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Abstract Title: Student Ideas around Vector Decomposition in the Upper-Division
Abstract: The Colorado Classical Mechanics/Math Methods Instrument (CCMI) is an open-ended assessment designed to investigate student skills in upper-division classical mechanics.  With a large number of student responses compiled (N=443), we conducted an analysis of student written work to identify student ideas and trends in student difficulties.  Here, we present our examination of student responses to one CCMI question that targets vector decomposition in multiple coordinate systems. Through iterative and cooperative efforts to hand-code student responses, we identified common patterns in students' final expressions, resulting in broad categories. We identified approaches to the problem inferred from features of student solutions. For example, when decomposing a velocity vector in a Cartesian coordinate system, we found that students either differentiated a position vector or used trigonometry to visualize the components. We observed that certain approaches more commonly resulted in particular errors. Investigating productive student approaches is a step towards pedagogical improvement.
Abstract Type: Contributed Poster Presentation

Author/Organizer Information

Primary Contact: Anna M Turnbull
Michigan State University
46651 Camelia Dr.
Canton, MI 48187
Phone: 7347489084
and Co-Presenter(s)
Leanne Doughty (2), Vashti Sawtelle (1,2), and Marcos D. Caballero (2,3)

(1) Lyman Briggs College, Michigan State University, East Lansing, MI 48824
(2) Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824
(3) CREATE for STEM Institute, Michigan State University, East Lansing, MI 48824