13,678 research outputs found

    Upper-division student difficulties with Separation of Variables

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    Separation of variables can be a powerful technique for solving many of the partial differential equations that arise in physics contexts. Upper-division physics students encounter this technique in multiple topical areas including electrostatics and quantum mechanics. To better understand the difficulties students encounter when utilizing the separation of variables technique, we examined students' responses to midterm exam questions and a standardized conceptual assessment, and conducted think-aloud, problem-solving interviews. Our analysis was guided by an analytical framework that focuses on how students activate, construct, execute, and reflect on the separation of variables technique when solving physics problems. Here we focus on student difficulties with separation of variables as a technique to solve Laplace's equation in both Cartesian and spherical coordinates in the context of junior-level electrostatics. Challenges include: recognizing when separation of variables is the appropriate tool; recalling/justifying the separated form of the potential and the need for the infinite sum; identifying implicit boundary conditions; and spontaneously reflecting on their solutions. Moreover, the type and frequency of errors was often different for SoV problems in Cartesian and spherical geometries. We also briefly discuss implication of these our findings for instruction.Comment: 13 pages, 3 figures, submitted to Phys. Rev. ST-PE

    Multiple-choice Assessment for Upper-division Electricity and Magnetism

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    The Colorado Upper-division Electrostatics (CUE) diagnostic was designed as an open-ended assessment in order to capture elements of student reasoning in upper-division electrostatics. The diagnostic has been given for many semesters at several universities resulting in an extensive database of CUE responses. To increase the utility and scalability of the assessment, we used this database along with research on students' difficulties to create a multiple-choice version. The new version explores the viability of a novel test format where students select multiple responses and can receive partial credit based on the accuracy and consistency of their selections. This format was selected with the goal of preserving insights afforded by the open-ended format while exploiting the logistical advantages of a multiple-choice assessment. Here, we present examples of the questions and scoring of the multiple-choice CUE as well as initial analysis of the test's validity, item difficulty, discrimination, and overall consistency with the open-ended version.Comment: 4 pages, 3 figures, accepted 2013 Physics Education Research Conference proceeding

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

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    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.Comment: 4 pages, 3 figures, 1 table; submitted to 2013 Proceedings of the Physics Education Research Conferenc

    Oviposition and development in the glass frog Hyalinobatrachium orientale (Anura: Centrolenidae)

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    Oviposition and development in the glass frog Hyalinobatrachium orientale (Anura: Centrolenidae). Oviposition and external embryonic developmental features are described in the Tobago glass frog, Hyalinobatrachium orientale. Egg clutches are nearly always laid on the undersides of leaves (one exception); usually leaves of Heliconia sp. are used, but Philodendron and palms may be used in the absence of Heliconia. Clutches contain 28.0 ± 5.3 eggs (mean ± SD) and eggs are 1.86 ± 0.11 mm in diameter. The behavior of one amplectant pair was followed for more than five hours; the pair rotated several times around a small area of the leaf depositing eggs in a tight spiral formation. External embryonic features were observed by scanning electron microscopy. Surface ciliation is extensive up to the time of hatching when it is lost; external gills are short and a cement gland is absent. Hatching gland cells were detectable on the anterodorsal surface of the head from Day 4 after deposition and persisted until at least Day 10, and hatching occurred between Days 9 and 16. During this period, progressive development in tail length, surface pigmentation, intestinal coiling, and oral disc features was observed. Post-hatching larvae reared for six weeks grew 37% in length and tripled in weight, but remained at Gosner Stage 25

    Effects of Neutron Spatial Distributions on Atomic Parity Nonconservation in Cesium

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    We have examined modifications to the nuclear weak charge due to small differences between the spatial distributions of neutrons and protons in the Cs nucleus. We derive approximate formulae to estimate the value and uncertainty of this modification based only on nuclear rms neutron and proton radii. Present uncertainties in neutron distributions in Cs are difficult to quantify, but we conclude that they should not be neglected when using atomic parity nonconservation experiments as a means to test the Standard Model.Comment: 5 pages, RevTeX, slightly revised, one figure adde

    Validation and analysis of the coupled multiple response Colorado upper-division electrostatics (CUE) diagnostic

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    Standardized conceptual assessment represents a widely-used tool for educational researchers interested in student learning within the standard undergraduate physics curriculum. For example, these assessments are often used to measure student learning across educational contexts and instructional strategies. However, to support the large-scale implementation often required for cross-institutional testing, it is necessary for these instruments to have question formats that facilitate easy grading. Previously, we created a multiple-response version of an existing, validated, upper-division electrostatics diagnostic with the goal of increasing the instrument's potential for large-scale implementation. Here, we report on the validity and reliability of this new version as an independent instrument. These findings establish the validity of the multiple-response version as measured by multiple test statistics including item difficulty, item discrimination, and internal consistency. Moreover, we demonstrate that the majority of student responses to the new version are internally consistent even when they are incorrect, and provide an example of how the new format can be used to gain insight into student difficulties with specific content in electrostatics.Comment: 8 pages, 6 figures, submitted to Phys. Rev. ST-PE

    Research-based course materials and assessments for upper-division electrodynamics (E&M II)

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    Favorable outcomes from ongoing research at the University of Colorado Boulder on student learning in junior-level electrostatics (E&M I) have led us to extend this work to upper-division electrodynamics (E&M II). We describe here our development of a set of research-based instructional materials designed to actively engage students during lecture (including clicker questions and other in-class activities); and an instrument for assessing whether our faculty-consensus learning goals are being met. We also discuss preliminary results from several recent implementations of our transformed curriculum, plans for the dissemination and further refinement of these materials, and offer some insights into student difficulties in advanced undergraduate electromagnetism.Postprin

    The Future of Charge Card Networks

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    The general-purpose charge card is now ubiquitous and largely taken for granted. Annual charge card volume exceeds $5 trillion worldwide. Within the United States, nearly one billion cards are in use (about eight per household), and more than two billion worldwide. But charge cards, or more specifically, the cooperative networks that serve the largest card systems, Visa and MasterCard, are under legal attack through multiple lawsuits and under regulatory challenge in other countries. We trace in this essay multiple possible future 'scenarios'. This focus on possible futures distinguishes our work from many earlier studies of this subject.
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