Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in writing before solving a problem. The CPS approach was implemented by high school physics teachers at three schools for major theorems and conservation laws in mechanics and CPS-taught classes were compared to control classes taught using traditional problem solving methods. Information about the teachers’ implementation of the approach was gathered from classroom observations and interviews, and the effectiveness of the approach was evaluated from a series of written assessments. Results indicated that teachers found CPS easy to integrate into their curricula, students engaged in classroom discussions and produced problem solutions of a higher quality than before, and students scored higher on conceptual and problem solving measures.

It is well known that introductory physics students often have alternative conceptions that are inconsistent with established physical principles and concepts. Invoking alternative conceptions in the quantitative problem-solving process can derail the entire process. In order to help students solve quantitative problems involving strong alternative conceptions correctly, appropriate scaffolding support can be helpful. The goal of this study is to examine how different scaffolding supports involving analogical problem-solving influence introductory physics students’ performance on a target quantitative problem in a situation where many students’ solution process is derailed due to alternative conceptions. Three different scaffolding supports were designed and implemented in calculus-based and algebra-based introductory physics courses involving 410 students to evaluate the level of scaffolding needed to help students learn from an analogical problem that is similar in the underlying principles involved but for which the problem-solving process is not derailed by alternative conceptions. We found that for the quantitative problem involving strong alternative conceptions, simply guiding students to work through the solution of the analogical problem first was not enough to help most students discern the similarity between the two problems. However, if additional scaffolding supports that directly helped students examine and repair their knowledge elements involving alternative conceptions were provided, e.g., by guiding students to contemplate related issues and asking them to solve the targeted problem on their own first before learning from the analogical problem provided, students were more likely to discern the underlying similarities between the problems and avoid getting derailed by alternative conceptions when solving the targeted problem. We also found that some scaffolding supports were more effective in the calculus-based course than in the algebra-based course. This finding emphasizes the fact that appropriate scaffolding support which is commensurate with students’ prior knowledge and skills must be determined via research in order to be effective.

It is known that experts identify or perceive meaningful patterns in visual stimuli related to their domain of expertise. This study explores the speed with which experts and novices detect changes in physics diagrams. Since change detection depends on where individuals direct their attention, differences in the speed with which experts and novices detect changes to diagrams would suggest differences in attention allocation between experts and novices. We present data from an experiment using the “flicker technique,” in which both physics experts and physics novices viewed nearly identical pairs of diagrams that are representative of typical introductory physics situations. The two diagrams in each pair contain a subtle difference that either does or does not change the underlying physics depicted in the diagram. Findings indicate that experts are faster at detecting physics-relevant changes than physics-irrelevant changes; however, there is no difference in response time for novices, suggesting that expertise guides attention for experts when inspecting physics diagrams. We discuss the cognitive implications of our findings.

We have conducted an investigation into how well students in introductory science classes (both physics and chemistry) are able to predict which questions they will or will not be able to answer correctly on an upcoming assessment. An examination of the data at the level of students’ overall scores reveals results consistent with the Dunning-Kruger effect, in which low-performing students tend to overestimate their abilities, while high-performing students estimate their abilities more accurately. Similar results have been widely reported in the science education literature. Breaking results out by students’ responses to individual questions, however, reveals that students of all ability levels have difficulty distinguishing questions which they are able to answer correctly from those that they are not able to answer correctly. These results have implications for the future study and reporting of students’ metacognitive abilities.

In this paper, we report about the development and validation of a learning progression about the Celestial Motion big idea. Existing curricula, research studies on alternative conceptions about these phenomena, and students’ answers to an open questionnaire were the starting point to develop initial learning progressions about change of seasons, solar and lunar eclipses, and Moon phases; then, a two-tier multiple choice questionnaire was designed to validate and improve them. The questionnaire was submitted to about 300 secondary students of different school levels (14 to 18 years old). Item response analysis and curve integral method were used to revise the hypothesized learning progressions. Findings support that spatial reasoning is a key cognitive factor for building an explanatory framework for the Celestial Motion big idea, but also suggest that causal reasoning based on physics mechanisms underlying the phenomena, as light flux laws or energy transfers, may significantly impact a students’ understanding. As an implication of the study, we propose that the teaching of the three discussed astronomy phenomena should follow a single teaching-learning path along the following sequence: (i) emphasize from the beginning the geometrical aspects of the Sun-Moon-Earth system motion; (ii) clarify consequences of the motion of the Sun-Moon-Earth system, as the changing solar radiation flow on the surface of Earth during the revolution around the Sun; (iii) help students moving between different reference systems (Earth and space observer’s perspective) to understand how Earth’s rotation and revolution can change the appearance of the Sun and Moon. Instructional and methodological implications are also briefly discussed.

