We describe the difficulties advanced undergraduate and graduate students have with concepts related to addition of angular momentum in quantum mechanics. We also describe the development and implementation of a research-based learning tool, Quantum Interactive Learning Tutorial (QuILT), to reduce these difficulties. The preliminary evaluation shows that the QuILT related to the basics of the addition of angular momentum is helpful in improving students’ understanding of these concepts.

We use visualization to find patterns in educational data. We represent student scores from high-stakes exams as flow vectors in fluids, define two types of streamlines and trajectories, and show that differences between streamlines and trajectories are due to regression to the mean. This issue is significant because it determines how quickly changes in long-term educational patterns can be deduced from score changes in consecutive years. To illustrate our methods, we examine a policy change in Texas that put increased pressure on public school students to pass several exams, and gave them resources to accomplish it. The response to this policy is evident from the changes in trajectories, although previous evaluation had concluded the program was ineffective. We pose the question of whether increased expenditure on education should be expected to correspond to improved student scores, or whether it should correspond to an increased rate of improvement in student scores.

We have given a group of 56 Massachusetts Institute of Technology (MIT) seniors who took mechanics as freshmen a written test similar to the final exam they took in their freshman course as well as the Mechanics Baseline Test (MBT) and the Colorado Learning Attitudes about Science Survey (CLASS). Students in majors unrelated to physics scored 60% lower on the written analytic part of the final than they would have as freshmen. The mean score of all participants on the MBT was insignificantly changed from their average on the posttest they took as freshmen. However, the students’ performance on 9 of the 26 MBT items (with 6 of the 9 involving graphical kinematics) represents a gain over their freshman posttest score (a normalized gain of about 70%), while their performance on the remaining 17 questions is best characterized as a loss of approximately 50% of the material learned in the freshman course. On multiple-choice questions covering advanced physics concepts, the mean score of the participants was about 50% lower than the average performance of freshmen. Although attitudinal survey results indicate that almost half the seniors feel the specific mechanics course content is unlikely to be useful to them, a significant majority (75%–85%) feel that physics does teach valuable problem solving skills, and an overwhelming majority believe that mechanics should remain a required course at MIT.

In this paper, we examine student success on three variants of a test item given in different representational formats (verbal, pictorial, and graphical), with an isomorphic problem statement. We confirm results from recent papers where it is mentioned that physics students’ problem-solving competence can vary with representational format and that solutions can be triggered by particular details of the representation. Previous studies are complemented with a fine grained analysis of solution strategies. We find that students use different problem-solving strategies, depending on the representational format in which the problem is stated.

A seminal study by Chi et al. firmly established the paradigm that novices categorize physics problems by “surface features” (e.g., “incline,” “pendulum,” “projectile motion,” etc.), while experts use “deep structure” (e.g., “energy conservation,” “Newton 2,” etc.). Yet, efforts to replicate the study frequently fail, since the ability to distinguish experts from novices turns out to be highly sensitive to the problem set being used. Exactly what properties of problems are most important in problem sets that discriminate experts from novices in a measurable way? To answer this question, we studied the categorizations by known physics experts and novices using a large, diverse set of problems. This set needed to be large so that we could determine how well experts and novices could be discriminated by considering both small subsets using an exhaustive Monte Carlo approach and larger subsets using simulated annealing. We found that the number of questions required to accurately classify experts and novices can be surprisingly small so long as the problem set is carefully crafted to be composed of problems with particular pedagogical and contextual features. Finally, we found that not only was what you ask (deep structure) important, but also how you ask it (problem context).

The Energy Project at Seattle Pacific University has developed representations that embody the substance metaphor and support learners in conserving and tracking energy as it flows from object to object and changes form. Such representations enable detailed modeling of energy dynamics in complex physical processes. We assess student learning by means of representations that learners invent to explain energy dynamics in specific real-world scenarios. Refined versions of these learner-generated representations have proven valuable for our own teaching, physics understanding, and research.

The nature of energy is not typically an explicit topic of physics instruction. Nonetheless, verbal and graphical representations of energy articulate models in which energy is conceptualized as a quasimaterial substance, a stimulus, or a vertical location. We argue that a substance ontology for energy is particularly productive in developing understanding of energy transfers and transformations. We analyze classic representations of energy—bar charts, pie charts, and others—to determine the energy ontologies that are implicit in those representations, and thus their affordances for energy learning. We find that while existing representations partially support a substance ontology for energy and thus the learning goal of energy conservation, they have limited utility for tracking the flow of energy among objects.

Technology has been widely involved in science research. Researchers are now applying it to science education in an attempt to bring students’ science activities closer to authentic science activities. The present study synthesizes the research to discuss the development of technology-enhanced laboratories and how technology may contribute to fulfilling the instructional objectives of laboratories in physics. To be more specific, this paper discusses the engagement of technology to innovate physics laboratories and the potential of technology to promote inquiry, instructor and peer interaction, and learning outcomes. We then construct a framework for teachers, scientists, and programmers to guide and evaluate technology-integrated laboratories. The framework includes inquiry learning and openness supported by technology, ways of conducting laboratories, and the diverse learning objectives on which a technology-integrated laboratory may be focused.

