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A Thousand Problems in Cosmology. Chapter 4: Black holes

The fourth chapter of the collection of problems in cosmology, devoted to black holes. Consists of basic introduction, sections on Schwarzschild and Kerr black holes, a section on particles' motion and collisions in general black hole space-times, and the astrophysical part. This version contains only formulations of 137 problems. The full collection, with solutions included, is available in the form of a wiki-based resource at www.universeinproblems.com. The cosmological community is welcome to contribute to its development.

physics.ed-ph↗

The benefits of completing homework for students with different aptitudes in an introductory physics course

We examine the relationship between homework completion and exam performance for students having different physics aptitudes for five different semesters of an introductory electricity and magnetism course. In our analysis, we plot exam scores versus homework completion scores and calculate the slopes of the line fits and the Pearson correlations. On average, completing many homework problems correlated to better exam scores only for students with high physics aptitude. Low aptitude physics students had a negative correlation between exam performance and completing homework; the more homework problems they did, the worse their performance was on exams. One explanation for this effect is that the assigned homework problems placed an excessive cognitive load on low aptitude students. As a result, no learning or even negative learning might have taken place when low aptitude students attempted to do assigned homework. Another explanation is based on the fact that the negative benefit effects first appeared when magnetism concepts were introduced. According to this explanation, low aptitude students had difficulty consolidating knowledge of magnetic fields with previously-learned knowledge of electric fields. A third possibility, that a high homework copying rate by low aptitude students impeded learning, is rejected because two different analyses revealed no evidence of homework copying.

physics.ed-ph↗

Assessing Student Learning in Middle-Division Classical Mechanics/Math Methods

Reliable and validated assessments of introductory physics have been instrumental in driving curricular and pedagogical reforms that lead to improved student learning. As part of an effort to systematically improve our sophomore-level Classical Mechanics and Math Methods course (CM 1) at CU Boulder, we are developing a tool to assess student learning of CM 1 concepts in the upper-division. The Colorado Classical Mechanics/Math Methods Instrument (CCMI) builds on faculty-consensus learning goals and systematic observations of student difficulties. The result is a 9-question open-ended post-test that probes student learning in the first half of a two-semester classical mechanics / math methods sequence. In this paper, we describe the design and development of this instrument, its validation, and measurements made in classes at CU Boulder.

physics.ed-ph↗

Contrastive Sets and Framing: A Case Study in Scientific Writing

I describe an activity created to help our students learn how to write a scientific paper by reverse engineering a contrastive set of existing papers. I look at three recent implementations of this activity and use a multiple cognitive models approach to begin understanding the variance. This leads to a reasonable strategy for further investigation. First, I describe the conception and design of the activity structure, and how a contrastive set was constructed. I create an initial coding scheme to characterize group behavior in the three implementations, with special attention paid to analyzing student dialog on the structure of scientific papers and their ideas about the reasons for the peculiar features they observe. There is a striking difference in the way students engaged with the activity between the implementations not all of which can be ascribed to differences in activity structures, and the remainder of the paper is concerned with the use of resources and framing, case-based reasoning and Gibson's ecological perspective to understand the reason for this difference.

physics.ed-ph↗

How to Demonstrate the Voltage on a charged object in Physics Laboratory

Common Objects like a comb or a pen get charged when rubbed against something like human hair or garment clothing. Charged objects exhibit noticeable attractive or repulsive force lifting small pieces of paper or pushing/pulling a suspended light object charged with the same/opposite(uncharged) polarity respectively. This indicates the strong electrical nature of charged objects. Flashes due to spark between oppositely charged objects can be seen in total darkness. Implying a large potential difference between these charged objects which is not possible at lower voltages. This article describes a method to measure the voltage on commonly charged objects with respect to earth using simple instrumentation based on capacitors and CMOS voltmeter. Once the potential difference is known the average charge on the object can be calculated as well. The article also suggests a simple femto-farad capacitance meter for electrostatics work.

physics.ed-ph↗

Implicit scaffolding in interactive simulations: Design strategies to support multiple educational goals

