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.

At the University of Maryland we videotaped several semesters of tutorials as part of a large research project. A particular research task required us to locate examples of students calling the teaching assistants (TAs) over for assistance with a physics question. To our surprise, examples of this kind of interaction were difficult to find. We undertook a systematic study of TA-student interactions in tutorial: In particular, how are the interactions initiated? Do the students call the TA over for help with a particular issue, does the TA stop by spontaneously, or does the worksheet require a discussion with the TA at that point? The initiation of the interaction is of particular interest because it provides evidence of the motivation for and purpose of the interaction. This paper presents the results of that systematic investigation. We discovered that the majority of student-TA interactions in tutorial are initiated by teaching assistants, confirmed our initial observation that relatively few interactions are initiated by students, and found, further, that even fewer interactions are worksheet initiated. Perhaps most importantly, we found that our sense of who initiates tutorial interactions—based on extensive but informal observations—is not necessarily accurate. We need systematic investigations to uncover the reality of our classroom experiences.

Coordination class theory is used to explain college students’ judgments about animated depictions of moving objects. diSessa’s coordination class theory models a “concept” as a complex knowledge system that can reliably determine a particular type of information in widely varying situations. In the experiment described here, fifty individually interviewed college students judged the realism of two sets of computer animations depicting balls rolling on a pair of tracks. The judgments of students from an introductory physics class were strongly affected by the number of balls depicted (one or two), but the judgments of students from an educational psychology class were not. Coordination analysis of interview transcripts supports the interpretation that physics students’ developing physics knowledge led them to consistently miss or ignore some observations that the other students consistently paid attention to. The analysis highlights the context sensitivity and potential fragility of coordination systems, and leads to the conclusion that students’ developing knowledge systems might not necessarily result in consistently improving performance.

How can one increase the awareness of teachers to the existence and importance of knowledge gained through physics education research (PER) and provide them with capabilities to use it? How can one enrich teachers’ physics knowledge and the related pedagogical content knowledge of topics singled out by PER? In this paper we describe a professional development model that attempts to respond to these needs. We report on a study of the model’s implementation in a program for 22 high-school experienced physics teachers. In this program teachers (in teams of 5-6) developed during a year and a half (about $330\mathrm{h}$), several lessons (minimodules) dealing with a topic identified as problematic by PER. The teachers employed a systematic research-based approach and used PER findings. The program consisted of three stages, each culminating with a miniconference: 1. Defining teaching and/or learning goals based on content analysis and diagnosis of students’ prior knowledge. 2. Designing the lessons using PER-based instructional strategies. 3. Performing a small-scale research study that accompanies the development process and publishing the results. We describe a case study of one of the groups and bring evidence that demonstrates how the workshop advanced: (a) Teachers’ awareness of deficiencies in their own knowledge of physics and pedagogy, and their perceptions about their students’ knowledge; (b) teachers’ knowledge of physics and physics pedagogy; (c) a systematic research-based approach to the design of lessons; (d) the formation of a community of practice; and (e) acquaintance with central findings of PER. There was a clear effect on teachers’ practice in the context of the study as indicated by the materials brought to the workshop. The teachers also reported that they continued to use the insights gained, mainly in the topics that were investigated by themselves and by their peers.

We introduce resource graphs, a representation of linked ideas used when reasoning about specific contexts in physics. Our model is consistent with previous descriptions of coordination classes and resources. It represents mesoscopic scales that are neither knowledge-in-pieces nor large-scale concepts. We use resource graphs to describe several forms of conceptual change: incremental, cascade, wholesale, and dual construction. For each, we give evidence from the physics education research literature to show examples of each form of conceptual change. Where possible, we compare our representation to models used by other researchers. Building on our representation, we analyze another form of conceptual change, differentiation, and suggest several experimental studies that would help understand the differences between reform-based curricula.

We report on the development of students’ ideas of probability and probability density in a University of Maine laboratory-based general education physics course called Intuitive Quantum Physics. Students in the course are generally math phobic with unfavorable expectations about the nature of physics and their ability to do it. We describe a set of activities used to teach concepts of probability and probability density. Rudimentary knowledge of mechanics is needed for one activity, but otherwise the material requires no additional preparation. Extensions of the activities include relating probability density to potential energy graphs for certain “touchstone” examples. Students have difficulties learning the target concepts, such as comparing the ratio of time in a region to total time in all regions. Instead, they often focus on edge effects, pattern match to previously studied situations, reason about necessary but incomplete macroscopic elements of the system, use the gambler’s fallacy, and use expectations about ensemble results rather than expectation values to predict future events. We map the development of their thinking to provide examples of problems rather than evidence of a curriculum’s success.