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theses

The purpose of this study was to examine how upper level students in astrophysics connect mathematical equations to concepts. Only a few studies in physics education research (PER) have investigated connections between student understanding of physics equations with physics concepts and none of those were in the field of astrophysics. As in many upper level physics classrooms, problem solving is a main part of astrophysics education. In upper level astrophysics classrooms, learning physics is about learning the ways physics describes, explains and predicts behavior of celestial objects by building mathematical models. This study evolved from a desire to improve student's conceptual understanding in an upper level physics course, which is highly mathematical in nature. The broad scope of this research is to understand how the students connect astrophysics equations to astrophysics concepts. This study presents a systematic examination on how students who were enrolled in an upper level astrophysics class at Rutgers University understand astrophysics equations using the framework proposed by Domert et al. (2012) as well as how they frame their mathematical use of equations based on examining the symbolic forms of their mathematical arguments (the framework of Sherin, 2001). A symbolic form, according to Sherin, is composed of two components: a conceptual schema - the idea to be expressed in the equation - and a symbol template - how the idea is written in symbols (Sherin, 2001). The majority of participants in this study were selected from the first of a two-semester sequence called Principles of Astrophysics (additional participants are experts in the field of astrophysics). The data for this dissertation include multiple homework assignments, two exams, a final essay, and video recordings of interviews of astrophysics students as well as experts working on solving problems involving gravitational potential energy and the virial theorem. Through the systematic examination of the collected data I was able to determine how students connect mathematical equations to concepts within the framework of Domert et al. (understanding of physics equations) and Sherin (symbolic forms). I found that most upper level undergraduate students in astrophysics have the potential to make meaningful connections between concepts and equations but need more purposeful instruction in order to make these connections.

ETD_8706

Ed.D.

Includes bibliographical references

by Heather Anne Rave

doi:10.7282/T36T0R27

ETD doctoral

The author owns the copyright to this work.