In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the recitation in which they had to first learn from a solved problem provided and take advantage of what they learned from it to solve another problem (which we call the quiz problem) which was isomorphic. Previous research suggests that the multiple-concept quiz problem is challenging for introductory students. Students in different recitation classes received different interventions in order to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. We also conducted think-aloud interviews with four introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. We found that most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem. However, they were not necessarily able to apply the principles correctly. Research suggests that more scaffolding is needed to help students in applying these principles appropriately. We outline a few possible strategies for future investigation.

Our previous research showed that students’ mental models of friction at the atomic level are significantly influenced by their macroscopic ideas. For most students, friction is due to the meshing of bumps and valleys and rubbing of atoms. The aforementioned results motivated us to further investigate how students can be helped to improve their present models of microscopic friction. Teaching interviews were conducted to study the dynamics of their model construction as they interacted with the interviewer, the scaffolding activities, and/or with each other. In this paper, we present the different scaffolding activities and the variation in the ideas that students generated as they did the hands-on and minds-on scaffolding activities. Results imply that through a series of carefully designed scaffolding activities, it is possible to facilitate the refinement of students’ ideas of microscopic friction.

In this paper, we discuss the first phase of a multiphase study aimed at investigating the dynamics of students’ knowledge construction in the context of unfamiliar physical phenomenon—microscopic friction. The first phase of this study involved the investigation of the variations in students’ mental models of microscopic friction. Clinical interviews were conducted with 11 students enrolled in conceptual modern physics to elicit their ideas and generate themes of explanations. A phenomenographic approach of data analysis was employed to establish the variations in students’ explanations. Results show that students’ mental models of friction at the atomic level are dominated by their macroscopic experiences. Friction at the atomic level according to most students is due to mechanical interactions (interlocking or rubbing of atoms).

We recently developed a multiple-choice conceptual survey in mechanical waves. The development, evaluation, and demonstration of the use of the survey were reported elsewhere [A. Tongchai et al., Developing, evaluating and demonstrating the use of a conceptual survey in mechanical waves, Int. J. Sci. Educ. 31, 2437 (2009)]. We administered the survey to 902 students from seven different groups ranging from high school to second year university. As an outcome of that analysis we were able to identify several conceptual models which the students seemed to be using when answering the questions in the survey. In this paper we attempt to investigate the strength with which the students were committed to these conceptual models, as evidenced by the consistency with which they answered the questions. For this purpose we focus on the patterns of student responses to questions in one particular subtopic, wave propagation. This study has three main purposes: (1) to investigate the consistency of student conceptions, (2) to explore the relative usefulness of different analysis techniques, and (3) to determine what extra information a study of consistency can give about student understanding of basic concepts. We used two techniques: first, categorizing and counting, which is widely used in the science education community, and second, model analysis, recently introduced into physics education research. The manner in which categorizing and counting is used is very diverse while model analysis has been employed only in prescriptive ways. Research studies have reported that students often use their conceptual models inconsistently when solving a series of questions that test the same idea. Our results support their conclusions. Moreover, our findings suggest that students who have had more experiences in physics learning seem to use the scientifically accepted models more consistently. Further, the two analysis techniques have different advantages and disadvantages. Our findings show that model analysis can be used in more diverse ways, provides flexibility in analyzing multiple-choice questions, and provides more information about consistency and inconsistency of student conceptions. An unexpected finding is that studying waves in other contexts (for example, quantum mechanics or electromagnetism) leads to more consistent answers about mechanical waves. The suggestion is that studying more abstract topics may solidify students’ understanding of more concrete waves. While this might be considered to be intuitive, we have not actually found direct empirical studies supporting this conjecture.

The Concise Data Processing Assessment (CDPA) was developed to probe student abilities related to the nature of measurement and uncertainty and to handling data. The diagnostic is a ten question, multiple-choice test that can be used as both a pre-test and post-test. A key component of the development process was interviews with students, which were used to both uncover common modes of student thinking and validate item wording. To evaluate the reliability and discriminatory power of this diagnostic, we performed statistical tests focusing on both item analysis (item difficulty index, item discrimination index, and point-biserial coefficient) and on the entire test (test reliability and Ferguson’s delta). Scores on the CDPA range from chance (for novices) to about 80% (for experts), indicating that it possesses good dynamic range. Overall, the results indicate that the CDPA is a reliable assessment tool for measuring targeted abilities in undergraduate physics students.

This study investigates the common difficulties that students in introductory physics experience when solving problems involving integration in the context of electricity. We conducted teaching-learning interviews with 15 students in a second-semester calculus-based introductory physics course on several problems involving integration. We found that although most of the students could recognize the need for an integral in solving the problem, they failed to set up the desired integral. We provide evidence that this failure can be attributed to students’ inability to understand the infinitesimal term in the integral and/or failure to understand the notion of accumulation of an infinitesimal physical quantity. This work supports and extends previous research on students’ difficulties with integration in physics.

