. Raimi at:
>>
>> >http://mathforum.org/kb/thread.jspa?forumID=206&threadID=478108
>>
>> >contains various references that may provide information about the
>> >extensive role of the NSF in funding and promoting SMSG.
>[snip]
>
>> That NSF funded and promoted SMSG is of course irrelevant. 锟絋he
>> question was who were the people who were in charge of adopting
>> textbooks and curricula. 锟絀n pretty much all cases, they were school
>> boards and textbook agencies. 锟絀n some cases, teachers and former
>> teachers were probably consulted (sometimes the textbooks themselves
>> are written by such teachers).
>
>The NSF-funded promoters played a key role in the demise of the
>traditional mathematics curriculum in the U.S.
[yawn]
Textbook salesmen attempt to sell textbooks. So what?
>One such promoter made
>several visits to our 7th-grade math class in fall 1960. Despite his
>pitches about "new math," sets, and subsets, our teacher didn't buy
>it. Two years later, our 64-year-old Algebra I teacher refused to
>adopt a "new math" book and taught us a traditional course.
Sounds like the teachers did have the say in the matter.
>After she retired the next year, the Dolciani book was adopted.
Presumably by a new teacher who CHOSE to adopt the book, since you
have demonstrated that the choice of textbook was up to the teacher in
the prior years. That you disagree with the new teacher's decision
does not mean that the teacher did not make the decision.
Michael Stemper
>On Sep 2, 4:52=A0pm, Bob LeChevalier <loj...@lojban.org> wrote:
>> Dom <DR...@teikyopost.edu> wrote:
>The NSF-funded promoters played a key role in the demise of the
>traditional mathematics curriculum in the U.S. One such promoter made
>several visits to our 7th-grade math class in fall 1960. Despite his
>pitches about "new math," sets, and subsets, our teacher didn't buy
>it.
So, if you hadn't learned about sets by seventh grade, when did you
learn about them?
--
Michael F. Stemper
#include <Standard_Disclaimer>
COFFEE.SYS not found. Abort, Retry, Fail?
Dom
wrote:
> In article <132943ff-b1e1-4c3c-9182-617eb24a6...@38g2000yqr.googlegroups.com>, Dom <DR...@teikyopost.edu> writes:
>
> >On Sep 2, 4:52=A0pm, Bob LeChevalier <loj...@lojban.org> wrote:
> >> Dom <DR...@teikyopost.edu> wrote:
> >The NSF-funded promoters played a key role in the demise of the
> >traditional mathematics curriculum in the U.S. One such promoter made
> >several visits to our 7th-grade math class in fall 1960. Despite his
> >pitches about "new math," sets, and subsets, our teacher didn't buy
> >it.
>
> So, if you hadn't learned about sets by seventh grade, when did you
> learn about them?
Prior to my sophomore year in College, the extent of my dealing with
sets was limited to one class at the beginning of Algebra II. I still
have a copy of the first test. In one problem we are given the
elements of two sets and we are asked to fing the union and
intersection.
Larry Hewitt
Strange.
I was introduced to sets in the 5th grade in the mid 60's. By the 7th
grade sets were a significant part of the curriculum even touching on a
basis of a set. It raised a lot of consternation in the community ---
resistance to "new math" by parents nearly ended the program.
When I was teaching a few years ago the state curriculum guidelines
introduced sets in the 6th grade, building year by year even in the
grade level classes (non-algebra middle school classes).
Larry
Herman Rubin
Dom <DR...@teikyopost.edu> wrote:
>On Sep 4, 1:49=A0pm, mstem...@walkabout.empros.com (Michael Stemper)
>wrote:
>> In article <132943ff-b1e1-4c3c-9182-617eb24a6...@38g2000yqr.googlegroups.=
>com>, Dom <DR...@teikyopost.edu> writes:
>> >On Sep 2, 4:52=3DA0pm, Bob LeChevalier <loj...@lojban.org> wrote:
>> >> Dom <DR...@teikyopost.edu> wrote:
>> >The NSF-funded promoters played a key role in the demise of the
>> >traditional mathematics curriculum in the U.S. One such promoter made
>> >several visits to our 7th-grade math class in fall 1960. Despite his
>> >pitches about "new math," sets, and subsets, our teacher didn't buy
>> >it.
>> So, if you hadn't learned about sets by seventh grade, when did you
>> learn about them?
>Prior to my sophomore year in College, the extent of my dealing with
>sets was limited to one class at the beginning of Algebra II. I still
>have a copy of the first test. In one problem we are given the
>elements of two sets and we are asked to fing the union and
>intersection.
My objection to the original "new math" was not the use of
sets, although this wasted a lot of time. It was the failure
to use the ordinal approach, which is essential to really
understanding the integers.
The cardinal approach LOOKS simple, but only to those who
do not realize what it leaves out, which is counting. The
ordinal approach uses only counting, but not assuming the
usual names for the integers. It can be learned quickly
and rigorously, including proofs, and can introduce the
cardinal and magnitude approaches, which should be there.
Dedekind's answer to the question as to what are the integers
is that if it looks like the integers and acts like the
integers, it is a version of the integers. Finite sets work,
but the cardinal approach by itself cannot define finite.
Dom
> An Interview with James Stewart, by Ivars Peterson is posted at:
>
> http://www.maa.org/news/061809stewart.html
>
> is at:http://www.maa.org/pubs/augsept09pgs4-6.pdf)
[snip]
The Oct/Nov 2009 issue of FOCUS contains two letters--by Stephen B.
