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We used a sequential synthesis problem to investigate novice teachers’ conceptual difficulties in hydrodynamics. Twenty-one new secondary level physics teachers from various regions of China, who had been in service for no more than 2 years, participated in the study. Each participant completed a written hydrodynamics problem consisting of four questions, all of which were related to a situation about water flowing in a long, nonuniform tube of different cross sections, heights, and orientations. Analysis of the teachers’ written performances exposed a number of errors. To further investigate their underlying notions about hydrodynamics, we conducted one-on-one interviews with 13 teachers selected randomly from those making such errors on the written test. The interviews revealed three major categories of errors about hydrodynamics held by our novice teachers. These relate to (a) ontological confusions and misuse of properties associated with solid, liquid, and gas; (b) deficient perceptions of force-motion and work-energy analysis; and (c) mischaracterizations about the nature of Bernoulli’s equation and the quantities therein. Here, we not only replicated some of the literature-reported misconceptions but also uncovered new ontological notions of hydrodynamics held by physics teachers, an underresearched population on this topic.

This study examines students’ visual behaviors when they tackle two types of synthesis problems, sequential and simultaneous problems. Sequential synthesis tasks can be solved by applying pertinent concepts consecutively, whereas simultaneous synthesis tasks require concurrent application of multiple concepts. Twenty-two students from an introductory calculus-based physics course participated in the study. We used an eye-tracker to record the students’ eye movements when they silently reflected on how to solve the problems and subsequently when they talked aloud their problem-solving strategies. We found that the students made more gaze transitions between text and diagram for the simultaneous problems than for the sequential ones. However, they spent more time looking at the diagram and making within-diagram eye transitions in the sequential tasks than in the simultaneous tasks. Further, most students invoked two concepts to solve the sequential tasks but only one for the simultaneous tasks. These findings indicate that the students made less effort to link text and diagram in solving sequential problems but frequently attempted to integrate information within each diagram. The pattern for the simultaneous problems appeared to be reversed. Our results suggest that different types of synthesis (i.e., sequential and simultaneous) may differentially influence the ways students handle tasks. As suggested by the eye-tracker data and confirmed by the participants’ verbal explanations, students tend to divide the situation in sequential problems into subtasks but treat simultaneous problems as a single-step task.

[This paper is part of the Focused Collection on Quantitative Methods in PER: A Critical Examination.] The notion of quantitative physics education research (PER) so far has been mostly limited to the mere use of statistical methods or use of computational tools for analyzing numerical data. Little attention, in fact, has been given to the underpinnings of this research paradigm. To fill the gap, this theoretical paper addresses key and yet often tacit (or even misunderstood) principles of three commonly used quantitative genres in PER, which I, respectively, refer to as measurement (quantification of individual constructs), controlled exploration of relations (quantification of relationships between multiple constructs through controlled experiments), and data mining (quantification of new information from large datasets). For each genre, I elucidate the paradigmatic basis by focusing on its ontological assumptions (theories about the reality under quantitative investigation), epistemological commitments (views about the knowledge gained through quantitative investigation), and methodological implications for empirical investigations. Although framed in the context of physics education research, the discussions herein are applicable to other discipline-based or general education research employing quantitative methods.

[This paper is part of the Focused Collection on Quantitative Methods in PER: A Critical Examination.] While other fields such as statistics and education have examined various issues with quantitative work, few studies in physics education research (PER) have done so. We conducted a two-phase study to identify and to understand the extent of these issues in quantitative PER. During phase 1, we conducted a focus group of three experts in this area, followed by six interviews. Subsequent interviews refined our plan. Both the focus group and interviews revealed issues regarding the lack of details in sample descriptions, lack of institutional or course contextual information, lack of reporting on limitation, and overgeneralization or overstatement of conclusions. During phase 2, we examined 72 manuscripts that used four conceptual or attitudinal assessments (Force Concept Inventory, Conceptual Survey of Electricity and Magnetism, Brief Electricity and Magnetism Assessment, and Colorado Learning Attitudes about Science Survey). Manuscripts were coded on whether they featured various sample descriptions, institutional or course context information, limitations, and whether they overgeneralized conclusions. We also analyzed the data to see if reporting has changed from the earlier periods to more recent times. We found that not much has changed regarding sample descriptions and institutional or course context information, but reporting and overgeneralizing conclusions have improved over time. We offer some questions for researchers, reviewers, and readers in PER to consider when conducting or using quantitative work.

