## PERC 2019 Abstract Detail Page

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Abstract Title: | Representing student reasoning about math in physics |
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Abstract: | Much of the teaching and learning of physics involves incorporating mathematical reasoning and principles. This extends beyond the use of math as a computational tool to how it contributes to interpreting physical systems and shapes our thinking in physics. Over the past decade, physics education researchers have made strides towards understanding this connection with the development of several frameworks to help analyze student responses to questions that involve mathematics. In this session we invite a group of researchers to advance our understanding of the interactions between math and physics in our curriculum and how students' nuanced understanding of mathematics affects their ability to do physics. This session will have a focus on the frameworks used in research to represent students' use and understanding of math in physics. The session will bring together researchers from the Research in Mathematics Education (RUME) community with researchers in PER to share their findings on the interface of math and physics. The session will conclude with extended time for a broader discussion and questions of all speakers. |

Abstract Type: | Talk Symposium |

Session Time: | Parallel Sessions Cluster I |

Room: | Cascade D |

## Author/Organizer Information | |

Primary Contact: |
Gina Passante CSU Fullerton |

Co-Author(s) and Co-Presenter(s) |
Co-moderators: Homeyra Sadaghiani and Steven Pollock Presenters: Steven Jones, Suzanne White, Benjamin Schermerhorn, and Kevin Watson |

## Symposium Specific Information | |

Presentation 1 Title: | Adapting the structural features framework to address computation: Exploring student preferences when calculating expectation value |

Presentation 1 Authors: | Benjamin Schermerhorn |

Presentation 1 Abstract: | A common activity in undergraduate quantum mechanics (QM) involves calculating expectation values. Analysis of written exam data given at three universities (teaching spins-first QM) showed students had a tendency to use matrix or integral calculation in situations where it is much simpler to use the summation method. To investigate students' use of and preferences for the various methods, interviews were conducted at two universities in the middle and end of the semester. Adapting Gire and Price's framework for categorizing structural features of different quantum mechanical notation, we analyze student responses to expectation value problems to highlight specific areas of difficulty and features of the methods which led to students' choices of one method over another. |

Presentation 2 Title: | How most calculus concepts seem to be grounded in meanings in math classes that do not align well with how those same concepts are used in science |

Presentation 2 Authors: | Steven Jones |

Presentation 2 Abstract: | Beginning in the mid 1900's, the academic departments of mathematics and natural sciences have been drifting apart, leading to the following problem. Because many mathematical concepts can have multiple meanings associated with them, it is possible for certain meanings to be developed and focused on within mathematics classes in a way that does not align well with how those same concepts are used or reasoned about in science. This appears to be true for several calculus concepts, including the derivative, the integral, and Taylor series, among others. I use pieces of frameworks on "centers of focus," "ways of thinking," and "concept projection" to briefly illustrate (a) the conceptual grounding given to these concepts within typical calculus classes, (b) the resulting types of meanings many students may develop for these concepts in their calculus classes, and (c) why that can lead to difficulty for students in using these concepts in science coursework. The hope is that by knowing what kinds of meanings their students have developed within their calculus classes, science instructors would be in a better position to work with students' current understanding -- and to develop that understanding -- in ways that can better help those student in using calculus concepts in science classes. |

Presentation 3 Title: | Assessing the math+physics conceptual blend: A new mathematical reasoning inventory for introductory physics |

Presentation 3 Authors: | Suzanne White Brahmia |

Presentation 3 Abstract: | Mathematical reasoning flexibility across physics contexts is a desirable learning outcome of introductory physics, where the "math world" and "physical world" meet. Physics Quantitative Literacy (PQL) is a set of interconnected skills and habits of mind that support quantitative reasoning about the physical world. We present the PIQL, Physics Inventory of Quantitative Literacy, which is currently under development in a multi-institution collaboration. PIQL assesses students' proportional reasoning, co-variational reasoning, and reasoning with signed quantities in physics contexts. Unlike concept inventories, which assess conceptual mastery of specific physics ideas, PIQL is a reasoning inventory that can provide snapshots of student ideas that are continuously developing. Item distractors are constructed based on the different established natures of the mathematical objects in physics contexts (e.g. the negative sign as a descriptor of charge type and the negative sign as indicator of opposition in Hooke's law). An analysis of student responses on PIQL will allow for assessment of hierarchical reasoning patterns, and thereby potentially map the emergence of mathematical reasoning flexibility throughout the introductory sequence. (NSF DUE-IUSE # 1832836) |

Presentation 4 Title: | Student Meanings for Eigenequations in Mathematics and in Quantum Mechanics |

Presentation 4 Authors: | Megan Wawro |

Presentation 4 Abstract: | Students encounter advanced mathematical concepts in both mathematics classes and physics classes. What meanings do they develop about the concepts across the various contexts? Our research project investigates students' meanings for eigentheory in quantum mechanics and how their language for eigentheory compares and contrasts across mathematics and quantum physics contexts. We present results regarding students' interpretations of a canonical mathematical 2x2 eigenequation, a spin-½ operator eigenequation, and a spin-½ operator equation in which the operation "flips" the spin state. The data consist of video, transcript, and written work from individual, semistructured interviews with 9 students from a quantum mechanics course. Students were asked to explain what the first two equations meant to them and then to compare and contrast how they conceptualize eigentheory in the two contexts. They were then asked to discuss the third equation. Using discourse analysis and symbolic form analysis, results characterize students' nuanced imagery for the various equations and highlight instances of both synergistic and potentially incompatible interpretations. |