Student learning in upper-division physics courses is a growing area of research in the field of Physics Education. Developing effective new curricular materials and pedagogical techniques to improve student learning in upper-division courses requires knowledge of both what material students struggle with and what curricular approaches help to overcome these struggles. To facilitate the course transformation process for one specific content area — upper-division electrostatics — this thesis presents two new methodological tools: (1) an analytical framework designed to investigate students' struggles with the advanced physics content and mathematically sophisticated tools/techniques required at the junior and senior level, and (2) a new multiple-response conceptual assessment designed to measure student learning and assess the effectiveness of different curricular approaches.
We first describe the development and theoretical grounding of a new analytical framework designed to characterize how students use mathematical tools and techniques during physics problem solving. We apply this framework to investigate student difficulties with three specific mathematical tools used in upper-division electrostatics: multivariable integration in the context of Coulomb's law, the Dirac delta function in the context of expressing volume charge densities, and separation of variables as a technique to solve Laplace's equation. We find a number of common themes in students' difficulties around these mathematical tools including: recognizing when a particular mathematical tool is appropriate for a given physics problem, mapping between the specific physical context and the formal mathematical structures, and reflecting spontaneously on the solution to a physics problem to gain physical insight or ensure consistency with expected results.
We then describe the development of a novel, multiple-response version of an existing conceptual assessment in upper-division electrostatics courses. The goal of this new version is to provide an easily-graded electrostatics assessment that can potentially be implemented to investigate student learning on a large scale. We show that student performance on the new multiple-response version exhibits a significant degree of consistency with performance on the free-response version, and that it continues to provide significant insight into student reasoning and student difficulties. Moreover, we demonstrate that the new assessment is both valid and reliable using data from upper-division physics students at multiple institutions. Overall, the work described in this thesis represents a significant contribution to the methodological tools available to researchers and instructors interested in improving student learning at the upper-division level.
Physics Teaching Assistants (TAs) serve a critical role in supporting student learning in various classroom environments, including discussions and laboratories. As research-based instructional strategies become more widespread in these settings, the TA's role is expanding beyond simply presenting physics content to encompass facilitating student discussion and attending to student reasoning. At the same time, we recognize that these TAs are physics professionals and future faculty, and their teaching experiences in graduate school have the potential for long-term impact on their professional identities. Consequently, there is a need to enhance traditional forms of preparation to support TAs in this expanded role in ways that complement broader professional development opportunities. Enhancing TA preparation requires understanding how TAs make sense of their roles as instructors so that we may identify potential avenues for intervention that support the development of practices that are (1) supportive of curricular goals and (2) consistent with the TAs' overall pedagogical model. The intent of this thesis is to develop a single overarching framework for analyzing how TAs talk about and carry out their roles as instructors. We then apply this framework to a set of interview and video data from multiple semesters, and make claims regarding instances of coordination and dis-coordination between TAs' beliefs and practices. Furthermore, we are able to track changes in beliefs and practices along various time scales. Finally, we return to the issue of TA preparation by identifying features of enhanced professional and pedagogical development, drawn from results of these studies, that could operate within existing institutional structures
An investigation into student and expert perspectives on the physical interpretation of quantum mechanics, with implications for modern physics instruction.
A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively realist perspectives of introductory students, and a lack of ontological flexibility in their conceptions of light and matter. We have developed a framework for understanding and characterizing student perspectives on the physical interpretation of quantum mechanics, and demonstrate the differential impact on student thinking of the myriad ways instructors approach interpretive themes in their introductory courses. Like expert physicists, students interpret quantum phenomena differently, and these interpretations are significantly influenced by their overall stances on questions central to the so-called measurement problem: Is the wave function physically real, or simply a mathematical tool? Is the collapse of the wave function an ad hoc rule, or a physical transition not described by any equation? Does an electron, being a form of matter, exist as a localized particle at all times? These questions, which are of personal and academic interest to our students, are largely only superficially addressed in our introductory courses, often for fear of opening a Pandora’s Box of student questions, none of which have easy answers. We show how a transformed modern physics curriculum (recently implemented at the University of Colorado) may positively impact student perspectives on indeterminacy and wave-particle duality, by making questions of classical and quantum reality a central theme of our course, but also by making the beliefs of our students, and not just those of scientists, an explicit topic of discussion.
