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Re: Calculus texts





On Fri, 27 Dec 1996, JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439 wrote:

Hi all-
I've come to the conclusion that there are no calculus texts
the hew, even approximately, to the pedagogical lines laid out by Arons
for the teaching of introductory physics. The apparent reason that
teachers can get away with using the clone texts, such as Anton's (which
I used last semester -as sparingly as possible), is that the texts are
full of worked out examples. Students can follow the examples almost
verbatim in doing many of the exercises at the end of each chapter.

And not only are students seduced into the illusion that they've learned
calculus, the teachers are suckered into thinking their course is a
success.

The end result is that the students, many of them deficient in algebra
skills, can "satisfactorily" complete a calculus course without understanding,
or even reading, any of the textual material. As for understanding any of
the underlying concepts - forget it!

The same criticism is applicable to most physics texts I've seen.

Students with such calculus preparation find themselves almost
totally lost when they enter our calculus-based physics classes. The
frustration with the math preparation of our students has been expressed
frequently on the physics-l net.
My solution to this problem is to write a "decent" introductory
calculus text. The text would adhere to the principles of:
a unifying theme
less is more
write at the level of the students' understanding
concept first, names later
avoid concepts that are unnecessary to the main theme
introduce concepts only as needed in the development of
main theme
continuous "circling back" and revisiting earlier concepts
including those learned in algebra and arithmetic
short, literate chapters, each dealing with a single principle
idea; each followed by relatively few exercises and problems.
The expectation is that a student will do all of the exercises
(and problems).

A very good list of qualities a text should have. With only slight
modification it could apply to physics texts as well. Having just
completed a review of one of these bloated encyclopedias masquerading as
textbooks, I heartily second your suggestion that 'less is more'. But try
to tell that to publishers. They come back with the observation that the
ideal text I'd like simply would not sell. They tell me that the books
which sell are those with lots of color, lots of worked examples,
instructor's solutions manuals, overhead transparencies, exam banks, and
coverage of all topics which are in anyone's syllabus, and on any
standardized exam the students might have to take. One editor told me in a
moment of candor that most teachers choose the book which will be the
least work for the teacher. Those of us who really want students to
*understand* are, she said, in the minority.

At the end of a two semester course the student who completes the
text should be able to apply the first and second fundamental theorems of
the calculus to elementary (separable) problems in one and two dimensions.
The student should also be able to derive the rules of calculus and to
work out complicated, unfamiliar integrals. (Maybe less).

I've asked my college students to clearly state three of the fundamental
theorems of calculus, or as many as they can remember. Not one can
remember even one! And some of these folks got A grades in calculus. When
they are given broad hints, they still can't reconstruct a statement of
even one of the theorems. But, how many high school physics teachers
could? Just as in physics courses, students get no sense of what is
fundamental and what is derived, what is empirical and what arises from
theory.

It points out that what's lacking in so many courses, both physics and
math, is any sense of the logical progression of ideas, and a clear
understanding of the difference between axioms and theorems, and the
logical steps to get from one to another. In physics there's a lack of
understanding the difference between definitions, empirical laws, theory,
hypothesis, and the logical connections between them.

Students in math courses are no longer expected to understand or to
independently construct proofs of theorems.

Look at the exams. Look at your exams. Suppose you had a student with
perfect eidetic imagery, who could look at a book and remember every word
in it, every diagram, right down to the punctuation. This is what some
call "photographic memory"--the ideal memorization. Assume that person
could also copy patterns and follow recipes and procedures faultlessly,
but didn't really understand anything. What score could this person get on
one of your exams? If your answer is any score larger than zero, then
something is wrong with your exams. Many exams reward mere memorization,
cramming of definitions and slogans, slavishly carrying out procedures and
recipes and pattern-following. These do not measure understanding, and do
not promote or encourage understanding.

The only exams which test understanding are those which ask the student to
apply physics and math to *new* situations, never seen before.

I am looking for one or two people to collaborate on such a text.
An ideal team, I think, would be two physicists (to keep it simple) and
one mathematician (to keep it honest).

Since when have physics textbook authors been noted for keeping things
simple?

-- Donald

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Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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