arXiv subjects

Steven J. Pollock

Publications and source records attributed to Steven J. Pollock.

32 records · Page 2Linked to original sources

arXiv2014

Student Difficulties with the Dirac Delta Function

The Dirac delta function is a standard mathematical tool used in multiple topical areas in the undergraduate physics curriculum. While Dirac delta functions are usually introduced in order to simplify a problem mathematically, students often struggle to manipulate and interpret them. To better understand student difficulties with the delta function at the upper-division level, we examined responses to traditional exam questions and conducted think-aloud interviews. Our analysis was guided by an analytical framework that focuses on how students activate, construct, execute, and reflect on the Dirac delta function in physics. Here, we focus on student difficulties using the delta function to express charge distributions in the context of junior-level electrostatics. Challenges included: invoking the delta function spontaneously, constructing two- and three-dimensional delta functions, integrating novel delta function expressions, and recognizing that the delta function can have units.

physics.ed-ph↗

arXiv2014

Coupled Multiple-response vs. Free-response Conceptual assessment: An Example from upper-division Physics

Free-response research-based assessments, like the Colorado Upper-division Electrostatics Diagnostic (CUE), provide rich, fine-grained information about students' reasoning. However, because of the difficulties inherent in scoring these assessments, the majority of the large-scale conceptual assessments in physics are multiple-choice. To increase the scalability and usability of the CUE, we set out to create a new version of the assessment that preserves the insights afforded by a free-response format while exploiting the logistical advantages of a multiple-choice assessment. We used our extensive database of responses to the free-response CUE to construct distractors for a new version where students can select multiple responses and receive partial credit based on the accuracy and consistency of their selections. Here, we describe the development of this modified CUE format, which we call coupled multiple-response (CMR), and present data from direct comparisons of both versions. We find that the two formats have the same average score and perform similarly on multiple measures of validity and reliability, suggesting that the new version is a potentially viable alternative to the original CUE for the purpose of large-scale research-based assessment. We also compare the details of student responses on each of the two versions. While the CMR version does not capture the full scope of potential student responses, nearly three-quarters of our students' responses to the free-response version contained one or more elements that matched options provided on the CMR version.

physics.ed-ph↗

arXiv2014

Development and Uses of Upper-division Conceptual Assessment

The use of validated conceptual assessments alongside more standard course exams has become standard practice for the introductory courses in many physics departments. These assessments provide a more standard measure of certain learning goals, allowing for comparisons of student learning across instructors, semesters, and institutions. Researchers at the University of Colorado Boulder have developed several similar assessments designed to target the more advanced physics content of upper-division classical mechanics, electrostatics, quantum mechanics, and electrodynamics. Here, we synthesize the existing research on our upper-division assessments and discuss some of the barriers and challenges associated with developing, validating, and implementing these assessments as well as some of the strategies we have used to overcome these barriers.

physics.ed-ph↗

arXiv2014

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.

physics.ed-ph↗

arXiv2014

Validation of a Conceptual Assessment Tool in E&M II

As part of an ongoing project to investigate student learning in upper-division electrodynamics (E&M II), the PER research group at the University of Colorado Boulder has developed a tool to assess student conceptual understanding: the CURrENT (Colorado UppeR-division ElectrodyNamics Test). The result is an open-ended post-test diagnostic with 6 multi-part questions, an optional 3-question pretest, and an accompanying grading rubric. This instrument is motivated in part by our faculty-consensus learning goals, and is intended to help measure the effectiveness of transformed pedagogy. In addition, it provides insights into student thinking and student difficulties in the covered topical areas. In this paper, we present preliminary measures of the validity and reliability of the instrument and scoring rubric. These include expert validation and student interviews, inter-rater reliability measures, and classical test statistics.

physics.ed-ph↗

arXiv2013

A Model for Incorporating Computation Without Changing the Course: An example from middle-division classical mechanics