This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving the area under the curve concept. We found that only a few students could recognize that the concept of area under the curve was applicable in physics problems. Even when students could invoke the area under the curve concept, they did not necessarily understand the relationship between the process of accumulation and the area under a curve, so they failed to apply it to novel situations. We also found that when presented with several graphs, students had difficulty in selecting the graph such that the area under the graph corresponded to a given integral, although all of them could state that “the integral equaled the area under the curve.” The findings in this study are consistent with those in previous mathematics education research and research in physics education on students’ use of the area under the curve.

The Maryland Physics Expectations (MPEX) survey was designed to probe students’ expectations about their understanding of the process of learning physics and the structure of physics knowledge—cognitive expectations. This survey was administered to first-year university students in Thailand in the first semester of an introductory calculus-based physics course during academic years 2007 and 2008, to assess their expectations at the beginning of the course. The precourse MPEX results were compared and correlated with two separate measures of student learning: (1) individual students’ normalized gains from pre and post Force and Motion Conceptual Evaluation (FMCE) results, which measure students’ conceptual understanding, and (2) student’s scores on the final exam, which measure their more general problem-solving ability. The results showed a significant positive correlation between their overall MPEX score and five of the six MPEX cluster scores, with their normalized learning gains on the FMCE for both academic years. The results also showed significant positive correlations between student MPEX scores and their final exam scores for the overall MPEX score and all MPEX cluster scores except for the effort cluster. We interviewed two groups of five students each, one group with small favorable scores on the precourse MPEX effort cluster and one with high favorable scores on the precourse MPEX effort cluster, to see how the students’ learning efforts compared with their MPEX results. We concluded from the interviews that what the students think or expect about the MPEX effort involved in learning physics does not match what they actually do.

Large-scale assessments of student achievement in physics are often approached with an intention to discriminate students based on the attained level of their physics competencies. Therefore, for purposes of test design, it is important that items display an acceptable discriminatory behavior. To that end, it is recommended to avoid extraordinary difficult and very easy items. Knowing the factors that influence physics item difficulty makes it possible to model the item difficulty even before the first pilot study is conducted. Thus, by identifying predictors of physics item difficulty, we can improve the test-design process. Furthermore, we get additional qualitative feedback regarding the basic aspects of student cognitive achievement in physics that are directly responsible for the obtained, quantitative test results. In this study, we conducted a secondary analysis of data that came from two large-scale assessments of student physics achievement at the end of compulsory education in Bosnia and Herzegovina. Foremost, we explored the concept of “physics competence” and performed a content analysis of 123 physics items that were included within the above-mentioned assessments. Thereafter, an item database was created. Items were described by variables which reflect some basic cognitive aspects of physics competence. For each of the assessments, Rasch item difficulties were calculated in separate analyses. In order to make the item difficulties from different assessments comparable, a virtual test equating procedure had to be implemented. Finally, a regression model of physics item difficulty was created. It has been shown that 61.2% of item difficulty variance can be explained by factors which reflect the automaticity, complexity, and modality of the knowledge structure that is relevant for generating the most probable correct solution, as well as by the divergence of required thinking and interference effects between intuitive and formal physics knowledge structures. Identified predictors point out the fundamental cognitive dimensions of student physics achievement at the end of compulsory education in Bosnia and Herzegovina, whose level of development influenced the test results within the conducted assessments.

In 2006 a new type of tutorial, called Map Meeting, was successfully trialled with novice first year physics students at the University of Sydney, Australia. Subsequently, in first semester 2007 a large-scale experiment was carried out with 262 students who were allocated either to the strongly scaffolding Map Meetings or to the less scaffolding Workshop Tutorials, which have been run at the University of Sydney since 1995. In this paper we describe what makes Map Meetings more scaffolding than Workshop Tutorials—where the level of scaffolding represents the main difference between the two tutorial types. Using a mixed methods approach to triangulate results, we compare the success of the two with respect to both student tutorial preference and examination performance. In summary, Map Meetings had a higher retention rate and received more positive feedback from students—students liked the strongly scaffolding environment and felt that it better helped them understand physics. A comparison of final examination performances of students who had attended at least 10 out of 12 tutorials revealed that only 11% of Map Meeting students received less than 30 out of 90 marks compared to 21% of Workshop Tutorial students, whereas there were no differences amongst high-achieving students. Map Meetings was therefore particularly successful in helping low-achieving novices learn physics.

