Upper-division student difficulties with Separation of Variables

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

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

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

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

Mark-recapture estimators for dual frame population size of prominent nesting structures: the effect of uncertain detection probability

The combined mark-recapture and line transect sampling methodology proposed by Alpizar- Jara and Pollock [Journal of Environmental and Ecological Statistics, 3(4), 311–327, 1996; In Marine Mammal Survey and Assessment Methods Symposium. G.W. Garner, S.C. Amstrup, J.L. Laake, B.F.J. Manly, L.L. McDonald, and D.C. Robertson (Eds.), A.A. Balkema, Rotterdam, Netherlands, pp. 99–114, 1999] is used to illustrate the estimation of population size for populations with prominent nesting structures (i.e., bald eagle nests). In the context of a bald eagle population, the number of nests in a list frame corresponds to a ‘‘pre-marked’’ sample of nests, and an area frame corresponds to a set of transect strips that could be regularly monitored. Unlike previous methods based on dual frame methodology using the screening estimator [Haines and Pollock (Journal of Environmental and Ecological Statistics, 5, 245–256, 1998a; Survey Methodology, 24(1), 79–88, 1998b)], we no longer need to assume that the area frame is complete (i.e., all the nests in the sampled sites do not need to be seen). One may use line transect sampling to estimate the probability of detection in a sampled area. Combining information from list and area frames provides more efficient estimators than those obtained by using data from only one frame. We derive an estimator for detection probability and generalize the screening estimator. A simulation study is carried out to compare the performance of the Chapman modification of the Lincoln–Petersen estimator to the screening estimator. Simulation results show that although the Chapman estimator is generally less precise than the screening estimator, the latter can be severely biased in presence of uncertain detection. The screening estimator outperforms the Chapman estimator in terms of mean squared error when detection probability is near 1 wheareas the Chapman estimator outperforms the screening estimator when detection probability is lower than a certain threshold value depending on particular scenarios

Gas chromatograph injection system

An injection system for a gas chromatograph is described which uses a small injector chamber (available in various configurations). The sample is placed in the chamber while the chamber is not under pressure and is not heated, and there is no chance of leakage caused by either pressure or heat. It is injected into the apparatus by changing the position of a valve and heating the chamber, and is volatilized and swept by a carrier gas into the analysis apparatus

Development of single crystal beta-alumina membrane

Feasibility of crystal growth technique for beta alumina membrane from molybdenum, tungsten, and iridiu