Calculus-based Physics Course Research Articles

Utilizing network analysis to explore student qualitative inferential reasoning chains

Over the course of the introductory calculus-based physics course, students are often expected to build conceptual understanding and develop and refine skills in problem solving and qualitative inferential reasoning. Many of the research-based materials developed over the past 30 years by the physics education research community use sequences of scaffolded questions to step students through a qualitative inferential reasoning chain. It is often tacitly assumed that, in addition to building conceptual understanding, such materials improve qualitative reasoning skills. However, clear documentation of the impact of such materials on qualitative reasoning skills is critical. New methodologies are needed to better study reasoning processes and to disentangle, to the extent possible, processes related to physics content from processes general to all human reasoning. As a result, we have employed network analysis methodologies to examine student responses to reasoning-related tasks in order to gain deeper insight into the nature of student reasoning in physics. In this paper, we show that network analysis metrics are both interpretable and valuable when applied to student reasoning data generated from . We also demonstrate that documentation of improvements in the articulation of specific lines of reasoning can be obtained from a network analysis of responses to reasoning chain construction tasks. Published by the American Physical Society 2024

Electrostatic potential of a uniformly charged annulus

The calculation of the electrostatic potential and/or electrostatic field due to a continuous distribution of charge is a well-covered topic in all calculus-based undergraduate physics courses. The most common approach is to consider bodies with uniform charge distribution and obtain the quantity of interest by integrating over the contributions from all the differential charges. The examples of a uniformly charged disk and ring are prominent in many physics textbooks since they illustrate well this technique at least for special points or directions of symmetry where the calculations are relatively simple. Surprisingly, the case of a uniformly charged annulus, namely, an annular disk, is largely absent from the literature. One might speculate that a uniformly charged annulus is not extremely interesting since after all, it is a uniformly charged disk with a central circular hole. However, we show in this work that the electrostatic potential created by a uniformly charged annulus has features that are much more interesting than one might have expected. A uniformly charged annulus interpolates between a uniformly charged disk and ring. However, the results of this work suggest that a uniformly charged annulus has such electrostatic features that may be essentially viewed as ring-like. The ring-like characteristics of the electrostatic potential of a uniformly charged annulus are evident as soon as a hole is present no matter how small the hole might be. The solution of this problem allows us to draw attention to the pedagogical aspects of this overlooked, but very interesting case study in electrostatics. In our opinion, the problem of a uniformly charged annulus and its electrostatic properties deserves to be treated at more depth in all calculus-based undergraduate physics courses covering electricity and magnetism.

Could an artificial-intelligence agent pass an introductory physics course?

Massive pre-trained language models have garnered attention and controversy due to their ability to generate human-like responses: attention due to their frequent indistinguishability from human-generated phraseology and narratives, and controversy due to the fact that their convincingly presented arguments and facts are frequently simply false. Just how human-like are these responses when it comes to dialogues about physics, in particular about the standard content of introductory physics courses? This study explores that question by having ChatGTP, the pre-eminent language model in 2023, work through representative assessment content of an actual calculus-based physics course and grading the responses in the same way human responses would be graded. As it turns out, ChatGPT would narrowly pass this course while exhibiting many of the preconceptions and errors of a beginning learner.

Evolution of grades and social comparison concern within an introductory physics course

This study investigates the evolution and associations between exam grades and social comparison concern (SCC) among students in an introductory calculus-based physics course. We begin with a descriptive characterization of midterm and final exam scores as well as pre-post SCC scores, including the concurrent evolution of these scores during the course. We hypothesize a feedback loop in which changes in SCC scores are mediated by exam grades, and changes in exam scores are mediated by SCC scores. We employ a structural equation model to determine whether the data are consistent with these hypotheses. Results indicate that there were significant within-student changes in the relative grade standing from exam to exam and that changes in SCC scores depended on both the pre-SCC scores and scores on the first midterm exam. Further, we find evidence that exam scores partially mediate the association between pre- and post-SCC scores, and in turn, post-SCC scores partially mediate associations between midterm and final exam scores, though the mediation effects are somewhat small, comprising 5%–10% of the total effects between exam scores and SCC. We also find that while SCC scores are somewhat correlated with exam scores, they are only very weakly correlated with nonexam grade components, consistent with the idea that exam scores (rather than nonexam scores) are driving changes in SCC and vice versa. Overall, the results provide empirical, correlational evidence to motivate further experimental investigation into a hypothesized dynamic and iterative feedback loop in which student concern about ability or performance compared to others (SCC) can either negatively or positively interfere with student performance on exams.1 MoreReceived 5 January 2023Accepted 28 March 2023DOI:https://doi.org/10.1103/PhysRevPhysEducRes.19.010129Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDiversity & inclusionLearning environmentPhysics Education Research

