This study investigates university students’ graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the Faculty of Science, University of Zagreb. Students were asked to provide explanations and/or mathematical procedures with their answers. Students’ main strategies and difficulties identified through the analysis of those explanations and procedures are described. Student strategies of graph interpretation were found to be largely context dependent and domain specific. A small fraction of students have used the same strategy in all three domains (mathematics, physics, and other contexts) on most sets of parallel questions. Some students have shown indications of transfer of knowledge in the sense that they used techniques and strategies developed in physics for solving (or attempting to solve) other context problems. In physics, the preferred strategy was the use of formulas, which sometimes seemed to block the use of other, more productive strategies which students displayed in other domains. Students’ answers indicated the presence of slope-height confusion and interval-point confusion in all three domains. Students generally better interpreted graph slope than the area under a graph, although the concept of slope still seemed to be quite vague for many. The interpretation of the concept of area under a graph needs more attention in both physics and mathematics teaching.

The combination of modern computing power, the interactivity of web applications, and the flexibility of object-oriented programming may finally be sufficient to create computer coaches that can help students develop metacognitive problem-solving skills, an important competence in our rapidly changing technological society. However, no matter how effective such coaches might be, they will only be useful if they are attractive to students. We describe the design and testing of a set of web-based computer programs that act as personal coaches to students while they practice solving problems from introductory physics. The coaches are designed to supplement regular human instruction, giving students access to effective forms of practice outside class. We present results from large-scale usability tests of the computer coaches and discuss their implications for future versions of the coaches.

Lab activities are an important element of an undergraduate physics course. In these lab activities, students construct and interpret graphs in order to connect the procedures of the lab with an understanding of the related physics concepts. This study investigated undergraduate students’ construction and interpretation of graphs with best-fit lines in the context of two physics lab activities. Students’ graphs were evaluated for overall graph quality and for the quality of the best-fit line. The strategies students used and their understanding of the meaning of the graph were accessed through interviews. The results suggest that undergraduate introductory physics students can successfully construct graphs with best-fit lines while not connecting the meaning of the graph to the underlying physics concepts. Furthermore, results indicated that the most challenging aspect of constructing a graph is setting up the scale, and that graphing is situated in specific contexts.

While many innovative teaching strategies exist, integration into undergraduate science teaching has been frustratingly slow. This study aims to understand the low uptake of research-based instructional innovations by studying 21 successful implementations of the Student Centered Active Learning with Upside-down Pedagogies (SCALE-UP) instructional reform. SCALE-UP significantly restructures the classroom environment and pedagogy to promote highly active and interactive instruction. Although originally designed for university introductory physics courses, SCALE-UP has spread to many other disciplines at hundreds of departments around the world. This study reports findings from in-depth, open-ended interviews with 21 key contact people involved with successful secondary implementations of SCALE-UP throughout the United States. We defined successful implementations as those who restructured their pedagogy and classroom and sustained and/or spread the change. Interviews were coded to identify the most common enabling and challenging factors during reform implementation and compared to the theoretical framework of Kotter’s 8-step Change Model. The most common enabling influences that emerged are documenting and leveraging evidence of local success, administrative support, interaction with outside SCALE-UP user(s), and funding. Many challenges are linked to the lack of these enabling factors including difficulty finding funding, space, and administrative and/or faculty support for reform. Our focus on successful secondary implementations meant that most interviewees were able to overcome challenges. Presentation of results is illuminated with case studies, quotes, and examples that can help secondary implementers with SCALE-UP reform efforts specifically. We also discuss the implications for policy makers, researchers, and the higher education community concerned with initiating structural change.

Students in introductory physics struggle with vector algebra and these challenges are often associated with contextual and representational features of the problems. Performance on problems about cross product direction is particularly poor and some research suggests that this may be primarily due to misapplied right-hand rules. However, few studies have had the resolution to explore student use of right-hand rules in detail. This study reviews literature in several disciplines, including spatial cognition, to identify ten contextual and representational problem features that are most likely to influence performance on problems requiring a right-hand rule. Two quantitative measures of performance (correctness and response time) and two qualitative measures (methods used and type of errors made) were used to explore the impact of these problem features on student performance. Quantitative results are consistent with expectations from the literature, but reveal that some features (such as the type of reasoning required and the physical awkwardness of using a right-hand rule) have a greater impact than others (such as whether the vectors are placed together or separate). Additional insight is gained by the qualitative analysis, including identifying sources of difficulty not previously discussed in the literature and revealing that the use of supplemental methods, such as physically rotating the paper, can mitigate errors associated with certain features.

