This article describes how the author successfully adapted techniques drawn from the literature on active learning for use in a graduate-level course on quantum field theory. Students completed readings and online questions ahead of each class and spent class time working through problems that required them to practice the decisions and skills typical of a theoretical physicist. The instructor monitored these activities and regularly provided timely feedback to guide their thinking. Instructor-student interactions and student enthusiasm were similar to that encountered in one-on-one discussions with advanced graduate students. Course coverage was not compromised. The teaching techniques described here are well suited to other advanced courses.
An important goal of graduate physics core courses is to help students develop expertise in problem solving and improve their reasoning and meta-cognitive skills. We explore the conceptual difficulties of physics graduate students by administering conceptual problems on topics covered in undergraduate physics courses before and after instruction in related first year core graduate courses. Here, we focus on physics graduate students' difficulties manifested by their performance on two qualitative problems involving diagrammatic representation of vector fields. Some graduate students had great …
Project-based assessment, in the form of take-home exams, was trialed in an honours/masters level electromagnetic theory course. This assessment formed an integral part of the learning experience of the students, and students felt that this was effective method of learning.
We describe a course designed to help future educators build an integrated understanding of the different elements of physics education research (PER), including: research into student learning, content knowledge from the perspective of how it is learned, and reform-based curricula together with evidence of their effectiveness. Course elements include equal parts of studying physics through proven curricula and discussion of research results in the context of the PER literature. We provide examples of the course content and structure as well as representative examples of student learning in th…
Laboratory courses for upper-division undergraduates often involve sophisticated equipment, relatively small class sizes, and extended hands-on projects. These courses present distinct challenges and opportunities for the physics education research community as these features are not often present in other undergraduate courses. Here, we focus on an upper-division lab-based electronics course. As a first step in establishing learning goals for upper-division electronics, we interviewed graduate students and faculty at the University of Colorado Boulder about the use of electronics in their own…
In experimental physics, lab notebooks play an essential role in the research process. For all of the ubiquity of lab notebooks, little formal attention has been paid to addressing what is considered `best practice' for scientific documentation and how researchers come to learn these practices in experimental physics. Using interviews with practicing researchers, namely physics graduate students, we explore the different experiences researchers had in learning how to effectively use a notebook for scientific documentation. We find that very few of those interviewed thought that their undergrad…
We address four main areas in which graduate quantum mechanics education can be improved: course content, textbook, teaching methods, and assessment tools. We report on a three year longitudinal study at the Colorado School of Mines using innovations in all these areas. In particular, we have modified the content of the course to reflect progress in the field in the last 50 years, used textbooks that include such content, incorporated a variety of teaching techniques based on physics education research, and used a variety of assessment tools to study the effectiveness of these reforms. We pres…
This essay discusses the effectiveness of a graduate course for physics students, with a course goal to write a publishable article on a modern research topic (graphene). I analyze the tools used to this end, which included Web 2.0 methods, in-class discussions and presentation, as well as extensive peer-review. In addition to producing a published article, this course led students to not only advance their mastery of a modern research topic but also to significantly improve their writing, discussion and presentation skills.
