Frequently, quantum mechanics is taught toward the end of the first year of physics -if it is taught at all. The reason for delaying the study is that quantum mechanics is a very abstract idea without much practical purpose. Therefore, students cannot understand it until they have learned all the rest of physics. We are challenging that way of thinking by creating instructional materials for quantum mechanics that can be integrated throughout the first physics course rather than just tacked on at the end. In addition, we have transferred some of the materials and the basic learning approach to higher-level courses. The result is a hands-on approach to learning and teaching quantum mechanics for a broad spectrum of students. We describe here some of our materials, as well as results of using these materials with students.

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, different from the medium through which it propagates. All other observed alternative models contain elements of both Entity and Wave models, but at the same time are distinct from each of the constituent models. We called these models “hybrid” or “blend” models. We discuss how students use these models in various contexts before and after instruction and how our findings contribute to the understanding of conceptual change. Implications of our findings for teaching are summarized

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 investigated students' mental models of sound propagation in introductory physics classes. In addition to the scientifically accepted wave model, students used the "entity" model. In this model sound is a self-standing entity, different from the medium, and propagating through it. All other observed alternative models are composed of entity and wave ingredients, but at the same time they are distinct from each of the constituent models. We called these models "hybrid" models. We will discuss how students use these models in various contexts before and after instruction.

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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 that although most of the students could recognize the need for an integral in solving the problem, they failed to set up the desired integral. We provide evidence that this failure can be attributed to students' inability to understand the infinitesimal term in the integral and/or failure to understand the notion of accumulation of an infinitesimal physical quantity. This work supports and extends previous research on students' difficulties with integration in physics.

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 the area under the curve concept. We found that only a few students could recognize that the concept of area under the curve was applicable in physics problems. Even when students could invoke the area under the curve concept, they did not necessarily understand the relationship between the process of accumulation and the area under a curve, so they failed to apply it to novel situations. We also found that when presented with several graphs, students had difficulty in selecting the graph such that the area under the graph corresponded to a given integral, although all of them could state that ''the integral equaled the area under the curve.'' The findings in this study are consistent with those in previous mathematics education research and research in physics education on students' use of the area under the curve.

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.