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“Field” & Stream Experiencing 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
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“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 • Break into groups of three or four. • Design (and build) a cheap apparatus that measures the direction of water flow. • 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. • Use the combined set of class data to create a velocity flow vector field. • Write an essay about your results, including your thoughts on the concept of a “vector field”.
Equipment for the River Project Compass Lanyard Vernier Probeware Velocity Meter
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