Download - “Field” & Stream Experiencing a Vector Field
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“Field” & StreamExperiencing a Vector Field
Steven Zides & Dr. Anne Catlla Wofford College [email protected]
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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
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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.
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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”.
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Wofford’s Glendale Environmental Studies Center
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Usable Section of the Lawson Fork Creek
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Equipment for the River Project
Vernier Probeware Velocity Meter Compass Lanyard
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Students at Work
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Raw Data
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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.
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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.
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“Field” & StreamExperiencing a Vector Field
Steven Zides & Dr. Anne Catlla Wofford College [email protected]