This article describes the development and field test of the Sound Concept Inventory Instrument (SCII), designed to measure middle school students’ concepts of sound. The instrument was designed based on known students’ difficulties in understanding sound and the history of science related to sound and focuses on two main aspects of sound: sound has material properties, and sound has process properties. The final SCII consists of 71 statements that respondents rate as either true or false and also indicate their confidence on a five-point scale. Administration to 355 middle school students resulted in a Cronbach alpha of 0.906, suggesting a high reliability. In addition, the average percentage of students’ answers to statements that associate sound with material properties is significantly higher than the average percentage of statements associating sound with process properties ($p<0.001$). The SCII is a valid and reliable tool that can be used to determine students’ conceptions of sound.

This paper describes an investigation into student reasoning about potential energy in the context of introductory electrostatics. Similar incorrect reasoning patterns emerged both in written questions administered after relevant instruction and in one-on-one interviews. These reasoning patterns are also prevalent in responses to questions posed about gravitational potential energy in the context of universal gravitation in introductory mechanics. This finding is relevant for interdisciplinary research, because many courses in multiple disciplines first introduce the concept of electric potential energy in analogy to gravitational potential energy. The results suggest that in introductory courses students do not gain an understanding of potential energy that is sufficiently robust to apply in more advanced physics courses or in disciplines other than physics, in which students must frequently reason with energy in the context of interactions between atoms and molecules.

Several studies in recent years have demonstrated that upper-division students struggle with the mathematics of thermodynamics. This paper presents a task analysis based on several expert attempts to solve a challenging mathematics problem in thermodynamics. The purpose of this paper is twofold. First, we highlight the importance of cognitive task analysis for understanding expert performance and show how the epistemic games framework can be used as a tool for this type of analysis, with thermodynamics as an example. Second, through this analysis, we identify several issues related to thermodynamics that are relevant to future research into student understanding and learning of the mathematics of thermodynamics.

We review the literature on the gender gap on concept inventories in physics. Across studies of the most commonly used mechanics concept inventories, the Force Concept Inventory and Force and Motion Conceptual Evaluation, men’s average pretest scores are always higher than women’s, and in most cases men’s posttest scores are higher as well. The weighted average gender difference on these tests is 13% for pretest scores, 12% for posttest scores, and 6% for normalized gain. This difference is much smaller than the average difference in normalized gain between traditional lecture and interactive engagement (25%), but it is large enough that it could impact the results of studies comparing the effectiveness of different teaching methods. There is sometimes a gender gap on commonly used electricity and magnetism concept inventories, the Brief Electricity and Magnetism Assessment and Conceptual Survey of Electricity and Magnetism, but it is usually much smaller and sometimes is zero or favors women. The weighted average gender difference on these tests is 3.7% for pretest scores, 8.5% for posttest scores, and 6% for normalized gain. There are far fewer studies of the gender gap on electricity and magnetism concept inventories and much more variation in the existing studies. Based on our analysis of 26 published articles comparing the impact of 30 factors that could potentially influence the gender gap, no single factor is sufficient to explain the gap. Several high-profile studies that have claimed to account for or reduce the gender gap have failed to be replicated in subsequent studies, suggesting that isolated claims of explanations of the gender gap should be interpreted with caution. For example, claims that the gender gap could be eliminated through interactive engagement teaching methods or through a “values affirmation writing exercise” were not supported by subsequent studies. Suggestions that the gender gap might be reduced by changing the wording of “male-oriented” questions or refraining from asking demographic questions before administering the test are not supported by the evidence. Other factors, such as gender differences in background preparation, scores on different kinds of assessment, and splits between how students respond to test questions when answering for themselves or for a “scientist” do contribute to a difference between male and female responses, but the size of these differences is smaller than the size of the overall gender gap, suggesting that the gender gap is most likely due to the combination of many small factors rather than any one factor that can easily be modified.