In this paper, we show data from the Colorado Learning Attitudes about Science Survey that suggests that Georgetown physics majors become increasingly expert in their attitudes towards physics learning and knowing after taking a course that combines two reformed curricula, Matter and Interactions (M&I) and Tutorials in Introductory Physics (TIPs). This occurs even though the two curricula do not send a consistent epistemological message to students. We analyze interview video data of two of these students to illustrate examples of this growth. We examine video data of one of these students in a tutorial session to describe a possible mechanism that may have contributed to the growth. Finally, we compare this qualitative video data with quantitative data from the newly developed Perceptions of Physics Classes survey and discuss aggregate responses to this survey in considering the ways in which other students developed more expertlike attitudes in this course. We conclude that the attitudinal growth observed cannot be explained simply “as the result of” either M&I or of TIPs but rather find the most plausible explanation to be that the growth is an emergent phenomena produced by M&I and TIPs working together in concert with other factors.

Students’ epistemologies affect how and what they learn: do they believe physics is a list of equations, or a coherent and sensible description of the physical world? In order to study these epistemologies as part of curricular assessment, we adopt the resources framework, which posits that students have many productive epistemological resources that can be brought to bear as they learn physics. In previous studies, these epistemologies have been either inferred from behavior in learning contexts or probed through surveys or interviews outside of the learning context. We argue that stimulated recall interviews provide a contextually and interpretively valid method to access students’ epistemologies that complement existing methods. We develop a stimulated recall interview methodology to assess a curricular intervention and find evidence that epistemological resources aptly describe student epistemologies.

In this study we investigated how two different approaches to drawing free body diagrams influence the development of students’ understanding of Newton’s laws, including their ability to identify real forces. For this purpose we developed a 12-item two-tier multiple choice survey and conducted a quasiexperiment. This experiment included two groups of first-year physics students from Rijeka (RG) ($n_e=27$) and Split (SG) ($n_c=25$) Universities. Students from both groups solved mechanics problems for a period of two class hours. The only difference was that RG students used the superposition of forces approach to solving mechanics problems and in SG the decomposition of forces approach has been used. The ANCOVA ($n_c=17$, $n_e=17$) showed a statistically significant difference in favor of RG, whereby the effect sizes were moderate to large, and the largest differences have been observed in the ability of identifying real forces. Students from the control group (SG) more often exhibited the misconception that forces and their components act on a body independently and simultaneously. Our results support the idea that the practice of resolving forces into the components may not be the most effective way to develop understanding of Newton’s laws and the concept of force.

This study was based on the hypothesis that students’ epistemological beliefs could become more expertlike with a combination of appropriate instructional activities: (i) preclass reading with metacognitive reflection, and (ii) in-class active learning that produces cognitive dissonance. This hypothesis was tested through a five-year study involving close to 1000 students at two institutions, in four physics courses. Using an experimental design, data from student interviews, writing product assessments, and the Discipline-Focused Epistemological Beliefs Questionnaire (DFEBQ) we demonstrate that the beliefs of novice science learners became more expertlike on 2 of the 4 DFEBQ factors. We conclude that a combination of an activity that gets students to examine textual material metacognitively (Reflective Writing) with one or more types of in-class active learning interventions can promote positive change in students’ epistemological beliefs.

Superposition gives rise to the probabilistic nature of quantum mechanics and is therefore one of the concepts at the heart of quantum mechanics. Although we have found that many students can successfully use the idea of superposition to calculate the probabilities of different measurement outcomes, they are often unable to identify the experimental implications of a superposition state. In particular, they fail to recognize how a superposition state and a mixed state (sometimes called a “lack of knowledge” state) can produce different experimental results. We present data that suggest that superposition in quantum mechanics is a difficult concept for students enrolled in sophomore-, junior-, and graduate-level quantum mechanics courses. We illustrate how an interactive lecture tutorial can improve student understanding of quantum mechanical superposition. A longitudinal study suggests that the impact persists after an additional quarter of quantum mechanics instruction that does not specifically address these ideas.