Many topics in introductory astronomy at the college or high-school level rely implicitly on using astronomical photographs and visual data in class. However, students bring many preconceptions to their understanding of these materials that ultimately lead to misconceptions, and research about students’ interpretation of astronomical images has been scarcely conducted. In this study we probed college students’ understanding of astronomical photographs and visual data about galaxies and spectra, and developed a set of concept questions based on their common misconceptions. The study was conducted mainly in three successive surveys: (i) open-ended questions looking for students’ ideas and common misconceptions, (ii) combined multiple-choice and open-ended questions seeking to explore student reasoning and to improve concept questions for clickers, and (iii) a finalized version of the concept questions used to investigate the strength of each misconception among the students in introductory astronomy courses. This study reports on the procedures and the development of the concept questions with the investigated common misconceptions about galaxies and spectra. We also provide the set of developed questions for teachers and instructors seeking to implement in their classes for the purpose of formative assessment with the use of classroom response systems. These questions would help them recognize the gap between their teaching and students’ understanding, and ultimately improve teaching of the concepts.

The term “weight” has multiple related meanings in both scientific and everyday usage. Even among experts and in textbooks, weight is ambiguously defined as either the gravitational force on an object or operationally as the magnitude of the force an object exerts on a measuring scale. This poses both conceptual and language difficulties for learners, especially for accelerating objects where the scale reading is different from the gravitational force. But while the underlying physical constructs behind the two referents for the term weight (and their relation to each other) are well understood scientifically, it is unclear how the concept of weight should be introduced to students and how the language ambiguities should be dealt with. We investigated treatments of weight in a sample of twenty introductory college physics textbooks, analyzing and coding their content based on the definition adopted, how the distinct constructs were dealt with in various situations, terminologies used, and whether and how language issues were handled. Results indicate that language-related issues, such as different, inconsistent, or ambiguous uses of the terms weight, “apparent weight,” and “weightlessness,” were prevalent both across and within textbooks. The physics of the related constructs was not always clearly presented, particularly for accelerating bodies such as astronauts in spaceships, and the language issue was rarely addressed. Our analysis of both literature and textbooks leads us to an instructional position which focuses on the physics constructs before introducing the term weight, and which explicitly discusses the associated language issues.

We investigate the development of expert identities through the use of the sociocultural perspective of learning as participating in a community of practice. An ethnographic case study of biophysics graduate students focuses on the experiences the students have in their research group meetings. The analysis illustrates how the communities of practice-based identity constructs of competencies characterize student expert membership. A microanalysis of speech, sound, tones, and gestures in video data characterize students’ social competencies in the physics community of practice. Results provide evidence that students at different stages of their individual projects have opportunities to develop social competencies such as mutual engagement, negotiability of the repertoire, and accountability to the enterprises as they interact with group members. The biophysics research group purposefully designed a learning trajectory including conducting research and writing it for publication in the larger community of practice as a pathway to expertise. The students of the research group learn to become socially competent as specific experts of their project topic and methodology, ensuring acceptance, agency, and membership in their community of practice. This work expands research on physics expertise beyond the cognitive realm and has implications for how to design graduate learning experiences to promote expert identity development.

