Trevor I. Smith

Applying a Resources Framework to Analysis of the Force and Motion Conceptual Evaluation.

We suggest one redefinition of common clusters of questions used to analyze student responses on the Force and Motion Conceptual Evaluation (FMCE). Our goal is to move beyond the expert/novice analysis of student learning based on pre-/post-testing and the correctness of responses (either on the overall test or on clusters of questions defined solely by content). We use a resources framework, taking special note of the contextual and representational dependence of questions with seemingly similar physics content. We analyze clusters in ways that allow the most common incorrect answers to give as much, or more, information as the correctness of responses in that cluster. Furthermore, we show that false positives can be found, especially on questions dealing with Newtons Third Law.

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.

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.

Student Understanding of Taylor Series Expansions in Statistical Mechanics.

One goal of physics instruction is to have students learn to make physical meaning of specific mathematical ideas, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann factor, using a Taylor series expansion of entropy. Using results from written surveys, classroom observations, and both individual think-aloud and teaching interviews, we present evidence that many students can recognize and interpret series expansions, but they often lack fluency with the Taylor series despite previous exposures in both calculus and physics courses. We present students successes and failures both using and interpreting Taylor series expansions in a variety of contexts.

Identifying Student Difficulties with Entropy, Heat Engines, and the Carnot Cycle

We report on several specific student difficulties regarding the Second Law of Thermodynamics in the context of heat engines within upper-division undergraduates thermal physics courses. Data come from ungraded written surveys, graded homework assignments, and videotaped classroom observations of tutorial activities. Written data show that students in these courses do not clearly articulate the connection between the Carnot cycle and the Second Law after lecture instruction. This result is consistent both within and across student populations. Observation data provide evidence for myriad difficulties related to entropy and heat engines, including students struggles in reasoning about situations that are physically impossible and failures to differentiate between differential and net changes of state properties of a system. Results herein may be seen as the application of previously documented difficulties in the context of heat engines, but others are novel and emphasize the subtle and complex nature of cyclic processes and heat engines, which are central to the teaching and learning of thermodynamics and its applications. Moreover, the sophistication of these difficulties is indicative of the more advanced thinking required of students at the upper division, whose developing knowledge and understanding give rise to questions and struggles that are inaccessible to novices.

Identifying student difficulties with conflicting ideas in statistical mechanics

In statistical mechanics there are two quantities that directly relate to the probability that a system at a temperature fixed by a thermal reservoir has a particular energy. The density of states function is related to the multiplicity of the system and indicates that occupation probability increases with energy. The Boltzmann factor is related to the multiplicity of the reservoir and indicates that occupation probability decreases with energy. This seems contradictory until one remembers that a complete probability distribution is determined by the total multiplicity of the system and its surroundings, requiring the product of these two functions. We present evidence from individual and group interviews that students knew how each of these functions relates to multiplicity but did not recognize the need to combine the two to characterize the physical scenario.

Comparing Three Methods for Teaching Newton’s Second Law

As a follow‐up to a study comparing learning of Newton’s Third Law when using three different forms of tutorial instruction, we have compared student learning of Newton’s Second Law (NSL) when students use the Tutorials in Introductory Physics, Activity‐Based Tutorials, or Open Source Tutorials. We split an algebra‐based, life sciences physics course in 3 groups and measured students’ pre‐ and post‐instruction scores on the Force and Motion Conceptual Evaluation (FMCE). We look at only the NSL‐related clusters of questions on the FMCE to compare students’ performance and normalized gains. Students entering the course are not significantly different, and students using the Tutorials in Introductory Physics show the largest normalized gains in answering question on the FMCE correctly. These gains are significant in only one cluster of questions, the Force Sled cluster.

Student Understanding of the Boltzmann Factor

We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable, nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations on student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.