“Field” & StreamExperiencing a Vector Field

Steven Zides & Dr. Anne Catlla Wofford College zidessb@wofford.edu

Student’s Background

Calculus I & II (all students)• One variable differentiation• One variable integration• Scalar functions of one variable• Implicit differentiation with two

variables

Physics (most students)• Graphical vector addition/subtraction• Vector addition with components

Conceptual Difficulties with Vector Fields

• Students think of vectors as objects that start at the origin.

• Students have trouble (in general) visualizing in 3D.

• Students think that the visualization of every function is a smooth graph.

Outline of the Glendale Project

1) Break into groups of three or four.2) Design (and build) a cheap apparatus that measures the

direction of water flow.3) Using a velocity meter and your direction device,

measure the velocity of the water at four locations along a defined cross section of the creek. Submit this data.

4) Use the combined set of class data to create a velocity flow vector field.

5) Write an essay about your results, including your thoughts on the concept of a “vector field”.

Wofford’s Glendale Environmental Studies Center

Usable Section of the Lawson Fork Creek

Equipment for the River Project

Vernier Probeware Velocity Meter Compass Lanyard

Students at Work

Raw Data

Project Strengths

• The student groups bonded very well.• Some of the direction apparatus were interesting and

creative• The students had a great time and talked about the

experience often.• The students realized the difficulty of collecting a uniform

set of data.• Most of the essays implied that the student’s

understanding of a vector field was more robust after the experience.

Project Weaknesses

• Although helpful, the data really only allows you to make a 2D vector field.

• It is hard for the students to judge ¼ intervals along their cross section.

• Not everyone documented their direction apparatus.• The vector diagrams, in the final essays, were not as good

as I hoped they might be.• The project does require transportation and equipment.• There is the potential for injury. Someone wore flip flops

and badly stubbed their toe.

“Field” & StreamExperiencing a Vector Field

Steven Zides & Dr. Anne Catlla Wofford College zidessb@wofford.edu