Using Student-Selected Projects in Second Semester Calculus
In
Spring 2003, I assigned my second semester calculus class of 31 students a
research project. After meeting with
me, the students were to create a problem on a calculus-related topic of
personal interest. Many selected an
application of calculus, either to mathematics or to a natural or social
science or engineering. Then they
designed a problem within that topic and used Calculus to solve the
problem. The better projects went on to
generalize their problem in some way.
There
were a variety of topics, including: determining the optimal admission price
for a public beach, deriving Fourier coefficients, finding the volume of
intersection of two cylinders, and estimating the volume of a human head.
In
end-of-semester evaluations, students stated that they “learned a lot”
(although not necessarily about mathematics) (95% confidence interval of 3.84
+/- 0.33 on a 1 to 5 scale, with 5 being “strongly agree”) and they “enjoyed”
the project (95% CI of 4.02 +/- 0.37).
Several claimed that that they had gained an understanding of how
calculus related to their major or to the real world.
Selected
student comments follow:
· [M]y project gave me a chance
to expand calculus to something that is more related to my major.
· The [p]roject is a really
good way to learn how calculus deals more with the real world.
· I enjoyed the opportunity to
relate what we are learning in math to other subjects of our interest. It was a nice “preview” to our major.
· [The best aspect of the class
was] learning the different methods used in calculus and how it relates to the
real world.
The
results from this experience are promising.
It seems that students not only enjoyed the project, but also found it
to be a useful part of their overall education.