What do a roller coaster, a rocket, an artillery shell, and a three-point shot have in common? Maybe vector calculus doesn't immediately spring to mind, but Mississippi State University students can use mathematical calculations to predict the success or failure of each.
Now, through a $125,000 National Science Foundation Instrumentation and Laboratory Improvement grant, the university has a new vector calculus laboratory where students can more easily understand--and actually have fun calculating--the daunting subject.
The grant proposal was written in 1993 by mathematics professors William England, Michael Neumann, Michael Pearson, and Betty Scarborough, who served as principal investigator for the project.
"It's a completely new way of doing mathematics for the students," said Pearson, assistant professor of mathematics and statistics. "And, in turn, it has led to a completely new style of teaching mathematics."
Sophomores no longer are tied to long numerical calculations that can take days to finish. With the latest Mathematica computer software, they watch their calculations become 3-D graphics, letting them see the success--or failure--of their efforts.
The approach is so new, in fact, that Mississippi State is among fewer than 10 American universities using it.
This reality led professors to search for a textbook that combined computers and vector calculus. Finding none, Neumann, along with math professor Len Miller, were left to write their own. The text functions more as a workbook and accompanies the computer software, offering various projects for the students to complete.
"We didn't have projects before in vector calculus," Neumann explained. "Now we let the students work on these projects, like in other disciplines, and they are excited about it. Because of the computer they can 'see' what they are creating and get their feedback from the graphics on the screen."
Some projects in the text include: location of the exact center of an irregularly bordered lake, calculation of roller coaster's speed, and determination of the trajectory needed to shoot a rocket as far as possible.
"Previously, students could spend days working on numerical calculations and they were so complicated, they may never know for sure if it would work," Pearson said. "It could be correct, mathematically, but there was no way for the student to 'see.'
"Now, with 3-D graphics, they can see the image on the screen and know what's working and what's not. It becomes very concrete for them."
Neumann added, "The students find the projects challenging, but they like them."
In addition to working the problems, the students must also develop writing skills as they explain their results, which are discussed in exit interviews.
"We feel strongly this is providing a big service to the College of Engineering and other colleges that require this course, which is not just for math majors," Pearson said. "It's not just numerical calculations, but adds graphics and algebraic computations. The students can really see what's going on."
He and Neumann said the new process involves more teaching time on their part, but "the results are worth it." They next hope to expand the course to other classes and to train other professors in the new way of teaching.