Numerical problem solving in classical mechanics in university physics education offers a learning situation where students have many possibilities of control and creativity. In this study, expertlike beliefs about physics and learning physics together with prior knowledge were the most important predictors of the quality of performance of a task with many degrees of freedom. Feelings corresponding to control and concentration, i.e., emotions that are expected to trigger students’ intrinsic motivation, were also important in predicting performance. Unexpectedly, intrinsic motivation, as indicated by enjoyment and interest, together with students’ personal interest and utility value beliefs did not predict performance. This indicates that although a certain degree of enjoyment is probably necessary, motivated behavior is rather regulated by integration and identification of expertlike beliefs about learning and are more strongly associated with concentration and control during learning and, ultimately, with high performance. The results suggest that the development of students’ epistemological beliefs is important for students’ ability to learn from realistic problem-solving situations with many degrees of freedom in physics education.

During a one-semester-long research project with high school students, we deployed and gauged efficiency of two different reform teaching methods: reading, presenting, and questioning (RPQ) and experimenting and discussion (ED). In this paper we report on changes in students’ attitudes and beliefs about physics and learning physics. We used the Colorado Learning Attitudes about Science Survey (CLASS v3) to assess the relative effectiveness of the two methods. The data show that both methods improved student attitudes and beliefs but to different extents. The RPQ group (91 students) achieved an overall improvement of $+5.8\%$ in attitudes and beliefs, while the ED group (85 students) attained an improvement of $+25.6\%$. These results suggest that both methods may have a substantial potential for improving students’ attitudes and beliefs about physics and physics learning, with the ED method being more promising than the RPQ. method

We have found that non-STEM (science, technology, engineering, and mathematics) majors taking either a conceptual physics or astronomy course at two regional comprehensive institutions score significantly lower preinstruction on the Lawson’s Classroom Test of Scientific Reasoning (LCTSR) in comparison to national average STEM majors. Based on LCTSR score, the majority of non-STEM students can be classified as either concrete operational or transitional reasoners in Piaget’s theory of cognitive development, whereas in the STEM population formal operational reasoners are far more prevalent. In particular, non-STEM students demonstrate significant difficulty with proportional and hypothetico-deductive reasoning. Prescores on the LCTSR are correlated with normalized learning gains on various concept inventories. The correlation is strongest for content that can be categorized as mostly theoretical, meaning a lack of directly observable exemplars, and weakest for content categorized as mostly descriptive, where directly observable exemplars are abundant. Although the implementation of research-verified, interactive engagement pedagogy can lead to gains in content knowledge, significant gains in theoretical content (such as force and energy) are more difficult with non-STEM students. We also observe no significant gains on the LCTSR without explicit instruction in scientific reasoning patterns. These results further demonstrate that differences in student populations are important when comparing normalized gains on concept inventories, and the achievement of significant gains in scientific reasoning requires a reevaluation of the traditional approach to physics for non-STEM students.

Physics students can encounter difficulties in physics problem solving as a result of failing to use knowledge that they have but do not perceive as relevant or appropriate. In previous work we have demonstrated that some of these difficulties may be epistemological. Students may limit the kinds of knowledge that they use. For example, they may use formal manipulations and ignore physical sense making or vice versa. Both beginning (novice) and intermediate (journeymen) students demonstrate these difficulties. Learning both to switch one’s epistemological lens on a problem and to integrate different kinds of knowledge is a critical component of learning to solve problems in physics effectively. In this paper, we present two case studies in which journeyman students (upper-division physics majors) demonstrate switching between epistemological resources in approaching a complex problem. We conjecture that mastering these epistemological skills is an essential component of learning complex problem solving in physics.

This study explored how researchers’ views about the form of students’ epistemologies influence how the researchers develop and refine surveys and how they interpret survey results. After running standard statistical analyses on 505 physics students’ responses to the Turkish version of the Maryland Physics Expectations-II survey, probing students’ epistemologies and expectations, we interpreted the results through two different theoretical lenses, the beliefs perspective and the resources perspective. We showed that the beliefs and resources frameworks provided different interpretations of the psychometric analyses, leading to different conclusions about how the survey results should be interpreted and how the survey should be improved.