The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple-choice test developed by Beichner in 1994 to assess students’ understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which correspond to students’ common difficulties with kinematics graphs. Instruction is unlikely to be effective if instructors do not know the common difficulties of introductory physics students and explicitly take them into account in their instructional design. We evaluate one aspect of the pedagogical content knowledge of first-year physics graduate students enrolled in a teaching assistant training course related to topics covered in the TUG-K. In particular, for each item on the TUG-K, the graduate students were asked to identify which incorrect answer choice they thought would be most commonly selected by introductory physics students if they did not know the correct answer after instruction in relevant concepts. We used the graduate student data and the data from Beichner’s original paper for introductory physics students (which was collected from over 500 college and high school students) to assess this aspect of the pedagogical content knowledge of the graduate students, i.e., knowledge of student difficulties related to kinematics graphs as they are revealed by the TUG-K. We find that, although the graduate students, on average, performed better than random guessing at identifying introductory student difficulties on the TUG-K, they did not identify many common difficulties that introductory students have with graphs in kinematics. In addition, we find that the ability of graduate students to identify the difficulties of introductory students is context dependent and that discussions among the graduate students improved their understanding of student difficulties related to kinematics graphs. Moreover, we find that the ability of American graduate students in identifying common student difficulties is comparable with that of foreign graduate students.

Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and researchers in characterizing students’ difficulties with specific mathematical tools when solving the long and complex problems that are characteristic of upper division. In this paper, we present this framework, including its motivation and development. We also describe an application of the framework to investigations of student difficulties with direct integration in electricity and magnetism (i.e., Coulomb’s law) and approximation methods in classical mechanics (i.e., Taylor series). These investigations provide examples of the types of difficulties encountered by advanced physics students, as well as the utility of the framework for both researchers and instructors.

Calculus is used across many physics topics from introductory to upper-division courses. The fundamental concepts of differentiation and integration are important tools for solving real-world problems involving nonuniformly distributed quantities. Research in physics education has reported students’ lack of ability to transfer their calculus knowledge to physics. In order to better understand students’ deficiencies, we collected data from group teaching or learning interviews as students solved physics problems requiring setting up integrals. We adapted the conceptual blending framework from cognitive science to make sense of the ways in which students combined their knowledge from calculus and physics to set up integrals. We found that many students were not able to blend their mathematics and physics knowledge in a productive way though they have the required mathematics knowledge. We discussed the productive and unproductive blends that students created when setting up integrals. The results of the study also suggested possible strategies to shifting students’ constructing of blends to more powerful ones.

We analyze the development in students’ understanding of fundamental principles in the context of learning a current interdisciplinary research topic—soft matter—that was adapted to the level of high school students. The topic was introduced in a program for interested 11th grade high school students majoring in chemistry and/or physics, in an off-school setting. Soft matter was presented in a gradual increase in the degree of complexity of the phenomena as well as in the level of the quantitative analysis. We describe the evolution in students’ use of fundamental thermodynamics principles to reason about phase separation—a phenomenon that is ubiquitous in soft matter. In particular, we examine the impact of the use of free energy analysis, a common approach in soft matter, on the understanding of the fundamental principles of thermodynamics. The study used diagnostic questions and classroom observations to gauge the student’s learning. In order to gain insight on the aspects that shape the understanding of the basic principles, we focus on the responses and explanations of two case-study students who represent two trends of evolution in conceptual understanding in the group. We analyze changes in the two case studies’ management of conceptual resources used in their analysis of phase separation, and suggest how their prior knowledge and epistemological framing (a combination of their personal tendencies and their prior exposure to different learning styles) affect their conceptual evolution. Finally, we propose strategies to improve the instruction of these concepts.

We report on a multiyear study of student attitudes measured with the Colorado Learning Attitudes about Science Survey in calculus-based introductory physics taught with the Modeling Instruction curriculum. We find that five of six instructors and eight of nine sections using Modeling Instruction showed significantly improved attitudes from pre- to postcourse. Cohen’s $d$ effect sizes range from 0.08 to 0.95 for individual instructors. The average effect was $d=0.45$, with a 95% confidence interval of (0.26–0.64). These results build on previously published results showing positive shifts in attitudes from Modeling Instruction classes. We interpret these data in light of other published positive attitudinal shifts and explore mechanistic explanations for similarities and differences with other published positive shifts.

