Student Difficulties Regarding Symbolic and Graphical Representations of Vector Fields

The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person's understanding of mathematical and physical concepts. This paper describes a study of studen...

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Bibliographic Details
Published in:Physical review. Physics education research 2017-08, Vol.13 (2), p.020109, Article 020109
Main Authors: Bollen, Laurens, van Kampen, Paul, Baily, Charles, Kelly, Mossy, De Cock, Mieke
Format: Article
Language:English
Subjects:
Cognitive Ability
College Mathematics
Colleges & universities
Computer Graphics
Coordinates
Educational Practices
Engineering education
Fields (mathematics)
Foreign Countries
Graphical representations
Instructional Innovation
Knowledge Representation
Learning Problems
Learning Strategies
Mathematical analysis
Physics
Problem Solving
Qualitative Research
Semi Structured Interviews
Student Surveys
Students
Switching
Symbols (Mathematics)
Teaching Methods
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Summary:The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person's understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing, and switching between representations of vector fields, using both qualitative and quantitative methods. We first identified to what extent students are fluent with the use of field vector plots, field line diagrams, and symbolic expressions of vector fields by conducting individual student interviews and analyzing in-class student activities. Based on those findings, we designed the Vector Field Representations test, a free response assessment tool that has been given to 196 second- and third-year physics, mathematics, and engineering students from four different universities. From the obtained results we gained a comprehensive overview of typical errors that students make when switching between vector field representations. In addition, the study allowed us to determine the relative prevalence of the observed difficulties. Although the results varied greatly between institutions, a general trend revealed that many students struggle with vector addition, fail to recognize the field line density as an indication of the magnitude of the field, confuse characteristics of field lines and equipotential lines, and do not choose the appropriate coordinate system when writing out mathematical expressions of vector fields.
ISSN:2469-9896
2469-9896
DOI:10.1103/PhysRevPhysEducRes.13.020109