Research has shown that students have tremendous difficulties developing a qualitative understanding of wave optics, at all educational levels. In this study, we investigate how three different approaches to visualizing light waves affect students’ understanding of wave optics. In the first, the conventional, approach light waves are represented by sinusoidal curves. The second teaching approach includes representing light waves by a series of static images, showing the oscillating electric field vectors at characteristic, subsequent instants of time. Within the third approach phasors are used for visualizing light waves. A total of $N=85$ secondary school students were randomly assigned to one of the three teaching approaches, each of which lasted a period of four class hours. Students who learned with phasors and students who learned from the series of static images outperformed the students learning according to the conventional approach, i.e., they showed a much better understanding of basic wave optics, as measured by a conceptual survey administered to the students one week after the treatment. Our results suggest that visualizing light waves with phasors or oscillating electric field vectors is a promising approach to developing a deeper understanding of wave optics for students enrolled in conceptual level physics courses.

In experiments including over 450 university-level students, we studied the effectiveness and time efficiency of several levels of feedback complexity in simple, computer-based training utilizing static question sequences. The learning domain was simple vector math, an essential skill in introductory physics. In a unique full factorial design, we studied the relative effects of “knowledge of correct response” feedback and “elaborated feedback” (i.e., a general explanation) both separately and together. A number of other factors were analyzed, including training time, physics course grade, prior knowledge of vector math, and student beliefs about both their proficiency in and the importance of vector math. We hypothesize a simple model predicting how the effectiveness of feedback depends on prior knowledge, and the results confirm this knowledge-by-treatment interaction. Most notably, elaborated feedback is the most effective feedback, especially for students with low prior knowledge and low course grade. In contrast, knowledge of correct response feedback was less effective for low-performing students, and including both kinds of feedback did not significantly improve performance compared to elaborated feedback alone. Further, while elaborated feedback resulted in higher scores, the learning rate was at best only marginally higher because the training time was slightly longer. Training time data revealed that students spent significantly more time on the elaborated feedback after answering a training question incorrectly. Finally, we found that training improved student self-reported proficiency and that belief in the importance of the learned domain improved the effectiveness of training. Overall, we found that computer based training with static question sequences and immediate elaborated feedback in the form of simple and general explanations can be an effective way to improve student performance on a physics essential skill, especially for less prepared and low-performing students.

We report on progress towards the development of an Action Concept Inventory (ACI), a test that measures student understanding of action principles in introductory mechanics and optics. The ACI also covers key concepts of many-paths quantum mechanics, from which classical action physics arises. We used a multistage iterative development cycle for incorporating expert and student feedback into successive revisions of the ACI. The student feedback, including think-aloud interviews, enabled us to identify their misconceptions about action physics.

Our study sets out to identify the difficulties that high school students, teachers, and university students encounter when trying to explain atomic spectra. To do so, we identify the key concepts that any quantum model for the emission and absorption of electromagnetic radiation must include to account for the gas spectra and we then design two questionnaires, one for teachers and the other for students. By analyzing the responses, we conclude that (i) teachers lack a quantum model for the emission and absorption of electromagnetic radiation capable of explaining the spectra, (ii) teachers and students share the same difficulties, and (iii) these difficulties concern the model of the atom, the model of radiation, and the model of the interaction between them.

The Force Concept Inventory (FCI) has been widely used to assess student understanding of introductory mechanics concepts by a variety of educators and physics education researchers. One reason for this extensive use is that many of the items on the FCI have strong distractor choices which correspond to students’ alternate conceptions in mechanics. Instruction is unlikely to be effective if instructors do not know the common alternate conceptions of introductory physics students and explicitly take into account students’ initial knowledge states in their instructional design. Here, we discuss research involving the FCI to evaluate one aspect of the pedagogical content knowledge of teaching assistants (TAs): knowledge of introductory student alternate conceptions in mechanics as revealed by the FCI. For each item on the FCI, the TAs were asked to identify the most common incorrect answer choice of introductory physics students. This exercise was followed by a class discussion with the TAs related to this task, including the importance of knowing student difficulties in teaching and learning. Then, we used FCI pretest and post-test data from a large population ($\sim 900$) of introductory physics students to assess the extent to which TAs were able to identify alternate conceptions of introductory students related to force and motion. In addition, we carried out think-aloud interviews with graduate students who had more than two semesters of teaching experience in recitations to examine how they reason about the task. We find that while the TAs, on average, performed better than random guessing at identifying introductory students’ difficulties with FCI content, they did not identify many common difficulties that introductory physics students have after traditional instruction. We discuss specific alternate conceptions, the extent to which TAs are able to identify them, and results from the think-aloud interviews that provided valuable information about why TAs sometimes select certain alternate conceptions as the most common, which are instead very rare among introductory students. We also briefly compare the performance of the TAs with physics instructors in identifying common introductory student difficulties with FCI content using the same task and find that their performances are comparable. Furthermore, our data suggest that the ability to identify introductory students’ difficulties was not correlated with whether the TAs obtained their undergraduate degree in the U.S. or elsewhere.

Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic classroom work. It is also useful if such tools can be employed by instructors to guide their pedagogy. We describe the design, development, and testing of a simple rubric to assess written solutions to problems given in undergraduate introductory physics courses. In particular, we present evidence for the validity, reliability, and utility of the instrument. The rubric identifies five general problem-solving processes and defines the criteria to attain a score in each: organizing problem information into a Useful Description, selecting appropriate principles (Physics Approach), applying those principles to the specific conditions in the problem (Specific Application of Physics), using Mathematical Procedures appropriately, and displaying evidence of an organized reasoning pattern (Logical Progression).

A virtual learning environment can engage university students in the learning process in ways that the traditional lectures and lab formats cannot. We present our virtual learning environment StudentResearcher, which incorporates simulations, multiple-choice quizzes, video lectures, and gamification into a learning path for quantum mechanics at the advanced university level. StudentResearcher is built upon the experiences gathered from workshops with the citizen science game Quantum Moves at the high-school and university level, where the games were used extensively to illustrate the basic concepts of quantum mechanics. The first test of this new virtual learning environment was a 2014 course in advanced quantum mechanics at Aarhus University with 47 enrolled students. We found increased learning for the students who were more active on the platform independent of their previous performances.

Students’ attitudes and approaches to physics problem solving can impact how well they learn physics and how successful they are in solving physics problems. Prior research in the U.S. using a validated Attitude and Approaches to Problem Solving (AAPS) survey suggests that there are major differences between students in introductory physics and astronomy courses and physics experts in terms of their attitudes and approaches to physics problem solving. Here we discuss the validation, administration, and analysis of data for the Turkish version of the AAPS survey for high school and university students in Turkey. After the validation and administration of the Turkish version of the survey, the analysis of the data was conducted by grouping the data by grade level, school type, and gender. While there are no statistically significant differences between the averages of various groups on the survey, overall, the university students in Turkey were more expertlike than vocational high school students. On an item by item basis, there are statistically differences between the averages of the groups on many items. For example, on average, the university students demonstrated less expertlike attitudes about the role of equations and formulas in problem solving, in solving difficult problems, and in knowing when the solution is not correct, whereas they displayed more expertlike attitudes and approaches on items related to metacognition in physics problem solving. A principal component analysis on the data yields item clusters into which the student responses on various survey items can be grouped. A comparison of the responses of the Turkish and American university students enrolled in algebra-based introductory physics courses shows that on more than half of the items, the responses of these two groups were statistically significantly different, with the U.S. students on average responding to the items in a more expertlike manner.

Epistemological studies generally focus on how students think about their construction of knowledge compared to how experts think about the same ideas. Instruments such as the MPEX and CLASS use a Likert scale to gauge whether students agree or disagree with how experts think about the same ideas. During analysis, five point scale responses are typically reduced to favorable, neutral, and unfavorable with neutral being treated as a nonresponse. What if students are actively selecting neutral and not treating it as a “does not apply?” To address this question we chose to analyze the postinstruction neutral responses of students in our Physics I course using data from multiple years, multiple sections, and multiple instructors. We found that classroom average postinstruction neutral responses were consistently within a band of 15%–25% and that this was also consistent with other published results. It is not yet clear what this pattern means. Is this a measure of students receiving mixed messages from instructors or a measure of a transitional stage that students go through when learning how to be a good college physics student? These initial findings are interesting enough that we are presenting them here with a more detailed question-by-question analysis to be published in the near future. For example, high levels of neutral responses to applied questions (e.g., “All I need to do is. …”) may indicate that students are receiving mixed messages from instructors. On the other hand, high levels of neutral responses to conceptual questions (e.g., “Knowledge in physics…”) may indicate that students are in a transitional stage between novice and expert.

Although physics education research (PER) has improved instructional practices, there are not agreed upon principles for designing effective instructional materials. Here, we illustrate how close comparison of instructional materials could support the development of such principles. Specifically, in discussion sections of a large, introductory physics course, a pair of studies compare two instructional strategies for teaching a physics concept: having students (i) explain a set of contrasting cases or (ii) apply and build on previously learned concepts. We compare these strategies for the teaching of Faraday’s law, showing that explaining a set of related contrasting cases not only improves student performance on Faraday’s law questions over building on a previously learned concept (i.e., Lorentz force), but also prepares students to better learn subsequent topics, such as Lenz’s law. These differences persist to the final exam. We argue that early exposure to contrasting cases better focuses student attention on a key feature related to both concepts: change in magnetic flux. Importantly, the benefits of contrasting cases for both learning and enjoyment are enhanced for students who did not first attend a Faraday’s law lecture, consistent with previous research suggesting that being told a solution can circumvent the benefits of its discovery. These studies illustrate an experimental approach for understanding how the structure of activities affects learning and performance outcomes, a first step toward design principles for effective instructional materials.

