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