In this meta-analysis, we synthesize the results of 24 studies using the Colorado Learning Attitudes about Science Survey (CLASS) and the Maryland Physics Expectations Survey (MPEX) to answer several questions: (1) How does physics instruction impact students’ beliefs? (2) When do physics majors develop expert-like beliefs? and (3) How do students’ beliefs impact their learning of physics? We report that in typical physics classes, students’ beliefs deteriorate or at best stay the same. There are a few types of interventions, including an explicit focus on model-building and (or) developing expertlike beliefs that lead to significant improvements in beliefs. Further, small courses and those for elementary education and nonscience majors also result in improved beliefs. However, because the available data oversamples certain types of classes, it is unclear whether these improvements are actually due to the interventions, or due to the small class size, or student populations typical of the kinds of classes in which these interventions are most often used. Physics majors tend to enter their undergraduate education with more expertlike beliefs than nonmajors and these beliefs remain relatively stable throughout their undergraduate careers. Thus, typical physics courses appear to be selecting students who already have strong beliefs, rather than supporting students in developing strong beliefs. There is a small correlation between students’ incoming beliefs about physics and their gains on conceptual mechanics surveys. This suggests that students with more expertlike incoming beliefs may learn more in their physics courses, but this finding should be further explored and replicated. Some unanswered questions remain. To answer these questions, we advocate several specific types of future studies: measuring students’ beliefs in courses with a wider range of class sizes, student populations, and teaching methods, especially large classes with very innovative pedagogy and small classes with more typical pedagogy; analysis of the relationship between students’ beliefs and conceptual understanding including a wide variety of variables that might influence each; and analysis of large data sets from a variety of classes that track individual students rather than averaging over classes.

This paper is part of a series of studies to improve the efficacy of online physics homework activities by integrating narrated animated solutions with mastery inspired exercises. In a clinical study using first- and second-year university students, the mastery group attempted question sets in four levels, with animated solutions between each attempt, until mastery was achieved on each level. This combined elements of formative assessment, the worked example effect, and mastery learning. The homework group attempted questions with immediate feedback and unlimited tries. The two groups took a similar amount of time to complete the activity. The mastery group significantly outperformed the homework group on a free response post-test that required students to show their work in solving near and far transfer problems.

We examine Illinois educational data from standardized exams and analyze primary factors affecting the achievement of public school students. We focus on the simplest possible models: representation of data through visualizations and regressions on single variables. Exam scores are shown to depend on school type, location, and poverty concentration. For most schools in Illinois, student test scores decline linearly with poverty concentration. However, Chicago must be treated separately. Selective schools in Chicago, as well as some traditional and charter schools, deviate from this pattern based on poverty. For any poverty level, Chicago schools perform better than those in the rest of Illinois. Selective programs for gifted students show high performance at each grade level, most notably at the high school level, when compared to other Illinois school types. The case of Chicago charter schools is more complex. Up to 2008, Chicago charter and neighborhood schools had similar performance scores. In the last few years, charter students’ scores overtook those of students in traditional schools as the number of charter school locations increased.

The Force Concept Inventory (FCI) is a 30-question multiple-choice assessment that has been a building block for much of the physics education research done today. In practice, there are often concerns regarding the length of the test and possible test-retest effects. Since many studies in the literature use the mean score of the FCI as the primary variable, it would be useful then to have different shorter tests that can produce FCI-equivalent scores while providing the benefits of being quicker to administer and overcoming the test-retest effects. In this study, we divide the 1995 version of the FCI into two half-length tests; each contains a different subset of the original FCI questions. The two new tests are shorter, still cover the same set of concepts, and produce mean scores equivalent to those of the FCI. Using a large quantitative data set collected at a large midwestern university, we statistically compare the assessment features of the two half-length tests and the full-length FCI. The results show that the mean error of equivalent scores between any two of the three tests is within 3%. Scores from all tests are well correlated. Based on the analysis, it appears that the two half-length tests can be a viable option for score based assessment that need to administer tests quickly or need to measure short-term gains where using identical pre- and post-test questions is a concern.

We observe teachers in professional development courses about energy constructing mechanistic accounts of energy transformations. We analyze a case in which teachers investigating adiabatic compression develop a model of the transformation of kinetic energy to thermal energy. Among their ideas is the idea that thermal energy is generated as a byproduct of individual particle collisions, which is represented in science education research literature as an obstacle to learning. We demonstrate that in this instructional context, the idea that individual particle collisions generate thermal energy is not an obstacle to learning, but instead is productive: it initiates intellectual progress. Specifically, this idea initiates the reconciliation of the teachers’ energy model with mechanistic reasoning about adiabatic compression, and leads to a canonically correct model of the transformation of kinetic energy into thermal energy. We claim that the idea’s productivity is influenced by features of our particular instructional context, including the instructional goals of the course, the culture of collaborative sense making, and the use of certain representations of energy.