We describe courses designed to help future teachers reflect on and discuss both physics content and student knowledge thereof. We use three kinds of activities: reading and discussing the literature, experiencing research-based curricular materials, and learning to use the basic research methods of physics education research. We present a general overview of the two courses we have designed as well as a framework for assessing student performance on physics content knowledge and one aspect of pedagogical content knowledge—knowledge of student ideas—about one particular content area: electric circuits. We find that the quality of future teachers’ responses, especially on questions dealing with knowledge of student ideas, can be successfully categorized and may be higher for those with a nonphysics background than those with a physics background.

We developed a web-based tool to provide students with access to old exam problems and solutions. By controlling the order in which students saw the problems, as well as their access to solutions, we obtained data about student learning by studying old exam problems. Our data suggest that in general students learn from doing old exam problems, and that having access to the problem solutions increases their learning. However, the data also suggest the depth of learning may be relatively shallow. In addition, the data show that doing old exam problems provides important formative assessment about the student’s overall preparedness for the exam and their particular areas of strength and weakness.

We describe an inquiry-based course in physics and chemistry for preservice K-8 teachers developed at California State University Fullerton. The course is one of three developed primarily to enhance the science content understanding of prospective teachers. The course incorporates a number of innovative instructional strategies and is somewhat unusual for its interdisciplinary focus. We describe the course structure in detail, providing examples of course materials and assessment strategies. Finally, we provide research data illustrating both the need for the course and the effectiveness of the course in developing student understanding of selected topics. Student responses to various questions reflect a lack of understanding of many relatively simple physical science concepts, and a level of performance that is usually lower than that in comparable courses serving a general education audience. Additional data suggest that course activities improve student understanding of selected topics, often dramatically.

In this paper we present the results of two experiments designed to understand how physics students’ learning of the concept of refraction is influenced by the cognitive phenomenon of “specificity.” In both experiments participants learned why light bends as it travels from one optical medium to another with an analogy made to a car driving from paved road into mud and vice versa. They then learned how to qualitatively draw the direction of refracted light rays with an example of a glass prism. One group learned with a rectangular prism example while a second group learned with a triangular prism example. In a transfer test, the participants revealed how, even when they seemed able to implement the refraction concept, their responses were biased by the example they had seen. Participants frequently violated the refraction principle they had just learned (reversing the bend direction) in order to make sure their response matched the surface features of their learning example. This tended to happen when their test question looked superficially similar to their learning example. We discuss the implications of these results for physics instruction.

We investigate student confusion of concepts of electric and magnetic force. At various times during a traditional university-level course, we administered a series of simple questions about the direction of force on a charged particle moving through either an electric or a magnetic field. We find that after electric force instruction but before magnetic force instruction most students answer electric force questions correctly, and we replicate well-known results that many students incorrectly answer that magnetic forces are in the same direction as the magnetic field. After magnetic force instruction, most students answer magnetic force questions correctly, but surprisingly many students incorrectly answer that electric forces are perpendicular to electric fields, as would happen if a student confused electric forces with magnetic forces. As a further indication of interference between electric and magnetic concepts, we also find that students’ responses depend on whether electric or magnetic force questions are posed first, and this effect depends on whether electric or magnetic force was most recently taught.

Novice problem solvers are rather sensitive to surface problem features, and they often resort to trial and error formula matching rather than identifying an appropriate solution approach. These observations have been interpreted to imply that novices structure their knowledge according to surface features rather than according to problem type categories. However, it may also be the case that novices do know problem types, but cannot map the problem at hand to a known type, because they fail to create a sufficiently well-elaborated problem representation. This study aims to distinguish between these explanations. In this study novice physics students at high and low levels of proficiency completed two problem-sorting tasks from the domain of electricity and magnetism, one with and one without elaboration support. Results confirm that these students do distinguish problem types in accordance with their required solution approaches, and that their problem-sorting performance improves with elaboration support. Therefore, it was concluded that their major difficulty lies in the process of matching concrete problems to a proper category. Within-group analysis revealed that the performance of proficient novices clearly improved with elaboration support, whereas the effect for less proficient novices remained inconclusive. The latter finding is explained from the less proficient novices’ problem representations being too fragmented to integrate new information. These results suggest that, in order to promote schema-based problem solving, instruction in the domain of electricity and magnetism should be based not so much on restructuring the conceptual knowledge base but rather on enriching situational knowledge.

We have been piloting web-based multimedia learning modules (MLMs), developed by the Physics Education Research Group at the University of Illinois at Urbana Champaign (UIUC), as a “prelecture assignment” in several introductory physics courses at California State Polytechnic University at Pomona. In this study, we report the results from a controlled study utilizing modules on electricity and magnetism as a part of a blended hybrid-online course. We asked students in the experimental section to view the MLMs prior to attending the face-to-face class, and to make sure this would not result in additional instructional time, we reduced the weekly class time by one-third. We found that despite reduced class time, student-learning outcomes were not hindered; in fact, the implementation of the UIUC MLMs resulted in a positive effect on student performance on conceptual tests and classroom discussion questions.