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Tangible Metaphors 
  
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PER Literature
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C. Manogue, E. Gire, and D. Roundy, PERC 2013 Proceedings, 27-30.
Upper-division physics requires students to use abstract mathematical objects to model measurable properties of physical entities. We have developed activities that engage students…
https://www.per-central.org/document/ServeFile.cfm?ID=13088&DocID=3623
"Surprisingly, there is an actual physical application…" Student understanding in Math Methods 
  
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M. Loverude and S. Li, PERC 2013 Proceedings, 229-232.
Among the canonical physics core courses taken by most undergraduate majors is a course in mathematical methods. Physics education research has begun to explore upper division…
https://www.per-central.org/document/ServeFile.cfm?ID=13172&DocID=3719
SEI: Classical Mechanics/Math Methods I Course Materials 
  
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S. Pollock, S. Chasteen, R. Pepper, A. Marino, and M. Caballero - Online Resource
This web site provides research-based materials for a sophomore-level course in classical mechanics and mathematical methods. This material focuses on the mathematical foundation of…
https://www.physport.org/curricula/CUBoulder/classical
Student difficulties with complex numbers 
  
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E. Smith, J. Zwolak, and C. Manogue, PERC 2015 Proceedings, 311-314.
Complex numbers and functions are used in multiple subfields in undergraduate physics. We use pretests, quizzes, and exams administered throughout the junior year to identify…
https://www.per-central.org/document/ServeFile.cfm?ID=13897&DocID=4315