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Topic: calc. reform
Replies: 3   Last Post: Jun 4, 1997 11:06 PM

 Messages: [ Previous | Next ]
 jerry rosen Posts: 244 Registered: 12/6/04
calc. reform
Posted: Jun 4, 1997 9:42 AM

Let me give an example illustrating some points from my last message.

My first job after getting my doctorate, in 82 and was at the University
of Iowa in Iowa City. At that time the University of Iowa did some
recruitment of undergraduates from Japan. The first course I ever taught
as a professor was three quarters Japanese. Every one of these students
knew traditional pre-calculus material backwards and forwards and they
were all hard workers.

We did very little "drill and kill" stuff - it would have been a waste of
their time. Instead I proved a lot of things - but not everything and did
a lot of conceptual stuff. But the conceptual stuff was tied into the
theory. For example, I would try to explain why a continuous function
would have extreme values on a closed interval. Then after a physical
motivation for Rolle's theorem, it and the MVT could be proved.

Now the reformers say - "you have to assume the completeness property of
the real line, so you're not really proving the MVT"

But this is where reformers miss a few BIG points by a mile

(1) It isn't the logical presentation of the MVT that matters here, but
rather it introduces the students to a proof which can be motivated
physically and geometrically

(2) The MVT may be the most important theorem in analysis and it is
crucial that many students know it. Theorems are always understood better
when they are proved.

I also spent a lot of time motivating derivative through instantaneous
velocity and we approximated this by hand - nobody had calculators and it
didn't matter - they could compute better than me - after all I was
American educated.

WE also spent a lot of time solving the hard word problems. Who care if
they were realistic or not - many were - I can not imagine better
training for a scientific career.

Also I didn't have to lump problems into types. For example, when doing
curve sketching we didn't do parabolas then cubics then quartics then
rational functions and later on transcendental ones. Since these students
truly knew pre-calculus I could "mix it up". This was also true for word
problems.

It was a real challenge to teach these students and it was a total joy.
The traditional book had a good balance between all these things. One of
the big lies of the reform movement is that the traditional programs we
heavy on rote stuff and left out conceptual stuff. The older Calculus
texts were not heavy on rote stuff at all - check out Courant and John or
many written in the '50's. Even those written in the '60's were not heavy
on rote. But even if they were, so what? Some students may need a lot of
rote stuff. In any case, many of the traditional texts could be used to
give several types of courses.

Someone in the group mentioned to me that he uses the HC text
successfully. This may be true and the people in this group seem very
intelligent and may be able to supplement it where necessary - of course,
it leaves out so much I doubt it can be successfully supplemented - this
is definitely the case if it is used in a mainstream college calculus
course. But I seriously doubt whether many future HS AP calculus teachers
will be able to give a good course out of the HC or books like it.

Here at CSUN the prospective HS math teachers are not required to take
advanced calculus (it was taken off the required list in 82 by the math
education people in my dept. at that time) and they take a watered-down
version of the math major. Half of our majors use the HC text and many of
the "feeder" JC's use it too. Hence it is safe to say many future AP
Calculus teachers in the Valley and the greater LA area will not know
what a limit is, will not know what a series is and will have a huge
number of topics - including L'hopital's rule, parametric equations,
polar coordinates, sequences, MVT (which is not mentioned until towards
the end of the HC book, etc. ... omitted from their education. How can
such people teach an honest AP-Calculus course? Reform educated teachers
all over the country will not have the background for teaching AP
Calculus and will lack the ability to "make up ground". Since the HC text
and ones like it are so lacking in topics and proofs they are also
useless as reference books and many future teachers won't even have
proper Calculus books in their personal libraries.

This is why I think all of you should oppose the HC text and similar
reform texts. I truly believe you can cover the conceptual problems from
a more traditional book. I know Dan Hart has had some success with Saxon
for AP Calculus. In any case, the intense negative reaction against HC
will result in different books being written and perhaps you will find
one which won't need supplementation. Perhaps some of you can get
involved in writing projects with college teachers - this would be
valuable for all.

But if AP teachers get caught up in this reform bandwagon then progress
will be slower. Also, as I indicated in my last message, the reform stuff
just masks the bigger problems which start in K-8. I teach our math
courses for prospective K-8 teachers and believe me there are some very
serious problems here which need to be dealt with.

I appreciate the comments I have gotten from this group. Everyone here
seems open to different points of view. Like you, I experience a certain
amount of displeasure in teaching and the nature of my teaching has
changed drastically since I started at CSUN in 84.

I know that the appeal of the HC text for HS teachers and college
teachers is, in part, due to the fact that it is different and people
may feel that any change is good. But as with my Japanese students,
teaching a group of motivated students who are prepared and know how to
study will always be fun and with such a group new things can be tried
from time to time.

But this reform calculus is highly detrimental to anything good happening
in the long run as well as the not so long run. I notice some of you
discuss including and omitting certain topics - at least you are aware of
various topics. Your successors will not be if they have gone through
reform minded programs.

I have great respect for HS math teachers and in fact it was such a
teacher who got me interested in math and in being a good student. I owe
a huge amount to this person (as well as to a school system which had
standards and assessment).

Like the Whole Language Learning movement, the Calculus Reform Movement
is completely lacking in balance in the direction of dumbing down. The HC
text is extremely bad for all science oriented students including future
teachers. I hope I can convince some of you to see my point of view.

Jerry Rosen

Date Subject Author
6/4/97 jerry rosen
6/4/97 Geoff Hagopian
6/4/97 jerry rosen
6/4/97 Carl Gagliardi