Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations). Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction. Starting from an overall distinction between a technical approach, which involves an instrumental (tool-like) use of mathematics, and a structural one, focused on reasoning about the physical world mathematically, the goal of this study is to characterize the development of the latter in didactic contexts. For this purpose, a case study was conducted on the electromagnetism course given by a distinguished physics professor. The analysis of selected teaching episodes with the software Videograph led to the identification of a set of categories that describe different strategies used by the professor to emphasize the structural role of mathematics in his lectures. As a consequence of this research, an analytic tool to enable future comparative studies between didactic approaches regarding the way mathematics is treated in physics teaching is provided.

Item response theory (IRT) becomes an increasingly important tool when analyzing “big data” gathered from online educational venues. However, the mechanism was originally developed in traditional exam settings, and several of its assumptions are infringed upon when deployed in the online realm. For a large-enrollment physics course for scientists and engineers, the study compares outcomes from IRT analyses of exam and homework data, and then proceeds to investigate the effects of each confounding factor introduced in the online realm. It is found that IRT yields the correct trends for learner ability and meaningful item parameters, yet overall agreement with exam data is moderate. It is also found that learner ability and item discrimination is robust over a wide range with respect to model assumptions and introduced noise. Item difficulty is also robust, but over a narrower range.

Developing expertise in physics problem solving requires the ability to use mathematics effectively in physical scenarios. Novices and experts often perceive the use of mathematics in physics differently. Students’ perceptions and how they frame the use of mathematics in physics play an important role in their physics problem solving. In this study, we examined students’ epistemological framing about using mathematics in physics in two types of problems: a conventional problem and a hypothetical debate problem. We found that when solving a conventional physics problem, students tended to frame problem solving in physics as rote equation chasing, i.e., plugging quantities into a memorized physics equation. In hypothetical debate problems, students were more likely to be involved in quantitative or qualitative sense making. We conclude that hypothetical debate problems might be used as an instructional tool for engaging students in sense making while using mathematics in physics. Thus, it might be potentially useful for developing more expertlike problem solving expertise.

Technology-rich student-centered classrooms such as SCALE-UP and TEAL are designed to actively engage students. We examine what happens when the design of the classroom (conventional or teacher-centered versus student-centered classroom spaces) is consistent or inconsistent with the teacher’s epistemic beliefs about learning and teaching (traditional or teacher-centered versus student-centered pedagogies). We compare two types of pedagogical approaches and two types of classroom settings through a quasiexperimental $2\times 2$ factorial design. We collected data from 214 students registered in eight sections of an introductory calculus-based mechanics course given at a Canadian publicly funded two-year college. All students were given the Force Concept Inventory at the beginning and at the end of the 15-week-long course. We then focused on six teachers assigned to teach in the student-centered classroom spaces. We used qualitative observations and the Approaches to Teaching Inventory (ATI), a self-reported questionnaire, to determine the teachers’ epistemic beliefs (teacher-centered or student-centered) and how these beliefs affected their use of the space and their students’ conceptual learning. We report four main findings. First, the student-centered classroom spaces are most effective when used with student-centered pedagogies. Second, student-centered classrooms are ineffective when used with teacher-centered pedagogies and may have negative effects for students with low prior knowledge. Third, we find a strong correlation between six instructors’ self-reported epistemic beliefs of student centeredness and their classes’ average normalized gain ($r=0.91$; $p=0.012$). Last, we find that some instructors are more willing to adopt student-centered teaching practices after using student-centered classroom spaces. These data suggest that student-centered classrooms are effective only when instructors’ epistemic framework of teaching and learning is consistent with a student-centered pedagogy. However, the use of the student-centered classrooms may change instructors’ epistemic frameworks over time. Further research should focus on how to better support teachers with shifting epistemic frameworks as well as helping students with lower prior knowledge in student-centered classroom spaces.

Tabular presentations of student data often hide information about the switches in responses by individual students over the course of a semester. We extend unpublished work by Kanim on “escalator diagrams,” which show changes in student responses from correct to incorrect (and vice versa) while representing pre- and postinstruction results on questions. We introduce the representation of “consistency plots,” containing three pieces of information: each student’s method of solution and correctness of solution and the shift from before to after instruction. We present data from students in an intermediate mechanics class answering (nearly) identical midterm and final examination questions. These data serve as a proof of concept of the method; we suggest other possible uses of consistency plots in physics education research, as well.

Many science education researchers have argued that learners’ commitment to a substance (matter-based) ontology impedes the learning of scientific concepts that scientists typically conceptualize as processes or interactions, such as force, electric current, and heat. By this account, students’ tendency to classify these entities as substances or properties of substances leads to robust misconceptions, and instruction should steer novices away from substance-based reasoning. We argue that substance-based reasoning can contribute to the learning and understanding of these very same physics concepts. Our case study focuses on a group of elementary school science teachers in our professional development program. Starting from substance-based metaphors for gravity, the teachers build a sophisticated explanation for why objects of different masses fall with the same acceleration. We argue that, for conceptual, epistemological, and affective reasons, instructional interventions should focus on tapping these productive substance-based resources when they arise rather than attempting to suppress them.

We have studied the correlation of student performance in a large first year university physics course with their reasons for taking the course and whether or not the student took a senior-level high school physics course. Performance was measured both by the Force Concept Inventory and by the grade on the final examination. Students who took the course primarily for their own interest outperformed students who took the course primarily because it was required, both on the Force Concept Inventory and on the final examination; students who took a senior-level high school physics course outperformed students who did not, also both on the Force Concept Inventory and on the final exam. Students who took the course for their own interest and took high school physics outperformed students who took the course because it was required and did not take high school physics by a wide margin. However, the normalized gain on the Force Concept Inventory was the same within uncertainties for all groups and subgroups of students.