We have investigated the impact of using multimedia learning modules (MLM) on the learning of students enrolled in introductory physics courses at California State Polytechnic University, Pomona. One hundred fifty-nine students were randomly registered in two sections of an introductory mechanics course, one of which featured the MLMs. Both sections had the same instructor, participated in class discussions on identical topics, and used the same problem-solving examples. The students in the multimedia group outperformed the students who did not experience the MLMs in a final course examination and across identical discussion questions.

Recent publications have documented positive attitudinal shifts on the Colorado Learning Attitudes about Science Survey (CLASS) among students enrolled in courses with an explicit epistemological focus. We now report positive attitudinal shifts in classes using the Physics by Inquiry (PbI) curriculum, which has only an implicit focus on student epistemologies and nature of science issues. These positive shifts have occurred in several different implementations of the curriculum, across multiple institutions and multiple semesters. In many classes, students experienced significant attitudinal shifts in the problem-solving categories of the CLASS, despite the conceptual focus of most PbI courses.

Developing a sense of community among students is one of the three pillars of an overall reform effort to increase participation in physics, and the sciences more broadly, at Florida International University. The emergence of a research and learning community, embedded within a course reform effort, has contributed to increased recruitment and retention of physics majors. We utilize social network analysis to quantify interactions in Florida International University’s Physics Learning Center (PLC) that support the development of academic and social integration. The tools of social network analysis allow us to visualize and quantify student interactions and characterize the roles of students within a social network. After providing a brief introduction to social network analysis, we use sequential multiple regression modeling to evaluate factors that contribute to participation in the learning community. Results of the sequential multiple regression indicate that the PLC learning community is an equitable environment as we find that gender and ethnicity are not significant predictors of participation in the PLC. We find that providing students space for collaboration provides a vital element in the formation of a supportive learning community.

This paper examines the educational impact of the implementation of the tutorial activity “Changes in Energy and Momentum” from The Tutorials in Introductory Physics in five different instructional settings. These settings include (1) a completely computer-based learning environment and (2) use of cooperative learning groups with varying levels of instructor support. Pre- and post-tests provide evidence that a computer-based implementation falls significantly short of classroom implementations which involve both collaborative learning groups and interactions with a teaching assistance. Other findings provide insight into the importance of certain elements of instructor training and the appropriate use of the tutorial as an initial introduction to a new concept.

We have investigated preservice science teachers’ qualitative understanding of circuits consisting of multiple batteries in single and multiple loops using a pretest and post-test method and classroom observations. We found that most students were unable to explain the effects of adding batteries in single and multiple loops, as they tended to use reasoning based on current and resistance where reasoning based on voltage is a necessity. We also found that problems such as thinking of the battery as a source of constant current resurfaced in this new context, and that answers given were inconsistent with current conservation. We describe the curriculum we developed that enables students to model circuits with multiple batteries qualitatively. Post-test results show that the majority of students were able to apply their newly developed model to make accurate predictions for complex circuits.

We present results of a pseudolongitudinal study of attitudes and beliefs about physics from different cohort groups ranging from final-year high school students in the UK to physics faculty ($N=637$), using the Colorado Learning Attitudes about Science Survey (CLASS) instrument. In terms of overall degree of expertlike thinking, we find little change in cohorts at different stages of their undergraduate degrees, with a flat profile of expertlike thinking across the years of an undergraduate degree. Significant differences in overall CLASS scores occur for cohorts across entry and exit points of the undergraduate program. At the entry boundary, our data for high school students provides strong evidence of a selection effect, with students who intend to major in physics at university displaying more expertlike views than those students who are merely studying the subject to final year in high school. A similar effect is suggested at the exit boundary but is not definitive.