This study examined the evolution of student responses to seven contextually different versions of two Force Concept Inventory questions in an introductory physics course at the University of Arkansas. The consistency in answering the closely related questions evolved little over the seven-question exam. A model for the state of student knowledge involving the probability of selecting one of the multiple-choice answers was developed. Criteria for using clustering algorithms to extract model parameters were explored and it was found that the overlap between the probability distributions of the model vectors was an important parameter in characterizing the cluster models. The course data were then clustered and the extracted model showed that students largely fit into two groups both pre- and postinstruction: one that answered all questions correctly with high probability and one that selected the distracter representing the same misconception with high probability. For the course studied, 14% of the students were left with persistent misconceptions post instruction on a static force problem and 30% on a dynamic Newton’s third law problem. These students selected the answer representing the predominant misconception slightly more consistently postinstruction, indicating that the course studied had been ineffective at moving this subgroup of students nearer a Newtonian force concept and had instead moved them slightly farther away from a correct conceptual understanding of these two problems. The consistency in answering pairs of problems with varied physical contexts is shown to be an important supplementary statistic to the score on the problems and suggests that the inclusion of such problem pairs in future conceptual inventories would be efficacious. Multiple, contextually varied questions further probe the structure of students’ knowledge. To allow working instructors to make use of the additional insight gained from cluster analysis, it is our hope that the physics education research community will make these methods available though their Web sites.

We present a method of analyzing the development of self-efficacy in real time using a framework of self-efficacy opportunities (SEOs). Considerable research has shown a connection between self-efficacy, or the confidence in one’s own ability to perform a task, and success in science fields. Traditional methods of investigating the development of self-efficacy have required participants to recollect past events. This reliance on participant memory makes it difficult to understand what impact particular events may have on developing self-efficacy in the moment. We use video recordings of three undergraduate Modeling Instruction students solving a physics problem to characterize SEOs in a moment-by-moment analysis. We then validate these characterizations of the development of self-efficacy by reviewing the problem-solving session with the participants and find evidence that the SEOs identified are taken up and impact self-efficacy. This characterization and validation of SEOs in the moment represents a first step towards establishing a methodology for analyzing the development of self-efficacy in real time.

“Self-diagnosis tasks” aim at fostering students’ learning in an examination context by requiring students to present diagnoses of their solutions to quiz problems. We examined the relationship between students’ learning from self-diagnosis and the typicality of the problem situation. Four recitation groups in an introductory physics class ($\sim 200$ students) were divided into a control group and three intervention groups in which different levels of guidance were provided to aid students in their performance of self-diagnosis activities. The self-diagnosis task was administered twice, first in an atypical problem situation and then in a typical one. In a companion paper we reported our findings in the context of an atypical problem situation. Here we report our findings in the context of a typical problem situation and discuss the effect of problem typicality on students’ self-diagnosis performance and subsequent success in solving transfer problems. We show that the self-diagnosis score was correlated with subsequent problem-solving performance only in the context of a typical problem situation, and only when textbooks and notebooks were the sole means of guidance available to the students for assisting them with diagnosis.

“Self-diagnosis tasks” are aimed at fostering diagnostic behavior by explicitly requiring students to present diagnosis as part of the activity of reviewing their problem solutions. Recitation groups in an introductory physics class of about 200 college students were distributed into a control group and three intervention groups in which different levels of guidance were provided for performing self-diagnosis activities. We investigated how well students self-diagnose their solutions in the different interventions and examined the effect of students’ self-diagnosis on subsequent problem solving in the different intervention groups. We found that in the context of an atypical quiz, while external support altered the self-diagnosis performance, the self-diagnosis score was not correlated with subsequent problem-solving performance on a transfer problem. We discuss possible explanations for our findings.

As part of an effort to systematically improve our junior-level E&M I course, we have developed a tool to assess student conceptual learning of electrostatics at the upper division. Together with a group of physics faculty, we established a list of learning goals for the course that, with results from student observations and interviews, served as a guide in creating the Colorado Upper-Division Electrostatics (CUE) assessment. The result is a 17-question open-ended post-test diagnostic (with an optional 7-question pretest) and an accompanying grading rubric. We present measures of the validation and reliability of the instrument and grading rubric, plus results from 535 students in both standard and interactive-engagement courses across seven institutions as a baseline for the instrument. Overall, we find that the CUE is a valid and reliable measure, and the data herein are intended to be of use to researchers and faculty interested in using the CUE to measure student learning.

