## PERC 2017 Abstract Detail Page

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Abstract Title: | Vectors and unit vectors in non-cartesian coordinate systems |
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Abstract: | This session will present several studies examining student understanding of vectors and unit vectors in non-Cartesian coordinate systems. Throughout upper-division physics, students are required to reason in coordinate systems including plane polar, cylindrical, and spherical. Most students learn the fundamentals of vector notation in the context of Cartesian coordinates and have little specific instruction on how these ideas are generalized to other systems. Research has shown that generalizing from Cartesian coordinates is not simple for many students. Talks in this session will highlight aspects of the research, including studies to investigate student thinking and tasks designed to improve student understanding. |

Abstract Type: | Talk Symposium |

## Author/Organizer Information | |

Primary Contact: |
Michael Loverude California State University Fullerton |

## Symposium Specific Information | |

Moderator: | Michael Loverude |

Presentation 1 Title: | Helping Students Make Sense of non-Cartesian Unit Vectors in Upper Level E&M |

Presentation 1 Authors: | Brant E. Hinrichs Department of Physics Drury University |

Presentation 1 Abstract: | An upper level E&M course (i.e. based on Griffiths) involves the extensive integration of vector calculus concepts and notation with abstract physics concepts like field and potential. We hope that students take what they have learned in their math classes and apply it to help represent and make sense of the physics. In 2010 we showed that students at different levels (pre-E&M course, post-E&M course, 1st year graduate students) and in different disciplines (physics, electrical engineering) had great difficulty using non-Cartesian unit vectors appropriately in a particular context. Since then we have developed a set of four linked problems that students work on in groups and discuss as a class, to help them confront and resolve some of their difficulties. This talk presents those problems, typical student responses, and three years of post-tests (given on quizzes or exams) that were used to assess their effectiveness. |

Presentation 2 Title: | A tale of two differential length vector constructions in non-Cartesian multivariable systems |

Presentation 2 Authors: | Benjamin Schermerhorn, John Thompson Department of Physics University of Maine |

Presentation 2 Abstract: | Given the significance of vector calculus and non-Cartesian coordinate systems to physics understanding in junior-level Electricity and Magnetism (E&M), the course provides a rich context to explore student understanding and determination of multivariable differential vector elements. Two interview tasks were administered in which students construct differential length elements for a given scenario. In the first task, student pairs reasoned about an unconventional spherical coordinate system. While no pair initially constructed the correct length element, they paid particular attention to the need for multiple components to represent the multiple directions of possible motion. The second task, more aligned with typical E&M problems, asked individual students to determine a differential length vector to calculate the electric potential difference over a spiral path. In contrast to the previous task, students were more likely to acknowledge only the theta component of the differential length vector, ignoring the change in the r-hat direction. |

Presentation 3 Title: | Investigating and addressing student ideas about coordinate systems in the upper division |

Presentation 3 Authors: | Brian Farlow, Warren Christensen Department of Physics North Dakota State University |

Presentation 3 Abstract: | Initial investigations have identified ideas upper-division undergraduate physics students bring to bear while attempting to solve non-Cartesian coordinate system problems. We identify specific resources for unit vectors, resources connecting polar vector elements to Cartesian vector elements, and the orthogonality of basis vectors in various coordinate systems. While not all of these resources are used productively by students, they constitute a set of ideas that can be explicitly addressed through instructional materials. We report on these findings as well as early development of instructional materials intended to promote productive student thinking about non-Cartesian unit and position vectors specifically among junior/senior-level undergraduate students. |

Presentation 4 Title: | Student resources in polar coordinates |

Presentation 4 Authors: | Marlene Vega, Michael Loverude Department of Physics California State University Fullerton |

Presentation 4 Abstract: | In upper-division physics courses students work with various coordinate systems, but research has shown that students are less comfortable with non-Cartesian systems. This study began with a difficulties framework, in which we sought to document difficulties with non-Cartesian coordinates. However, we found that a resources framework allowed us to see more than just the difficulties students have. It allowed us to identify the different pieces of knowledge that the students assemble when answering these physics questions. This study aims to identify different resources students activate when answering questions in various contexts regarding unit vectors in polar coordinates. We will present data from written responses and interviews of students in upper division physics courses at two universities. |