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Re: Foerster book
Posted:
Oct 15, 1997 12:28 AM
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As a teacher of the Thomas series for years, and now a user of the Foerster
text, I don't fully understand the basis of some of these comments. It
seems to me that the new text embodies many contemporary techniques, and it
hardly seems that it is dominated by "old-fashioned, out of date ideas."
The course differs dramatically from the calculus courses I studied in the
60's and have taught in the decades since, yet clearly it does embody
critical, traditional topics as well. None of the older texts referred to
relied heavily on graphing calculator techniques, had major emphasis on
numerical methods, required much verbalization of understanding by the
student, incorporated group learning activities, included regular
exploratory exercises, or included such topics as slope fields and Euler's
method. Most likely the Foerster book, or any other, is not the "Bible" of
calculus for the next decade, but having done a thorough search / review of
available books last year, I found it to be an excellent alternative for
these transition years of reform in calculus education. It seems to me to
be an attractive compromise between the out-of-date, symbolic manipulative
texts and others that are ready to leap ahead and immediately abandon all
traditional topics. Especially in these years when the AP test is steadily
changing, essentially requiring high school students to be able to do it
all -- traditional and contemporary -- from my limited experience (with the
first four chapters, so far) Foerster is working well. From the teacher's
standpoint, working with this book is very different from using older ones,
and it is apparent on a daily basis in class that it demands of the student
much more conceptual understanding and non-traditional, non-manipulative
techniques. With the exception of the few topics that have been eliminated
recently from the AP syllabus, however, I feel that I must have a text that
"does it all". It must include plenty of practice, without overkill, in
many of the basic, traditional calculus topics, while simultaneously
incorporating the contemporary approaches as well.
>I have just had the opportunity to look at Paul Foerster's new calculus book.
>Here are some quick impressions:
>
>
>Although all the traditional calculus books today are clones of George
>Thomas's book from the fifties, Forester's book is a clone of the
>Granville,Smith and Longley the dominant calculus book for 1920-1960 . (The
>younger folks might not realize that Thomas was the reform calculus of its
>time.)
>
>
>
>Like Granville, Foerster's emphasis is hand symbol manipulation and
>Forester presents this very well - including some neat tricks at doing
>repeated integration. and partial fractions. And Foerster caps this off
>with some great calculus probems highly appropriate in the context of the
>book. I think the book is
>i) thoughtfully planned,
>ii) well written and
>iii) well produced.
>
>It would have been a great book back in the fifties; I wish the calculus
>course I took in 1959 had been based on this book. I do not think Foerster
>is a good book for a 1997 calculus course. It has too much emphasis on
>old=fashioned and out of date ideas and has little indication of where
>calculus will be in the future.
>
>Still, if you want to emphasize hand manipulations, I predict Foerster will
>deliver better than Stewart, Thomas-Finney,
>Saxon, etc.
>
>-Jerry Uhl
>
>
>----------------------------------------------------------------------
>Jerry Uhl juhl@ncsa.uiuc.edu
>Professor of Mathematics 1409 West Green Street
>University of Illinois Urbana,Illinois 61801
>Calculus&Mathematica Development Team
>http://www-cm.math.uiuc.edu
>http://www-cm.math.uiuc.edu/dep
>
>
>[If] logic is the hygiene of the mathematician, it is not his source of food.
>---Andre Weil
>
>Only professional mathematicians learn anything from proofs. Other people
>learn from explanations.
>---R. P. Boas
Wayne Murrah
Porter-Gaud School
Charleston, SC
School: wmurrah@porter.portergaud.edu
Home: wmurrah@awod.com
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