Microworld: Stay
Afloat!
Click the Hyperlink
above to download the Microworld.
Author:James
E. White
This
7-page work, first written in 1997 as a Mathwright WorkBook, emerged from
a student's question in a Calculus II course taught by the author. It is one
of our new free Visualization Studio Interactive
Web Books in the Math Cafe, and all visitors are invited to check it out before
joining the Library to get a glimpse of what is possible with Mathwright.
It exemplifies the applications of object-oriented design to geometry by placing
the student in a carpentry shop where she cuts the wood to build a boat that
will carry two children across Monet Pond.
The
aim is to take account of Archimedes' bouyancy principle, and to solve the
resulting optimization problem, i.e. guarantee that the boat will not sink,
while testing the resulting 3D model of the boat. This hands-on approach to
optimization succeeds well by making the task a challenge in a game-like environment.
Later, we "do the math" so that students can appreciate the role
of implicit differentiation in solving the problem.
The
goals of structured discovery learning worked so well that we have translated
it and extended it to our Microworld format so that you may view it either
in your browser or offline.
This playbook explores Archimedes' bouyancy principle, implicit differentiation,
and optimization problems in a game/story in which players build a boat by
cutting and assembling planks from a board and putting them together. They
may view their product in three dimensions and get statistics on weight and
volume that helps them decide how to proceed.
Students
learn about bouyancy and make calculations that will optimize the volume of
the boat. We use implicit differentiation to solve the problem as a last resort.
This is a nice way to motivate the study of the derivative. The playbook uses
animation in the carpentry shop, 3D animation to test the boat, and sprite
animation to enliven the tasks.
Return to the listing of MathwrightWeb Microworlds
| - James E. White, Ph.D. , Library Director, | ||
| author of this website, Mathwright 2000, MindScapes, | ||
| MathwrightWeb, and Mathwright32 |
