A detailed derivation of analytic solutions is presented for overlap, kinetic, nuclear attraction and electron repulsion integrals involving Cartesian Gaussian-type orbitals. It is demonstrated how s-type orbitals can be used to evaluate integrals with higher angular momentum via the properties of Hermite polynomials and differentiation with…

The Lorentz transformation applies directly to the kinematics of moving particles viewed as geometric points. Wave propagation, on the other hand, involves moving planes which are extended objects defined by simultaneity. By treating a plane wave as a geometric object moving at the phase velocity, novel results are obtained that illustrate the…

Research on the learning and teaching of science is an important field for scholarly inquiry by faculty in science departments. Such research has proved to be an efficient means for improving the effectiveness of instruction in physics. A basic topic in introductory physics is used to illustrate how discipline-based education research has helped…

Video recordings of Year 11 physics lessons were analyzed to identify key features of teacher explanations. Important features of the explanations used included teachers' ability to move between qualitative and quantitative modes of discussion, attention to what students require to succeed in high stakes examinations, thoughtful use of…

This paper describes a method aimed at pointing out the quality of the mental models undergraduate engineering students deploy when asked to create explanations for phenomena or processes and/or use a given model in the same context. Student responses to a specially designed written questionnaire are quantitatively analyzed using…

We have developed simple data-mining algorithms to assess the consistency and the randomness of student responses to problems consisting of multiple true or false statements. In this paper we describe the algorithms and use them to analyze data from introductory physics courses. We investigate statements that emerge as outliers because the class…

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…

Previous research suggests that students; prior knowledge can interfere with how they observe and remember lecture demonstrations. We measured students' prior knowledge in introductory mechanics and electricity and magnetism at two large universities. Students were then asked to predict the outcome of lecture demonstrations. We compare…

With the increased availability of modern technology and handheld probeware for classrooms, the iPad and the Video Physics application developed by Vernier are used to capture and analyze the motion of an ice hockey puck within secondary-level physics education. Students collect, analyze, and generate digital modes of representation of physics…

As educators we are facing an unprecedented challenge to prepare our students not only for traditional careers but also for future careers that don't exist today. Many of these careers will require a firm grounding in disciplines such as physics, along with multidisciplinary, Global, and systems thinking skill sets. Our Multidisciplinary…

Each year our physical science class for pre-service elementary teachers launches water-powered rockets based on the activity from NASA. We analyze the rocket flight using data from frame-by-frame video analysis of the launches. Before developing the methods presented in this paper, we noticed our students were mired in calculation details while…

Using a quasi-experimental design, we integrated systematic learning from problematic and successful experiences into teachers' preparatory programs and examined how such learning affected preservice physics teachers' capacity to teach students self-regulated learning (SRL). Results indicated that preservice teachers who contemplated both…

In teaching physics, the history of physics offers fruitful starting points for designing instruction. I introduce here an approach that uses historical cognitive processes to enhance the conceptual development of pre-service physics teachers' knowledge. It applies a method called cognitive-historical approach, introduced to the cognitive sciences…

When students reason during school science, they often refer to conceptions that are derived from out-of-school experiences and are poor proxies for science orthodoxy. However, for some areas of science, these conceptions represent only a proportion of students' full conceptual knowledge, for tacit understanding exists that is superior to the…

In college level chemistry courses, reasoning using molecular and particulate descriptions of matter becomes central to understanding physical and chemical properties. In this study, we used a qualitative approach to analyzing classroom discourse derived from Toulmin's model of argumentation in order to describe the ways in which students develop…