877 research outputs found
Representing uncertainty on model analysis plots
Model analysis provides a mechanism for representing student learning as
measured by standard multiple-choice surveys. The model plot contains
information regarding both how likely students in a particular class are to
choose the correct answer and how likely they are to choose an answer
consistent with a well-documented conceptual model. Unfortunately Bao's
original presentation of the model plot did not include a way to represent
uncertainty in these measurements. I present details of a method to add error
bars to model plots by expanding the work of Sommer and Lindell. I also provide
a template for generating model plots with error bars.Comment: Accepted for publication in Phys. Rev. Phys. Edu. Res. Published
version will include supplementary file
Identifying and Addressing Specific Student Difficulties in Advanced Thermal Physics
As part of an ongoing multi-university research study on student understanding of concepts in thermal physics at the upper division, I identified several student difficulties with topics related to heat engines (especially the Carnot cycle), as well as difficulties related to the Boltzmann factor. In an effort to address these difficulties, I developed two guided-inquiry worksheet activities (a.k.a. tutorials) for use in advanced undergraduate thermal physics courses. Both tutorials seek to improve student understanding of the utility and physical background of a particular mathematical expression. One tutorial focuses on a derivation of Carnot\u27s theorem regarding the limit on thermodynamic efficiency, starting from the Second Law of Thermodynamics. The other tutorial helps students gain an appreciation for the origin of the Boltzmann factor and when it is applicable; focusing on the physical justification of its mathematical derivation, with emphasis on the connections between probability, multiplicity, entropy, and energy. Student understanding of the use and physical implications of Carnot\u27s theorem and the Boltzmann factor was assessed using written surveys both before and after tutorial instruction within the advanced thermal physics courses at the University of Maine and at other institutions. Classroom tutorial sessions at the University of Maine were videotaped to allow in-depth scrutiny of student successes and failures following tutorial prompts. I also interviewed students on various topics related to the Boltzmann factor to gain a more complete picture of their understanding and inform tutorial revisions. Results from several implementations of my tutorials at the University of Maine indicate that students did not have a robust understanding of these physical principles after lectures alone, and that they gain a better understanding of relevant topics after tutorial instruction; Fisher\u27s exact tests yield statistically significant improvement at the = 0:05 level. Results from other schools indicate that difficulties observed before tutorial instruction in our classes (for both tutorials) are not unique, and that the Boltzmann factor tutorial can be an effective replacement for lecture instruction. Additional research is suggested that would further examine these difficulties and inform instructional strategies to help students overcome them
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
A framework for the natures of negativity in introductory physics
Mathematical reasoning skills are a desired outcome of many introductory
physics courses, particularly calculus-based physics courses. Positive and
negative quantities are ubiquitous in physics, and the sign carries important
and varied meanings. Novices can struggle to understand the many roles signed
numbers play in physics contexts, and recent evidence shows that unresolved
struggle can carry over to subsequent physics courses. The mathematics
education research literature documents the cognitive challenge of
conceptualizing negative numbers as mathematical objects--both for experts,
historically, and for novices as they learn. We contribute to the small but
growing body of research in physics contexts that examines student reasoning
about signed quantities and reasoning about the use and interpretation of signs
in mathematical models. In this paper we present a framework for categorizing
various meanings and interpretations of the negative sign in physics contexts,
inspired by established work in algebra contexts from the mathematics education
research community. Such a framework can support innovation that can catalyze
deeper mathematical conceptualizations of signed quantities in the introductory
courses and beyond
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
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 expressions, 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 in creating and using a Taylor series appropriately, despite previous exposures in both calculus and physics courses
Identifying Student Difficulties with Heat Engines, Entropy, 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 undergraduate 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
Quantitatively ranking incorrect responses to multiple-choice questions using item response theory
Research-based assessment instruments (RBAIs) are ubiquitous throughout both
physics instruction and physics education research. The vast majority of
analyses involving student responses to RBAI questions have focused on whether
or not a student selects correct answers and using correctness to measure
growth. This approach often undervalues the rich information that may be
obtained by examining students' particular choices of incorrect answers. In the
present study, we aim to reveal some of this valuable information by
quantitatively determining the relative correctness of various incorrect
responses. To accomplish this, we propose an assumption that allow us to define
relative correctness: students who have a high understanding of Newtonian
physics are likely to answer more questions correctly and also more likely to
choose better incorrect responses, than students who have a low understanding.
Analyses using item response theory align with this assumption, and Bock's
nominal response model allows us to uniquely rank each incorrect response. We
present results from over 7,000 students' responses to the Force and Motion
Conceptual Evaluation
Comparing three methods for teaching Newton’s third law
Although guided-inquiry methods for teaching introductory physics have been individually shown to be more effective at improving conceptual understanding than traditional lecture-style instruction, researchers in physics education have not studied differences among reform-based curricula in much detail. Several researchers have developed University of Washington–style tutorial materials, but the different curricula have not been compared against each other. Our study examines three tutorials designed to improve student understanding of Newton’s third law: the University of Washington’s Tutorials in Introductory Physics (TIP), the University of Maryland’s Activity-Based Tutorials (ABT), and the Open Source Tutorials (OST) also developed at the University of Maryland. Each tutorial was designed with different goals and agendas, and each employs different methods to help students understand the physics. We analyzed pretest and post-test data, including course examinations and data from the Force and Motion Conceptual Evaluation (FMCE). Using both FMCE and course data, we find that students using the OST version of the tutorial perform better than students using either of the other two
- …