The under representation and under performance of females in physics has been well documented and has long concerned policy-makers, educators, and the physics community. In this thesis, we focus on gender disparities in the first- and second-semester introductory, calculus-based physics courses at the University of Colorado. Success in these courses is critical for future study and careers in physics (and other sciences). Using data gathered from roughly 10,000 undergraduate students, we identify and model gender differences in the introductory physics courses in three areas: student performance, retention, and psychological factors. We observe gender differences on several measures in the introductory physics courses: females are less likely to take a high school physics course than males and have lower standardized mathematics test scores; males outscore females on both pre- and post-course conceptual physics surveys and in-class exams; and males have more expert-like attitudes and beliefs about physics than females. These background differences of males and females account for 60% to 70% of the gender gap that we observe on a post-course survey of conceptual physics understanding. In analyzing underlying psychological factors of learning, we find that female students report lower self-confidence related to succeeding in the introductory courses (self-efficacy) and are less likely to report seeing themselves as a “physics person”. Students’ self-efficacy beliefs are significant predictors of their performance, even when measures of physics and mathematics background are controlled, and account for an additional 10% of the gender gap. Informed by results from these studies, we implemented and tested a psychological, self-affirmation intervention aimed at enhancing female students’ performance in Physics 1. Self-affirmation reduced the gender gap in performance on both in-class exams and the post-course conceptual physics survey. Further, the benefit of the self-affirmation was strongest for females who endorsed the stereotype that men do better than women in physics. The findings of this thesis suggest that there are multiple factors that contribute to the under performance of females in physics. Establishing this model of gender differences is a first step towards increasing females’ participation and performance in physics, and can be used to guide future interventions to address the disparities.
This study reports the results of the first systematic investigation into Astro 101 students' conceptual and reasoning difficulties with cosmology. We developed four surveys with which we measured students' conceptual knowledge of the Big Bang, the expansion and evolution of the universe, and the evidence for dark matter. Our classical test theory and item response theory analyses of over 2300 students' pre- and post-instruction responses, combined with daily classroom observations, videotapes of students working in class, and one-on-one semi-structured think-aloud interviews with nineteen Astro 101 students, revealed several common learning difficulties. In order to help students overcome these difficulties, we used our results to inform the development of a new suite of cosmology lecture-tutorials. In our initial testing of the new lecture-tutorials at the University of Colorado at Boulder and the University of Arizona, we found many cases in which students who used the lecture-tutorials achieved higher learning gains (as measured by our surveys) at statistically significant levels than students who did not. Subsequent use of the lecture-tutorials at a variety of colleges and universities across the United States produced a wide range of learning gains, suggesting that instructors' pedagogical practices and implementations of the lecture-tutorials significantly affect whether or not students achieve high learning gains.
While research-based curricula and instructional strategies in introductory physics are becoming more widespread, how these strategies are implemented by educators is less well understood. Understanding classroom implementation of these strategies is further complicated by the fact that they are being used beyond the institutions at which they were developed. This thesis examines how educational innovations are taken up, take root, and transform educational practice. Data is analyzed from two case studies in educational change at the University of Colorado: the use of Peer Instruction (PI) and the use of the Tutorials in Introductory Physics. Our research studies on PI establish that 1) professors’ actual practices involving the use of PI differ strikingly, thus exposing students to different scientific practices, 2) variations in classroom practices create different classroom norms, and 3) students perceive PI classrooms differently in ways that are associated with corresponding PI implementation. Investigations into the use of the Tutorials in Introductory Physics (Tutorials) reveal that focusing purely on individual faculty members’ experiences does not fully capture the complexity of the change processes associated with Tutorials adoption. Although individual faculty members play important roles in the adoption and institutionalization process, other changes occur simultaneously throughout the educational system (i.e. shifts in internal and external funding, as well as expanding partnerships between the physics department, other STEM departments, the School of Education, and other university programs). By examining faculty within the situations that they work, we have found that structural changes in how institutions operate are coupled with changes in how individual faculty members’ teach their courses. These findings call into question the common assumption of dissemination approaches that focus solely on individual faculty members’ adoption and individual use of curricular materials and suggest that approaches to educational change might be more successful by coordinating and addressing multiple levels of the educational system simultaneously.