Equitable approach to introductory calculus-based physics courses focused on problem solving

Introductory calculus-based mechanics (“Physics 1”) is an important gateway course for students desiring to pursue a science, technology, engineering, and mathematics (STEM) career. A major challenge with this course is the large spread in the students’ incoming physics preparation. This level of preparation is strongly predictive of a students’ performance because of the overlap between Physics 1 and high school physics courses. Because the level of students’ incoming preparation is largely determined by the quality of their high school physics courses, Physics 1 can amplify K–12 educational inequities and be a barrier for marginalized students wishing to pursue a STEM career. Here, we present a novel introductory course design to address this equity challenge. The design and implementation are based on the concept of deliberate practice as applied to learning real-world problem solving. Students explicitly practice research-identified decision-based skills required for problem solving in the context of solving real-world problems. The problems used in the course and their solutions have little resemblance to what students encounter in high school physics, thereby reducing the dependence of course performance on the high school physics preparation. Versions of this course were taught at a highly selective private and a lightly selective public university. The students who took the course learned the physics content knowledge they needed for future courses, particularly in engineering, and their problem-solving skills improved substantially. Furthermore, their course performance had much less correlation with their incoming physics preparation than was the case for the outcomes from the traditional Physics 1 courses at both institutions: in one case the correlation dropped from r=0.62 to 0.14, and on the other case the correlation dropped from r=0.56 to 0.26. These findings suggest this course design can be a more equitable version of the traditional Physics 1 course, and hence particularly beneficial for marginalized students.Received 8 August 2022Accepted 23 September 2022DOI:https://doi.org/10.1103/PhysRevPhysEducRes.18.020124Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDiversity & inclusionInstructional strategiesStudent preparationPhysics Education Research

Calculation of the Coulomb Self-Energy of a Spherical Surface with Uniform Surface Charge Density Using the Fourier Transform Method

Undergraduate students in upper levels of physics or engineering programs learn the theory of Fourier series and integral transform method from mathematics courses. Nevertheless, they rarely see the application of such a method to solving problems in calculus-based physics courses that deal with topics such as electrostatics or magnetism. In this work, we illustrate the utility of the Fourier transform method by considering and solving via such a technique a representative problem that arises in electrostatics. The chosen case study is that of a spherical surface with uniform surface charge density and the calculation of its electrostatic Coulomb self-energy. By solving this problem by using the Fourier transform technique we also draw attention to the pedagogical aspects of the treatment. In particular, we stress the point that the Fourier transform method should be treated at more depth in calculus-based physics courses for undergraduate students.

Comparison of student performance between virtual and in-person modalities of introductory calculus-based physics

Physics educators keep adding many skill developments to science and engineering students during their education as individuals and groups including critical thinking, conceptual understanding, problem-solving, mathematical implementation, computational implementation, etc. Here, we are discussing how to reach and analyse students’ outcomes within the context of introductory calculus-based physics courses by investigating two different teaching modalities. We found that there is no significant impact of teaching modality on student learning. By performing two different assessments: chapter-ending midterm assessments and unit-based (three to four chapters) midterm assessments, shows that students can perform much better with short-time assessments in contrast to the long-time assessments. Further, we study any possible effects on students’ final grades from students’ prior knowledge of calculus and conceptual physics. This investigation shows that although there is no correlation between student’s prior proficiency in calculus the class performance, however, there is a correlation of conceptual physics understanding towards class performance.

Comparing Science and Engineering Students Using the Force Concept Inventory in Introductory Physics Courses

This work is intended to analyze and compare the performance of two groups of students on the understanding of force and motion concepts using the Force Concept Inventory (FCI). The FCI test serves questions on basic Newtonian concepts where the answers inclyde the correct response and commonly misconceived alternatives. The FCI test was implemented twice as pre and post-tests for two introductory calculus-based physics courses offered at the Sultan Qaboos University (SQU) in Oman for students mainly from the Colleges of Sciences, Education and Agriculture and the students from the College of Enginerring in the Spring 2017 and Spring 2018 semesters. These courses cover the traditional first-year level kinematics and dynamics in translational and rotational motions based on the same syllabus and the same textbook. Hake's normalized gain, defined as the change in class averages divided by the maximum possible increase, was used to compare the students'performances. The normalized gains for both groups of students were in the low gain category. Female students in both courses performed better on the FCI in general, but the difference was only statistically significant in the course offered to Science students.