As part of an ongoing investigation of students’ learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum mechanics assessment tool (QMAT) to a multiple-choice (MC) format. Further question refinement, development of effective distractors, adding new questions, and robust statistical analysis has led to a 31-item quantum mechanics concept assessment (QMCA) test. The QMCA is used as post-test only to assess students’ knowledge about five main topics of quantum measurement: the time-independent Schrödinger equation, wave functions and boundary conditions, time evolution, and probability density. During two years of testing and refinement, the QMCA has been given in alpha ($N=61$) and beta versions ($N=263$) to students in upper division quantum mechanics courses at 11 different institutions with an average post-test score of 54%. By allowing for comparisons of student learning across different populations and institutions, the QMCA provides instructors and researchers a more standard measure of effectiveness of different curricula or teaching strategies on student conceptual understanding of quantum mechanics. In this paper, we discuss the construction of effective distractors and the use of student interviews and expert feedback to revise and validate both questions and distractors. We include the results of common statistical tests of reliability and validity, which suggest the instrument is presently in a stable, usable, and promising form.

Research has demonstrated that many students and some teachers do not consistently apply the conservation of energy principle when analyzing mechanical scenarios. In observing elementary and secondary teachers engaged in learning activities that require tracking and conserving energy, we find that challenges to energy conservation often arise in dissipative scenarios in which kinetic energy transforms into thermal energy (e.g., a ball rolls to a stop). We find that teachers expect that when they can see the motion associated with kinetic energy, they should be able to perceive the warmth associated with thermal energy. Their expectations are violated when the warmth produced is imperceptible. In these cases, teachers reject the idea that the kinetic energy transforms to thermal energy. Our observations suggest that apparent difficulties with energy conservation may have their roots in a strong and appropriate association between forms of energy and their perceptible indicators. We see teachers resolve these challenges by relating the original scenario to an exaggerated version in which the dissipated thermal energy is associated with perceptible warmth. Using these exaggerations, teachers infer that thermal energy is present to a lesser degree in the original scenario. They use this exaggeration strategy to track and conserve energy in dissipative scenarios.

The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them. To characterize student difficulties with the delta function at the upper-division level, we examined students’ responses to traditional exam questions and a standardized conceptual assessment, and conducted think-aloud interviews. Our analysis was guided by an analytical framework that focuses on how students activate, construct, execute, and reflect on the Dirac delta function in the context of problem solving in physics. Here, we focus on student difficulties using the delta function to express charge distributions in the context of junior-level electrostatics. Common challenges included invoking the delta function spontaneously, translating a description of a charge distribution into a mathematical expression using delta functions, integrating 3D or non-Cartesian delta function expressions, and recognizing that the delta function can have units. We also briefly discuss implications of these difficulties for instruction.

Although confusion is generally perceived to be negative, educators dating as far back as Socrates, who asked students to question assumptions and wrestle with ideas, have challenged this notion. Can confusion be productive? How should instructors interpret student expressions of confusion? During two semesters of introductory physics that involved Just-in-Time Teaching (JiTT) and research-based reading materials, we evaluated performance on reading assignments while simultaneously measuring students’ self-assessment of their confusion over the preclass reading material ($N=137$; $N_{\text{fall}}=106$, $N_{\text{spring}}=88$). We examined the relationship between confusion and correctness, confidence in reasoning, and (in the spring) precourse self-efficacy. We find that student expressions of confusion before coming to class are negatively related to correctness on preclass content-related questions, confidence in reasoning on those questions, and self-efficacy, but weakly positively related to final grade when controlling for these factors ($\beta =0.23$, $p=0.03$).

We modified the Just-in-Time Teaching approach and developed a dual safeguard web-based interactive (DGWI) teaching system for an introductory physics course. The system consists of four instructional components that improve student learning by including warm-up assignments and online homework. Student and instructor activities involve activities both in the classroom and on a designated web site. An experimental study with control groups evaluated the effectiveness of the DGWI teaching method. The results indicate that the DGWI method is an effective way to improve students’ understanding of physics concepts, develop students’ problem-solving abilities through instructor-student interactions, and identify students’ misconceptions through a safeguard framework based on questions that satisfy teaching requirements and cover all of the course material. The empirical study and a follow-up survey found that the DGWI method increased student-teacher interaction and improved student learning outcomes.