Calculus-based Introductory Physics Course Research Articles

Investigation of students repeating calculus-based introductory physics courses by gender, ethnicity and race

Abstract We analyze institutional data from large introductory calculus-based physics courses at a large public research university in the US in which the students enrolled in these courses majored in engineering, chemistry, physics, and mathematics. The data was analyzed from two introductory physics courses that are required for most of these students and they are often considered “weed out” courses in that a poor performance in these courses can severely hinder students’ long term career goal achievement. In particular, these courses can act as gatekeepers for many students and those who do not perform to their satisfaction the first time often repeat these courses, particularly if they aspire to remain in their major. We present findings by analyzing data from different demographic groups based upon gender, ethnicity and race for how likely were the students from different demographic groups to repeat these introductory calculus-based physics courses and we compared outcomes of students who repeated with those who did not. We also analyzed and found similar patterns in the calculus courses that are co-requisites for the physics courses. However, the students who failed and repeated physics courses were not necessarily those who failed and repeated the calculus courses. These findings can help physics departments contemplate strategies for providing support to help all students excel in these calculus-based physics courses so that students do not have to repeat these courses, which are pivotal for accomplishing their long-term career goals.

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

Investigating students’ self-identified and reflected appraisal of femininity, masculinity, and androgyny in introductory physics courses

In the field of physics education research, numerous studies have been dedicated to investigating the relationship between gender identity and physics learning. However, these studies have predominantly employed binary gender measurement methods, which may limit the range of research questions that can be explored and impede the discovery of crucial insights. In this study, we adapted gradational measures from prior research to investigate students’ self-identified femininity, masculinity, and androgyny, as well as their reflected appraisal of femininity, masculinity, and androgyny (i.e., perceptions of how others perceive them) in both algebra-based and calculus-based introductory physics courses. The use of gradational measures revealed significant variation in students’ self-identified femininity, masculinity, and androgyny within the binary categories of women and men, providing new insights into gender dynamics in physics. We found that self-identified women in the calculus-based courses, where they are underrepresented, tend to perceive themselves as more masculine and less feminine than how they believe others perceive them. Similarly, students of color are also more likely than White students to perceive themselves as more masculine than they believe others perceive them. Using structural equation modeling, we found that students’ gender stigma consciousness plays an important role in mediating the effects of identifying as women and students of color on the observed discrepancies. Additionally, we found that women also exhibit a tendency to perceive themselves as more androgynous than they believe others perceive them in both algebra-based and calculus-based physics courses, and this phenomenon is also related to gender stigma consciousness. Moreover, our analyses revealed that students in the calculus-based courses tend to have a higher level of gender stigma consciousness even after controlling for gender and race. Our findings underscore the potential of gradational gender measurements in deepening our understanding of gender-related issues in physics education, shedding light on the complex interplay between students’ gender identity, perceptions from others, and their educational experiences in the field. Published by the American Physical Society 2024

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

Charging a Capacitor with Another Capacitor by Using Arduino

Resistor–capacitor (RC) circuit labs help students, but most courses don’t include them because of complications and cost. This work presents an easy and inexpensive Arduino-based lab on the charge and energy transfer between two capacitors with different values of the initial electric charge when they are connected through a resistor. Capacitors are electromagnetic devices widely described in calculus-based introductory physics courses. The concept of capacitance, the determination of the capacitance in planar and cylindrical geometries, the description of the series and parallel combinations of capacitors, or the evaluation of the electric energy stored in them are classic topics studied under electrostatic equilibrium conditions. Charge and discharge of a capacitor through a resistor is also studied in order to experimentally determine the capacitance of the capacitor or measure the electric charge stored in it. Energy balances in the charging and discharging processes of a capacitor are also widely discussed in textbooks. To get a better understanding of the basic concepts, other complex exercises are included in these courses. Among them, one can find the determination of the final charge and energy stored in each of the two capacitors, with different initial charge states, which are combined in parallel. In addition, the study of the charge through a resistor of a discharged capacitor by using a charged capacitor is also a classical exercise when one studies in depth the RC circuit. However, lab exercises covering these last topics are lacking in introductory physics courses. This is mainly due to the need to use complex experimental setups to simultaneously handle various power sources and various multimeters.

