“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.

Research on physics problem categorization has established that proficient problem solvers are able to group together physics problems that would be solved by similar principles and use conceptual approaches when solving problems, whereas weak solvers rely more heavily upon surface features (objects, contexts, and quantities provided) to identify specific equations that match to the problem situation. This study explores the degree to which novices are able to shift their categorization strategies toward one that is more principle based as a result of a brief, computer-based intervention designed to highlight the role of principles as categorization criteria. Students finishing an introductory algebra-based mechanics course were presented with a sequence of problem pairs, asked to judge whether each pair would be solved similarly, and provided with feedback. Students in one condition received feedback that was very sparse and only indicated correctness, whereas students in a second condition viewed elaborate feedback that linked problem features to the appropriate concepts and principles to solve each problem. We found an increased use of physics principles in the reasoning provided by students who received the elaborate feedback whereas students who did not view this elaboration primarily cited quantities in the problem statement. Although these results suggest it is possible to increase students’ attention to principles when approaching problems, poor performance on the items indicates that considering the appropriateness of principles remains a difficult task for beginning physics students.

Research in student knowledge and learning of science has typically focused on explaining conceptual change. Recent research, however, documents the great degree to which student thinking is dynamic and context-sensitive, implicitly calling for explanations not only of change but also of stability. In other words, when a pattern of student reasoning is sustained in specific moments and settings, what mechanisms contribute to sustaining it? We characterize student understanding and behavior in terms of multiple local coherences in that they may be variable yet still exhibit local stabilities. We attribute stability in local conceptual coherences to real-time activities that sustain these coherences. For example, particular conceptual understandings may be stabilized by the linguistic features of a worksheet question or by feedback from the students’ spatial arrangement and orientation. We document a group of university students who engage in multiple local conceptual coherences while thinking about motion during a collaborative learning activity. As the students shift their thinking several times, we describe mechanisms that may contribute to local stability of their reasoning and behavior.

Previous studies have reported that students employed different problem solving approaches when presented with the same task structured with different representations. In this study, we explored and compared students’ strategies as they attempted tasks from two topical areas, kinematics and work. Our participants were 19 engineering students taking a calculus-based physics course. The tasks were presented in linguistic, graphical, and symbolic forms and requested either a qualitative solution or a value. The analysis was both qualitative and quantitative in nature focusing principally on the characteristics of the strategies employed as well as the underlying reasoning for their applications. A comparison was also made for the same student’s approach with the same kind of representation across the two topics. Additionally, the participants’ overall strategies across the different tasks, in each topic, were considered. On the whole, we found that the students prefer manipulating equations irrespective of the representational format of the task. They rarely recognized the applicability of a “qualitative” approach to solve the problem although they were aware of the concepts involved. Even when the students included visual representations in their solutions, they seldom used these representations in conjunction with the mathematical part of the problem. Additionally, the students were not consistent in their approach for interpreting and solving problems with the same kind of representation across the two topical areas. The representational format, level of prior knowledge, and familiarity with a topic appeared to influence their strategies, their written responses, and their ability to recognize qualitative ways to attempt a problem. The nature of the solution does not seem to impact the strategies employed to handle the problem.

We designed a sequence of seven lessons to facilitate learning of integration in a physics context. We implemented this sequence with a single college sophomore, “Amber,” who was concurrently enrolled in a first-semester calculus-based introductory physics course which covered topics in mechanics. We outline the philosophy underpinning these lessons, which characterizes integration in terms of layers and representations. We describe how Amber learned to give oral presentations in which she told a story about how integration comes from products, sums, and limits in a variety of physics contexts. We conclude that by the end of our lessons, Amber was able to conceptualize and explain integrals using multiple representations. In one case, she was able to solve a novel problem about integration in an unfamiliar context (center of mass.) Based on our previous research about integration, we suggest that these achievements would have been unattainable with the use of a single one or two hour lesson.

Since it was first published 30 years ago, the seminal paper of Chi et al. on expert and novice categorization of introductory problems led to a plethora of follow-up studies within and outside of the area of physics [Cogn. Sci. 5, 121 (1981)]. These studies frequently encompass “card-sorting” exercises whereby the participants group problems. While this technique certainly allows insights into problem solving approaches, simple descriptive statistics more often than not fail to find significant differences between experts and novices. In moving beyond descriptive statistics, we describe a novel microscopic approach that takes into account the individual identity of the cards and uses graph theory and models to visualize, analyze, and interpret problem categorization experiments. We apply these methods to an introductory physics (mechanics) problem categorization experiment, and find that most of the variation in sorting outcome is not due to the sorter being an expert versus a novice, but rather due to an independent characteristic that we named “stacker” versus “spreader.” The fact that the expert-novice distinction only accounts for a smaller amount of the variation may explain the frequent null results when conducting these experiments.