This work reviews the literature on analogy, introduces a new model of analogy, and presents a series of experiments that test and confirm the utility of this model to describe and predict student learning in physics with analogy. Pilot studies demonstrate that representations (e.g., diagrams) can play a key role in students’ use of analogy. A new model of analogy, Analogical Scaffolding, is developed to explain these initial empirical results. This model will be described in detail, and then applied to describe and predict the outcomes of further experiments. Two large-scale (N>100) studies will demonstrate that: (1) students taught with analogies, according to the Analogical Scaffolding model, outperform students taught without analogies on pre- post assessments focused on electromagnetic waves; (2) the representational forms used to teach with analogy can play a significant role in student learning, with students in one treatment group outperforming students in other treatment groups by factors of two or three. It will be demonstrated that Analogical Scaffolding can be used to predict these results, as well as finer-grained results such as the types of distracters students choose in different treatment groups, and to describe and analyze student reasoning in interviews. Abstraction in physics is reconsidered using Analogical Scaffolding. An operational definition of abstraction is developed within the Analogical Scaffolding framework and employed to explain (a) why physicists consider some ideas more abstract than others in physics, and (b) how students conceptions of these ideas can be modeled. This new approach to abstraction suggests novel approaches to curriculum design in physics using Analogical Scaffolding.
The purpose of my research was to produce a problem solving evaluation tool for physics. To do this it was necessary to gain a thorough understanding of how students solve problems. Although physics educators highly value problem solving and have put extensive effort into understanding successful problem solving, there is currently no efficient way to evaluate problem solving skill. Attempts have been made in the past; however, knowledge of the principles required to solve the subject problem are so absolutely critical that they completely overshadow any other skills students may use when solving a problem. The work presented here is unique because the evaluation tool removes the requirement that the student already have a grasp of physics concepts. It is also unique because I picked a wide range of people and picked a wide range of tasks for evaluation. This is an important design feature that helps make things emerge more clearly.
This dissertation includes an extensive literature review of problem solving in physics, math, education and cognitive science as well as descriptions of studies involving student use of interactive computer simulations, the design and validation of a beliefs about physics survey and finally the design of the problem solving evaluation tool. I have successfully developed and validated a problem solving evaluation tool that identifies 44 separate skills (skills) necessary for solving problems. Rigorous validation studies, including work with an independent interviewer, show these skills identified by this content-free evaluation tool are the same skills that students use to solve problems in mechanics and quantum mechanics. Understanding this set of component skills will help teachers and researchers address problem solving within the classroom.
Skill with different representations and multiple representations is highly valued in physics, and prior work has shown that novice physics students can struggle with the representations typically used in solving physics problems. There exists work in PER examining student use of representations and multiple representations, but there have been no comprehensive attempts to understand what factors influence how introductory students succeed or fail in using representations in physics. This thesis is such an attempt, and is organized around four main goals and results. First, we establish that representation is a major factor in student performance, and uncover some of the mechanisms by which representation can affect performance, including representation-dependent cueing. Second, we study the effect of different instructional environments on student learning of multiple representation use during problem solving, and find that courses that are rich in representations can have significant impacts on student skills. Third, we evaluate the role of meta-representational skills in solving physics problems at the introductory level, and find that the meta-representational abilities that we test for in our studies are poorly developed in introductory students. Fourth, we characterize the differences in representation use between expert and novice physics problem solvers, and note that the major differences appear not to lie in whether representations are used, but in how they are used.
With these results in hand, we introduce a model of student use of representations during physics problem solving. This model consists of a set of practical heuristics plus an analysis framework adapted from cultural-constructivist theory. We demonstrate that this model can be useful in understanding and synthesizing our results, and we discuss the instructional implications of our findings.
The importance of informal science education to the field of Physics Education Research includes extending to a broader range of ages and environments than formal science and focusing on broader goals such as participants' identities as scientists. This paper describes 3 aspects of informal science education: programming, research, and curriculum development. A summer camp was run through JILA's PISEC (Partnerships of Informal Science in the Community) program. Participants' use of representations, in particular drawings, in response to different types of prompting was analyzed in both lab notebooks and stop-motion videos made by the participants. In light of the results of this study, a new curriculum was developed for use in the fall 2012 semester of the PISEC program.
The use of simulations in learning physics is a topic of growing interest in physics education research circles. While prior research has been conducted to understand the factors that promote engaging and interacting with sims in an interview setting, little work has been done to understand how assignments affect students' interactions with the sims in various environments. This paper explores this issue through analyzing two different case studies in radically different settings. One is a study done in a middle school classroom using the build-a-molecule PhET simulation, and the other investigates the use of a PhET quantum tunneling sim used in a college-level modern physics course. These assignments were created with a tentative list of "heuristics" we felt would be useful in writing these assignments, and through these studies we present a list of refined and expanded heuristics that are more representative of our findings. In addition to these heuristics, we present a framework which is more inclusive than the set of heuristics alone in accounting for the design of these assignments across different contexts.
