This paper describes ongoing research investigating student approaches to quantitative and qualitative problem solving in physics. This empirical study was conducted using a phenomenographic approach to analyze data from individual semistructured problem solving interviews with 22 introductory college physics students. The main result of the study is a hierarchical set of categories that describe the students’ problem solving approaches in the context of introductory physics.

We use clustering, an analysis method not presently common to the physics education research community, to group and characterize student responses to written questions about two-dimensional kinematics. Previously, clustering has been used to analyze multiple-choice data; we analyze free-response data that includes both sketches of vectors and written elements. The primary goal of this paper is to describe the methodology itself; we include a brief overview of relevant results.

National studies of science education have unanimously concluded that preparing our students for the demands of the 21st century workplace is one of the major goals. This paper describes a study of student activities in introductory college physics labs, which were designed to help students acquire abilities that are valuable in the workplace. In these labs [called Investigative Science Learning Environment (ISLE) labs], students design their own experiments. Our previous studies have shown that students in these labs acquire scientific abilities such as the ability to design an experiment to solve a problem, the ability to collect and analyze data, the ability to evaluate assumptions and uncertainties, and the ability to communicate. These studies mostly concentrated on analyzing students’ writing, evaluated by specially designed scientific ability rubrics. Recently, we started to study whether the ISLE labs make students not only write like scientists but also engage in discussions and act like scientists while doing the labs. For example, do students plan an experiment, validate assumptions, evaluate results, and revise the experiment if necessary? A brief report of some of our findings that came from monitoring students’ activity during ISLE and nondesign labs was presented in the Physics Education Research Conference Proceedings. We found differences in student behavior and discussions that indicated that ISLE labs do in fact encourage a scientistlike approach to experimental design and promote high-quality discussions. This paper presents a full description of the study.

Although guided-inquiry methods for teaching introductory physics have been individually shown to be more effective at improving conceptual understanding than traditional lecture-style instruction, researchers in physics education have not studied differences among reform-based curricula in much detail. Several researchers have developed University of Washington–style tutorial materials, but the different curricula have not been compared against each other. Our study examines three tutorials designed to improve student understanding of Newton’s third law: the University of Washington’s Tutorials in Introductory Physics (TIP), the University of Maryland’s Activity-Based Tutorials (ABT), and the Open Source Tutorials (OST) also developed at the University of Maryland. Each tutorial was designed with different goals and agendas, and each employs different methods to help students understand the physics. We analyzed pretest and post-test data, including course examinations and data from the Force and Motion Conceptual Evaluation (FMCE). Using both FMCE and course data, we find that students using the OST version of the tutorial perform better than students using either of the other two.

Previously, we proposed a model of student reasoning which combines the roles of representation, analogy, and layering of meaning—analogical scaffolding [Podolefsky and Finkelstein, Phys. Rev. ST Phys. Educ. Res. 3, 010109 (2007)]. The present empirical studies build on this model to examine its utility and demonstrate the vital intertwining of representation, analogy, and conceptual learning in physics. In two studies of student reasoning using analogy, we show that representations couple to students’ existing prior knowledge and also lead to the dynamic formation of new knowledge. Students presented with abstract, concrete, or blended (both abstract and concrete) representations produced markedly different response patterns. In the first study, using analogies to scaffold understanding of electromagnetic (EM) waves, students in the blend group were more likely to reason productively about EM waves than students in the abstract group by as much as a factor of 3 (73% vs 24% correct, $p=0.002$). In the second study, examining representation use within one domain (sound waves), the blend group was more likely to reason productively about sound waves than the abstract group by as much as a factor of 2 (48% vs 23% correct, $p=0.002$). Using the analogical scaffolding model we examine when and why students succeed and fail to use analogies and interpret representations appropriately.

