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Matrix algebra and eigentheory are important to students&#39; learning of physics in upper division physics courses. In this study, we investigated how students apply matrix algebra and eigentheory in various physics contexts, excluding quantum mechanics. The data collected consist of student written responses taken from a math methods course. We used the Physical-Mathematical Model (Uhden et al, 2011) to categorize each question by the three skills the model presents: mathematization, interpretation, and technical operation. The results from our data show that students have difficulty with mathematizing and interpreting the mathematical and physical system of a matrix equation, but are fluent in technical operations. We will present examples of student responses illustrating student reasoning, and discuss implications for classroom instruction.

PERC SM 20

Examining student understanding of matrix algebra and eigentheory

eigentheory

matrix algebra

skills

linear algebra

math

application

physics

The 2020 AAPT Virtual Summer Meeting brought together physics educators from around the globe to learn about the latest in physics theory, research methodology and education from leaders in their field. The program featured plenary speakers, sessions, workshops and many special activities.

For more information please visit the 2020 AAPT Virtual Summer Meeting page at: https://www.aapt.org/Conferences/SM2020/index.cfm.


AAPT SM 20

The 2020 AAPT Virtual Summer Meeting brought together physics educators from around the globe to learn about the latest in physics theory, research methodology and education from leaders in their field. 

Matrix algebra and eigentheory are important to students' learning of physics in upper division physics courses. In this study, we investigated how students apply matrix algebra and eigentheory in various physics contexts, excluding quantum mechanics. The data collected consist of student written responses taken from a math methods course. We used the Physical-Mathematical Model (Uhden et al, 2011) to categorize each question by the three skills the model presents: mathematization, interpretation, and technical operation. The results from our data show that students have difficulty with mathematizing and interpreting the mathematical and physical system of a matrix equation, but are fluent in technical operations. We will present examples of student responses illustrating student reasoning, and discuss implications for classroom instruction.

poster

Join us in exploring emergent themes in PER as a scholarly endeavor and as a research community!  Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?
Following the lead of AAPT for the summer meeting, PERC 20/20 was virtual. Enjoy browsing the content.

Since its inception, PER has served as a confluence of discipline, theory, research methodology, practice, and application.  How have these facets and the interplays among them been fruitful for physics education globally, regionally, locally, or otherwise?  And, how have our successes and interactions influenced the very nature of PER itself?

We are interviewing students in a second semester introductory physics course as well as graduate physics students about the generation of electromagnetic waves. We have interviewed 43 intro level students and 20 graduate students. We found that only 10 of 43 intro students could identify accelerating charges as a source for electromagnetic radiation. 15 of these students came from a course that used the Matter and Interactions text and 7 were able to identify accelerating charges as a source of EM waves. Fully half of the grad students could not answer correctly. If you restrict to graduate students that do not work with radiation as part of their research, 7 of 8 graduate students could not answer correctly. We are continuing to search for specific difficulties as well as reasons why students do not seem to grasp this core concept. Additional details of methodology and findings will be presented.

What do Students Know about Electromagnetic Wave Generation? (PERC)

Most students find difficulty in visualizing 3D concepts in physics courses. Some of these include electric and magnetic fields, the divergence theorem, RC circuits, electric flux, Gausss law, electromagnetic induction, and three-dimensional integration. A solution to this issue is to present these concepts in augmented reality to allow for better visualization of them. The augmented reality activities presented in this paper were created by a team of undergraduate physics and computer science students using the software Unity and the Merge Cube. We present a systematic process of creating and improving specialized apps that can be utilized in a classroom environment.

Developing Augmented Reality Modules to Teach Electromagnetism (PERC)

Group work during lab instruction can be a source of inequity between male and female students. In this preliminary study, we explored the activities male and female students take on during a lab session at a university in Denmark. Different from many studies, the class was majority-female, so three of the seven groups were all female and the rest were mixed-gender. We found that students in mixed-gender groups divide tasks in similar ways to mixed-gender groups at North American institutions, with men handling the equipment and women handling the computer more often. We also found that women in single-gender groups took on each of the available roles with approximately equal frequency. We interpret the results through poststructual gender theory and the notion of 'doing physics' and 'doing gender' in physics labs.

Preliminary evidence for available roles in mixed-gender and all-women lab groups

It has been well documented that introductory physics students struggle with vector addition and subtraction. We use the results of a multiple-choice assessment on one-dimensional vector addition and subtraction, administered to students in a large-enrollment algebra-based physics sequence, to explore the consistency in the types of errors students make. The assessment was analyzed using Module Analysis for Multiple Choice Responses, a type of network analysis that highlights groups of responses commonly given together. We find evidence for five distinct modules that are consistent across multiple semesters. Of these groups, two support the method of "closing-the-loop", two are consistent with students performing the wrong operation, and one suggests that students provide an answer independently of whether they were prompted to add or subtract two vectors, though only for vectors that are anti-aligned.

