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

Cutting tool condition monitoring using multiple sensors and artificialintelligence techniques on a computer numerical controlled milling machine

This work documents an investigation of the degradation of a variety of different tools whilst conducting milling operations on a computer numerical controlled (CNC) milling machine. The potential of a range of sensors to detect tool degradation has been investigated and the outputs have been incorporated into a monitoring system. Progressive degradation under nominal rough and finish face milling and rough groove milling has been investigated using a two point grooving tool and four and eight point face milling tools on En8, En24 and En24T workpiece materials. Rapid degradation of the cutting tool has also been observed under rough milling conditions using four and eight point face milling tools, whilst machining n8 and En24T materials in a variety of simulated and actual tool breakage situations. A limited investigation of the effect of the individual wear geometries associated with both progressive and instantaneous tool degradation has been conducted by simulating these geometries and carrying out rough miffing tests using a four point face milling tool on a workpiece of En8 material. Similarly, a limited investigation of the effect of machining on different machines has also been undertaken. A number of different sensing technologies have been used, including conventional sensors such as spindle current and cutting force but also novel sensing techniques such as Acoustic Emission. These have been combined using artificial intelligence techniques to provide automatic recognition of the tool wear state. Similarly, the feasibility of breakage detection/prediction has also been demonstrated.CEC - BRITE EURAM Programm

Student behavior and test security in online conceptual assessment

Historically, the implementation of research-based assessments (RBAs) has been a driver of education change within physics and helped motivate adoption of interactive engagement pedagogies. Until recently, RBAs were given to students exclusively on paper and in-class; however, this approach has important drawbacks including decentralized data collection and the need to sacrifice class time. Recently, some RBAs have been moved to online platforms to address these limitations. Yet, online RBAs present new concerns such as student participation rates, test security, and students' use of outside resources. Here, we report on a pilot study addressing these concerns. We gave two upper-division RBAs to courses at five institutions; the RBAs were hosted online and featured embedded JavaScript code which collected information on students' behaviors (e.g., copying text, printing). With these data, we examine the prevalence of these behaviors, and their correlation with students' scores, to determine if online and paper-based RBAs are comparable. We find that browser loss of focus is the most common online behavior while copying and printing events were rarer.We found no statistically significant correlation between any of these online behaviors and students scores. We also found that participation rates for our upper-division population went up when the RBA was given online. These results indicates that, for our upper-division population, scores on online administrations of these RBAs were comparable to in-class versions.Comment: 6 pages, 0 figures, submitted to the 2019 Physics Education Research Conferenc

Upper-division Student Understanding of Coulomb's Law: Difficulties with Continuous Charge Distributions

Utilizing the integral expression of Coulomb's Law to determine the electric potential from a continuous charge distribution is a canonical exercise in Electricity and Magnetism (E&M). In this study, we use both think-aloud interviews and responses to traditional exam questions to investigate student difficulties with this topic at the upper-division level. Leveraging a theoretical framework for the use of mathematics in physics, we discuss how students activate, construct, execute and reflect on the integral form of Coulomb's Law when solving problems with continuous charge distributions. We present evidence that junior-level E&M students have difficulty mapping physical systems onto the mathematical expression for the Coulomb potential. Common challenges include difficulty expressing the difference vector in appropriate coordinates as well as determining expressions for the differential charge element and limits of integration for a specific charge distribution. We discuss possible implications of these findings for future research directions and instructional strategies.Comment: 5 pages, 1 figure, 2 tables, accepted to 2012 PERC Proceeding

ACER: A Framework on the Use of Mathematics in Upper-division Physics

At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics, electromagnetism, and quantum mechanics. Unsurprisingly, a number of difficulties are related to students' use of mathematical tools (e.g., approximation methods). Previous work has documented a number of challenges that students must overcome to use mathematical tools fluently in introductory physics (e.g., mapping meaning onto mathematical symbols). We have developed a theoretical framework to facilitate connecting students' difficulties to challenges with specific mathematical and physical concepts. In this paper, we motivate the need for this framework and demonstrate its utility for both researchers and course instructors by applying it to frame results from interview data on students' use of Taylor approximations.Comment: 10 pages, 1 figures, 2 tables, accepted to the 2012 PERC Proceeding

Analytic Framework for Students' Use of Mathematics in Upper-Division Physics

Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and researchers in characterizing students' difficulties with specific mathematical tools when solving the long and complex problems that are characteristic of upper-division. In this paper, we present this framework, including its motivation and development. We also describe an application of the framework to investigations of student difficulties with direct integration in electricity and magnetism (i.e., Coulomb's Law) and approximation methods in classical mechanics (i.e., Taylor series). These investigations provide examples of the types of difficulties encountered by advanced physics students, as well as the utility of the framework for both researchers and instructors.Comment: 17 pages, 4 figures, 3 tables, in Phys. Rev. - PE