Search Results (9 total)

It is generally believed that students should use multiple representations in solving certain physics problems, and earlier work in PER has begun to outline how experts and novices differ in their use of multiple representations. In this study, we build on this foundation by interviewing expert and novice physicists as they solve two types of multiple representation problems: those in which multiple representations are provided for them and those in which the students must construct their own representations. We analyze in detail the types of representations subjects use and the order and manner in which they are used. Expert and novice representation use is surprisingly similar in some ways, especially in that both experts and novices make significant use of multiple representations. Some significant differences also emerge. Experts are more flexible in terms of starting point and move between the available representations more quickly, and novices tend to move between more representations in total. In addition, we find that an examination of how often and when multiple representations are used is inadequate to fully characterize a problem-solving episode; one must also consider the purpose behind the use of the available representations. This analysis of how experts and novices use representations sharpens the differences between the two groups, demonstrates analysis techniques that may be useful in future work, and suggests possible paths for instruction.

Good use of multiple representations is considered key to learning physics, and so there is considerable motivation both to learn how students use multiple representations when solving problems and to learn how best to teach problem solving using multiple representations. In this study of two large-lecture algebra-based physics courses at the University of Colorado (CU) and Rutgers, the State University of New Jersey, we address both issues. Students in each of the two courses solved five common electrostatics problems of varying difficulty, and we examine their solutions to clarify the relationship between multiple representation use and performance on problems involving free-body diagrams. We also compare our data across the courses, since the two physics-education-research-based courses take substantially different approaches to teaching the use of multiple representations. The course at Rutgers takes a strongly directed approach, emphasizing specific heuristics and problem-solving strategies. The course at CU takes a weakly directed approach, modeling good problem solving without teaching a specific strategy. We find that, in both courses, students make extensive use of multiple representations, and that this use (when both complete and correct) is associated with significantly increased performance. Some minor differences in representation use exist, and are consistent with the types of instruction given. Most significant are the strong and broad similarities in the results, suggesting that either instructional approach or a combination thereof can be useful for helping students learn to use multiple representations for problem solving and concept development.

Recent papers document that student problem-solving competence varies (often strongly) with representational format, and that there are significant differences between the effects that traditional and reform-based instructional environments have on these competences [Kohl and Finkelstein, Phys. Rev. ST Phys. Educ. Res. 1, 010104 (2005); Kohl and Finkelstein, Phys. Rev. ST Phys. Educ. Res. 2, 010102 (2006)]. These studies focused on large-lecture introductory physics courses, and included aggregate data on student performance on quizzes and homeworks. In this paper, we complement previous papers with finer-grained in-depth problem-solving interviews. In 16 interviews of students drawn from these classes, we investigate in more detail how and when student problem-solving performance varies with problem representation (verbal, mathematical, graphical, or pictorial). We find that student strategy often varies with representation, and that in this environment students who show more strategy variation tend to perform more poorly. We also verify that student performance depends sensitively on the particular combination of representation, topic, and student prior knowledge. Finally, we confirm that students have generally robust opinions of their representational skills, and that these opinions correlate poorly with their actual performances.

In a recent study we showed that physics students’ problem-solving performance can depend strongly on problem representation, and that giving students a choice of problem representation can have a significant impact on their performance [P. B. Kohl and N. D. Finklestein, Phys. Rev. ST. Phys. Educ. Res. 1, 010104 (2005)] In this paper, we continue that study in an attempt to separate the effect of instructional technique from the effect of content area. We determine that students in a reform-style introductory physics course are learning a broader set of representational skills than those in a more traditional course. We also analyze the representations used in each course studied and find that the reformed course makes use of a richer set of representations than the traditional course and also makes more frequent use of multiple representations. We infer that this difference in instruction is the source of the broader student skills. These results provide insight into how macrolevel features of a course can influence student skills, complementary to the microlevel picture provided by the first study.

Student success in solving physics problems is related to the representational format of the problem. We study student representational competence in two large-lecture algebra-based introductory university physics courses with approximately 600 participants total. We examined student performance on homework problems given in four different representational formats (mathematical, pictorial, graphical, verbal), with problem statements as close to isomorphic as possible. In addition to the homeworks, we examine students’ assessment of representations by providing follow-up quizzes in which they chose between various problem formats. As a control, some parts of the classes were assigned a random-format follow-up quiz. We find that there are statistically significant performance differences between different representations of nearly isomorphic statements of quiz and homework problems. We also find that allowing students to choose which representational format they use improves student performance under some circumstances and degrades it in others. Notably, one of the two courses studied shows much greater performance differences between the groups that received a choice of format and those that did not, and we consider possible causes. Overall, we observe that student representational competence is tied to both micro- and macrolevel features of the task and environment.

This paper examines the effects of substituting a computer simulation for real laboratory equipment in the second semester of a large-scale introductory physics course. The direct current circuit laboratory was modified to compare the effects of using computer simulations with the effects of using real light bulbs, meters, and wires. Two groups of students, those who used real equipment and those who used a computer simulation that explicitly modeled electron flow, were compared in terms of their mastery of physics concepts and skills with real equipment. Students who used the simulated equipment outperformed their counterparts both on a conceptual survey of the domain and in the coordinated tasks of assembling a real circuit and describing how it worked.

We have calculated the single-particle eigenstates of a system designed to model a two-dimensional channel obstructed by a pair of anti-dots, under a transverse magnetic field. The model is relevant to recent experiments in which the conductance of the two-antidot system reveals a conductance minimum which is modulated by oscillations of a constant period in a magnetic field, contrary to the predictions of semiclassical calculations. We show that the modulations are due to the evolution with applied magnetic field of the eigenstates occupying the Fermi level, which alternate between cyclotron resonant states and states which are pinched off in the constricted region between the antidots and the channel edge. The phenomenon is an example of the interplay of the semiclassical cyclotron behavior and the quantum-mechanical nature of the constrictions.