United States

Problem solving is an important aspect of physics education. To become skilled problem solvers students do not only need sufficient conceptual and procedural knowledge, they also need metacognitive skills in order to monitor their solution process. We present a prototype for an online tool that aims at stimulating students’ metacognitive skills for problem solving by offering them problem-specific reflection questions. We discuss a case study of the implementation of the tool within a 1st year mechanics course.

AAPT SM 21

Supporting Metacognition in Physics Problem Solving.

metacognition

reflection

problem solving

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technical paper

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

We discuss an investigation of student difficulties with the representation in which a Hermitian operator corresponding to a physical observable (e.g., the Hamiltonian operator corresponding to energy) is diagonal in the context of degenerate perturbation theory involving the Zeeman effect in the hydrogen atom. This investigation was carried out in advanced quantum mechanics courses by administering written free-response and multiple-choice questions and conducting individual interviews with students. We discuss the common student difficulties related to these concepts, knowledge of which can be useful for developing research-validated learning tools.

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

In study of synthesis problem solving, we distinguished two types of synthesis tasks: sequential and simultaneous. To capture their distinctive characteristics and differing impacts on problem solvers’ sensemaking behaviors, we investigated students’ gaze transitions between problem text and diagram as well as between different components within a diagram. Our work is underpinned by the cognitive theory of multi-media learning; that is, greater gaze transitions indicate greater mental efforts in information integration. We found that when multiple events were integrated sequentially, students made great cognitive efforts to connect information within a diagram. When events occurred simultaneously, students’ mental efforts focused mainly on linking text and diagram. Regardless, in both cases students sought to connect information for comprehending the problem situation, which is a core of effective problem solving and deep learning. We maintain that synthesis tasks can support student development of expert-like habits of mind.

Pedagogical implications of synthesis problem solving

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.

Instructional implications of findings on students’ mathematics difficulties

Physics education is facing challenges in terms of ensuring student engagement with physics. This can be due to the techno-centric approach in physics education when little or no attention is devoted to exploring the relationship between physics concepts and human needs. To change this may require that in addition to examining questions of “what” and “how” required for developing skills in abstract problem-solving, we may also need to leverage a techno-centric approach to teaching physics curriculum to enhance student engagement with physics by helping them to understand the “why” that inspires STEM undergraduates to learn physics. The essence of the socio-technical approach to physics education is based on contextualizing physics in real-world applications that reveals impact of physics on human and humanity. We will discuss the results the connection between Physics Innovation and Entrepreneurship computational and laboratory skillset that can offer an enhanced model for teaching physics.

Fostering synergy among mindset and skillset

Physics for Tomorrow talk 3 of 3. Lab courses can meet the ideals of a “Physics for Tomorrow” curriculum by integrating theory, computation, and experimentation in ways that emphasize social impact and career-relevant applications. COVID-19 served as the catalyst for a significant overhaul of the 2nd-year electronics lab at Rochester Institute of Technology, which is taken by about 45 physics majors. The course now uses low-cost lab kits (130 USD), which increase the hands-on lab experience for every student, whether they are in-person or remote. Circuit simulations in LTspice (free) provide experience with commercial circuit simulators, while Jupyter notebooks are used as electronic lab notebooks and to incorporate scientific Python. An optical heart rate monitor is the focus of a culminating 2-week lab showing human-centered interdisciplinary applications of physics and electronics. Finally, multi-week final projects are proposed and executed by students to reinforce that physics is a creative and applied discipline.

Integrating computation, experimentation, projects, and human-centered applications in lab courses

In order to prepare students as future professionals, reforming science, technology, engineering, and mathematics (STEM) education has been demanded by education committees and government bodies alike. To become successful and effective scientists, medical professionals, or engineers, students must be skilled in science application, peer collaboration, science-based critical thinking, and effective communication. As misinformation spreads quickly and resistance to scientific knowledge thrives, the future of science depends on preparing students to overcome this opposition. In order to foster these skills, we used the Deliberative Democracy (DD) active-learning model. Each module focuses on a socially relevant and sometimes controversial scientific problem (e.g. climate change), tasking students to collaborate with their peers to identify the scientific issues, building physics models, researching & deliberating solutions through policies and regulations, and effectively communicating these in a written report. We will walk through the development process and share early results from this project in this talk.

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Supporting Metacognition in Physics Problem Solving.

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

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