There are many hypotheses regarding factors that may encourage female students to pursue careers in the physical sciences. Using multivariate matching methods on national data drawn from the Persistence Research in Science and Engineering (PRiSE) project ($n=7505$), we test the following five commonly held beliefs regarding what factors might impact females’ physical science career interest: (i) having a single-sex physics class, (ii) having a female physics teacher, (iii) having female scientist guest speakers in physics class, (iv) discussing the work of female scientists in physics class, and (v) discussing the underrepresentation of women in physics class. The effect of these experiences on physical science career interest is compared for female students who are matched on several factors, including prior science interests, prior mathematics interests, grades in science, grades in mathematics, and years of enrollment in high school physics. No significant effects are found for single-sex classes, female teachers, female scientist guest speakers, and discussing the work of female scientists. However, discussions about women’s underrepresentation have a significant positive effect.

In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation in which they had to learn from a solved problem provided and take advantage of what they learned from it to solve another isomorphic problem (which we call the quiz problem). The solved problem provided has two subproblems while the quiz problem has three subproblems, which is known from previous research to be challenging for introductory students. In addition to the solved problem, students also received extra scaffolding supports that were intended to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. The data analysis suggests that students had great difficulty in transferring what they learned from a two-step problem to a three-step problem. Although most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem, they were not necessarily able to apply the principles correctly. We also conducted think-aloud interviews with six introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. The interviews suggest that students often superficially mapped the principles employed in the solved problem to the quiz problem without necessarily understanding the governing conditions underlying each principle and examining the applicability of the principle in the new situation in an in-depth manner. Findings suggest that more scaffolding is needed to help students in transferring from a two-step problem to a three-step problem and applying the physics principles appropriately. We outline a few possible strategies for future investigation.

We have examined the teaching practices of faculty members who adopted research-based instructional strategies (RBIS) as part of the Carl Wieman Science Education Initiative (CWSEI) at the University of British Columbia (UBC). Of the 70 that adopted such strategies with the support of the CWSEI program, only one subsequently stopped using these strategies. This is a tiny fraction of the 33% stopping rate for physics faculty in general [Phys. Rev. ST Phys. Educ. Res. 8, 020104 (2012)]. Nearly all of these UBC faculty members who had an opportunity to subsequently use RBIS in other courses (without CWSEI support) did so. We offer speculations for the difference in quitting rates. The direct support of the faculty member by a trained science education specialist in the discipline during the initial implementation of the new strategies is a particularly notable factor.

Previous research suggests that students’ prior knowledge can interfere with how they observe and remember lecture demonstrations. We measured students’ prior knowledge in introductory mechanics and electricity and magnetism at two large universities. Students were then asked to predict the outcome of lecture demonstrations. We compare students’ predictions before having seen the demonstration to what they report having seen both right after the demonstration and several weeks later. We report four main findings. First, roughly one out of every five observations of a demonstration is inconsistent with the actual outcome. Second, students who understand the underlying concepts before observing the demonstration are more likely to observe it and remember it correctly. Third, students are roughly 20% (23%) more likely to observe a demonstration correctly if they predict the outcome first, regardless of whether the prediction is correct or not. Last, conceptual learning is contingent on the student making a correct observation. This study represents an initial step towards understanding the disconnect reported between demonstrations and student learning.

As has been shown by previous research, students may possess various misconceptions in the area of thermal physics. In order to help them overcome misconceptions observed prior to instruction, we implemented a one-hour lecture-based intervention in their introductory thermal physics course. The intervention was held after the conventional lectures and homework sessions, and it consisted of three phases: individual working, hinting, and peer discussion. To probe students’ conceptual understanding before, during, and after the intervention, use was made of a diagnostic test related to the multiphased process of an ideal gas [D. E. Meltzer, Am. J. Phys. 72, 1432 (2004)]. The students’ conceptions were monitored by analyzing the explanations they provided and by recording the peer discussions of five voluntary pairs. The intervention helped students to realize the flaws in their explanations and increased the proportion of their scientific explanations, the increase being statistically significant in five tasks out of seven. When the same themes were addressed in a post-test, it was shown that the level of accurate explanations remained almost constant after the intervention, and hence it could be deduced that the impact had not been short-lived. In comparison with earlier studies conducted with the same material, our intervention produced a better learning outcome, the difference being 15–20 percentage points. In addition, the number of misconceptions on the part of the students was smaller in our study, although with individual exceptions. Hence, we conclude that the intervention was successful and that similar interventions could also be designed and implemented in other areas of physics.

