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 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 to evaluate the level of scaffolding needed to help students learn from an analogical problem that is similar in the underlying principles 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, 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 must be determined via research in order to be effective.
[This paper is part of the Focused Collection on Upper Division Physics Courses.] In response to the need for a scalable, institutionally supported model of educational change, the Science Education Initiative (SEI) was created as an experiment in transforming course materials and faculty practices at two institutions - University of Colorado Boulder (CU) and University of British Columbia. We find that this departmentally focused model of change, which includes an explicit focus on course transformation as supported by a discipline-based postdoctoral education specialist, was generally effective in impacting courses and faculty across the institution. In CU's Department of Physics, the SEI effort focused primarily on upper-division courses, creating high-quality course materials, approaches, and assessments, and demonstrating an impact on student learning. We argue that the SEI implementation in the CU Physics Department, as compared to that in other departments, achieved more extensive impacts on specific course materials, and high-quality assessments, due to guidance by the physics education research group-but with more limited impact on the departmental faculty as a whole. We review the process and progress of the SEI Physics at CU and reflect on lessons learned in the CU Physics Department in particular. These results are useful in considering both institutional and faculty-led models of change and course transformation.
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.
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.
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 paper is part of the Focused Collection on Upper Division Physics Courses.] The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing the key role of the energy eigenbasis in determining the time dependence of wave functions. Through analysis of student responses to a set of four interrelated tasks, we categorize some of the difficulties that underlie common errors. The conceptual and reasoning difficulties that have been identified are illustrated through student responses to four sets of questions administered at different points in a junior-level course on quantum mechanics. Evidence is also given that the problems persist throughout undergraduate instruction and into the graduate level.
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.
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 expert- like beliefs that lead to significant improvements in beliefs. Further, small courses and those for elementary education and non-science 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 population typical of the kinds of classes in which these interventions are most often used. Physics majors tend to enter their undergraduate education with more expert-like beliefs than non-majors 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 expert-like 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.
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.
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.
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.
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.
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.
[This paper is part of the Focused Collection on Upper Division Physics Courses.] Energy measurements play a fundamental role in the theory of quantum mechanics, yet there is evidence that the underlying concepts are difficult for many students, even after all undergraduate instruction. We present results from an investigation into student ability to determine the possible energies that can be measured for a given wave function and Hamiltonian, to determine the probabilities of each energy measurement and how they depend on time, and to recognize how a measurement of energy affects the state. By analyzing student responses to open-ended questions, we identify five broad, interrelated sets of conceptual and reasoning difficulties related to energy measurements. Data are drawn from sophomore-, junior-, and graduate-level quantum mechanics courses. Particular attention is paid to incorrect ideas that persist across all levels.
[This paper is part of the Focused Collection on Upper Division Physics Courses.] Students learning to separate variables in order to solve a differential equation have multiple ways of correctly doing so. The procedures involved in separation include division or multiplication after properly grouping terms in an equation, moving terms (again, at times grouped) from one location on the page to another, or simply carrying out separation as a single act without showing any steps. We describe student use of these procedures in terms of Hammer’s resources, showing that each of the previously listed procedures is its own “piece” of a larger problem solving activity. Our data come from group examinations of students separating variables while solving an air resistance problem in an intermediate mechanics class. Through detailed analysis of four groups of students, we motivate that the mathematical procedures are resources and show the issues that students must resolve in order to successfully separate variables. We use this analysis to suggest ways in which new resources (such as separation) come to be.
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.
[This paper is part of the Focused Collection on Upper Division Physics Courses.] This study concentrates on evaluating the consistency of upper-division students' use of the second law of thermodynamics at macroscopic and microscopic levels. Data were collected by means of a paper and pencil test (N = 48) focusing on the macroscopic and microscopic features of the second law concerned with heat transfer processes. The data analysis was based on a qualitative content analysis where students' responses to the macroscopic-and microscopic-level items were categorized to provide insight into the consistency of the students' ideas; if students relied on the same idea at both levels, they ended up in the same category at both levels, and their use of the second law was consistent. The most essential finding is that a majority of students, 52%-69% depending on the physical system under evaluation, used the second law of thermodynamics consistently at macroscopic and microscopic levels; approximately 40% of the students used it correctly in terms of physics while others relied on erroneous ideas, such as the idea of conserving entropy. The most common inconsistency harbored by 10%-15% of the students (depending on the physical system under evaluation) was students' tendency to consider the number of accessible microstates to remain constant even if the entropy was stated to increase in a similar process; other inconsistencies were only seen in the answers of a few students. In order to address the observed inconsistencies, we would suggest that lecturers should utilize tasks that challenge students to evaluate phenomena at macroscopic and microscopic levels concurrently and tasks that would guide students in their search for contradictions in their thinking.
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.