Over the course of four years, we have researched and transformed a key course in the career of an undergraduate physics major—junior-level electricity and magnetism. With the aim of educating our majors based on a more complete understanding of the cognitive and conceptual challenges of upper-division courses, we used principles of active engagement and learning theory to develop course materials and conceptual assessments. Our research results from student and faculty interviews and observations also informed our approach. We present several measures of the outcomes of this work at the University of Colorado at Boulder and external institutions. Students in the transformed courses achieved higher learning gains compared to those in the traditionally taught courses, particularly in the areas of conceptual understanding and ability to articulate their reasoning about a problem. The course transformations appear to close a gender gap, improving female students’ scores on conceptual and traditional assessments so that they are more similar to those of male students. Students enthusiastically support the transformations, and indicate that several course elements provide useful scaffolding in conceptual understanding, as well as physicists’ “habits of mind” such as problem-solving approaches and work habits. Despite these positive outcomes, student conceptual learning gains do not fully meet faculty expectations, suggesting that it is valuable to further investigate how the content and skills indicative of “thinking like a physicist” can be most usefully taught at the upper division.

Students taking introductory physics are rarely exposed to computational modeling. In a one-semester large lecture introductory calculus-based mechanics course at Georgia Tech, students learned to solve physics problems using the VPython programming environment. During the term, 1357 students in this course solved a suite of 14 computational modeling homework questions delivered using an online commercial course management system. Their proficiency with computational modeling was evaluated with a proctored assignment involving a novel central force problem. The majority of students (60.4%) successfully completed the evaluation. Analysis of erroneous student-submitted programs indicated that a small set of student errors explained why most programs failed. We discuss the design and implementation of the computational modeling homework and evaluation, the results from the evaluation, and the implications for computational instruction in introductory science, technology, engineering, and mathematics (STEM) courses.

We perform a factor analysis on a “Force Concept Inventory” (FCI) data set collected from 2109 respondents. We address two questions: the appearance of conceptual coherence in student responses to the FCI and some consequences of this factor analysis on the teaching of Newtonian mechanics. We will highlight the apparent conflation of Newton’s third law with Newton’s first law in one of the FCI questions and suggest an approach to teaching that may avoid this issue. We also note the absence of a distinct factor interpretable as relating specifically to kinematics. Furthermore, we identify and discuss some of the technical difficulties which may be encountered when performing factor analysis on categorical data sets, such as is the case with FCI data sets.

During the fall of 2008 a web survey, designed to collect information about pedagogical knowledge and practices, was completed by a representative sample of 722 physics faculty across the United States (50.3% response rate). This paper presents partial results to describe how 20 potential predictor variables correlate with faculty knowledge about and use of research-based instructional strategies (RBIS). The innovation-decision process was conceived of in terms of four stages: knowledge versus no knowledge, trial versus no trial, continuation versus discontinuation, and high versus low use. The largest losses occur at the continuation stage, with approximately $1/3$ of faculty discontinuing use of all RBIS after trying one or more of these strategies. Nine of the predictor variables were statistically significant for at least one of these stages when controlling for other variables. Knowledge and/or use of RBIS are significantly correlated with reading teaching-related journals, attending talks and workshops related to teaching, attending the physics and astronomy new faculty workshop, having an interest in using more RBIS, being female, being satisfied with meeting instructional goals, and having a permanent, full-time position. The types of variables that are significant at each stage vary substantially. These results suggest that common dissemination strategies are good at creating knowledge about RBIS and motivation to try a RBIS, but more work is needed to support faculty during implementation and continued use of RBIS. Also, contrary to common assumptions, faculty age, institutional type, and percentage of job related to teaching were not found to be barriers to knowledge or use at any stage. High research productivity and large class sizes were not found to be barriers to use of at least some RBIS.

By analysis of student use of mathematics in responses to conceptual physics questions, as well as analogous math questions stripped of physical meaning, we have previously found evidence that students often enter upper-level physics courses lacking the assumed prerequisite mathematics knowledge and/or the ability to apply it productively in a physics context. As an extension from this work on students’ mathematical competency at the upper level in physics, we report on a preliminary investigation of mathematical understanding of fundamental concepts of slope and derivative among students in a third-semester multivariable calculus course. Among the first published findings of physics education research are investigations on students’ understanding of kinematics, with particular attention to graphical representations of position-, velocity-, and acceleration-versus-time graphs. Underlying these physical quantities are relationships that depend on derivatives and slopes. We report on our findings as we attempt to isolate students’ understanding of these mathematical concepts.

We present three models of equity and show how these, along with the statistical measures used to evaluate results, impact interpretation of equity in education reform. Equity can be defined and interpreted in many ways. Most equity education reform research strives to achieve equity by closing achievement gaps between groups. An example is given by the study by Lorenzo et al. that shows that interactive engagement methods lead to increased gender equity. In this paper, we reexamine the results of Lorenzo et al. through three models of equity. We find that interpretation of the results strongly depends on the model of equity chosen. Further, we argue that researchers must explicitly state their model of equity as well as use effect size measurements to promote clarity in education reform.