Quantum mechanics is often thought to be a difficult subject to understand, not only in the complexity of its mathematics but also in its conceptual foundation. In this paper we emphasize students’ depictions of the uncertainty principle and wave-particle duality of quantum events, phenomena that could serve as a foundation in building an understanding of quantum mechanics. A phenomenographic study was carried out to categorize a picture of students’ descriptions of these key quantum concepts. Data for this study were obtained from a semistructured in-depth interview conducted with undergraduate physics students ($N=25$) from Bahir Dar, Ethiopia. The phenomenographic data analysis revealed that it is possible to construct three qualitatively different categories to map students’ depictions of the concept wave-particle duality, namely, (1) classical description, (2) mixed classical-quantum description, and (3) quasiquantum description. Similarly, it is proposed that students’ depictions of the concept uncertainty can be described with four different categories of description, which are (1) uncertainty as an extrinsic property of measurement, (2) uncertainty principle as measurement error or uncertainty, (3) uncertainty as measurement disturbance, and (4) uncertainty as a quantum mechanics uncertainty principle. Overall, we found students are more likely to prefer a classical picture of interpretations of quantum mechanics. However, few students in the quasiquantum category applied typical wave phenomena such as interference and diffraction that cannot be explained within the framework classical physics for depicting the wavelike properties of quantum entities. Despite inhospitable conceptions of the uncertainty principle and wave- and particlelike properties of quantum entities in our investigation, the findings presented in this paper are highly consistent with those reported in previous studies. New findings and some implications for instruction and the curricula are discussed.

We developed an instrument to systematically investigate student conceptual understanding of the relationships between the directions of net force, velocity, and acceleration in one dimension and report on data collected on the final version of the instrument from over 650 students. Unlike previous work, we simultaneously studied all six possible conditional relations between force, velocity, and acceleration in order to obtain a coherent picture of student understanding of the relations between all three concepts. We present a variety of evidence demonstrating the validity and reliability of the instrument. An analysis of student responses from three different course levels revealed three main findings. First, a significant fraction of students chose “partially correct” responses, and from pre- to post-test, many students moved from “misconception” to partially correct responses, or from partially correct to fully correct responses. Second, there were asymmetries in responding to conditional relations. For example, students answered questions of the form “Given the velocity, what can be inferred about the net force?” differently than converse questions “Given the net force, what can be inferred about the velocity?” Third, there was evidence of hierarchies in student responses, suggesting, for example, that understanding the relation between velocity and acceleration is necessary for understanding the relation between velocity and force, but the converse is not true. Finally, we briefly discuss how these findings might be applied to instruction.

This study compared the educational effects of computer simulations developed in a hyper-realistic virtual environment with the educational effects of either traditional schematic simulations or a traditional optics laboratory. The virtual environment was constructed on the basis of Java applets complemented with a photorealistic visual output. This new virtual environment concept, which we call hyper-realistic, transcends basic schematic simulation; it provides the user with a more realistic perception of a physical phenomenon being simulated. We compared the learning achievements of three equivalent, homogeneous groups of undergraduates—an experimental group who used only the hyper-realistic virtual laboratory, a first control group who used a schematic simulation, and a second control group who used the traditional laboratory. The three groups received the same theoretical preparation and carried out equivalent practicals in their respective learning environments. The topic chosen for the experiment was optical aberrations. An analysis of variance applied to the data of the study demonstrated a statistically significant difference ($p$ value $<0.05$) between the three groups. The learning achievements attained by the group using the hyper-realistic virtual environment were 6.1 percentage points higher than those for the group using the traditional schematic simulations and 9.5 percentage points higher than those for the group using the traditional laboratory.

The ability to categorize problems based upon underlying principles, rather than surface features or contexts, is considered one of several proxy predictors of expertise in problem solving. With inspiration from the classic study by Chi, Feltovich, and Glaser, we assess the distribution of expertise among introductory physics students by asking three introductory physics classes, each with more than a hundred students, to categorize mechanics problems based upon similarity of solution. We compare their categorization with those of physics graduate students and faculty members. To evaluate the effect of problem context on students’ ability to categorize, two sets of problems were developed for categorization. Some problems in one set included those available from the prior study by Chi et al. We find a large overlap between calculus-based introductory students and graduate students with regard to their categorizations that were assessed as “good.” Our findings, which contrast with those of Chi et al., suggest that there is a wide distribution of expertise in mechanics among introductory and graduate students. Although the categorization task is conceptual, introductory students in the calculus-based course performed better than those in the algebra-based course. Qualitative trends in categorization of problems are similar between the non-Chi problems and problems available from the Chi study used in our study although the Chi problems used are more difficult on average.

