John R. Thompson

Student Understanding Of The Physics And Mathematics Of Process Variables In P‐V Diagrams

Students in an upper‐level thermal physics course were asked to compare quantities related to the First Law of Thermodynamics along with similar mathematical questions devoid of all physical context. We report on a comparison of student responses to physics questions involving interpretation of ideal gas processes on P‐V diagrams and to analogous mathematical qualitative questions about the signs of and comparisons between the magnitudes of various integrals. Student performance on individual questions combined with performance on the paired questions shows evidence of isolated understanding of physics and mathematics. Some difficulties are addressed by instruction.

Assessing Student Understanding of Partial Derivatives in Thermodynamics

We are engaged in a research project to study teaching and learning in upper‐level thermal physics courses. We have begun to explore student functional understanding of mathematical concepts when applied in thermal physics contexts. We report here preliminary findings associated with partial differentiation and the Maxwell relations, which equate mixed second partial derivatives of various state functions. Our results suggest that students are often unable to apply the appropriate mathematical concepts and operations to the physical situations encountered in the course, despite having taken the prerequisite mathematics courses.

Student (Mis)application of Partial Differentiation to Material Properties

Students in upper‐level undergraduate thermodynamics courses were asked about the relationship between the complementary partial derivatives of the isothermal compressibility and the thermal expansivity of a substance. Both these material properties can be expressed with first partial derivatives of the system volume. Several of the responses implied difficulty with the notion of variables held fixed in a partial derivative. Specifically, when asked to find the partial derivative of one of these quantities with respect to a variable that was initially held fixed, a common response was that this (mixed second) partial derivative must be zero. We have previously reported other related difficulties in the context of the Maxwell relations, indicating persistent confusion applying partial differentiation to state functions. We present results from student homework and examination questions and briefly discuss an instructional strategy to address these issues.

What Is Entropy? Advanced Undergraduate Performance Comparing Ideal Gas Processes

We report data on upper‐level student understanding of entropy and the Second Law of Thermodynamics when comparing the isothermal and free expansions of an ideal gas. Data from pre‐ and post‐instruction written questions are presented, and several noteworthy features of student performance are identified and discussed. These features include ways students think about these topics prior to instruction as well as specific difficulties and other interesting aspects of student thought that persist after instruction. Implications for future research are also addressed.

Effectiveness of Ninth-Grade Physics in Maine: Conceptual Understanding

The Physics First movement—teaching a true physics course to ninth-grade students—is gaining popularity in high schools. There are several different rhetorical arguments for and against this movement, and it is quite controversial in physics education. However, there is no actual evidence to assess the success, or failure, of this substantial shift in the science teaching sequence. We have undertaken a comparison study of physics classes taught in ninth- and 12th-grade classes in Maine. Comparisons of student understanding and gains with respect to mechanics concepts were made with excerpts from well-known multiple-choice surveys and individual student interviews. Results indicate that both populations begin physics courses with similar content knowledge and specific difficulties, but when learning concepts, ninth-graders are more sensitive to the instructional method used.

Student Understanding of Tunneling in Quantum Mechanics: Examining Interview and Survey Results for Clues to Student Reasoning

Members of the University of Maine Physics Education Research Laboratory are studying student understanding of the phenomenon of quantum tunneling through a potential barrier, a standard topic in most introductory quantum physics courses. When a series of interviews revealed that many students believe energy is lost in the tunneling process, a survey was designed to investigate the prevalence of the energy‐loss idea. This survey was administered to populations of physics majors at the sophomore and senior levels. Data indicate that interview results are shared by a somewhat larger population of students and give insight into additional models of reasoning (e.g. analogies to macroscopic tunnels) not found in the interviews.

Addressing Student Difficulties with Concepts Related to Entropy, Heat Engines and the Carnot Cycle

We report the rationale behind and preliminary results from a guided‐inquiry conceptual worksheet (a.k.a. tutorial) dealing with Carnot’s efficiency and the Carnot cycle. The tutorial was administered in an upper‐level thermodynamics course at the University of Maine. The tutorial was implemented as the third in a three‐tutorial sequence designed to improve students’ understanding of entropy and its applications. Initial pre‐ and post‐tutorial assessment data suggest that student understanding of heat engines and the Carnot cycle improved as a result of tutorial instruction.

Representations of partial derivatives in thermodynamics

One of the mathematical objects that students become familiar with in thermodynamics, often for the first time, is the partial derivative of a multivariable function. The symbolic representation of a partial derivative and related quantities present difficulties for students in both mathematical and physical contexts, most notably what it means to keep one or more variables fixed while taking the derivative with respect to a different variable. Material properties are themselves written as partial derivatives of various state functions (e.g., compressibility is a partial derivative of volume with respect to pressure). Research in courses at the University of Maine and Oregon State University yields findings related to the many ways that partial derivatives can be represented and interpreted in thermodynamics. Research has informed curricular development that elicits many of the difficulties using different representations (e.g., geometric) and different contexts (e.g., connecting partial derivatives to specific experiments).

Resource Selection in Nearly‐Novel Situations

We developed an iterative survey to study the process of resource selection in a specific nearly‐novel situation — the design of vacuum tube diodes. Preliminary data from upper‐level undergraduate physics majors suggest that the ability to identify diode function in simple circuits predicts the ability to construct diodes.

Addressing Student Difficulties with Statistical Mechanics: The Boltzmann Factor

As part of research into student understanding of topics related to thermodynamics and statistical mechanics at the upper division, we have identified student difficulties in applying concepts related to the Boltzmann factor and the canonical partition function. With this in mind, we have developed a guided‐inquiry worksheet activity (tutorial) designed to help students develop a better understanding of where the Boltzmann factor comes from and why it is useful. The tutorial guides students through the derivation of both the Boltzmann factor and the canonical partition function. Preliminary results suggest that students who participated in the tutorial had a higher success rate on assessment items than students who had only received lecture instruction on the topic. We present results that motivate the need for this tutorial, the outline of the derivation used, and results from implementations of the tutorial.