For over 30 years, researchers have investigated students’ ideas about energy with the intent of reforming instructional practice. In this pursuit, Watts contributed an influential study with his 1983 paper “Some alternative views of energy” [Phys. Educ. 18, 213 (1983)]. Watts’ “alternative frameworks” continue to be used for categorizing students’ non-normative ideas about energy. Using a resources framework, we propose an alternate analysis of student responses from Watts’ interviews. In our analysis, we show how students’ activated resources about energy are disciplinarily productive. We suggest that fostering seeds of scientific understandings in students’ ideas about energy may play an important role in their development of scientific literacy.

This study reports on a content course for science immersion teacher candidates that emphasized authentic practice of science and thinking scientifically in the context of introductory astrophysics. We explore how 122 science teacher candidates spanning three cohorts did and did not reason scientifically and how this evolved in our program. Our primary method of exploring teacher candidate reasoning is through analysis of responses to an apparently simple multiple-choice question. The question asks for the relative motion between the Sun and Earth and then for a scientific argument supporting the response. To explore these participants’ reasoning and its potential impact on classroom practice, we also describe qualitative observations of how the teacher candidates were reasoning while participating in a science course, participant evaluations, and long-term follow-up with select program graduates after they had taught science in middle or high school. Our results suggest that participant ability to reason scientifically improved significantly and that this can impact classroom practice in a positive way.

One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann factor using a Taylor series expansion of entropy. Using results from written surveys, classroom observations, and both individual think-aloud and teaching interviews, we present evidence that many students can recognize and interpret series expansions, but they often lack fluency in creating and using a Taylor series appropriately, despite previous exposures in both calculus and physics courses.

The role of student interactions in learning situations is a foundation of sociocultural learning theory, and social network analysis can be used to quantify student relations. We discuss how self-reported student interactions can be viewed as processes of meaning making and use this to understand how quantitative measures that describe the position in a network, called centrality measures, can be understood in terms of interactions that happen in the context of a university physics course. We apply this discussion to an empirical data set of self-reported student interactions. In a weekly administered survey, first year university students enrolled in an introductory physics course at a Danish university indicated with whom they remembered having communicated within different interaction categories. For three categories pertaining to (1) communication about how to solve physics problems in the course (called the PS category), (2) communications about the nature of physics concepts (called the CD category), and (3) social interactions that are not strictly related to the content of the physics classes (called the ICS category) in the introductory mechanics course, we use the survey data to create networks of student interaction. For each of these networks, we calculate centrality measures for each student and correlate these measures with grades from the introductory course, grades from two subsequent courses, and the pretest Force Concept Inventory (FCI) scores. We find highly significant correlations ($p<0.001$) between network centrality measures and grades in all networks. We find the highest correlations between network centrality measures and future grades. In the network composed of interactions regarding problem solving (the PS network), the centrality measures hide and PageRank show the highest correlations ($r=-0.32$ and $r=0.33$, respectively) with future grades. In the CD network, the network measure target entropy shows the highest correlation ($r=0.45$) with future grades. In the network composed solely of noncontent related social interactions, these patterns of correlation are maintained in the sense that these network measures show the highest correlations and maintain their internal ranking. Using hierarchical linear regression, we find that a linear model that adds the network measures hide and target entropy, calculated on the ICS network, significantly improves a base model that uses only the FCI pretest scores from the beginning of the semester. Though one should not infer causality from these results, they do point to how social interactions in class are intertwined with academic interactions. We interpret this as an integral part of learning, and suggest that physics is a robust example.

This study focuses on students’ use of the mathematical concept of differentials in physics problem solving. For instance, in electrostatics, students need to set up an integral to find the electric field due to a charged bar, an activity that involves the application of mathematical differentials (e.g., $dr$, $dq$). In this paper we aim to explore students’ reasoning about the differential concept in physics problems. We conducted group teaching or learning interviews with 13 engineering students enrolled in a second-semester calculus-based physics course. We amalgamated two frameworks—the resources framework and the conceptual metaphor framework—to analyze students’ reasoning about differential concept. Categorizing the mathematical resources involved in students’ mathematical thinking in physics provides us deeper insights into how students use mathematics in physics. Identifying the conceptual metaphors in students’ discourse illustrates the role of concrete experiential notions in students’ construction of mathematical reasoning. These two frameworks serve different purposes, and we illustrate how they can be pieced together to provide a better understanding of students’ mathematical thinking in physics.