We report some of the common, prevalent conceptual resources that students used to reason about energy, based on our analysis of written responses to questions given to 807 introductory physics students. These resources include, for example, associating forms of energy with indicators, relating forces and energy, and representing energy quantitatively. This research responds to a need for large-scale, resources-oriented research on students’ conceptual understanding and has the potential to support the development of an underexplored dimension of pedagogical content knowledge–knowledge of student resources for understanding energy. Our aim is to promote instructor take-up of the resources theory of knowledge, and we suggest a number of ways in which instructors might capitalize on the resources we report.

Over the past few decades, a growing body of evidence demonstrates that students learn best in engaging, interactive, collaborative, and inquiry-based environments. However, most college science classes are still taught with traditional methods suggesting the existing selection of research-based instructional materials has not widely transformed undergraduate education. SCALE-UP is a renovated pedagogy and classroom environment that has achieved a greater impact than most, used extensively throughout the United States and abroad. SCALE-UP is not a simple collection of lesson plans or a textbook that can be easily adopted, and instead instructors are encouraged to customize main pedagogical principles to their unique instructional situation. This flexibility along with promotion of instructor autonomy may have assisted its spread. This paper uses case studies of five successful secondary implementations in the United States to examine how instructors gather information about reform, create a curriculum, and achieve sustained use. Many people learned about research-based resources that formed the composite of their curricula through interpersonal connections. Time constraints and misunderstandings between developers and instructors limited which resources were chosen and how they were used. Once instructors created a “working form” of the curriculum, three out of five instructors did not make significant changes. This could lead to the preservation of a more conservative curriculum. Implications include that disseminators should articulate core principles of the reform that should be retained to uphold the integrity of the reform as well as the areas where adopters have flexibility to innovate. Strategically involving other secondary users in the dissemination process could facilitate important interpersonal exchanges that could provide an additional layer of support for faculty.

This study examined the regulation of out-of-class time invested in the academic activities associated with a physics class for 20 consecutive semesters. The academic activities of 1676 students were included in the study. Students reported investing a semester average of $6.5\pm 2.9\mathrm{h}$ out of class per week. During weeks not containing an examination, a total of $4.3\pm 2.1\mathrm{h}$ was reported which was divided between $2.5\pm 1.2\mathrm{h}$ working homework and $1.8\pm 1.4\mathrm{h}$ reading. Students reported spending $7.6\pm 4.8\mathrm{h}$ preparing for each in-semester examination. Students showed a significant correlation between the change in time invested in examination preparation ($r=-0.12$, $p<0.0001$) and their score on the previous examination. The correlation increased as the data were averaged over semester ($r=-0.70$, $p=0.0006$) and academic year ($r=-0.82$, $p=0.0039$). While significant, the overall correlation indicates a small effect size and implies that an increase of 1 standard deviation of test score (18%) was related to a decrease of 0.12 standard deviations or 0.9 h of study time. Students also modified their time invested in reading as the length of the textbook changed; however, this modification was not proportional to the size of the change in textbook length. Very little regulation of the time invested in homework was detected either in response to test grades or in response to changes in the length of homework assignments. Patterns of regulation were different for higher performing students than for lower performing students with students receiving a course grade of “C” or “D” demonstrating little change in examination preparation time in response to lower examination grades. This study suggests that homework preparation time is a fixed variable while examination preparation time and reading time are weakly mutable variables.

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four “pseudophysics” problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.

Student learning in instructional physics labs represents a growing area of research that includes investigations of students’ beliefs and expectations about the nature of experimental physics. To directly probe students’ epistemologies about experimental physics and support broader lab transformation efforts at the University of Colorado Boulder and elsewhere, we developed the Colorado Learning Attitudes about Science Survey for experimental physics (E-CLASS). Previous work with this assessment has included establishing the accuracy and clarity of the instrument through student interviews and preliminary testing. Several years of data collection at multiple institutions has resulted in a growing national data set of student responses. Here, we report on results of the analysis of these data to investigate the statistical validity and reliability of the E-CLASS as a measure of students’ epistemologies for a broad student population. We find that the E-CLASS demonstrates an acceptable level of both validity and reliability on measures of item and test discrimination, test-retest reliability, partial-sample reliability, internal consistency, concurrent validity, and convergent validity. We also examine students’ responses using principal component analysis and find that, as expected, the E-CLASS does not exhibit strong factors (a.k.a. categories).

