Matthew J. Moelter

A Direct Comparison of Conceptual Learning and Problem Solving Ability in Traditional and Studio Style Classrooms

We present data on student performance on conceptual understanding and on quantitative problem-solving ability in introductory mechanics in both studio and traditional classroom modes. The conceptual measures used were the Force Concept Inventory and the Force and Motion Conceptual Evaluation. Quantitative problem-solving ability was measured with standard questions on the final exam. Our data compare three different quarters over the course of 2 years. In all three quarters, the normalized learning gain in conceptual understanding was significantly larger for students in the studio sections. At the same time, students in the studio sections performed the same or slightly worse on quantitative final exam problems.

The implications of a robust curriculum in introductory mechanics

We have developed a curriculum for introductory mechanics that emphasizes interactive engagement and conceptual understanding using the studio format. As previously reported, we have shown in three different quarters that the curriculum much improved the students’ conceptual understanding compared to the traditional course without significantly affecting the scores on a traditional final exam. Here we report the results for the entire three-year period during which the course was taught, 34 sections of the course were taught with 11 different instructors to over 1200 students. In each term, these sections had common exams, syllabus, and schedule. Student experiences were very similar in terms of activities. Student performance was measured using the force and motion conceptual evaluation or the force concept inventory; the average pre/post normalized gain was 0.59. There was no significant correlation with any instructor characteristics, including teaching experience, knowledge of interactive-engagement m...

Electric potential in the classical Hall effect: An unusual boundary-value problem

The classical Hall effect presents a surprisingly unusual and challenging problem in electrostatics, with boundary conditions that are not of Dirichlet, Neumann, or of mixed Dirichlet and Neumann type. These unusual boundary conditions create several difficulties not normally encountered in standard problems, and ultimately lead to expansion of the electric potential in a nonorthogonal basis set. We derive the boundary conditions for the potential in a rectangular geometry, construct a solution for the potential, and discuss the relation between this problem and problems of the standard mixed type. We also address a commonly encountered misconception about the current distribution.

A laboratory-based nonlinear dynamics course for science and engineering students

We describe the implementation of a new laboratory-based interdisciplinary undergraduate course on nonlinear dynamical systems. Geometrical methods and data visualization techniques are especially emphasized. A novel feature of the course is a required laboratory where the students analyze the behavior of a number of dynamical systems. Most of the laboratory experiments can be economically implemented using equipment available in many introductory physics microcomputer-based laboratories.

Computational problems in introductory physics: Lessons from a bead on a wire

We have found that incorporating computer programming into introductory physics requires problems suited for numerical treatment while still maintaining ties with the analytical themes in a typical introductory-level university physics course. In this paper, we discuss a numerical adaptation of a system commonly encountered in the introductory physics curriculum: the dynamics of an object constrained to move along a curved path. A numerical analysis of this problem that includes a computer animation can provide many insights and pedagogical avenues not possible with the usual analytical treatment. We present two approaches for computing the instantaneous kinematic variables of an object constrained to move along a path described by a mathematical function. The first is a pedagogical approach, appropriate for introductory students in the calculus-based sequence. The second is a more generalized approach, suitable for simulations of more complex scenarios.

Formulas in Physics Have a “Standard” Form

We discuss the importance of the ordering of symbols in physics formulas and identify implicit conventions that govern the “standard” form for how formulas are written and interpreted. An important part of writing and reading this form is understanding distinctions among constants, parameters, and variables. We delineate these conventions and encourage instructors to make them explicit for students.

Calculating and visualizing the density of states for simple quantum mechanical systems

We present a graphical approach to understanding the degeneracy, density of states, and cumulative state number for some simple quantum systems. By taking advantage of basic computing operations, we define a straightforward procedure for determining the relationship between discrete quantum energy levels and the corresponding density of states and cumulative level number. The density of states for a particle in a rigid box of various shapes and dimensions is examined and graphed. It is seen that the dimension of the box, rather than its shape, is the most important feature. In addition, we look at the density of states for a multi-particle system of identical bosons built on the single-particle spectra of those boxes. A simple model is used to explain how the N-particle density of states arises from the single particle system it is based on.

Exposing Students to the Idea that Theories Can Change

The scientific method is arguably the most reliable way to understand the physical world, yet this aspect of science is rarely addressed in introductory science courses. Students typically learn about the theory in its final, refined form, and seldom experience the experiment‐to‐theory cycle that goes into producing the theory. One exception to this is the Powerful Ideas in Physical Science curriculum (PIPS) developed by the American Association of Physics Teachers.1 In this curriculum students develop theories based on experiments. The “Heat and Conservation of Energy” unit illustrates the experiment‐to‐theory cycle in a set of experiments introducing the conservation of energy. The idea of conservation of energy is developed early in the unit; however, students must expand their idea of energy in order to incorporate new phenomenon, namely the specific heat and phase transitions. Yet even with these experiments, the ideas of energy and of a theory remain abstract. In order to address the abstractness of...