We developed an instrument to systematically investigate student conceptual understanding of the relationships between the directions of net force, velocity, and acceleration in one dimension and report on data collected on the final version of the instrument from over 650 students. Unlike previous work, we simultaneously studied all six possible conditional relations between force, velocity, and acceleration in order to obtain a coherent picture of student understanding of the relations between all three concepts. We present a variety of evidence demonstrating the validity and reliability of the instrument. An analysis of student responses from three different course levels revealed three main findings. First, a significant fraction of students chose “partially correct” responses, and from pre- to post-test, many students moved from “misconception” to partially correct responses, or from partially correct to fully correct responses. Second, there were asymmetries in responding to conditional relations. For example, students answered questions of the form “Given the velocity, what can be inferred about the net force?” differently than converse questions “Given the net force, what can be inferred about the velocity?” Third, there was evidence of hierarchies in student responses, suggesting, for example, that understanding the relation between velocity and acceleration is necessary for understanding the relation between velocity and force, but the converse is not true. Finally, we briefly discuss how these findings might be applied to instruction.

This study compared the educational effects of computer simulations developed in a hyper-realistic virtual environment with the educational effects of either traditional schematic simulations or a traditional optics laboratory. The virtual environment was constructed on the basis of Java applets complemented with a photorealistic visual output. This new virtual environment concept, which we call hyper-realistic, transcends basic schematic simulation; it provides the user with a more realistic perception of a physical phenomenon being simulated. We compared the learning achievements of three equivalent, homogeneous groups of undergraduates—an experimental group who used only the hyper-realistic virtual laboratory, a first control group who used a schematic simulation, and a second control group who used the traditional laboratory. The three groups received the same theoretical preparation and carried out equivalent practicals in their respective learning environments. The topic chosen for the experiment was optical aberrations. An analysis of variance applied to the data of the study demonstrated a statistically significant difference ($p$ value $<0.05$) between the three groups. The learning achievements attained by the group using the hyper-realistic virtual environment were 6.1 percentage points higher than those for the group using the traditional schematic simulations and 9.5 percentage points higher than those for the group using the traditional laboratory.

The ability to categorize problems based upon underlying principles, rather than surface features or contexts, is considered one of several proxy predictors of expertise in problem solving. With inspiration from the classic study by Chi, Feltovich, and Glaser, we assess the distribution of expertise among introductory physics students by asking three introductory physics classes, each with more than a hundred students, to categorize mechanics problems based upon similarity of solution. We compare their categorization with those of physics graduate students and faculty members. To evaluate the effect of problem context on students’ ability to categorize, two sets of problems were developed for categorization. Some problems in one set included those available from the prior study by Chi et al. We find a large overlap between calculus-based introductory students and graduate students with regard to their categorizations that were assessed as “good.” Our findings, which contrast with those of Chi et al., suggest that there is a wide distribution of expertise in mechanics among introductory and graduate students. Although the categorization task is conceptual, introductory students in the calculus-based course performed better than those in the algebra-based course. Qualitative trends in categorization of problems are similar between the non-Chi problems and problems available from the Chi study used in our study although the Chi problems used are more difficult on average.

This paper describes a teaching experiment designed to examine the learning (i.e., retention of content and conceptual development) that takes place when public scientific web lectures delivered by scientists are utilized to present advanced ideas in physics to students with a high school background in physics. The students watched an exemplary public physics web lecture that was followed by a collaborative generic activity session. The collaborative session involved a guided critical reconstruction of the main arguments in the lecture, and a processing of the key analogical explanations. Then the students watched another exemplary web lecture on a different topic. The participants ($N=14$) were divided into two groups differing only in the order in which the lectures were presented. The students’ discussions during the activities show that they were able to reason and demonstrate conceptual progress, although the physics ideas in the lectures were far beyond their level in physics. The discussions during the collaborative session contributed significantly to the students’ understanding. We illustrate this point through an analysis of one of these discussions between two students on an analogical explanation of the Aharonov-Bohm effect that was presented in one of the lectures. The results from the tests that were administered to the participants several times during the intervention further support this contention.

It is well documented that when solving problems experts first search for underlying concepts while students tend to look for equations and previously worked examples. The overwhelming majority of end-of-chapter (EOC) problems in most introductory physics textbooks contain only material and examples discussed in a single chapter, rarely requiring a solver to conduct a general search for underlying concepts. Hypothesizing that complete reliance on EOC problems trains students to rely on a nonexpert approach, we designed and implemented “synthesis” problems, each combining two major concepts that are broadly separated in the teaching timeline. To provide students with guided conceptual scaffolding, we encapsulated each synthesis problem into a sequence with two preceding conceptually based multiple-choice questions. Each question contained one of the major concepts covered in the subsequent synthesis problem. Results from a small-scale interview study and two large-scale written tests showed that the scaffolding encouraged students to search for and apply appropriate fundamental principles in solving synthesis problems, and that repeated training using scaffolded synthesis problems also helped students to make cross-topic transfers.

This paper examines the results of the repeated administration of the Colorado Learning Attitudes about Science Survey (CLASS) in a large introductory physics course at a midsize, metropolitan Canadian university. We compare the results to those obtained previously in comparable courses at the University of British Columbia (Canada) and the University of Colorado (U.S.). Atypically, students in this study exhibited a positive shift in their attitudes about science over the semester. The change in students’ attitudes across the term appears to be moderated by their educational background—specifically, whether they had taken grade 12 physics or not. The correlation between students’ attitudes and their conceptual knowledge also appears to be influenced by students’ educational background. The results have pedagogical implications for instructors of introductory college and university physics and potentially for other science courses.

Utilizing an energy-as-substance conceptual metaphor as a central feature of the introductory physics curriculum affords students a wealth of conceptual resources for reasoning about energy conservation, storage, and transfer. This paper first establishes the utility and function of a conceptual metaphor in developing student understanding of energy concepts. Then a curricular framework with a prominent energy-as-substance conceptual metaphor is described. The curricular framework involves both a reorganization of the content of introductory physics as well as a renewed focus. Reorganizing includes treating energy early and spiraling back to energy treatments. The refocusing includes emphasizing energy’s role in modeling phenomena and attending to the tools for representing energy conservation, storage, and transfer. Implementation of the energy framework is then described in the context of a Modeling Instruction course. Finally, qualitative evidence is presented showing student use of energy conceptual resources which are promoted in the curricular implementation.

Florida International University has undergone a reform in the introductory physics classes by focusing on the laboratory component of these classes. We present results from the secondary implementation of two research-based instructional strategies: the implementation of the Learning Assistant model as developed by the University of Colorado at Boulder and the Open Source Tutorial curriculum developed at the University of Maryland, College Park. We examine the results of the Force Concept Inventory (FCI) for introductory students over five years ($n=872$) and find that the mean raw gain of students in transformed lab sections was 0.243, while the mean raw gain of the traditional labs was 0.159, with a Cohen’s $d$ effect size of 0.59. Average raw gains on the FCI were 0.243 for Hispanic students and 0.213 for women in the transformed labs, indicating that these reforms are not widening the gaps between underrepresented student groups and majority groups. Our results illustrate how research-based instructional strategies can be successfully implemented in a physics department with minimal department engagement and in a sustainable manner.

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.