Computer-automated assessment of students’ text responses to short-answer questions represents an important enabling technology for online learning environments. We have investigated the use of machine learning to train computer models capable of automatically classifying short-answer responses and assessed the results. Our investigations are part of a project to develop and test an interactive learning environment designed to help students learn introductory physics concepts. The system is designed around an interactive video tutoring interface. We have analyzed 9 with about 150 responses or less. We observe for 4 of the 9 automated assessment with interrater agreement of 70% or better with the human rater. This level of agreement may represent a baseline for practical utility in instruction and indicates that the method warrants further investigation for use in this type of application. Our results also suggest strategies that may be useful for writing activities and questions that are more appropriate for automated assessment. These strategies include building activities that have relatively few conceptually distinct ways of perceiving the physical behavior of relatively few physical objects. Further success in this direction may allow us to promote interactivity and better provide feedback in online learning systems. These capabilities could enable our system to function more like a real tutor.

An earlier investigation found that the performance of advanced students in a quantum mechanics course did not automatically improve from midterm to final exam on identical problems even when they were provided the correct solutions and their own graded exams. Here, we describe a study, which extended over four years, in which upper-level undergraduate students in a quantum physics course were given four identical problems in both the midterm exam and final exam. Approximately half of the students were given explicit incentives to correct their mistakes in the midterm exam. In particular, they could get back up to 50% of the points lost on each midterm exam problem. The solutions to the midterm exam problems were provided to all students in both groups but those who corrected their mistakes were provided the solution after they submitted their corrections to the instructor. The performance on the same problems on the final exam suggests that students who were given incentives to correct their mistakes significantly outperformed those who were not given an incentive. The incentive to correct the mistakes had greater impact on the final exam performance of students who had not performed well on the midterm exam.

Students often complain that they cannot see the relevance of what they are being taught in foundation physics classes. While revising and adjusting the curriculum and teaching are important, this study suggests it might also be useful to help students view their learning in relation to their future career aspirations. This paper reports on a study conducted with first-year students enrolled in a compulsory foundation physics unit with a history of low pass rates. Working within a “possible selves” framework, activities were designed to help students position their learning in relation to possible future lives and careers. Two cohorts of students ($N=93$) engaged in an intensive workshop comprising multiple activities relating to self and career. Self-reflection worksheets were analyzed using content analysis. The results indicate that students experience immediate benefits from these activities through self-reflection on the current self, future possible professional selves, and the role of current studies in narrowing the gap between the two.

This study investigated if and to what extent grade 8 and 9 students in Taiwan attributed materialistic properties to sound concepts, and whether they hold scientific views in parallel with materialistic views. Taiwanese middle school students are a special population since their scores in international academic comparison tests such as TIMSS and PISA are among the highest in the world. The “Sound Concept Inventory Instrument” with both materialistic and scientific statements of sound concepts was applied to explore Taiwanese students’ ideas and corresponding confidence. The results showed that although the subject of sound is taught extensively in grade 8 in Taiwan, students still hold materialistic views of sound. The participants agreed, on average, with 41% of the statements that associate sound with materialistic properties. Moreover, they were quite confident in their materialistic answers ($\text{mean}=3.27$ on a 5-point Likert scale). In parallel, they also agreed with 71% of the scientific statements in the questions. They were also confident of their scientific answers ($\text{mean}=3.21$). As for the difference between grade 8 and 9 students, it seems that in grade 9, when students do not learn about sound, there is a kind of regression to a more materialistic view of sound. The girls performed better than the boys ($t=3.59$, $p<0.001$). The paper uses Vosniadou and Brewer’s [Cogn. Sci. 18, 123 (1994).] framework theory to explain the results, and suggests some ideas for improving the teaching of sound.

This study investigates how elite Turkish high school physics students claim to approach learning physics when they are simultaneously (i) engaged in a curriculum that led to significant gains in their epistemological sophistication and (ii) subject to a high-stakes college entrance exam. Students reported taking surface (rote) approaches to learning physics, largely driven by college entrance exam preparation and therefore focused on algorithmic problem solving at the expense of exploring concepts and real-life examples more deeply. By contrast, in recommending study strategies to “Arzu,” a hypothetical student who doesn’t need to take a college entrance exam and just wants to understand physics deeply, the students focused more on linking concepts and real-life examples and on making sense of the formulas and concepts—deep approaches to learning that reflect somewhat sophisticated epistemologies. These results illustrate how students can epistemically compartmentalize, consciously taking different epistemic stances—different views of what counts as knowing and learning—in different contexts even within the same discipline.