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We have administered diagnostic tests covering pre-college mathematics to over 6700 introductory physics students at four state universities, with largely consistent results. Key findings include: (1) Use of symbols to replace numbers in otherwise identical algebraic equations significantly lowered correct-response rates, implying that instructors may want to be more cautious when employing symbolic manipulations; (2) Few physics students solved algebraic equations by “isolating the unknown variable,” implying that instructors’ standard and habitual approach to algebraic manipulation may appear confusing, and should be modified or better scaffolded; (3) Class-average scores on even a single diagnostic test item were highly predictive of average scores on other items covering varied topics, suggesting it may be possible to diagnose the level of students’ difficulties with very few pretest items; (4) During interviews, students tended to self-correct approximately 60% of their initial errors, suggesting that instruction on self-checking strategies may offer disproportionately high returns.

AAPT SM 21

Instructional implications of findings on students’ mathematics difficulties

problem-solving

mathematics

introductory

physics

reasoning

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In this talk, we qualitatively analyze physics majors’ identity development as they transfer from a community college to a four-year university. Students in the study attend a large, public four-year university in which a significant fraction of undergraduate physics majors are transfer students. Research participants had previously enrolled in a required 1-credit introduction to the physics major course designed to cultivate community and identity, as well as foster a broad set of physics-related skills. In one-on-one interviews, students discussed their academic and personal experiences before, during, and after their transition from community college to a four-year university. In this talk, we will discuss how their academic and personal experiences as well as their interactions with physics community members shaped their identity development as physics students. We then consider implications for building institutional supports for physics transfer students.

Research on Identity Development Among Physics Transfer Students

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Unpacking tensions in a pedagogical transition from lectures to modelling

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Impact of mathematical rigor on students’ understanding of quantum optics

The Conceptual Survey of Electricity and Magnetism (CSEM) is a multiple-choice survey that contains a variety of electricity and magnetism concepts at the level of introductory physics used to help inform instructors of student mastery of those concepts. Prior studies suggest that many concepts on the survey are challenging for introductory physics students and the average student scores after traditional instruction are low. The research presented here compares the performance of students in introductory, upper-level, and graduate-level physics courses on five CSEM questions to understand the cross-sectional evolution of student understanding of these concepts from the introductory to upper-level to graduate-level. We discuss five CSEM questions that remain challenging for many upper-level and graduate students.

Evolution in student conceptual understanding of electricity and magnetism

The solving of physics problems is often an important component of introductory physics courses. For many students, approaching a physics problem, organizing their thoughts, and reaching a solution is a novel skill which needs to be taught and mastered. Rubrics can be powerful tools to guide student development of new skills. Here we will discuss the development of problem solving rubric we have implemented in our large enrollment introductory physics course. We will discuss the particular challenges and advantages of using these rubrics in an online course. Finally, we will then discuss the extent to which these rubrics were successful in changing student behavior over the course of two semesters of instruction.

Rubrics to Teach Problem-Solving Strategies in Large Enrollment Online Courses

Selection and application of an appropriate equation is a key step in instructional problem-solving strategies. But what if one cannot exactly recall the relevant equation? We are currently investigating how coherence between physical and mathematical reasoning opens multiple solution pathways for qualitative physics problems. In one-on-one interviews, community college students, 4-year college undergraduates, and graduate students solved qualitative introductory-level E&M questions. Analysis of 18 interviews showed that while many students had initial difficulty in recalling a relevant equation, they demonstrated strategies for making progress. We present two cases from the data corpus. One interviewee was unsure whether the time constant for an RC circuit is RC or 1/(RC) and sought coherence with qualitative reasoning to determine the correct expression. Another student switched to reasoning qualitatively from a physical model after noting that they could not recall a relevant equation. These examples show how mathematical and physical reasoning is opportunistically incorporated in students’ problem solving.

Seeking coherence and switching reasoning after forgetting an equation

The entanglement between physical and mathematical reasoning can be exploited for problem solving, making physical/mathematical coherence seeking a desirable learning goal. We endeavor to enrich the empirical knowledge of students’ coherent physical/mathematical reasoning through a video analysis of problem solving. Drawing from a corpus of 18 interviews with students solving qualitative E&M problems, we discuss a case study of a student who undertakes multiple contradicting lines of reasoning and ultimately reconciles them. We discuss the types of coherent reasoning that they recruit and the central role of physical/mathematical coherence seeking in their problem solving and learning.

Resolving Inconsistencies in E&M by Seeking Coherence Between Physical/Mathematical Reasoning

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Student difficulties identifying diagonal operators for degenerate perturbation theory

In this study, we surveyed students from a calculus-based and an algebra-based introductory physics courses at a liberal arts college about their ability to draw conclusions from measurement data. Both courses are taught in studio mode and use the Workshop Physics curriculum. The survey was administered online before and after instruction on measurement uncertainty. In the survey, students considered two experiments that differ only by one setup. Students were first asked to make predictions about the experimental outcomes as to whether or not the outcomes agree with each other, and then were given data to analyze and draw conclusions. We evaluate the extent to which instruction impacts student ability to draw conclusions as well as reasoning about measurement uncertainty. We use the framework of point and set paradigms to characterize student reasoning. The set paradigm emphasizes a measurement distribution rather than a single measurement; it is considered more expert-like.

Evaluating student ability to draw conclusions from measurement data

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Instructional implications of findings on students’ mathematics difficulties

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Research on Identity Development Among Physics Transfer Students

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