Many proven research-based instructional strategies have been developed for introductory college-level physics. Significant efforts to disseminate these strategies have focused on convincing individual instructors to give up their traditional practices in favor of particular research-based practices. Yet evidence suggests that the findings of educational research are, at best, only marginally incorporated into typical introductory physics courses. In this paper we present partial results of an interview study designed to generate new ideas about why proven strategies are slow to integrate in mainstream instruction. Specifically we describe the results of open-ended interviews with five physics instructors who represent likely users of educational research. We found that these instructors have conceptions about teaching and learning that are more compatible with educational research than with their self-described instructional practices. Instructors often blamed this discrepancy on situational factors that favor traditional instruction. A theoretical model is introduced to explain these findings.

Although much is known about the differences between expert and novice problem solvers, knowledge of those differences typically does not provide enough detail to help instructors understand why some students seem to learn physics while solving problems and others do not. A critical issue is how students access the knowledge they have in the context of solving a particular problem. In this paper, we discuss our observations of students solving physics problems in authentic situations in an algebra-based physics class at the University of Maryland. We find that when these students are working together and interacting effectively, they often use a limited set of locally coherent resources for blocks of time of a few minutes or more. This coherence appears to provide the student with guidance as to what knowledge and procedures to access and what to ignore. Often, this leads to the students failing to apply relevant knowledge they later show they possess. In this paper, we outline a theoretical phenomenology for describing these local coherences and identify six organizational structures that we refer to as epistemic games. The hypothesis that students tend to function within the narrow confines of a fairly limited set of games provides a good description of our observations. We demonstrate how students use these games in two case studies and discuss the implications for instruction.

This paper describes a model of analogy, analogical scaffolding, which explains present and prior results of student learning with analogies. We build on prior models of representation, blending, and layering of ideas. Extending this model’s explanatory power, we propose ways in which the model can be applied to design a curriculum directed at teaching abstract ideas in physics using multiple, layered analogies. We report on a recent empirical study that motivates this model. Students taught about electromagnetic waves in a curriculum that builds on the model of analogical scaffolding posted substantially greater gains pre- to postinstruction than students taught using a more traditional (non-analogy-based) tutorial (21% vs 7%).

Good use of multiple representations is considered key to learning physics, and so there is considerable motivation both to learn how students use multiple representations when solving problems and to learn how best to teach problem solving using multiple representations. In this study of two large-lecture algebra-based physics courses at the University of Colorado (CU) and Rutgers, the State University of New Jersey, we address both issues. Students in each of the two courses solved five common electrostatics problems of varying difficulty, and we examine their solutions to clarify the relationship between multiple representation use and performance on problems involving free-body diagrams. We also compare our data across the courses, since the two physics-education-research-based courses take substantially different approaches to teaching the use of multiple representations. The course at Rutgers takes a strongly directed approach, emphasizing specific heuristics and problem-solving strategies. The course at CU takes a weakly directed approach, modeling good problem solving without teaching a specific strategy. We find that, in both courses, students make extensive use of multiple representations, and that this use (when both complete and correct) is associated with significantly increased performance. Some minor differences in representation use exist, and are consistent with the types of instruction given. Most significant are the strong and broad similarities in the results, suggesting that either instructional approach or a combination thereof can be useful for helping students learn to use multiple representations for problem solving and concept development.

Previous research [Lorenzo et al., Am. J. Phys. 74, 118 (2006)] demonstrated that the difference in performance between male and female students can be reduced and even eliminated, in consistent fashion, by using interactive engagement techniques in the introductory physics classroom. The present paper describes similar studies in a different, large research university and finds that the use of interactive engagement techniques does not necessarily reduce the gender gap. Furthermore, in the environments studied, there is a gap in learning gains between male and female students $(p<0.01)$ whether partially or fully interactive classroom techniques are used. Our findings suggest that engaging students in interactive educational environments is not sufficient to reduce the gender gap, and we find instances where despite significant learning gains by all students, the gender gap is increased. There is indication that there are both student and instructor effects that impact the gender gap, which are the subjects of ongoing studies.