Much of the research done by modern physicists would be impossible without the use of computation. And yet, while computation is a crucial tool of practicing physicists, physics curricula do not generally reflect its importance and utility. To more tightly connect undergraduate preparation with professional practice, we integrated computational instruction into middle-division classical mechanics at the University of Colorado Boulder. Our model for integration works within the constraints of faculty who do not specialize in computation teaching standard physics courses by placing a strong emphasis on {an adaptable curriculum}. Our model includes the construction of computational learning goals, the design of computational activities consistent with those goals, and the assessment of students' computational fluency. We present critiques of our model as we work to develop an effective and sustainable model for computational instruction in the undergraduate curriculum

physics.ed-ph↗

arXiv2013

Developing Tutorials for Advanced Physics Students: Processes and Lessons Learned

When education researchers describe newly developed curricular materials, they typically concentrate on the research base behind their design, and the efficacy of the final products, but do not highlight the initial stages of creating the actual materials. With the aim of providing useful information for faculty engaged in similar projects, we describe here our development of a set of in-class tutorials for advanced undergraduate electrodynamics students, and discuss factors that influenced their initial design and refinement. Among the obstacles to be overcome was the investigation of student difficulties within the short time frame of our project, and devising ways for students to engage in meaningful activities on advanced-level topics within a single 50-minute class period. We argue for a process that leverages faculty experience and classroom observations, and present several guidelines for tutorial development and implementation in upper-division physics classrooms.

physics.ed-ph↗

arXiv2013

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.

physics.ed-ph↗

arXiv2013

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↗

arXiv2012

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.

physics.ed-ph↗

arXiv2012

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.

physics.ed-ph↗

arXiv2012

Research-Based Course Materials and Assessments for Upper-Division Electrodynamics (E&M II)

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.

physics.ed-ph↗

arXiv2009

A longitudinal study of student conceptual understanding in Electricity and Magnetism

We have investigated the long-term effect of student-centered instruction at the freshman level on juniors' performance on a conceptual survey of Electricity and Magnetism (E&M). We measured student performance on a research-based conceptual instrument -- the Brief Electricity & Magnetism Assessment (BEMA) -- over a period of 8 semesters (2004-2007). Concurrently, we introduced the University of Washington's Tutorials in Introductory Physics as part of our standard freshman curriculum. Freshmen took the BEMA before and after this Tutorial-based introductory course, and juniors took it after completion of their traditional junior-level E&M I and E&M II courses. We find that, on average, individual BEMA scores do not change significantly after completion of the introductory course - neither from the freshman to the junior year, nor from upper-division E&M I to E&M II. However, we find that juniors who had completed a non-Tutorial freshman course scored significantly lower on the (post upper-division) BEMA than those who had completed the reformed freshman course - indicating a long-term positive impact of freshman Tutorials on conceptual understanding.

physics.ed-ph↗

arXiv2008

Sustaining Educational Reforms in Introductory Physics

While it is well known which curricular practices can improve student performance on measures of conceptual understanding, the sustaining of these practices and the role of faculty members in implementing these practices are less well understood. We present a study of the hand-off of Tutorials in Introductory Physics from initial adopters to other instructors at the University of Colorado, including traditional faculty not involved in physics education research. The study examines the impact of implementation of Tutorials on student conceptual learning across eight first-semester, and seven second-semester courses, for fifteen faculty over twelve semesters, and includes roughly 4000 students. It is possible to demonstrate consistently high, and statistically indistinguishable, student learning gains for different faculty members; however, such results are not the norm, and appear to rely on a variety of factors. Student performance varies by faculty background - faculty involved in, or informed by physics education research, consistently post higher student learning gains than less-informed faculty. Student performance in these courses also varies by curricula used - all semesters in which the research-based Tutorials and Learning Assistants are used have higher student learning gains than those semesters that rely on non-research based materials and do not employ Learning Assistants.

physics.ed-ph↗