Physics education research has consistently shown that students have higher learning outcomes when enrolled in interactive-engagement courses. Consequently, many schools are actively reforming their introductory curricula. For courses where the interactive sections (labs, tutorials, and/or workshops) are mostly taught by graduate student teaching assistants (TAs), good TAs are instrumental to the success of the reform. Many studies have investigated specific interactions between TAs and students, but more can be learned through a holistic examination of TA-student interactions. Over the course…
We developed and validated a conceptual survey that focuses on the formalism and postulates of quantum mechanics covered in upper-level undergraduate quantum mechanics courses. The concepts included in the Quantum Mechanics Formalism and Postulate Survey (QMFPS) focus on Dirac notation, the Hilbert space, state vectors, physical observables and their corresponding Hermitian operators, compatible and incompatible observables, quantum measurement, time-dependence of quantum states and expectation values, and spin angular momenta. Here we describe the validation and administration of the survey, …
Students' attitudes and approaches to problem solving in physics can profoundly influence their motivation to learn and development of expertise. We developed and validated an Attitudes and Approaches to Problem Solving survey by expanding the Attitudes towards Problem Solving survey of Marx and Cummings and administered it to physics graduate students. Comparison of their responses to the survey questions about problem solving in their own graduate level courses vs. problem solving in the introductory physics courses provides insight into their expertise in introductory and graduate level phy…
The Federal University of Santa Maria (UFSM - Universidade Federal de Santa Maria) has trained more than 600 undergraduate and 200 Ph.D. students, becoming a reference in physics training at the Rio Grande do Sul central region. In this work we present a gender analysis of the UFSM graduated students from both levels. The number of graduated students of the female gender has been rising with time and is significatively bigger than the number observed nationally in both levels. The mean values are 35%, 37%, 28%, 42% e 39% for the courses physics teaching (daytime), physics teaching (nightime), …
A survey was developed to probe student understanding of quantum mechanics at the beginning of graduate instruction. The survey was administered to 202 physics graduate students enrolled in first-year quantum mechanics courses from seven universities at the beginning of the first semester. We also conducted one-on-one interviews with fifteen graduate or advanced undergraduate students who had just completed a course in which all the content on the survey was covered. Although students from some universities performed better on average than others, we found that students share universal difficu…
Physics graduate teaching assistants (TAs) are often responsible for grading. Physics education research suggests that grading practices that place the burden of proof for explicating the problem solving process on students can help them develop problem solving skills and learn physics. However, TAs may not have developed effective grading practices and may grade student solutions in introductory and advanced courses differently. In the context of a TA professional development course, we asked TAs to grade student solutions to introductory physics and quantum mechanics problems and explain why…
Graduate Teaching Assistants (GTAs) are key partners in the education of undergraduates. Given the potentially large impact GTAs can have on undergraduate student learning, it is important to provide them with appropriate preparation for teaching. But GTAs are students themselves, and not all of them desire to pursue an academic career. Fully integrating GTA preparation into the professional development of graduate students lowers the barrier to engagement so that all graduate students may benefit from the opportunity to explore teaching and its applications to many potential career paths. In …
We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and administered it to more than 200 students at 10 institutions. The issues targeted in the survey include the set of possible wavefunctions, bound and scattering states, quantum measurement, expectation values, the role of the Hamiltonian, and the time-dependence of the wavefunction and expectation values. We find that undergraduate and graduate students have…
We developed a survey to probe student understanding of quantum mechanics concepts at the beginning of graduate instruction. The survey was administered to 202 graduate students in physics enrolled in first-year quantum mechanics courses from seven different universities at the beginning of the first semester. We also conducted one-on-one interviews with fifteen graduate students or advanced undergraduate students who had just finished a course in which all the content on the survey was covered. We find that students share universal difficulties about fundamental quantum mechanics concepts. Th…
Beginning in autumn 2008 the first generation of astronomy master students will start a 2 year course in Astrophysics offered by the Physics department of the University of Split, Croatia (http://fizika.pmfst.hr/astro/english/index.html). This unique master course in South-Eastern Europe, following the Bologna convention and given by astronomers from international institutions, offers a series of comprehensive lectures designed to greatly enhance students' knowledge and skills in astrophysics, and prepare them for a scientific career. An equally important aim of the course is to recognise the …
Student learning in upper division thermal physics has not been studied to the same extent as in other courses like electromagnetism and quantum mechanics. Studies addressing reasoning and learning at the graduate level are even more limited. In this study, we conducted think-aloud interviews with eight graduate students involving questions centered around a set of entropy related conceptual tasks, two of which are similar to tasks presented to undergraduates in other studies. We discuss patterns in student reasoning on each question then discuss themes that appeared across questions. We ident…
We investigate the dynamics of how graduate students coordinate their mathematics and physics knowledge within the context of solving a homework problem for a plasma physics survey course. Students were asked to obtain the complex dielectric function for a plasma with a specified distribution function and find the roots of that expression. While all the 16 participating students obtained the dielectric function correctly in one of two equivalent expressions, roughly half of them (7 of 16) failed to compute the roots correctly. All seven took the same initial step that led them to the incorrect…
This is a graduate course on elementary quantum mechanics written for the benefit of undergraduate and graduate students. It is the English version of physics/0003106, which I did at the suggestion of several students from different countries. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
First Internet graduate course on Classical Mechanics in Spanish (Castellano). This is about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. English and Romanian versions are in (slow) progress and hopefully will be arXived. For a similar course on Quantum Mechanics, see physics/9808031
Excerpts are presented from a graduate course on Classical Electrodynamics held during the spring semester of 2000 at the Institute of Physics, Guanajuato State University, Mexico
