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|| Electronic Proceedings of the Eighth Annual ||
|| International Conference on Technology in Collegiate Mathematics ||
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CONTRIBUTED PAPER: 8-C39
Calculus Remediation Using Databases
Russell Jay Hendel
Health Care Finance Administration
POB 34662
Philadelphia, PA 19101
Phone: (215) 596-6830, Fax: (215) 596-5084
E-mail: RHendel@Phi1.SSW.DHHS.GOV
ABSTRACT
This presentation will focus on a (typical) student problem: The
"WHERE DO I BEGIN," problem. It will be shown that remediation
can be accomplished using database theory.
Using Calculus II for purposes of illustration we may more
specifically define the problem as follows: There are many
students who KNOW how to implement the various integration
techniques---parts, partial fractions, trigonometric
substitutions,.... In other words, these students COULD SOLVE a
problem of the form "Integrate the following function using the
TECHNIQUE OF....". However some of these students may be unable
to solve a problem of the form"Integrate the following function."
We may describe these students as being INTERMEDIATE REMEDIAL--
they are better than those students who cannot implement
particular techniques but are inferior to those students who can
do problems without being prodded on which technique to use.
A characteristic symptom of INTERMEDIATE REMEDIALS is the typical
response, "WHERE DO I BEGIN." However, once informed of the right
technique these students can do the problems.
Having defined the problem we proceed to discuss the solution.
For purposes of illustration consider a problem requesting
integration of a rational function. It is reasonable to assume
that a good student goes thru a mental list of integration
techniques and selects that technique which is used when the
integrand is a rational function (partial fractions). Our goal
then is to give the intermediate remedial student the same skill.
Let us describe in further detail how the good student selects
the technique of partial fractions. Imagine a database table of
techniques. The first column of each row is labeled with a
TECHNIQUE NAME--parts, partial fractions... The second column of
each row is labeled with an INTEGRAND FORM---product of
exponential and powers, rational functions etc. The remaining
columns in each row give the STEPS by which the particular
TECHNIQUE is implemented. (The full paper contains the database)
The good student seeks that row whose integrand-form column has
"rational function." This results in the row beginning with
partial fractions. THE CRUCIAL POINT IS THAT THE GOOD STUDENT HAS
IN EFFECT PERFORMED THE FOLLOWING query ON THE technique
DATABASE: "SELECT * FROM techniques WHERE integrand = rational
function." It follows that one possible approach to helping the
intermediate remedial is to teach him/her to use the TECHNIQUE
database.