We build on theoretical foundations of tool-mediated learning, tool design, and human computer interaction to develop a framework for implicit scaffolding in learning environments. Implicit scaffolding employs affordances, constraints, cueing, and feedback in order to frame and scaffold student exploration without explicit guidance, and it is a particularly useful design framework for interactive simulations in science and mathematics. A key purpose of implicit scaffolding is to support a range of educational goals including affect, process, and content. In particular, the use of implicit scaffolding creates learning environments that are productive for content learning and are able to simultaneously support the affective goals of student agency and ownership over the learning process - goals that may not be addressed in more directed learning environments. We describe how the framework is applied in the context of the Energy Skate Park: Basics simulation, a simulation aimed at middle school student learning of energy concepts. Interview data provides an exemplar of the process by which implicit scaffolding can support productive student exploration with a computer simulation. While we present this framework for implicit scaffolding in the context of computer simulations, the framework can be extended and adapted to apply to a range of tool-mediated learning environments.

physics.ed-ph↗

Estimation of solar zenith passage on the Earth's surface by a simple harmonic motion

The kinematics of the Solar zenith passage on the Earth was shown as a simple harmonic motion. This analytical model used the uniform circular motion to describe the Earth's rotation relative to its axis and relative to the Sun, also this model considered the sunlight beams parallel and constant the obliquity of the ecliptic. We made a contrast between some data taken from of the software Stellarium 0.12.1 and the model, we obtained an uncertainty $Δt=1d$; this result allow to project the model as an astronomical context conducive to develop the kinematics of simple harmonic motion.

physics.pop-ph↗

pyro: A teaching code for computational astrophysical hydrodynamics

We describe pyro: a simple, freely-available code to aid students in learning the computational hydrodynamics methods widely used in astrophysics. pyro is written with simplicity and learning in mind and intended to allow students to experiment with various methods popular in the field, including those for advection, compressible and incompressible hydrodynamics, multigrid, and diffusion in a finite-volume framework. We show some of the test problems from pyro, describe its design philosophy, and suggest extensions for students to build their understanding of these methods.

astro-ph.IM↗

Physical Determination of the Action

The objective is a foundation of physics from the operationalization of its basic observables. We begin with classical and relativistic kinematics. Seizing on a programmatic proposal by Heinrich Hertz we arrive via quantification of energy-momentum at the equations of motion and the action functional. Finally we present a relativistic revision of energy, momentum and inertial mass. The goal is not primarily to change or improve the mathematical structure of mechanics, but to gain a deeper physical understanding of mechanics like Einstein with his gedanken experiments on relativistic kinematics. Starting from undisputed measurement operations and natural principles the mathematical formalism is only created and thus shown in a new light. This work is in the same context as current efforts to the "foundation of quantum mechanics", just with respect to the interpretation of the classical and relativistic calculuses.

physics.hist-ph↗

Toward affect-inclusive models of cognitive dynamics: Coupling epistemological resources and emotions

Many prominent lines of research on student's reasoning and conceptual change within learning sciences and physics education research have not attended to the role of learners' affect or emotions in the dynamics of their conceptual reasoning. This is despite evidence from psychology and cognitive- and neuro- sciences that emotions are deeply integrated with cognition and documented associations in education research between emotions and academic performance. The few studies that have aimed to integrate emotions within models of learners' cognition, have mostly done so at a coarse grain size. In this manuscript, toward the long-term goal of incorporating emotions into fine-grained models of in-themoment cognitive dynamics, we present a case study of Judy, an undergraduate electrical engineering and physics major. We argue that a fine-grained aspect of Judy's affect, her annoyance at a particular kind of homework problem, stabilizes a context-dependent epistemological stance she displays, about an unbridgeable gulf she perceives to exist between real and ideal circuits.

physics.ed-ph↗

Optimization Of Simulations And Activities For A New Introductory Quantum Mechanics Curriculum

The Institute of Physics New Quantum Curriculum (quantumphysics.iop.org) consists of online texts and interactive simulations with accompanying activities for an introductory course in quantum mechanics starting from two-level systems. Observation sessions and analysis of homework and survey responses from in-class trials were used to optimize the simulations and activities in terms of clarity, ease-of-use, promoting exploration, sense-making and linking of multiple representations. This work led to revisions of simulations and activities and general design principles which have been incorporated wherever applicable. This article describes the optimization of one of the simulation controls and the refinement of activities to help students make direct connections between multiple representations.

physics.ed-ph↗

The Initial State of Students Taking an Introductory Physics MOOC

As part of a larger research project into massively open online courses (MOOCs), we have investigated student background, as well as student participation in a physics MOOC with a laboratory component. Students completed a demographic survey and the Force and Motion Conceptual Evaluation at the beginning of the course. While the course is still actively running, we have tracked student participation over the first five weeks of the eleven-week course.

