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From: booker@network.ucsd.edu (Booker bense)
Newsgroups: sci.math,comp.sys.handhelds
Subject: Re: The use of calculators in teaching calculus
Keywords: Calculators, calculus
Message-ID: <4176@network.ucsd.edu>
Date: 6 Dec 90 17:12:04 GMT
References: <4608@umbc3.UMBC.EDU> <1990Dec4.153552.29699@javelin.es.com>
Followup-To: sci.math
Organization: San Diego Supercomputer Center @ UCSD
Lines: 89

In article <1990Dec4.153552.29699@javelin.es.com> pashdown@javelin.es.com (Pete Ashdown) writes:
>rouben@math13.math.umbc.edu writes:
>
>>I would like to hear your thoughts and comments on this.  Specifically:
>

>>A - Is the traditional U.S. style of teaching freshman calculus
>>    in need of reform?
>
	Yes, having taken and taught calculus ( 3-years in G-school ),
I think that most students don't learn any calculus in Freshman calc.
They (the ones that pass) brush up on their algebra and learn to jump
through symbolic hoops like trained monkey's, but they rarely get the
intuition needed to use calculus effectively. They most useful thing
we could teach a freshman student is a strong physical sense of what a
derivative and a integral are and some initution about when an answer
'looks right'. I tried very hard to teach this in my classes, but it's
not really possible in the 'barf back the formula' setting of most 
calculus courses.

>
>>B - Will the use of computer algebra systems (mathematica, maple,
>>    derive, mascsyma, mu-math, etc.) enhance the learning of calculus?
>
>Yes.  Broderbund's introductory calculus software is a good example of this.
>You get to see a visual representation of tangents, areas, derivatives, etc.
>Although it is pretty limited, I would imagine the packages you mentioned
>are much more capable.  Being able to "play around" with ideas to see how
>they work is extremely valuable.
	
	I think the key thing here is graphics. In the tv age, this is 
the only way to convey ideas that really gets to most students. One
example of this that I think is quite good is the 'Mechanical
Universe' tv course series that show up on PBS occasionally. They
portray the physical ideas that motived the development of calculus in
a very visually compelling manner .  

>
>>C - Will the use of programmable calculators enhance the learning
>>    of calculus?
>
	I would say no. In one course I taught, we did not allow
students to use calculators. What's needed is pictures and the
development of some physical notions that relate to the symbols. 
A calculator just provides numbers or answers faster , not better.

>
>>D - Should the cost of the calculator be a factor in deciding whether
>>    to prescribe it as a required tool for enrollment in a course?
>
	I think a calculator is an unnecessary tool, a PC-Lab with 
appropriate software would be far more useful.

>
>>E - Have you thought, or have you been a student in a "non-traditional"
>>    type calculus course?  What was your experience?
>
	Yes, I was a student in a Independently Paced calculus class
when I was a freshman at WPI those many years ago. The way it was set
up was that you had a series of tests to pass and you could take them 
whenever you wanted. There was no class , but tutors were available in
the lab were you took your test. I don't think that is a very good
situation, I only learned enough to pass one test and go on to the
next. It's too easy to get only a minimal understanding, particularly
if you're good at taking tests. 

>
>>E - Other thoughts and comments.
>
	Another poster mentioned that epsilon and delta's should be
part of 'any freshman course'. This is the most wasted week in
freshman calc. None of the students understand it , they just don't
have the background to understand an axiomatic proof. It would be 
far better just to leave it for the junior real analysis course, where
maybe you'll understand it. In my case , I really didn't get a good 
feeling for eps-delta proofs until my graduate analysis class. 

	I think this is another example of where math education has
adopted the wrong approach. IMHO, elementary math courses should be 
taught from a historical basis, not the axiomatic one familar to most 
mathematicians. I.e. a freshman calculus course should start with the 
problem of determining the path of a projectile and see how that
problem leads to the idea of a derivative. There is a place for
formalism and precision, but it should come after the intution is in
place not before. 


/* Booker C. Bense 
   benseb@grumpy.sdsc.edu */