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Topic: calc. reform
Replies: 27   Last Post: Jun 16, 1997 7:45 PM

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jerry rosen

Posts: 244
Registered: 12/6/04
calc. reform
Posted: Jun 2, 1997 1:28 PM
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I have been reading the posts in this group with great interest and it is
good to see teachers with such a genuine passion for their student's
education. However, I think many of you are terribly mis-guided with
respect to this calculus reform issue.

The Harvard Calculus (HC) text and ones like it are very one dimensional
and dangerous. They emphasize a few types of conceptual problems which
are based on calculators but (1) it omits almost all theory and some of
the theory and definitions which it contains are wrong - for example a
wrong proof of the quotient rule - with no explanation (2) it omits a
huge number of topics - see the MC web site for a list of about 20
serious omissions (3) it suffers from a de-emphasis on algebraic
manipulation and calculation in general. A world famous mathematician -
Donald Passman of the University of Wisconsin once told me, in his
negative evaluation of calculus reform - "at least with the traditional
calculus course we knew the engineering majors would know algebra by the
time they graduated college - now we don't even have that" (4) Because of
(1) and (2) the HC text is useless as a reference book.

Several of my friends in areo space and computer animation pointed (4)
out to me. BTW These people hated the book and thought it would be
terrible to use for CS and engineering majors. My neighbor is an
aerospace engineer and I gave him the HC book to look at - his reaction
was " they can't possibly mean that this book could be used for
scientific majors". These people - who use computers on a regular basis -
laugh at the way calculators are integrated into the material. They all
say they would feel better having colleagues who could compute by hand
and who know enough theory to be able learn a new topic if needed.

Here is some history: The calculus reform movement started in the mid
80's when it was found that about 50% of American students were flunking
calculus the first time they took it. One would have thought that, as a
first step, we look at what is happening before calculus. It was known
that algebra skills were weak. Instead of looking into this the reformers
said "hey, here is a good idea, let's not make calculus as algebra
intensive and take out the theory."

Now this is bad for several reasons (1) Calculus without algebra,
computation and some theory is not calculus and becomes useless for all
scientific majors and (2) it stops people from looking into the real
problems in education.

None of the reformers took the time to research educational issues - such
as studies done by E.D. Hirsch who found that reform like ideas in
education have been around for decades and are to blame for huge amount
of what is wrong.

I can see the immediate appeal of the HC book to HS math teachers.
Because it doesn't require facility with algebra and because it involves
pushing buttons it will have a knee-jerk appeal to students and the
teachers get excited. But you are missing the big picture. What is
important for success in college is that students have a firm base of
knowledge which must include a solid understanding of algebra and trig.
Furthermore students need to have good study skills. It is this last
thing which differentiates the good college students from the rest. Good
students will tell you that the act of learning isn't fun - it requires
sacrifice and struggle. Students who don't know this are not prepared for
college. Of course the rewards are great but a price must be paid. If
calculators are getting in the way of this I would advocate not using
them at all. I used to think they coul be used in HS, but reading these
posts is making me think otherwise.

As a math professor at CSUN I see hundreds of students who have received
a significant portion of their math training under reform programs - the
California Framework, as instituted in 92, is very reform minded. These
students are lacking in pre-requisites and have know idea how to study
independently. Since the inception of reform my students have gotten much
worse.

While I know many of you have the best interest of your students at
heart, I can tell you, from a college professor's perspective, you are
harming them if you don't develop their ability to do hard-core
calculation and give them dexterity with all the transcendental functions
and their inverses. Furthermore, you must develop their ability to
accumulate knowledge independently. If they are coming to you weak in the
basics this is a problem. But getting them to push more buttons is not
the solution and only masks the problem until a later date.

Some of you mentioned there has been no long term studies. This is no
argument to defend reform. Just because an idea is pushed (and in the
case of reform, some of it's biggest pushers, are those who are making a
profit off it) doesn't mean it deserves to be studied while it is being
forced on millions of unsuspecting students.

WLL was used for over a decade and we have now discovered that it has
ruined the reading ability of tens of thousands of children.

What if the problems our children have had nothing to do with the
traditional education that the reformers are so quick to attack? I and
every math professor I know had a traditional education. Many of my
friends from NYC had a traditional education and have gone on to highly
successful careers. Face it, millions of people in this country and
abroad were well-trained in a traditional manner.

What if the real problems in education were caused by schools of
education through pushing programs which are based on the very ideas in
common with calculus reform.

We would be in big trouble. We are in big trouble. If you are not
profiting from reform then I urge you to consider this very carefully.

Jerry Rosen
CSUN





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