Stretching a Hanging Chain without Work

We study a variation of the hanging chain problem. If one end (or both) of a hanging chain moves with stretching the chain along a path such that an external force(s) supporting the chain does not do any work, what path does the movable end draw? Sketching the path (“the workless curve”) will help students to acquire a qualitative understanding of work. In its mathematical derivation, one has to solve transcendental equations under an approximation including the Lambert [Formula: see text] function. It is suitable for undergraduate students in calculus-based physics courses.

Framework for the natures of negativity in introductory physics

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Positive and negative quantities are ubiquitous in physics, and the sign carries important and varied meanings. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. The mathematics education research literature documents the cognitive challenge of conceptualizing negative numbers as mathematical objects--both for experts, historically, and for novices as they learn. We contribute to the small but growing body of research in physics contexts that examines student reasoning about signed quantities and reasoning about the use and interpretation of signs in mathematical models. In this paper we present a framework for categorizing various meanings and interpretations of the negative sign in physics contexts, inspired by established work in algebra contexts from the mathematics education research community. Such a framework can support innovation that can catalyze deeper mathematical conceptualizations of signed quantities in the introductory courses and beyond.

We need to rethink lower-division physics teaching

We need to rethink lower-division physics teaching

Evaluating a predictive model of student performance in introductory calculus-based physics

Various factors are known to correlate with performance in physics and other STEM courses. In this study, we report on students’ performance in an introductory calculus-based physics course at the university level and correlate their performance (as measured by final grade) with a variety of measures of academic and cognitive ability. These measures include mathematical and English language ability (as measured by the SAT), incoming GPA, and spatial and scientific reasoning ability (as measured by the Mental Rotation Test and Classroom Test of Scientific Reasoning). We also consider the effect on student performance of factors such as employment status, and science and mathematics self-efficacy (as measured by a survey). In this study, we report the prediction efficiency of the ability of two multivariate linear models to predict student success in the course.

Students’ mental models of wave–particle duality

In this study, we investigated students’ mental models of wave–particle duality. We interviewed six engineering and premedical students enrolled in a calculus-based physics course. We conducted a qualitative examination of student interviews and found that students displayed four different mental models: quantum model (QM), semi-quantum model (SQM), wave model (WM), and in-between model (IM). We also found that 2/3 of the students had difficulty discriminating between classical and quantum ideas and held mental models that were inconsistent and context-specific. This work provides a much-needed detailed exploration of students’ conceptions of quantum theory, which will help instructors understand conceptual barriers frequently encountered by introductory students.

Sports, Smartphones, and Simulation as an Engaging Method to Teach Projectile Motion Incorporating Air Resistance

Much data, both published and anecdotal, have shown that students grasp scientific concepts more easily when they are directly involved in the learning via lab experiments or other hands-on activities. Hands-on or experiential learning also appears to aid in students’ ability to retain scientific theory. One way to engage students in a first-year calculus-based classical physics course is with the use of smartphones to validate or illustrate a variety of concepts covered in the lectures. It is true that almost all incoming students own or have access to a smartphone. This paper presents a method for students to use a smartphone app to track the trajectory of a sports projectile fired in real time (i.e., a basketball, volleyball, shot put, etc.). This experimental result was compared to a theoretical prediction of the trajectory of the projectile using an incremental air resistance algorithm implemented in Microsoft Excel. The students were required to estimate all of the parameters within the drag force equation (i.e., the drag coefficient, density of air, etc.) that made up part of the theoretical prediction. Ultimately, the goal was for the students to compare their experimental result with their prediction and gain an appreciation for the factors affecting the agreement (or lack of) between the two results.

Teaching Biophysics in an Undergraduate Curriculum

Simply put, the field of biophysics is the intersection of biology and physics. In this field, the concepts and principles of physics are used to explain biological processes. Also, physical principles and tools are used to solve biological and medical problems. Additionally, biophysics involves the development of instrumentation and methodologies to study biomedical and environmental phenomena. It is known that many institutions in the United States and around the world, do not offer biophysics courses at the undergraduate level. This is due, in part, to the need for a good exposure and mastery of both introductory and upper level physics courses before application to biological systems. The computational and mathematical skills needed for such applications are developed in these physics classes. While most physics programs do not require students to take biology courses, most biology programs do not require students to take calculus-based physics courses. This weakens the preparation of both the physics students and the biology students towards careers in biophysics. In most institutions, physics for life sciences is taught from the algebra-based approach, denying students exposure to advanced mathematical skills needed in biophysics. We propose that students interested in biophysics should take calculus-based physics at the introductory level, and that physics students should have some exposure to biology courses. This will ensure adequate preparation of students for upper level and graduate level biophysics classes.