In this paper we present a series of item response models of data collected using the Force Concept Inventory. The Force Concept Inventory (FCI) was designed to poll the Newtonian conception of force viewed as a multidimensional concept, that is, as a complex of distinguishable conceptual dimensions. Several previous studies have developed single-trait item response models of FCI data; however, we feel that multidimensional models are also appropriate given the explicitly multidimensional design of the inventory. The models employed in the research reported here vary in both the number of fitting parameters and the number of underlying latent traits assumed. We calculate several model information statistics to ensure adequate model fit and to determine which of the models provides the optimal balance of information and parsimony. Our analysis indicates that all item response models tested, from the single-trait Rasch model through to a model with ten latent traits, satisfy the standard requirements of fit. However, analysis of model information criteria indicates that the five-trait model is optimal. We note that an earlier factor analysis of the same FCI data also led to a five-factor model. Furthermore the factors in our previous study and the traits identified in the current work match each other well. The optimal five-trait model assigns proficiency scores to all respondents for each of the five traits. We construct a correlation matrix between the proficiencies in each of these traits. This correlation matrix shows strong correlations between some proficiencies, and strong anticorrelations between others. We present an interpretation of this correlation matrix.

Broad instructional methods like “interactive engagement” have been shown to be effective, but such general characterization provides little guidance on the details of how to structure instructional materials. In this study, we seek instructional specificity by comparing two ways of using an analogy to learn a target physical principle: (i) applying the analogy to the target physical domain on a case-by-case basis and (ii) using the analogy to create a general rule in the target physical domain. In the discussion sections of a large, introductory physics course ($N=231$), students who sought a general rule were better able to discover and apply a correct physics principle than students who analyzed the examples case by case. The difference persisted at a reduced level after subsequent direct instruction. We argue that students who performed case-by-case analyses were more likely to focus on idiosyncratic problem-specific features rather than the deep structural features. This study provides an example of investigations into how the specific structure of instructional materials can be consequential for what is learned.

We report on seven years of attitudinal data using the Colorado Learning Attitudes about Science Survey from University Modeling Instruction (UMI) sections of introductory physics at Florida International University. University Modeling Instruction is a curricular and pedagogical transformation of introductory university physics that engages students in building and testing conceptual models in an integrated lab and lecture learning environment. This work expands upon previous studies that reported consistently positive attitude shifts in UMI courses; here, we disaggregate the data by gender and ethnicity to look for any disparities in the pattern of favorable shifts. We find that women and students from statistically underrepresented ethnic groups have gains that are comparable to those of men and students from well-represented ethnic groups on this attitudinal measure, and that this result holds even when interaction effects of gender and ethnicity are included. We conclude with suggestions for future work in UMI courses and for attitudinal equity investigations generally. We encourage researchers to expand their scope beyond simple performance gaps when considering equity concerns, and to avoid relying on a single measure to evaluate student success. Finally, we conjecture that students’ social and academic networks are one means by which attitudinal and efficacy beliefs about the course are propagated.

Separation of variables can be a powerful technique for solving many of the partial differential equations that arise in physics contexts. Upper-division physics students encounter this technique in multiple topical areas including electrostatics and quantum mechanics. To better understand the difficulties students encounter when utilizing the separation of variables technique, we examined students’ responses to midterm exam questions and a standardized conceptual assessment and conducted think-aloud, problem-solving interviews. Our analysis was guided by an analytical framework that focuses on how students activate, construct, execute, and reflect on the separation of variables technique when solving physics problems. Here we focus on student difficulties with separation of variables as a technique to solve Laplace’s equation in both Cartesian and spherical coordinates in the context of junior-level electrostatics. Challenges include recognizing when separation of variables is the appropriate tool, recalling or justifying the separated form of the potential and the need for the infinite sum, identifying implicit boundary conditions, and spontaneously reflecting on their solutions. Moreover, the type and frequency of errors was often different for separation of variables problems in Cartesian and spherical geometries. We also briefly discuss implication of these findings for instruction.