We examine students’ mathematical performance on quantitative “synthesis problems” with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students’ mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students’ simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students’ formulation and combination of equations. Several reasons may explain this difference, including the students’ different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

The ability to solve physics problems that require multiple concepts from across the physics curriculum—“synthesis” problems—is often a goal of physics instruction. Three experiments were designed to evaluate the effectiveness of two instructional methods employing worked examples on student performance with synthesis problems; these instructional techniques, analogical comparison and self-explanation, have previously been studied primarily in the context of single-concept problems. Across three experiments with students from introductory calculus-based physics courses, both self-explanation and certain kinds of analogical comparison of worked examples significantly improved student performance on a target synthesis problem, with distinct improvements in recognition of the relevant concepts. More specifically, analogical comparison significantly improved student performance when the comparisons were invoked between worked synthesis examples. In contrast, similar comparisons between corresponding pairs of worked single-concept examples did not significantly improve performance. On a more complicated synthesis problem, self-explanation was significantly more effective than analogical comparison, potentially due to differences in how successfully students encoded the full structure of the worked examples. Finally, we find that the two techniques can be combined for additional benefit, with the trade-off of slightly more time on task.

A body of research on physics problem solving has focused on single-concept problems. In this study we use “synthesis problems” that involve multiple concepts typically taught in different chapters. We use two types of synthesis problems, sequential and simultaneous synthesis tasks. Sequential problems require a consecutive application of fundamental principles, and simultaneous problems require a concurrent application of pertinent concepts. We explore students’ conceptual performance when they solve quantitative synthesis problems with varying mathematical complexity. Conceptual performance refers to the identification, follow-up, and correct application of the pertinent concepts. Mathematical complexity is determined by the type and the number of equations to be manipulated concurrently due to the number of unknowns in each equation. Data were collected from written tasks and individual interviews administered to physics major students (N=179) enrolled in a second year mechanics course. The results indicate that mathematical complexity does not impact students’ conceptual performance on the sequential tasks. In contrast, for the simultaneous problems, mathematical complexity negatively influences the students’ conceptual performance. This difference may be explained by the students’ familiarity with and confidence in particular concepts coupled with cognitive load associated with manipulating complex quantitative equations. Another explanation pertains to the type of synthesis problems, either sequential or simultaneous task. The students split the situation presented in the sequential synthesis tasks into segments but treated the situation in the simultaneous synthesis tasks as a single event.

This paper analyzes pre-post matched gains in the epistemological views of science students taking the introductory physics course at Beijing Normal University (BNU) in China. In this study we examined the attitudes and beliefs of science majors (n=441) in four classes, one taught using traditional (lecture) teaching methods, and the other three taught with Peer Instruction (PI). In two of the PI classes, student peer groups were constantly changing throughout the semester, while in the other PI class student groups remained fixed for the duration of the semester. The results of the pre- and post-test using the Colorado Learning Attitudes about Science Survey showed that students in traditional lecture settings became significantly more novicelike in their beliefs about physics and learning physics over the course of a semester, a result consistent with what was reported in the literature. However, all three of the classes taught using the PI method improved student attitudes and beliefs about physics and learning physics. In the PI class with fixed peer groups, students exhibited a greater positive shift in attitudes and beliefs than in the other PI class with changing peer groups. The study also looked at gender differences in student learning attitudes. Gender results revealed that female science majors in the PI classes achieved a greater positive shift in attitudes and beliefs after instruction than did male students.

Previous literature on learners’ epistemological beliefs about physics has almost exclusively focused on analysis of university classroom instruction and its effects on students’ views. However, little is known about other populations or factors other than classroom instruction on learners’ epistemologies. In this study, we used a cross-sequential method, combining both longitudinal and cross-sectional designs, to investigate an epistemological progression trend from preservice to in-service teachers. Six cohorts of participants were studied, who either were then attending or had completed an undergraduate teacher preparation program in physics at a major Chinese university. These cohorts were incoming freshmen, end-of-year freshmen, end-of-year sophomores, end-of-year juniors, end-of-year seniors, and 1st-year high school physics teachers who were about to enter the 2nd year of teaching. We used the Colorado Learning Attitudes about Science Survey (CLASS) as both a pretest and a post-test to gauge the changes in the participants’ epistemological views over an entire academic year. Follow-up interviews were also conducted to explore factors responsible for such changes. Results showed that the epistemological trend as measured by CLASS did not increase monotonically. Instead, there was a decrease in the epistemological trend among the incoming freshmen in their first year undergraduate studies, followed by a long stasis until the end of the senior year. Then, there was a rebound for the end-of-year seniors in their 1st year of teaching, followed by another plateau. Interviews revealed that the competitive learning environment, increased content difficulty, and unfamiliar pedagogies in college were major factors that negatively influenced incoming freshmen’s views about physics. Conversely, a role change from student to teacher and relatively easy content in high school positively impacted end-of-year seniors’ views about physics and learning.