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Topic: Quotations from Andrei Toom
Replies: 6   Last Post: Mar 25, 2002 12:23 AM

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Posts: 308
Registered: 12/3/04
Re: Quotations from Andrei Toom
Posted: Mar 24, 2002 2:07 PM
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I too spend a lot of time ranting about educational quality in the US. I
allocate the blame somewhat differently. I actually like textbooks that
errors in them. It provides an opportunity to discuss how important it is
to think for one's self. A recent example: "The kinetic energy of the
roller coaster cars being lifted to the top is small." Well, it's only
small if you ignore the rotational, orbital, and galactic orbital
velocities, which are all large compared to the velocity that the text book
authors thought interesting. I actually tend to heap a large part of the
blame on parents, which is a bit unfair. Parents tend to accept what they
read in the newpapers and hear on the TV. The educational debate is
generally framed in terms of better books, better teachers, better schools,
better tests. Very rarely are better parents mentioned. There are a very
few public schools that test incoming students and then help the parents to
change what they have (not) been doing with their children. It is a
generally successful paradigm. But most parents blindly accept the party
line that if they just spend more of their tax dollars things will
radically change. I've reached the point where I'm ready to spend less of
my tax dollars on education. I've lost faith in the existing system.

My 10 year old is finishing up prealgebra with a smattering of analytic
geometry. His teacher supplements Dolciani et al. _Mathematics, Structure
and Method_ (because that is the book that the school has) with samples
from some of her own high school texts. (His teacher has a MS in
mathematics, is retired, and is teaching at a private school because
getting certified to teach in public schools would be a pain.) They rarely
use calculators or computers. I try to provide balance to that by using
Mathematica, MATLAB, and Excel for demos at home. In that context, the
NCTM standards are farcical. His teacher estimates he will be doing
calculus comfortably within 2 years. I've started to lay some of the
ground work for that. We spent a Saturday together working on his science
project. We dumped a capacitor bank into short lengths of various types of
wire, photographed the explosions, and collected current and voltage data
with a TDS 3014, transfered it to Excel in comma delimited (CSV) format and
approximated the integrated power as a sum. To consolidate the E=1/2Cv^2
relation for the capacitor energy, we looked at F=kx and E = 1/2kx^2 for
some real springs - more real data. As we talked about finding the area in
the triangle analytically and how we had approximated the area with Excel,
he made the conceptual leap that you could do it somehow with polynomial
functions of force in general. What's the point? You can get good results
in education with fair quality books, if there are compensating factors. A
good place to start is to simply ignore the NCTM standards - they're not
going away and trying to make them do so is just a waste of time. Get on
with life.

Friday, I took my kids to the San Diego Regional Science Fair. I'd
estimate that it was about 40,000 square feet of exhibits. I was able to
speak at length with one of the 8th graders. She had used ICP AA to look
at various metals leaching into foods from utensils. I probed a bit more
and found she really knew what ICP was and had sought out that capability
because "last year I used flame and you can't do aluminum with flame." I
asked her how she got so smart and what her parents did: "They're both
mathematicians and very supportive." Another exhibitor described how her
parents had rearranged their lives to drive her to lab at 3pm and pick her
up at 7pm every day for 4 months. It seemed to be a consistent link across
many schools and disciplines.

So just what is the worst problem with the US educational system? If you
had to pick a single thing to change tomorrow, what would it be?

From: Domenico Rosa <>
Subject: Quotations from Andrei Toom
Date: Thursday, March 21, 2002 14:05

The following excerpts are from an article written by Andrei Toom after
teaching a Calculus II course for business majors. This article came to
my attention when it was discussed by Albert Shanker, the late President
of the American Federation of Teachers, in his weekly New York Times
column ("Pseudo-education," Week in Review section, Oct. 10, 1993).

In my opinion, Toom did an oustanding job at exposing the
pseudo-educated students being produced in the US, and he is to be
commended for speaking up in such a forthright manner. Toom was also
quite outspoken in exposing the fraudulent promotions and incompetence
of the NCTM leadership, whom he described as "impostors of education."
Unfortunately, when Toom wrote the article, he was not aware of how our
textbooks and teaching methods had degenerated during the previous 30

It is clear to me that the situation has worsened since Toom wrote this
article. I am particularly appalled by the increasing number of students
whose high school math courses consisted of little more than idiotic
drills with graphing calculators. The continuing pseudo-education of
American students is a national disgrace, and it is important that
people speak up.

Dom Rosa

Andrei Toom, A Russian Teacher in America, Journal of Mathematical
Behavior, Vol. 12 (1993) pp.117-139.

An adapted version of Toom's article was reprinted in the Fall 1993
issue of The American Educator (beginning on page 9). A shorter version
appeared in the June and August 1996 issues of FOCUS, the newsletter of
the MAA.

"Never before had I seen so many young people in one place who were so
reluctant to meet challenges and to solve original problems. All they
wanted were high grades, and they wanted to get them with a conveyor
belt regularity." (p. 122)

"I had to learn that every technical calculation, which I was used to
ignoring, was a considerable obstacle for my students. It took a
considerable amount of time for me to understand how poor they were in
basic algebraic calculations." (p. 123)

"Of course, students are different. Many want to learn, because
curiosity is inherent in the human nature." (p. 125)

"They [students] are never carried away by the subject's charm for its
own sake, as they believe they must be 'practical', that is never forget
points and grades. As a result they never use the powerful potential of
creativity given to them by nature." (p. 126)

"Elementary mathematics is normally taught to children who looked like
children." (p. 127)

"The voluminous book … perfectly fits the max-min principle of the
market: maximal pretensions with minimal content." (p. 130)

"The moral status of those who designed the business calculus course is
like that of colonial-time hucksters who sold cheap beads, mirrors and
'fire-water' to ignorants, whose role is now played by students. I do
not blame rank-and-file teachers, because they have no choice." (p.

"The students grabbed their calculators, but seemed not to know what to
calculate. After a while, one produced a complicated and wrong answer.
... All they had learned was to follow a few recipes without thinking."
(p. 135)


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