Rodi and Steve Edwards--commenting on the Stewart interview. The two
letters are at:
Gordie La Forge
Wait, is he still the Captain of the Starship Enterprise?
Signed, Gordeo Fa Lorgeio galiele
Tim Norfolk
<snip>
>
> This was not the situation in Chicago, and I do not
> believe in Illinois.
Herman;
I consider myself a skeptic, and even I believe in Illinois.
pubkeybreaker
> In article <NdOdnRDiLZOjYQPXRVn_...@comporium.net>,
> Larry Hewitt <larryh...@comporium.net> wrote:
>
> As I said before, what experts? How many recognized researchers
> in mathematics, NOT "mathematics education", have been consulted?
>
> A head of a high school mathematics department said he used to
> ask his candidated for faculty positions to prove that 2+2=4.
> Not only could they not prove it, but they could not understand
> why such a question could be raised. Anyone who understands
> the counting numbers can understand it, and should be able to
> come up with a proof;
Uh huh. And how many pages did Whitehead & Russell take to prove
1+1 = 2???
The underlying question is: what axioms am I allowed to use in such a
proof? Peano Arithmetic? or: May it be assumed that the integers are
well-ordered
or must this be proved? (equivalent to assuming axiom of induction).
etc.
OTOH, I would expect that a high school teacher would know the Peano
axioms.
Gerry Myerson
<3fb1bc8f-73c3-41ff...@a6g2000vbp.googlegroups.com>,
pubkeybreaker <pubkey...@aol.com> wrote:
> OTOH, I would expect that a high school teacher would know the Peano
> axioms.
I'd be very surprised if any of my high school (math) teachers knew
the Peano axioms (and I went to a good high school).
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
Herman Rubin
Gerry Myerson <ge...@maths.mq.edi.ai.i2u4email> wrote:
>In article
><3fb1bc8f-73c3-41ff...@a6g2000vbp.googlegroups.com>,
> pubkeybreaker <pubkey...@aol.com> wrote:
>> OTOH, I would expect that a high school teacher would know the Peano
>> axioms.
>I'd be very surprised if any of my high school (math) teachers knew
>the Peano axioms (and I went to a good high school).
You may be both partly right. SOME high school math
teachers do learn the Peano axioms, but probably most
do not.
Tim Norfolk
> In article <gerry-1BAEBD.13035509102...@feeder.eternal-september.org>,
> Gerry Myerson �<ge...@maths.mq.edi.ai.i2u4email> wrote:
>
> >In article
> > pubkeybreaker <pubkeybrea...@aol.com> wrote:
> >> OTOH, �I would expect that a high school teacher would know the Peano
> >> axioms.
> >I'd be very surprised if any of my high school (math) teachers knew
> >the Peano axioms (and I went to a good high school).
>
> You may be both partly right. �SOME high school math
> teachers do learn the Peano axioms, but probably most
> do not.
> --
> 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
The ones that we graduate here have seen them, and done some small
problems. Whether they remember and understand is something else. On a
related note, I have to disagree with your contention that the 'good',
but not excellent, student can learn analysis before the calculus. I
am teaching a complex analysis course right now, and the homework that
I am grading suggests that the students cannot easily 'see' that 2(3x)
= 6x, because their manipulative skills are so weak. How can they
follow a good proof?
Herman Rubin
Tim Norfolk <tims...@aol.com> wrote:
>On Oct 9, 3:34=EF=BF=BDpm, hru...@odds.stat.purdue.edu (Herman Rubin) wrote=
>:
>> In article <gerry-1BAEBD.13035509102...@feeder.eternal-september.org>,
>> Gerry Myerson =EF=BF=BD<ge...@maths.mq.edi.ai.i2u4email> wrote:
>> >In article
>> ><3fb1bc8f-73c3-41ff-b2d7-1b7d371f2...@a6g2000vbp.googlegroups.com>,
>> > pubkeybreaker <pubkeybrea...@aol.com> wrote:
>> >> OTOH, =EF=BF=BDI would expect that a high school teacher would know th=
>e Peano
>> >> axioms.
>> >I'd be very surprised if any of my high school (math) teachers knew
>> >the Peano axioms (and I went to a good high school).
>> You may be both partly right. =EF=BF=BDSOME high school math
>> teachers do learn the Peano axioms, but probably most
>> do not.
>The ones that we graduate here have seen them, and done some small
>problems. Whether they remember and understand is something else. On a
>related note, I have to disagree with your contention that the 'good',
>but not excellent, student can learn analysis before the calculus. I
>am teaching a complex analysis course right now, and the homework that
>I am grading suggests that the students cannot easily 'see' that 2(3x)
>=3D 6x, because their manipulative skills are so weak. How can they
>follow a good proof?
If they UNDERSTOOD algebra, instead of just learning how
to solve problems, they would be. Also, if they had the
"Euclid" geometry, they would be. Every manipulative course
makes their ability to see relations worse.
If you asked them to simplify 2(3x), they would give you
the same expression which they cannot recognize as equal
to it. I would teach arithmetic from the Peano postulates
in the beginning, including some proofs.
I was considering real analysis. If taught without assuming
calculus, it can be understood. But by the time students
have had all that instruction in doing manipulations, it
gets much harder.