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 the Effects of Cookbook and Non-Cookbook Based Lab Activities In a Calculus-Based Introductory Physics Course

I have compared the effects of Cookbook based lab activities with the impacts of doing lab inquiry based on a small introductory engineering physics course. Performance in lab activities that did and did not require the Cookbook procedure was compared using a final questionnaire from the participating students in that course. The population of students who did the lab in each scenario was the same because they enrolled in the same course. In the course, I planned five lab activities of three different types. The first type, which I call “Cookbook” activities (CB) were prepared and then completed by students. The second type of activities, which I call” Non- Cookbook” (NCB) were inquiry-based and orally guide. The final activity type was called “Both” and was a combination of two other activities. I investigated the activities in two dimensions: “scientific skills” and “general skills”. The results for scientific skills showed in NCB “Predicting” have improved. In CB, “Measuring the quantity” and “Sorting/classifying” have positive points of improving scientific skills. For general skills, in NCB, “Recalling concepts” and “Conceptual understanding” were improved. In CB, “Conceptual understanding” and “Scientific writing skills” and “Self-efficacy” were improved. “Writing the lab report” is a tough skill in NCB, while it is easy for CB.

Students’ sense of belonging in introductory physics course for bioscience majors predicts their grade

Student sense of belonging in physics classes may not only play a key role in shaping course outcomes but also influence student persistence and future career aspirations. Prior research has shown that women have a lower sense of belonging than men in calculus-based introductory physics courses. However, prior research has generally not investigated students’ sense of belonging in introductory physics courses in which women are not underrepresented. We administered a validated survey to investigate the sense of belonging of 814 students and how it predicts student grades in a mandatory introductory physics course primarily for bioscience majors. In particular, we investigated how students’ sense of belonging predicts female and male students’ grade at the end of the mandatory physics course for bioscience majors using structural equation modeling. We found that women had a lower sense of belonging and grade than men in this course and that the students’ sense of belonging played a major role in predicting students’ grade in the course. In addition, while men’s sense of belonging significantly increased from the beginning to the end of the physics course, women’s sense of belonging did not significantly change by the end of the course.Received 11 October 2021Accepted 16 March 2022DOI:https://doi.org/10.1103/PhysRevPhysEducRes.18.010139Published 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 & inclusionEpistemology, attitudes, & beliefsLearning environmentPhysics Education Research

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.

Effect of gender, self-efficacy, and interest on perception of the learning environment and outcomes in calculus-based introductory physics courses

Current learning environments in introductory calculus-based physics influence all students' physics-related motivational belief in a negative way and are more detrimental for female students than male students.

The Scourge of Online Solutions and an Academic Hertzsprung–Russell Diagram

We report on preliminary results of a statistical study of student performance in more than a decade of calculus-based introductory physics courses. Treating average homework and test grades as proxies for student effort and comprehension, respectively, we plot comprehension versus effort in an academic version of the astronomical Hertzsprung–Russell diagram (which plots stellar luminosity versus temperature). We study the evolution of this diagram with time, finding that the “academic main sequence” has begun to break down in recent years as student achievement on tests has become decoupled from homework grades. We present evidence that this breakdown is likely related to the emergence of easily accessible online solutions to most textbook problems, and discuss possible responses and strategies for maintaining and enhancing student learning in the online era.

Gendered performance differences in introductory physics: A study from a large land-grant university

Studies examining gender differences in introductory physics show a consensus when it comes to a gender gap on conceptual assessments; however, the story is not as clear when it comes to differences in gendered performance on exams. This study examined whether gendered differences exist on midterm and final exams in introductory physics courses and if such differences were correlated with a gender difference in final course grades. The population for this study included more than 10 000 students enrolled in algebra- and calculus-based introductory physics courses between Spring 2007 and Spring 2019. We found a small but statistically significant difference, with a weak effect size, in final letter grades for only one out of four courses: algebra-based mechanics. By looking at midterm exam grades, statistically significant differences were noted for some exams in three out of four courses, with calculus-based electricity and magnetism being the exception. In all statistically significant cases, the effect size was small or weak, indicating that performance on exams and final letter grades was not strongly dependent on gender. As an added dimension examining gendered differences, we investigated if differences exist when accounting for instructor gender. Additionally, a questionnaire was administered in Fall 2019 to more than 1600 students in both introductory sequences to explore students’ perceptions of performance, class contributions, and inclusion. We observed some differences between students’ perception of their performance and contribution when grouped by gender, but no difference on perception of inclusion.Received 2 June 2020Accepted 4 January 2021DOI:https://doi.org/10.1103/PhysRevPhysEducRes.17.010106Published 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 AreasAssessmentDiversity & inclusionProfessional TopicsLower undergraduate studentsPhysics Education Research