The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple choice test developed by Beichner to assess students' understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which correspond to introductory students' common difficulties with kinematics graphs. Instruction is unlikely to be effective if instructors do not know these common difficulties and take them into account in their instructional design. We evaluate the performance of first year physics graduate students at identifying introductory students' common difficulties related to kine…
The Quantum Mechanics Conceptual Survey (QMCS) is a 12-question survey of students' conceptual understanding of quantum mechanics. It is intended to be used to measure the relative effectiveness of different instructional methods in modern physics courses. In this paper we describe the design and validation of the survey, a process that included observations of students, a review of previous literature and textbooks and syllabi, faculty and student interviews, and statistical analysis. We also discuss issues in the development of specific questions, which may be useful both for instructors who…
We investigated the difficulties that physics students in upper-level undergraduate quantum mechanics and graduate students after quantum and statistical mechanics core courses have with the Fermi energy, the Fermi-Dirac distribution and total electronic energy of a free electron gas after they had learned relevant concepts in their respective courses. These difficulties were probed by administering written conceptual and quantitative questions to undergraduate students and asking some undergraduate and graduate students to answer those questions while thinking aloud in one-on-one individual i…
We present two programs that address needs to better prepare graduate students for their roles as professional physicists, particularly in the areas of teaching and education research. The two programs, Preparing Future Physicists (PFP) and a course, Teaching and Learning Physics, are designed to be mutually supportive, address these broader graduate roles, and support the development of the field of physics education research. While voluntary, PFP has attracted the participation of roughly half the physics graduate students at each of two large research institutions. Compared to the national …
The Americans with Disabilities Act (ADA) mandates that U.S. institutions of higher education provide "reasonable accommodations" to students with disabilities to ensure equal educational opportunities. However, despite the key role of physics as a gateway to Science, Technology, Engineering and Mathematics (STEM) studies, only limited resources exist for teaching physics to students who are blind or visually impaired. Here we share lessons from our experience creating an accessible physics curriculum for a blind physics major. The authors include the student himself, a blind physics B.S. who …
Teaching assistants (TAs) are often responsible for grading student solutions. Since grading communicates instructors' expectations, TAs' grading decisions play a crucial role in forming students' approaches to problem solving (PS) in physics. We investigated the change in grading practices and considerations of 18 first-year graduate students participating in a TA professional development (PD) course. The TAs were asked to state their beliefs about the purpose of grading, to grade a set of specially designed student solutions, and to explain their grading decisions. We found that after one se…
This is the English version of a friendly graduate course on Classical Mechanics, containing about 80% of the material I covered during the January-June 1999 semester at IFUG in the Mexican city of Leon. For the Spanish version, see physics/9906066
This article tells the story of the founding of the Compass Project at UC Berkeley and describes its impacts. The Compass Project is a self-formed group of graduate and undergraduate students in the physical sciences. Its goals are to improve undergraduate physics education, provide our members with opportunities for professional development, and increase retention of students, especially those from populations typically underrepresented in the physical sciences. Compass fosters a diverse, collaborative student community by providing a wide range of services, including a summer program, fall a…
The physics instruction at UC Davis for life science majors takes place in a long-standing reformed large-enrollment physics course in which the discussion/lab instructors (primarily graduate student teaching assistants) implement the interactive-engagement (IE) elements of the course. Because so many different instructors participate in disseminating the IE course elements, we find it essential to the instructors professional development to observe and document the student-instructor interactions within the classroom. Out of this effort, we have developed a computerized real-time instructor o…
The Test of Understanding Graphs in Kinematics (TUG-K) is a multiple choice test developed by Beichner in 1994 to assess students' understanding of kinematics graphs. Many of the items on the TUG-K have strong distractor choices which correspond to students' common difficulties with kinematics graphs. Instruction is unlikely to be effective if instructors do not know the common difficulties of introductory physics students and explicitly take them into account in their instructional design. We evaluate the pedagogical content knowledge of first year physics graduate students enrolled in a teac…
Learning quantum mechanics is challenging, even for upper-level undergraduate and graduate students. Research-validated interactive tutorials that build on students' prior knowledge can be useful tools to enhance student learning. We have been investigating student difficulties with quantum mechanics pertaining to the double-slit experiment in various situations that appear to be counterintuitive and contradict classical notions of particles and waves. For example, if we send single electrons through the slits, they may behave as a "wave" in part of the experiment and as a "particle" in anothe…
Well-developed problem-solving skills are essential for any student enrolled in a science, technology, engineering or mathematics (STEM) course as well as for graduates in the workforce. One of the most essential skills is the ability to monitor one's own progress and understanding while solving a problem. Successful monitoring during the entire solution allows a solver to identify errors within a solution and make adjustments as necessary. To highlight this aspect of problem-solving, we have developed a framework and associated classroom activities that introduce students to monitoring (M) al…
A thoughtful approach to designing and improving labs, particularly at the advanced level, is critical for the effective preparation of physics majors for professional work in industry or graduate school. With that in mind, physics education researchers in partnership with the physics faculty at the University of Colorado Boulder have overhauled the senior-level Advanced Physics Lab course. The transformation followed a three part process of establishing learning goals, designing curricula that align with the goals, and assessment. Similar efforts have been carried out in physics lecture cours…
This article provides brief guidance for a successful graduate teaching assistantship at our school. Although the components mentioned in this article are primarily aimed at mathematics courses designated as the "Basic Science and Mathematics" (BSM) modules with multiple sections, the principle can also be applied and adapted to other courses and institutions as well.
