INTERACTIVE INTERNET-BASED
MULTIVARIABLE CALCULUS
Thomas Banchoff
June 26-29, 2005
Brown University
Providence, RI
Visualizing graphs of functions of two and more variables is a key
skill needed to deal with the main ideas of multivariable calculus.
Internet-based tools make it possible to engage students in the
interplay between analysis, algebra, and geometry in ways that lead to
deeper appreciation of the underlying principles and of real-world
applications.
New software developed by the workshop leader and his students provides
accessible and powerful tools for interactively investigating curves
and surfaces, and enables students to share their own demonstrations
with the instructor and with other students. Communication software
provides easy ways for students to respond online to homework
assignments and even examinations, and for instructors to submit online
comments that can be shared, after a time delay, with other
members of the class.
One student, describing her experience in the class, wrote: ’In the
beginning I really did not like the system of reading other students’
homework. It made me feel really
nervous and exposed and it made me want to leave problems blank rather
than put an incorrect answer. As the semester progressed I
realized what a useful tool it could be and I started reading other
people's homework responses more and more and felt more comfortable
with mine being read.â?
This workshop is intended for teachers of multivariable calculus who
wish to explore the possibilities of new software for helping students
develop a full range of geometric intuitions as well as formal skills
in algebra, in abstract
concepts in calculus (including continuity, differentiability, and
curvature) and in effective writing. Prior computer experience is not
required. The workshop will use Java applet software and laboratory
materials that will be available for the participants to use in their
courses in the fall.
In addition to the three-day intensive workshop, there will be online
follow-up activities at least once a month during the fall,
concentrating on different ways that the participants experiment with
the software in their courses. Members of the workshop will be
invited to participate in a session at the joint MAA-AMS national
meeting in January 2006 to share their experiences. For more
information, please visit the workshop webpage at
http://www.math.brown.edu/~banchoff/PREPReturn to List of PREP Workshops