Retention of conceptual learning after an interactive introductory mechanics course

The cyclic format of the undergraduate physics curriculum depends on students' ability to recall and utilize material covered in prior courses in order to reliably build on that knowledge in later courses. However, there is evidence to suggest that people often do not retain all, or even most, of what they learned previously. How much information is retained appears to be dependent both on the individuals' approach to learning as well as the style of instruction. In particular, there is evidence to suggest that active engagement techniques in the classroom can improve students' retention of the material over time. Here, we report the findings of a longitudinal investigation of students' retention of conceptual understanding as measured by the Force and Motion Conceptual Evaluation (FMCE) following a first-semester, calculus-based introductory physics course, which features significant active engagement in both lecture and recitation. By administering the FMCE at the end of a first-semester physics course and again at the beginning of the subsequent second-semester physics course, we examine students' knowledge retention over time periods ranging from 1-15 months. We find that the shift in students' FMCE scores between these two courses is positive but corresponds to a small effect size, indicating that students retained effectively all of their conceptual learning (as measured by the FMCE). This finding largely persists even as the length of the gap between the two courses increases. We also find that, when breaking out students' performance on individual questions, the majority of students maintain their score on individual questions. Averaged over all questions, roughly a fifth of the students switched their answers from right to wrong or wrong to right on any given item.

Calculus-enhanced energy-first curriculum for introductory physics improves student performance locally and in downstream courses

A calculus-based introductory physics course with an energy-first curriculum improves student learning and has lasting benefits for students entering with lower math ability.

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.

New video resource for calculus-based introductory physics, design and assessment. I. Electricity and magnetism

A new online video resource named Freshman Physics Classroom (FPC) was developed by a team in the Department of Physics & Astronomy at Texas A&M University to supplement calculus-based introductory physics courses. This article describes the development of this resource and reports the results from the first term of deployment, spring 2017, for student performance on both course examinations and the Brief Electricity & Magnetism Assessment (BEMA). The video modules received a high approval rating (>85%) from students according to anonymous clicker surveys administered twice over the course of the semester during lectures. Data from midterm exams show that students who engaged with the resource tended to outperform students who did not make use of the FPC video modules. Distributions of exam scores indicate that students with partial understanding of a subject from the course (lectures, recitations, and so forth) benefited from engagement with the video modules. Students from the spring semesters of 2015–2017 showed nearly identical levels of conceptual knowledge according to pre-testing conducted using BEMA, where spring 2015 and spring 2016 were used as a control group. Normalized gains were higher on average for those students who made use of the FPC video modules than for those who did not. Overall, the FPC video modules demonstrated a positive influence on student conceptual understanding and problem solving ability.

Disconnect between undergraduates’ understanding of the algebraic and geometric aspects of vectors

In this article, we present our findings on STEM undergraduates’ understanding of the fundamental concepts of vectors. The study was conducted on a sample of 166 undergraduates who either had or had not taken a calculus-based introductory physics course at a comprehensive private university in the USA. A quiz about vectors on both the algebraic aspects (with the coordinations for the head and tail of a vector and with unit vector notation) and geometric aspects (with arrow notation), along with a survey of their prior experience regarding vectors, was given. The results revealed that several learning difficulties are due to a lack of understanding of the connections between the algebraic and geometric aspects of vectors. This underlines the need for the implementation of effective teaching strategies that would better emphasize the connections between the algebraic and geometric aspects of vectors.

Speaking of E&M

This paper describes a new lab experiment where students explore the magnetic force on a permanent magnet placed inside a short solenoid. This lab is the fourth experiment performed in the second semester of the calculus-based introductory physics course at Washington University in St. Louis. The experiment is performed using a speaker (which students themselves have constructed), function generator, multimeter, and Vernier microphone while all analysis is done using Logger Pro. Experiments confirm a functional relationship similar to one that students have seen in class, while showing students the applicability of classroom physics to their world.

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.