This is the first graduate course on elementary quantum mechanics in Internet written in Romanian for the benefit of Romanian speaking students (Romania and Moldova). It is a translation (with corrections) of the Spanish version of the course (physics/9808031, English translation physics/0004072), which I did at the request of students of physics in Bucharest. The topics included refer to the postulates of quantum mechanics, one-dimensional barriers and wells, angular momentum and spin, WKB method, harmonic oscillator, hydrogen atom, quantum scattering, and partial waves
Quantum mechanics is a challenging subject, even for advanced undergraduate and graduate students. Here, we discuss the development and evaluation of research-based concept tests for peer instruction as a formative assessment tool in quantum mechanics (QM) courses. The preliminary evaluations show that these tools are effective in helping students develop a good grasp of quantum mechanics.
We discuss an investigation of student difficulties with degenerate perturbation theory (DPT) carried out in advanced quantum mechanics courses by administering free-response and multiple-choice questions and conducting individual interviews with students. We find that students share many common difficulties related to this topic. We used the difficulties found via research as resources to develop and evaluate a Quantum Interactive Learning Tutorial (QuILT) which strives to help students develop a functional understanding of DPT. We discuss the development of the DPT QuILT and its preliminary …
The workshop `Astrophysical Dynamics 1999/2000' followed a homonymous advanced research course, and both activities were organized by me. In this opening paper of the proceedings book, I describe them and document their strong impact on the academic life of the local institutions. The advanced research course was open to graduate students, senior researchers, and motivated under-graduate students with good background in physics and mathematics. The course covered several multi-disciplinary issues of modern research on astrophysical dynamics, and thus also of interest to physicists, mathematici…
Modeling Instruction (MI), an active-learning introductory physics curriculum, has been shown to improve student academic success. Peer-to-peer interactions play a salient role in the MI classroom. Their impact on student interest and self-efficacy -- preeminent constructs of various career theories -- has not been thoroughly explored. Our examination of three undergraduate MI courses (N=221) revealed a decrease in students' physics self-efficacy, physics interest, and general science interest. We found a positive link from physics interest to self-efficacy, and a negative relationship between…
Dirac notation is used commonly in quantum mechanics. However, many upper-level undergraduate and graduate students in physics have difficulties with representations of quantum operators corresponding to observables especially when using Dirac notation. To investigate these difficulties, we administered free-response and multiple-choice questions and conducted individual interviews with students in advanced quantum mechanics courses. We discuss the analysis of data on the common difficulties found.
Educational technology has attained significant importance as a mechanism for supporting experiential learning of science concepts. However, the growth of this mechanism is limited by the significant time and technical expertise needed to develop such products, particularly in specialized fields of science. We sought to test whether interactive, educational, online software modules can be developed effectively by students as a curriculum component of an advanced science course. We discuss a set of fifteen such modules developed by Harvard University graduate students to demonstrate various con…
This mini-course gives an introduction to the techniques used in experimental particle physics with an emphasis on the impact of technological advances. The basic detector types and particle accelerator facilities will be briefly covered with examples of their use and with comparisons. The mini-course ends with what can be expected in the near future from current technology advances. The mini-course is intended for graduate students and post-docs and as an introduction to experimental techniques for theorists.
Investigating student interpretations of the differences between classical and quantum computers: Are quantum computers just analog classical computers?