Standardized conceptual assessment represents a widely used tool for educational researchers interested in student learning within the standard undergraduate physics curriculum. For example, these assessments are often used to measure student learning across educational contexts and instructional strategies. However, to support the large-scale implementation often required for cross-institutional testing, it is necessary for these instruments to have question formats that facilitate easy grading. Previously, we created a multiple-response version of an existing, validated, upper-division electrostatics diagnostic with the goal of increasing the instrument’s potential for large-scale implementation. Here, we report on the validity and reliability of this new version as an independent instrument. These findings establish the validity of the multiple-response version as measured by multiple test statistics including item difficulty, item discrimination, and internal consistency. Moreover, we demonstrate that the majority of student responses to the new version are internally consistent even when they are incorrect and provide an example of how the new format can be used to gain insight into student difficulties with specific content in electrostatics.

Understanding Maxwell’s equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found that they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell’s equations in electrodynamics.

Students’ ability to effectively study for an exam, or to manage their time during an exam, is related to their metacognitive capacity. Prior research has demonstrated the effective use of metacognitive strategies during learning and retrieval is related to content expertise. Students also make judgments of their own learning and of problem difficulty to guide their studying. This study extends prior research by investigating the accuracy of novices’ and experts’ ability to judge problem difficulty across two experiments; here “accuracy” refers to whether or not their judgments of problem difficulty corresponds with actual exam performance in an introductory mechanics physics course. In the first experiment, physics education research (PER) experts judged the difficulty of introductory physics problems and provided the rationales behind their judgments. Findings indicate that experts use a number of different problem features to make predictions of problem difficulty. While experts are relatively accurate in judging problem difficulty, their content expertise may interfere with their ability to predict student performance on some question types. In the second experiment novices and “near experts” (graduate TAs) judged which question from a problem pair (taken from a real exam) was more difficult. The results indicate that judgments of problem difficulty are more accurate for those with greater content expertise, suggesting that the ability to predict problem difficulty is a trait of expertise which develops with experience.

Thermal science is challenging for students due to its largely imperceptible nature. Handheld infrared cameras offer a pedagogical opportunity for students to see otherwise invisible thermal phenomena. In the present study, a class of upper secondary technology students ($N=30$) partook in four IR-camera laboratory activities, designed around the predict-observe-explain approach of White and Gunstone. The activities involved central thermal concepts that focused on heat conduction and dissipative processes such as friction and collisions. Students’ interactions within each activity were videotaped and the analysis focuses on how a purposefully selected group of three students engaged with the exercises. As the basis for an interpretative study, a “thick” narrative description of the students’ epistemological and conceptual framing of the exercises and how they took advantage of the disciplinary affordance of IR cameras in the thermal domain is provided. Findings include that the students largely shared their conceptual framing of the four activities, but differed among themselves in their epistemological framing, for instance, in how far they found it relevant to digress from the laboratory instructions when inquiring into thermal phenomena. In conclusion, the study unveils the disciplinary affordances of infrared cameras, in the sense of their use in providing access to knowledge about macroscopic thermal science.

[This paper is part of the Focused Collection on Upper Division Physics Courses.] Partial derivatives are used in a variety of different ways within physics. Thermodynamics, in particular, uses partial derivatives in ways that students often find especially confusing. We are at the beginning of a study of the teaching of partial derivatives, with a goal of better aligning the teaching of multivariable calculus with the needs of students in STEM disciplines. In this paper, we report on an initial study of expert understanding of partial derivatives across three disciplines: physics, engineering, and mathematics. We report on the central research question of how disciplinary experts understand partial derivatives, and how their concept images of partial derivatives differ, with a focus on experimentally measured quantities. Using the partial derivative machine (PDM), we probed expert understanding of partial derivatives in an experimental context without a known functional form. In particular, we investigated which representations were cued by the experts’ interactions with the PDM. Whereas the physicists and engineers were quick to use measurements to find a numeric approximation for a derivative, the mathematicians repeatedly returned to speculation as to the functional form; although they were comfortable drawing qualitative conclusions about the system from measurements, they were reluctant to approximate the derivative through measurement. On a theoretical front, we found ways in which existing frameworks for the concept of derivative could be expanded to include numerical approximation.