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.

We present data from a between-student study on student response to questions on Newton’s third law given in two introductory calculus-based physics classes (Mechanics and Electromagnetism) at a large northeastern university. Construction of a response curve reveals subtle dynamics in student learning not capturable by pretesting and post-testing. We find a significant positive effect of instruction that diminishes by the end of the quarter. Two quarters later, a significant dip in correct response occurs when instruction changes from the vector quantities of electric forces and fields to the scalar quantity of electric potential. When instruction returns to vector topics, performance rebounds to initial values.

Solving physics problem in university physics education using a computational approach requires knowledge and skills in several domains, for example, physics, mathematics, programming, and modeling. These competences are in turn related to students’ beliefs about the domains as well as about learning. These knowledge and beliefs components are referred to here as epistemic elements, which together represent the students’ epistemic framing of the situation. The purpose of this study was to investigate university physics students’ epistemic framing when solving and visualizing a physics problem using a particle-spring model system. Students’ epistemic framings are analyzed before and after the task using a network analysis approach on interview transcripts, producing visual representations as epistemic networks. The results show that students change their epistemic framing from a modeling task, with expectancies about learning programming, to a physics task, in which they are challenged to use physics principles and conservation laws in order to troubleshoot and understand their simulations. This implies that the task, even though it is not introducing any new physics, helps the students to develop a more coherent view of the importance of using physics principles in problem solving. The network analysis method used in this study is shown to give intelligible representations of the students’ epistemic framing and is proposed as a useful method of analysis of textual data.

Student use of out-of-class time was measured for four years in the introductory second-semester calculus-based physics course at the University of Arkansas. Two versions of the course were presented during the time of the measurement. In both versions, the total out-of-class time a student invested in the course explained less than 1% of the variance in test average and in normalized gain on the Conceptual Survey in Electricity and Magnetism. The details of how students used their out-of-class time explained from 21% to 36% of the variance in test average and 19% to 37% of the variance in normalized gain. The amount of time spent on the course increased as the course was made more difficult, but less than would be expected based on the changes in the course. Students changed their allocation of out-of-class time based on their performance within the course as the course progressed.

Recent research results have failed to support the conventionally held belief that students learn physics best from hands-on experiences with physical equipment. Rather, studies have found that students who perform similar experiments with computer simulations perform as well or better on measures of conceptual understanding than their peers who used physical equipment. In this study, we explored how university-level nonscience majors’ understanding of the physics concepts related to pulleys was supported by experimentation with real pulleys and a computer simulation of pulleys. We report that when students use one type of manipulative (physical or virtual), the comparison is influenced both by the concept studied and the timing of the post-test. Students performed similarly on questions related to force and mechanical advantage regardless of the type of equipment used. On the other hand, students who used the computer simulation performed better on questions related to work immediately after completing the activities; however, the two groups performed similarly on the work questions on a test given one week later. Additionally, both sequences of experimentation (physical-virtual and virtual-physical) equally supported students’ understanding of all of the concepts. These results suggest that both the concept learned and the stability of learning gains should continue to be explored to improve educators’ ability to select the best learning experience for a given topic.

Educators and policy makers have advocated for reform of undergraduate biology education, calling for greater integration of mathematics and physics in the biology curriculum. While these calls reflect the increasingly interdisciplinary nature of biology research, crossing disciplinary boundaries in the classroom carries epistemological challenges for both instructors and students. In this paper we expand on the construct of authenticity to better describe and understand disciplinary practices, in particular, to examine those used in undergraduate physics and biology courses. We then apply these ideas to examine an introductory biology course that incorporates physics and mathematics. We characterize how instructors asked students to use interdisciplinary tools in this biology course and contrast them with the typical uses of these tools in physics courses. Finally, we examine student responses to the use of mathematics and physics in this course, to better understand the challenges and consequences of using interdisciplinary tools in introductory courses. We link these results to the reform initiatives of introductory physics courses for life-science students.

We discuss common difficulties in upper-division electricity and magnetism (E&M) in the areas of Gauss’s law, vector calculus, and electric potential using both quantitative and qualitative evidence. We also show that many of these topical difficulties may be tied to student difficulties with mathematics. At the junior level, some students struggle to combine mathematical calculations and physics ideas, to account for the underlying spatial situation when doing a mathematical calculation, and to access appropriate mathematical tools. We discuss the implications of our findings for E&M instruction at the junior level.

In this paper we discuss a study on the approaches to modeling of students of the 4-year elementary school teacher program at the University of Palermo, Italy. The answers to a specially designed questionnaire are analyzed on the basis of an a priori analysis made using a general scheme of reference on the epistemology of mathematics and physics. The study is performed by using quantitative data analysis methods, i.e. factorial analysis of the correspondences and implicative analysis. A qualitative analysis of key words and terms used by students during interviews is also used to examine some aspects that emerged from the quantitative analysis. The students have been classified on the basis of their different epistemological approaches to knowledge construction, and implications between different conceptual strategies used to answer the questionnaire have been highlighted. The study’s conclusions are consistent with previous research, but the use of quantitative data analysis allowed us to classify the students into three “profiles” related to different epistemological approaches to knowledge construction, and to show the implications of the different conceptual strategies used to answer the questionnaire, giving an estimation of the classification or implication “strength.” Some hints on how a course for elementary school physics and mathematics education can be planned to orient the future teachers to the construction of models of explanation are reported.

A perceived difficulty is associated with physics problem solving from a learner’s viewpoint, arising out of a multitude of reasons. In this paper, we have examined the microstructure of students’ thought processes during physics problem solving by combining the analysis of responses to multiple-choice questions and semistructured student interviews. Design of appropriate scaffoldings serves as pointers to the identification of student problem solving difficulties. An analysis of the results suggests the necessity of identification of the skill sets required for developing better problem solving abilities.