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…

In prior research, the classification of concepts into three types--descriptive, hypothetical and theoretical--has allowed for the association of students' use of different concept types with their level of understanding. Previous studies have also examined the ways in which students link concepts to determine whether students have a meaningful…

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…

In this paper, we report on a project concerned with the role of cognition during problem solving. We specifically explore the categories of mental representations that students work with during problem solving of different representational task formats. The sample, consisting of 19 engineering students taking a calculus-based physics course,…

This study focuses on students' use of the mathematical concept of differentials in physics problem solving. For instance, in electrostatics, students need to set up an integral to find the electric field due to a charged bar, an activity that involves the application of mathematical differentials (e.g., "dr," "dq"). In this…

We investigate the effects of visual cueing on students' eye movements and reasoning on introductory physics problems with diagrams. Participants in our study were randomly assigned to either the cued or noncued conditions, which differed by whether the participants saw conceptual physics problems overlaid with dynamic visual cues. Students in the…

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…

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…

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…

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…

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…

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…

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…

We investigated introductory physics students' mental models of sound propagation. We used a phenomenographic method to analyze the data in the study. In addition to the scientifically accepted Wave model, students used the "Entity" model to describe the propagation of sound. In this latter model sound is a self-standing entity,…