Networks identify productive forum discussions

Discussion forums provide a channel for students to engage with peers and course material outside of class, accessible even to commuter and non-traditional populations. As such, forums can build classroom community as well as aid learning, but students do not always take up these tools. We use network analysis to compare three semesters of forum logs from an introductory calculus-based physics course. The networks show dense structures of collaboration that differ significantly between semesters, even though aggregate participation statistics remain steady. After characterizing network structure for each semester, we correlate centrality with final course grade. Finally, we use a backbone extraction procedure to clean up "noise" in the network and clarify centrality/grade correlations. We find that network centrality is positively linked with course success in the two semesters with denser forum networks, and is a more reliable indicator than non-network measures such as post count. Backbone extraction destroys these correlations, suggesting that the "noise" is in fact signal and further analysis of the discussion transcripts is required.

Challenge of Helping Introductory Physics Students Transfer Their Learning by Engaging with a Self-Paced Learning Tutorial

With advances in digital technology, research-validated self-paced learning tools can play an increasingly important role in helping students with diverse backgrounds become good problem solvers and independent learners. Thus, it is important to ensure that all students engage with self-paced learning tools effectively in order to learn the content deeply, develop good problem-solving skills, and transfer their learning from one context to another. Here we first provide an overview of a holistic framework for engaging students with self-paced learning tools so that they can transfer their learning to solve novel problems. The framework not only takes into account the features of the self-paced learning tools but also how those tools are implemented, the extent to which the tools take into account student characteristics, and whether factors related to students’ social environments are accounted for appropriately in the implementation of those tools. We then describe an investigation in which we interpret the findings using the framework. In this study, a research-validated self-paced physics tutorial was implemented in both controlled one-on-one interviews and in large enrollment, introductory calculus-based physics courses as a self-paced learning tool. We find that students who used the tutorial in a controlled one-on-one interview situation performed significantly better on transfer problems than those who used it as a self-paced learning tool in the large-scale implementation. The findings suggest that critically examining and taking into account how the self-paced tools are implemented and incentivized, student characteristics including their self-regulation and time-management skills, and social and environmental factors can greatly impact the extent and manner in which students engage with these learning tools. Motivating and getting buy-in from students of the value of these tools and providing appropriate support while implementing them is critical for ensuring that students, who otherwise may be constrained by motivational, social, and environmental factors, engage effectively with the tools in order to learn deeply and transfer their learning.

Using a Ternary Diagram to Display a System's Evolving Energy Distribution

A ternary diagram is a graphical representation used for systems with three components. They are familiar to mineralogists (who typically use them to categorize varieties of solid solution minerals such as feldspar) but are not yet widely used in the physics community. Last year the lead author began using ternary diagrams in his introductory (calculus-based) physics course in a novel context—tracking the distribution of energy in a system as it transforms among three categories (e.g., gravitational, kinetic, and thermal) or transfers among three objects (e.g., inductor, capacitor, and resistor). The ternary diagram has some significant advantages over other graphical representations of energy distributions: an entire scenario can appear in a single plot, even when using very small time steps. This also means that the plot can be used to compare relative rates of energy change during various processes. Our goal for this paper is to introduce the ternary diagram and discuss these advantages in hopes that this will stimulate broader use of ternary diagrams and further research into their educational utility.

Generalizing a categorization of students’ interpretations of linear kinematics graphs

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.Received 23 September 2015DOI:https://doi.org/10.1103/PhysRevPhysEducRes.12.010108This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasConcepts & principlesEpistemology, attitudes, & beliefsPhysics Education Research

Active Learning Classroom Effectiveness Compared to Traditional Lecture

Beginning with the fall 2013 semester, George Mason University began teaching first-semester (PHYS 160) and second-semester (PHYS 260) calculus-based physics courses in an ALT (active learning with technology) environment simultaneously with traditional lectures. Previous results of students' performance comparisons consistently showed that ALT courses were more effective means for students' learning than traditional lecturing. Average final grades as well as the average exam grades in ALT courses regularly surpassed grades in traditional courses by 10-15%. We also cross-compared performance of our students in the PHYS 260 course in all four combinations of students coming from traditional PHYS 160 and cross-compared the ALT course to either style of the PHYS 260 courses. We did our analysis for all available pairs of consecutive semesterss starting from fall 2013 and ending with spring 2015. Results from this analysis clearly indicate that students' performance is greatly improved through the ALT experience.