Visual representations play a critical role in teaching physics. However, since we do not have a satisfactory understanding of how visual perception impacts the construction of abstract knowledge, most visual representations used in instructions are either created based on existing conventions or designed according to the instructor’s intuition, which leads to a significant variance in their effectiveness. In this paper we propose a cognitive mechanism based on grounded cognition, suggesting that visual perception affects understanding by activating “perceptual symbols”: the basic cognitive unit used by the brain to construct a concept. A good visual representation activates perceptual symbols that are essential for the construction of the represented concept, whereas a bad representation does the opposite. As a proof of concept, we conducted a clinical experiment in which participants received three different versions of a multimedia tutorial teaching the integral expression of electric potential. The three versions were only different by the details of the visual representation design, only one of which contained perceptual features that activate perceptual symbols essential for constructing the idea of “accumulation.” On a following post-test, participants receiving this version of tutorial significantly outperformed those who received the other two versions of tutorials designed to mimic conventional visual representations used in classrooms.

We use the theory of communities of practice and the concept of accountable disciplinary knowledge to describe how a learning community develops in the context of an upper-division physics laboratory course. The change in accountable disciplinary knowledge motivates students’ enculturation into a community of practice. The enculturation process is facilitated by four specific structural features of the course and supported by a primary instructional choice. The four structural features are “paucity of instructor time,” “all in a room together,” “long and difficult experiments,” and “same experiments at different times.” The instructional choice is the encouragement of the sharing and development of knowledge and understanding by the instructor. The combination of the instructional choice and structural features promotes the development of the learning community in which students engage in authentic practices of a physicist. This results in a classroom community that can provide students with the opportunity to have an accelerated trajectory towards being a more central participant of the community of a practice of physicists. We support our claims with video-based observations of laboratory classroom interactions and individual, semistructured interviews with students about their laboratory experiences and physics identity.

In this clinical study on helping students prepare for an exam, we compared three different treatments. All students were asked to take a practice exam. One group was then given worked-out solutions for that exam, another group was given the solutions and targeted exercises to do as homework based on the result of their practice exam, and the third group was given the solutions, homework, and also an hour of one-on-one tutoring. Participants from all three conditions significantly outperformed the control group on the midterm exam. However, participants that had one-on-one tutoring did not outperform the other two participant groups.

Ideally, instructors and their institutions would have a shared set of metrics by which they determine teaching effectiveness. And, ideally, these metrics would overlap with research findings on measuring teaching effectiveness. Unfortunately, the current situation at most institutions is far from this ideal. As part of a larger interview study, 72 physics instructors were asked to describe how they and their institutions assess teaching effectiveness. Results suggest that institutions typically base most or all of their assessment of teaching effectiveness on student evaluations of teaching. Instructors, on the other hand, base most or all of their assessment of teaching effectiveness on student exam performance and nonsystematic formative assessments. Few institutions and instructors use assessment practices suggested by the research literature. In general, instructors are much more positive about the methods they use to evaluate their teaching than the methods their institutions use to evaluate their teaching. Both instructors and institutions could benefit from broadening the assessment sources they use to evaluate teaching effectiveness through increased use of standardized measures based on student learning and greater reliance on systematic formative assessment.

This paper addresses the efficacy of an open-inquiry approach that allows students to build on traditionally received knowledge. A sample of thirty engineering undergraduates, having already attended traditional university physics instruction, was selected for this study. The students were involved in a six-week long learning experience of open-inquiry research activities within the highly motivating context of developing a thermodynamically efficient space base on Mars. They designed and carried out their own scientific investigations, which involved gathering information, collecting and analyzing data, providing explanations, and sharing results. A questionnaire containing fifteen open-ended real-world problems in thermal science was administered to the students both prior to and after all activities, with the aim of investigating the nature of their difficulties in problem solving. Students’ answers were classified into three epistemological profiles and a prepost instruction comparison was carried out, using methods of statistical implicative analysis. The students obtained significant benefits from their open-inquiry experiences, in terms of the strengthening of their practical and reasoning abilities, by proficiently applying the learned concepts to face and solve real-world problem situations.

Discipline-based science concept assessments are powerful tools to measure learners’ disciplinary core ideas. Among many such assessments, the Brief Electricity and Magnetism Assessment (BEMA) has been broadly used to gauge student conceptions of key electricity and magnetism (E&M) topics in college-level introductory physics courses. Differing from typical concept inventories that focus only on one topic of a subject area, BEMA covers a broad range of topics in the electromagnetism domain. In spite of this fact, prior studies exclusively used a single aggregate score to represent individual students’ overall understanding of E&M without explicating the construct of this assessment. Additionally, BEMA has been used to compare traditional physics courses with a reformed course entitled Matter and Interactions (M&I). While prior findings were in favor of M&I, no empirical evidence was sought to rule out possible differential functioning of BEMA that may have inadvertently advantaged M&I students. In this study, we used Rasch analysis to seek two missing pieces regarding the construct and differential functioning of BEMA. Results suggest that although BEMA items generally can function together to measure the same construct of application and analysis of E&M concepts, several items may need further revision. Additionally, items that demonstrate differential functioning for the two courses are detected. Issues such as item contextual features and student familiarity with question settings may underlie these findings. This study highlights often overlooked threats in science concept assessments and provides an exemplar for using evidence-based reasoning to make valid inferences and arguments.