This paper describes a teaching experiment designed to examine the learning (i.e., retention of content and conceptual development) that takes place when public scientific web lectures delivered by scientists are utilized to present advanced ideas in physics to students with a high school background in physics. The students watched an exemplary public physics web lecture that was followed by a collaborative generic activity session. The collaborative session involved a guided critical reconstruction of the main arguments in the lecture, and a processing of the key analogical explanations. Then the students watched another exemplary web lecture on a different topic. The participants ($N=14$) were divided into two groups differing only in the order in which the lectures were presented. The students’ discussions during the activities show that they were able to reason and demonstrate conceptual progress, although the physics ideas in the lectures were far beyond their level in physics. The discussions during the collaborative session contributed significantly to the students’ understanding. We illustrate this point through an analysis of one of these discussions between two students on an analogical explanation of the Aharonov-Bohm effect that was presented in one of the lectures. The results from the tests that were administered to the participants several times during the intervention further support this contention.

It is well documented that when solving problems experts first search for underlying concepts while students tend to look for equations and previously worked examples. The overwhelming majority of end-of-chapter (EOC) problems in most introductory physics textbooks contain only material and examples discussed in a single chapter, rarely requiring a solver to conduct a general search for underlying concepts. Hypothesizing that complete reliance on EOC problems trains students to rely on a nonexpert approach, we designed and implemented “synthesis” problems, each combining two major concepts that are broadly separated in the teaching timeline. To provide students with guided conceptual scaffolding, we encapsulated each synthesis problem into a sequence with two preceding conceptually based multiple-choice questions. Each question contained one of the major concepts covered in the subsequent synthesis problem. Results from a small-scale interview study and two large-scale written tests showed that the scaffolding encouraged students to search for and apply appropriate fundamental principles in solving synthesis problems, and that repeated training using scaffolded synthesis problems also helped students to make cross-topic transfers.

This paper examines the results of the repeated administration of the Colorado Learning Attitudes about Science Survey (CLASS) in a large introductory physics course at a midsize, metropolitan Canadian university. We compare the results to those obtained previously in comparable courses at the University of British Columbia (Canada) and the University of Colorado (U.S.). Atypically, students in this study exhibited a positive shift in their attitudes about science over the semester. The change in students’ attitudes across the term appears to be moderated by their educational background—specifically, whether they had taken grade 12 physics or not. The correlation between students’ attitudes and their conceptual knowledge also appears to be influenced by students’ educational background. The results have pedagogical implications for instructors of introductory college and university physics and potentially for other science courses.

Utilizing an energy-as-substance conceptual metaphor as a central feature of the introductory physics curriculum affords students a wealth of conceptual resources for reasoning about energy conservation, storage, and transfer. This paper first establishes the utility and function of a conceptual metaphor in developing student understanding of energy concepts. Then a curricular framework with a prominent energy-as-substance conceptual metaphor is described. The curricular framework involves both a reorganization of the content of introductory physics as well as a renewed focus. Reorganizing includes treating energy early and spiraling back to energy treatments. The refocusing includes emphasizing energy’s role in modeling phenomena and attending to the tools for representing energy conservation, storage, and transfer. Implementation of the energy framework is then described in the context of a Modeling Instruction course. Finally, qualitative evidence is presented showing student use of energy conceptual resources which are promoted in the curricular implementation.

Florida International University has undergone a reform in the introductory physics classes by focusing on the laboratory component of these classes. We present results from the secondary implementation of two research-based instructional strategies: the implementation of the Learning Assistant model as developed by the University of Colorado at Boulder and the Open Source Tutorial curriculum developed at the University of Maryland, College Park. We examine the results of the Force Concept Inventory (FCI) for introductory students over five years ($n=872$) and find that the mean raw gain of students in transformed lab sections was 0.243, while the mean raw gain of the traditional labs was 0.159, with a Cohen’s $d$ effect size of 0.59. Average raw gains on the FCI were 0.243 for Hispanic students and 0.213 for women in the transformed labs, indicating that these reforms are not widening the gaps between underrepresented student groups and majority groups. Our results illustrate how research-based instructional strategies can be successfully implemented in a physics department with minimal department engagement and in a sustainable manner.