Examining consistency of student errors in vector operations using module analysis

Proficiency in units/dimensional analysis is a useful skill in the sciences and engineering, and STEM instructors often presume competence from their students in this area. However, unit analysis techniques and unit systems are not always formally taught, and even with explicit emphasis during instruction, many students lack the repeated exposure necessary to master them. To assess student understanding of units and unit systems, we administered a brief, itemized survey to N=53 calculus-based introductory university physics students. The survey was intended to uncover possible misconceptions and identify previously unknown obstacles to student success within this topic. Our results suggest that as many as half of surveyed participants may not recognize the adaptability of symbolic physical equations to different unit systems. Furthermore, a similar proportion failed to eliminate non-viable answer choices involving analytic functions with units inside their arguments. Consequently, we believe units/dimensional analysis is a topic ripe for further investigation.

Excerpts from an exploratory survey of units/dimensional analysis in introductory physics

As a first step in a larger study of student difficulties in upper-division thermal physics, we conducted think-aloud interviews with 8 physics graduate students to probe their understanding of entropy. In this paper, we'll discuss results from a question which presented students with a novel system---a string in a bath of water---and asked students to rank the probabilities of particular arrangements of the string, define macrostates of the system, and discuss specifically what is meant by the entropy of the system. Exploring graduate students' understanding of entropy and their ability to solve problems and reason with entropic arguments will provide insights into how physicists develop a mature understanding of entropy as a physical quantity. We find a tendency for graduate students to project properties of macrostates onto constituent microstates and other similar difficulties. We discuss connections to other research in this field and identify observations warranting further study.

Investigating how graduate students connect microstates and macrostates with entropy (PERC)

Recent undergraduate laboratory recommendations emphasize the importance of helping students develop their scientific documentations skills throughout the curriculum. Learning proper lab notebook practices is important for students in preparation for graduate school and the STEM workforce. Laboratory notebooks can also be a valuable tool for instructors to assess a student's understanding of lab activities and the underlying physics principles. This study analyzes students' development of standard notebook practices during introductory physics lab courses. This research was conducted through a series of pre- and post-surveys given in introductory physics lab classes. The surveys cover topics of how students use lab notebooks, how they learned notebook practices, and their attitudes toward beliefs about using lab notebooks. This paper uses a mixed methods approach to examine student growth in specific laboratory notebook practices and reviews the instructional methods and feedback that were most effective for first semester physics students.

Evaluating and Improving Laboratory Notebook Practices

Group work provides valuable opportunities for students to actively participate in classroom conversations. Instructors often emphasize generating and sharing ideas in group work, but how these ideas are shared in small-group discussions can be complicated by social dynamics within that group. In this project, we applied techniques from Systemic Functional Linguistics (SFL) to analyze the interpersonal meanings in students discourse in a college physics lab section. By examining how students socially positioned themselves in the episode, we found that students steered the groups conversation not only by explicitly offering ideas, but also by positioning as not-knowing, raising questions, and appealing to authority. This episode provides another example to a growing body of research describing the consequential role of social dynamics in how physics students contribute to small-group discussions.

Examining the Social Dynamics of Small-Group Discussions (PERC)

[course name] is a flipped, problem-based learning course for introductory, calculus-based mechanics. [course name] was designed using the communities of practice framework, with a principle learning goal to develop scientific practices. To promote students' development of practices, students spend their in-class time working in groups of 4 to 5 members to solve complex physics problems. Scientific practice development is then facilitated through formative feedback and assessments aligned with the growth in these practice. Each student receives weekly, individualized feedback from their instructor (either a faculty member, teaching assistant or learning assistant) as a practice-based assessment. The feedback focuses on helping students improve their individual understanding and group collaboration through the development of key group-based practices such as decision making and planning. This paper reports on a series of semi-structured interviews that were conducted with students at various points in the semester to understand the impact feedback had on them.

Student perspective about the impacts of feedback

Although we have found that students in our Introductory Physics for Life Science (IPLS) course describe physics as more relevant to their primary interests than do their counterparts in a traditional introductory physics environment, we do not yet know whether IPLS courses better prepare life science students to use physical reasoning in contexts that extend beyond those explicitly encountered in IPLS. To answer this question of whether IPLS better prepared our students for future learning, we designed and administered a task related to fluid dynamics at the conclusion of both traditional and IPLS introductory physics courses. We describe the construction of the task and the ways in which IPLS students approached the task differently than did students in the traditional course. We interpret the results in light of the goal of the IPLS course, supporting transfer within the preparation for future learning paradigm around which our course is designed.

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Examining student understanding of matrix algebra and eigentheory

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