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Topic: Re: Calculus Reform: reply to De'Liberto
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Posts: 100
Registered: 12/3/04
Re: Calculus Reform: reply to De'Liberto
Posted: Jun 29, 1997 12:36 PM
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In a message dated 97-06-29 11:03:36 EDT, you write:

<< We -- mathematics teachers at all levels -- learned well and succeeded by
being taught by the lecture method. It's very efficient: the teacher
lectures, the student wants to learn what's being lectured about, he/she
studies and asks questions about what he/she doesn't know, the lecturer
answers the questions (by lecturing) etc. etc. Some people can learn this way
and we are them. We like to teach that way because we learned well that way.
It's difficult for us to consider (even as a point for discussion) that this
may not be the "best" way. But we are not everyone. The second sentence in
this paragraph contains a lot of assumptions which just do not apply to the
majority of high school students in math or many other areas.

Lin McMullin
Ballston Spa, NY


Thanks for your message. Your observation is indeed accurate in terms of my
experience. I might also add that we were GOOD math students and we found
the study of mathematics INTERESTING. If we had not really ENJOYED
mathematics, I do not think we would have decided to become mathematics
teachers. Many of our studnts neither like mathematics nor are they
necssarily good at it. I think that many math teachers "love" mathematics
and we can't understand why our students lack interest. Consider what it was
that motivated us to enjoy mathematics and you will surely find that what
motivated us is quite different than what it takes to motivate our current

Your last sentence is particularly intersesting because I have found at times
that students are not really interested in anything. Our generation, for
example, collected stamps, coins, stickers, and for the most part had
hobbies. We had something personal to connect our learning to and something
that we were proud of.

Getting back to the discussion of Calculus Reform, I must add that Calculus
was the first math course in which I really began to see what math was used
for in the real world. It is often hard to show this in the earlier math
courses because the students do not have enough of a foundation to really
understand real world problems much less solve them with real data. I think
that technology has made the teaching of Calculus (and higher level
mathematics courses) more accessible if it is used appropriately. I recall
taking a college level statistics course and the difficulty we had in
visualizing moment generating functions. That experience would not have
occurred if I was taking the course now. We now have an opportunity to make
concepts clear that at one time were very difficult to visualize.

In this sense, some degree of reform is needed. We as teachers need to
become more familiar with how to use technology appropriately in the
classroom. This is no easy task. Our methods of teaching and our
assessments will also need to change as a result. This last note has nothing
to do with the ability level of our Calculus students. This change is needed
because we now have additional tools that we can use to facilitate learning.

I agree with Martha Green's comment that "Even the "worst" HS
calculus student has got to be a better than average student or he/she
never would/could have arrived at "college level" math while in high
school! " But I do think that many more high school students that do not
take Calculus would be capable of being successful in Calculus if the points
I made in my long posting were addressed. And yes many of our Calculus
studnts are weak in Algebra. And again, I claim that we have three options -
we can continue to say that the Algebra teacher should not have passed them,
we can attempt to raise standards earlier on, or we can address this issue as
part of our discussion of Calculus Reform. Options 2 and 3 can be (and I
would suggest should be) done simultaneously so that eventually our students
will have a stronger foundation in Algebra and we can devote more time and
resources to the study of Calculus as we should.

Deanna M. De'Liberto
Assessment Specialist in Mathematics
Hazlet, NJ
(732) 888-9339

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