Previous physics education research has raised the question of “hidden variables” behind students’ success in learning certain concepts. In the context of the force concept, it has been suggested that students’ reasoning ability is one such variable. Strong positive correlations between students’ preinstruction scores for reasoning ability (measured by Lawson’s Classroom Test of Scientific Reasoning) and their learning of forces [measured by the Force Concept Inventory (FCI)] have been reported in high school and university introductory courses. However, there is no published research concerning the relation between students’ ability to interpret multiple representations consistently (i.e., representational consistency) and their learning of forces. To investigate this, we collected 131 high school students’ pre- and post-test data of the Representational Variant of the Force Concept Inventory (for representational consistency) and the FCI. The students’ Lawson pretest data were also collected. We found that the preinstruction level of students’ representational consistency correlated strongly with student learning gain of forces. The correlation (0.51) was almost equal to the correlation between Lawson prescore and learning gain of forces (0.52). Our results support earlier findings which suggest that scientific reasoning ability is a hidden variable behind the learning of forces. In addition, we suggest that students’ representational consistency may also be such a factor, and that this should be recognized in physics teaching.

This study investigated how visual attention differed between those who correctly versus incorrectly answered introductory physics problems. We recorded eye movements of 24 individuals on six different conceptual physics problems where the necessary information to solve the problem was contained in a diagram. The problems also contained areas consistent with a novicelike response and areas of high perceptual salience. Participants ranged from those who had only taken one high school physics course to those who had completed a Physics Ph.D. We found that participants who answered correctly spent a higher percentage of time looking at the relevant areas of the diagram, and those who answered incorrectly spent a higher percentage of time looking in areas of the diagram consistent with a novicelike answer. Thus, when solving physics problems, top-down processing plays a key role in guiding visual selective attention either to thematically relevant areas or novicelike areas depending on the accuracy of a student’s physics knowledge. This result has implications for the use of visual cues to redirect individuals’ attention to relevant portions of the diagrams and may potentially influence the way they reason about these problems.

We report on the adaptation of the small enrollment, lab and discussion based physical science course, Physical Science and Everyday Thinking (PSET), for a large-enrollment, lecture-style setting. Like PSET, the new Learning Physical Science (LEPS) curriculum was designed around specific principles based on research on learning to meet the needs of nonscience students, especially prospective and practicing elementary and middle school teachers. We describe the structure of the two curricula and the adaptation process, including a detailed comparison of similar activities from the two curricula and a case study of a LEPS classroom implementation. In LEPS, short instructor-guided lessons replace lengthier small group activities, and movies, rather than hands-on investigations, provide the evidence used to support and test ideas. LEPS promotes student peer interaction as an important part of sense making via “clicker” questions, rather than small group and whole class discussions typical of PSET. Examples of student dialog indicate that this format is capable of generating substantive student discussion and successfully enacting the design principles. Field-test data show similar student content learning gains with the two curricula. Nevertheless, because of classroom constraints, some important practices of science that were an integral part of PSET were not included in LEPS.

Gender differences in student learning in the introductory, calculus-based electricity and magnetism course were assessed by administering the Conceptual Survey of Electricity and Magnetism pre- and postcourse. As expected, male students outgained females in traditionally taught sections as well as sections that incorporated interactive engagement (IE) techniques. In two of the IE course sections, however, the gains of female students were comparable to those of male students. Classroom observations of the course sections involved were made over an extended period. In this paper, we characterize the observed instructor-student interactions using a framework from educational psychology referred to as wise schooling. Results suggest that instructor practices affect differential learning, and that wise schooling techniques may constitute an effective strategy for promoting gender equity in the physics classroom.

We describe the development and implementation of research-based learning tools such as the Quantum Interactive Learning Tutorials and peer-instruction tools to reduce students’ common difficulties with issues related to measurement in quantum mechanics. A preliminary evaluation shows that these learning tools are effective in improving students’ understanding of concepts related to quantum measurement.

We describe the difficulties that advanced undergraduate and graduate students have with quantum measurement within the standard interpretation of quantum mechanics. We explore the possible origins of these difficulties by analyzing student responses to questions from both surveys and interviews. Results from this research are applied to develop research-based learning tutorials to improve students’ understanding of quantum measurement.