Contextual framing in physics problems has been shown to generally affect student performance on assessments. This study seeks to identify some of the main influences of this effect, and to characterize how contextual framing may vary within a classroom. Students in summer introductory physics courses (algebra based and calculus based) are administered surveys that assess performance on problems that are contextually rich (more “real world”) vs. contextually bland (more abstract, “laboratory” descriptions). Initially females perform worse than do males on the contextually rich versions of the assessments when performance was equal on the contextually bland versions of the test. However further assessment reveals no clear trend how explicit contextual framing influences male and females differently. Students were polled on Attitudes and beliefs regarding the use of different kinds of context in the classroom, and the researcher’s observations of instructor practice correlated well with students’ opinions. Other roles of problem contextualization are identified, including the triggering of intuition and reasoning, albeit sometimes incorrect.
An accurate, nuanced capturing and characterization of student/teacher behavior inside and outside the classroom is a necessity in today’s education reform. In this paper, a new framework, called the BIAR (Beliefs, Intentions, Actions, and Reflections) Student-Teacher Interaction Model, is introduced. This tool incorporates the use of TDOP (Teaching Dimensions Observation Protocol) in classroom observations alongside student/faculty interviews, stimulated recall sessions, and electronic surveys. Once gathered, the data can be compared and rated for their degree of correlation. While the work in this project wasn’t aimed at making any specific claims about the practices of teachers or students, the introduction of the BIAR Model provides a structure for future work in this area.
The use of simulations in educational environments is a topic of growing interest, particularly in science education. While much research has been done to understand simulation use in interview settings, less has been done in the environments in which the majority of simulation use arises. The purpose of this thesis is to provide a framework for how simulations can be used in these natural environments, and analyze what can be done to promote effective use of simulations in these settings. We propose a list of heuristics or strategies that can be used when writing assignments to incorporate simulations, and additionally, provide a tentative theoretical view of how to implement these heuristics and why they work. This is done through a series of case studies that make use of the heuristics, as we first give an analysis of the heuristics that were used, and then provide a tentative theoretical view of how the heuristics were implemented, and why they work.
Educators devote most of their attention to students learning the subject matter of a course. What is less recognized by educators, is that beyond learning the content, students’ attitudes, beliefs, and values change too—sometimes in unexpected and unintended ways. When something is not explicitly taught, but students learn it anyway, it is part of the “hidden curriculum.” Because the explicit curriculum tends to focus on content, it’s the hidden curriculum that influences students’ beliefs about the nature of science, and the nature of learning science. This thesis presents a study of the hidden curricula in three different introductory physics courses. All three are second semester Electricity and Magnetism courses at the University of Colorado at Boulder. This research focuses on four dimensions of the hidden curriculum: Process vs. Product, Source of Knowledge, Real World vs. Abstract, and Gender Bias vs. Gender Neutral. In order to measure these four dimensions of the hidden curricula of three courses, rubrics have been developed, and course environments have been observed and measured using these rubrics. Additionally, the impact that varying hidden curricula have on students is addressed by surveying student beliefs. Results indicate that course practices implicitly affect student attitudes and beliefs in a way that might be predictable by measuring the hidden curriculum—especially for students with less strongly held beliefs. Furthermore, the hidden curriculum sends mixed messages to students, and certain course elements have greater influence on students’ beliefs than others (like lecture versus homework).
There are many different ways by which students learn physics and develop beliefs about physics. These range from exams to lectures, from labs to homework. Teachers have beliefs about the ideal content for each of these media to contain, as well as beliefs about what they typically do contain. The purpose of my thesis, therefore, is to examine in detail, a small but vital way that this information is conveyed from teacher to student: Homework. First, I design a survey to be administered to teachers of introductory university classes. This survey is designed to acquire data about teachers’expectations and beliefs about their homework content. Next, I administer the survey and simultaneously conduct an interview with each professor in my study. Then, I acquire homework sets from the teachers’ classes. I rate these homework sets along the same dimensions the teachers were asked to rate them. Finally, I compare the ratings and analyze them for agreement.