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Abstract Title: A Cross-sectional Study of Students’ Use of Mathematics
Abstract: Upper-division physics courses introduce quantitative models that require students to use sophisticated mathematical tools to develop an understanding of them. We have investigated students' in-the-moment math reasoning during physics problem solving, through observations in dyad interviews.  By conducting interviews over a range of students' physics experience, we enabled a cross-sectional analysis of how students employ mathematical tools, particularly the decomposition of vectors. In investigating students' reasoning underlying their use of those mathematical tools, we have catalogued student difficulties and identified productive approaches for pedagogical purposes. We observed some patterns in students' problem solving approaches and difficulties that propagate and/or evolve across levels. For example, introductory students may neglect to consider the sign a vector component while upper-level students are much more thorough in their analysis. However, we observe sign errors in work by both groups, but with different reasoning.
Abstract Type: Contributed Poster Presentation

Author/Organizer Information

Primary Contact: Anna Turnbull
Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824
575 N Hagadorn
East Lansing, MI 48823
Phone: 7347489084
Co-Author(s)
and Co-Presenter(s)
Leanne Doughty [1] and Marcos D. Caballero [2,3]

[1] School of Education and Human Development, University of Colorado Denver, Denver, CO 80204

[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