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Physics as a Mechanism for Including ELLs in Classroom Discourse

English Language Learners (ELLs) are frequently left on the periphery of classroom interactions. Due to misalignment of language skills, teachers and peers communicate with these students less often, decreasing the number of opportunities to engage. Exclusion can be avoided with learning activities that invite all students to participate and contribute ideas. We argue that environments and activities that privilege scientific inductive reasoning increase possibilities for emerging bilingual students to engage. This study investigated first-grade students' discussions about factors that affect how objects float. Students came from a variety of language backgrounds; all were considered beginner/intermediate ELLs. Results show that the goal of inducing principles from actual phenomena encouraged students to communicate their ideas and reasoning, boosting students' confidence in expressing themselves. Following the hybrid space argument of Vygotsky's theory of concept formation, we illustrate that physics can be particularly suitable context for the co-development of concepts and English language skills.

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Paradigms in Physics Education Research

In this paper, we describe two paradigms in physics education research (PER): recurrence-oriented and case-oriented PER. We connect theory on research methodologies in the social sciences to interviews with physics education researchers and examples of published PER to articulate the specific assumptions of recurrence- and case-oriented PER. We show that the different assumptions made in these two paradigms bear out in specific aims and research designs taken up by physics education researchers. In particular, recurrence-oriented research seeks reproducible, representative patterns and relationships; human behavior is modeled as governed by lawful (albeit probabilistic) relationships. Case-oriented research, in contrast, seeks to refine and develop theory by linking that theory to cases; human action is assumed to be shaped by the meanings that participants make of their local environments. We briefly offer examples in which researchers take up both the recurrence- and case-oriented research paradigms.

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Selection, Generalization, and Theories of Cause in Case-Oriented Physics Education Research

Case-oriented physics education research - which seeks to refine and develop theory by linking that theory to cases - incorporates distinct practices for selecting data for analysis, generalizing results, and making causal claims. Unanswered questions about these practices may constrain researchers more familiar with the recurrence-oriented research paradigm - which seeks to inform instructional predictions by discerning reproducible, representative patterns and relationships - from participating in or critically engaging with case-oriented research. We use results from interviews with physics education researchers, a synthesis of the literature on research methodologies, and published examples of case-oriented and recurrence-oriented research to answer "hard-hitting questions" that researchers may pose. In doing so, we aim to substantiate our position that both case-oriented and recurrence- oriented PER are rigorous but that the rigor is of a different nature in each paradigm.

physics.ed-ph↗

Software Carpentry: Lessons Learned

Over the last 15 years, Software Carpentry has evolved from a week-long training course at the US national laboratories into a worldwide volunteer effort to raise standards in scientific computing. This article explains what we have learned along the way the challenges we now face, and our plans for the future.

cs.GL↗

Development and results from a survey on students views of experiments in lab classes and research

The Colorado Learning Attitudes about Science Survey for Experimental Physics (E-CLASS) was developed as a broadly applicable assessment tool for undergraduate physics lab courses. At the beginning and end of the semester, the E-CLASS assesses students views about their strategies, habits of mind, and attitudes when doing experiments in lab classes. Students also reflect on how those same strategies, habits-of-mind, and attitudes are practiced by professional researchers. Finally, at the end of the semester, students reflect on how their own course valued those practices in terms of earning a good grade. In response to frequent calls to transform laboratory curricula to more closely align it with the skills and abilities needed for professional research, the E-CLASS is a tool to assess students' perceptions of the gap between classroom laboratory instruction and professional research. The E-CLASS has been validated and administered in all levels of undergraduate physics classes. To aid in its use as a formative assessment tool, E-CLASS provides all participating instructors with a detailed feedback report. Example figures and analysis from the report are presented to demonstrate the capabilities of the E-CLASS. The E-CLASS is actively administered through an online interface and all interested instructors are invited to administer the E-CLASS their own classes and will be provided with a summary of results at the end of the semester.

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