Observations on student difficulties with mathematics in upper-division electricity and magnetism

Self Cite

Over the course of four years, we have researched and transformed a key course in the career of an undergraduate physics major-junior-level electricity and magnetism. With the aim of educating our majors based on a more complete understanding of the cognitive and conceptual challenges of upperdivision courses, we used principles of active engagement and learning theory to develop course materials and conceptual assessments. Our research results from student and faculty interviews and observations also informed our approach. We present several measures of the outcomes of this work at the University of Colorado at Boulder and external institutions. Students in the transformed courses achieved higher learning gains compared to those in the traditionally taught courses, particularly in the areas of conceptual understanding and ability to articulate their reasoning about a problem. The course transformations appear to close a gender gap, improving female students' scores on conceptual and traditional assessments so that they are more similar to those of male students. Students enthusiastically support the transformations, and indicate that several course elements provide useful scaffolding in conceptual understanding, as well as physicists' ''habits of mind'' such as problem-solving approaches and work habits. Despite these positive outcomes, student conceptual learning gains do not fully meet faculty expectations, suggesting that it is valuable to further investigate how the content and skills indicative of ''thinking like a physicist'' can be most usefully taught at the upper division.

Section: Mathematical Sophisticationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Transforming the junior level: Outcomes from instruction and research in E&M

Chasteen

Pollock

Pepper

et al. 2012

Self Cite

“…There have been a number of papers on the transformation of upper-division courses that use novel methods or curriculum, but they have very limited measures of learning and, with one exception, no such comparative data indicating the superiority of one teaching method over another. For example, some PER work on upper-division courses has focused on the characterization of persistent difficulties with fundamental concepts [3] and mathematics [4] that hinder meaningful learning of advanced topics. This work motivated the creation and use of tutorials where the instructor has small groups of students work collaboratively on worksheets that guide them through proper reasoning to overcome misconceptions and gain physical insight or that simply provide supervised practice of key mathematical tools [3,5].…”

Section: A Existing Per Literature On the Effectiveness Of Upper-divmentioning

confidence: 99%

Transforming a fourth year modern optics course using a deliberate practice framework

Jones

Madison

Wieman

2015

[This paper is part of the Focused Collection on Upper Division Physics Courses.] We present a study of active learning pedagogies in an upper-division physics course. This work was guided by the principle of deliberate practice for the development of expertise, and this principle was used in the design of the materials and the orchestration of the classroom activities of the students. We present our process for efficiently converting a traditional lecture course based on instructor notes into activities for such a course with active learning methods. Ninety percent of the same material was covered and scores on common exam problems showed a 15% improvement with an effect size greater than 1 after the transformation. We observe that the improvement and the associated effect size is sustained after handing off the materials to a second instructor. Because the improvement on exam questions was independent of specific problem topics and because the material tested was so mathematically advanced and broad (including linear algebra, Fourier transforms, partial differential equations, and vector calculus), we expect the transformation process could be applied to most upper-division physics courses having a similar mathematical base.

“…The study of student understanding of advanced topics is becoming increasingly prevalent in physics education research [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Investigating upper-division undergraduate students provides a snapshot of the intellectual journey from novice introductory student to expert physicist that may reveal key components of this transition [19].…”

Section: Introductionmentioning

confidence: 99%

Student understanding of the Boltzmann factor

Smith

Mountcastle

Thompson

2015

[This paper is part of the Focused Collection on Upper Division Physics Courses.] We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations of student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students' abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students' appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.