Preinstruction SAT scores and normalized gains $\left(G\right)$ on the force concept inventory (FCI) were examined for individual students in interactive engagement (IE) courses in introductory mechanics at one high school $(N=335)$ and one university $(N=292)$, and strong, positive correlations were found for both populations ($r=0.57$ and $r=0.46$, respectively). These correlations are likely due to the importance of cognitive skills and abstract reasoning in learning physics. The larger correlation coefficient for the high school population may be a result of the much shorter time interval between taking the SAT and studying mechanics, because the SAT may provide a more current measure of abilities when high school students begin the study of mechanics than it does for college students, who begin mechanics years after the test is taken. In prior research a strong correlation between FCI $G$ and scores on Lawson’s Classroom Test of Scientific Reasoning for students from the same two schools was observed. Our results suggest that, when interpreting class average normalized FCI gains and comparing different classes, it is important to take into account the variation of students’ cognitive skills, as measured either by the SAT or by Lawson’s test. While Lawson’s test is not commonly given to students in most introductory mechanics courses, SAT scores provide a readily available alternative means of taking account of students’ reasoning abilities. Knowing the students’ cognitive level before instruction also allows one to alter instruction or to use an intervention designed to improve students’ cognitive level.

This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students and physicists talking and writing about the subject of quantum mechanics. We found that physicists’ language encodes different varieties of analogical models through the use of grammar and conceptual metaphor. We hypothesize that students categorize concepts into ontological categories based on the grammatical structure of physicists’ language. We also hypothesize that students overextend and misapply conceptual metaphors in physicists’ speech and writing. Using our theory, we will show how, in some cases, we can explain student difficulties in quantum mechanics as difficulties with language.

We present results from a comparative study of student understanding for students who attended recitation classes that used different teaching methods. Student volunteers from our introductory calculus-based physics course attended a special recitation class that was taught using one of four different teaching methods. A total of 272 students were divided into approximately equal groups for each method. Students in each class were taught the same topic, “Changes in Energy and Momentum,” from Tutorials in Introductory Physics. The different teaching methods varied in the amount of student and teacher engagement. Student understanding was evaluated through pre- and post-tests. Our results demonstrate the importance of the instructor’s role in teaching recitation classes. The most effective teaching method was for students working in cooperative learning groups with the instructors questioning the groups using Socratic dialogue. In addition, we investigated student preferences for modes of instruction through an open-ended survey. Our results provide guidance and evidence for the teaching methods that should be emphasized in training course instructors.

We present and describe the development of a framework for assessing or categorizing instructional practices and related conceptions in the context of introductory physics instruction. The purpose of the framework is for articulating practices and conceptions of individual instructors or of curricula. It was developed based on the research literature and interviews with physics faculty and contains ideas with widespread acceptance as well as some outside mainstream rhetoric. We provide an example of how this framework can be applied by using it to categorize aspects of three well-known research-based curricula. The results of this categorization highlight areas that are common in research-based curricular designs and other areas that are less embraced but worthy of consideration.

The force concept inventory and a 10-question context-modified test were given to 647 students enrolled in introductory physics classes at the University of Arkansas. Context changes had an effect ranging from $-3\%$ to 10% on the individual questions. The average student score on the ten transformed questions was 3% higher than the average student score on the corresponding 10 force concept inventory questions. Therefore, the effect of contextual changes on the total of the 10 questions is not sufficient to affect normal use of the force concept inventory as a diagnostic instrument.

An important result of physics education research is that students’ learning and success in a course is correlated with their beliefs, attitudes, and expectations regarding physics. However, it is hard to assess these beliefs for individual students, and traditional survey instruments such as the Maryland Physics Expectations Survey (MPEX) are intended to evaluate the impact of one or more semesters of instruction on an overall class and improve teaching. In this study, we investigate the possibility of using the analysis of online student discussion behavior as an indicator of an individual student’s approach to physics. These discussions are not tainted by the effects of self-reporting, and are gathered in authentic nonresearch settings, where students attempt to solve problems in the way that they believe is most efficient and appropriate. We calculate the correlation of both MPEX and student discussions with different measures of student learning, and find that on an individual base, student discussions are a stronger predictor of success than MPEX outcomes.