# Education Commons™

Electronic Theses and Dissertations

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Science and Mathematics Education

The University of Maine

Physics

Publication Year

Articles 1 - 4 of 4

## Full-Text Articles in Education

#### Investigating Student Understanding Of Vector Calculus In Upper-Division Electricity And Magnetism: Construction And Determination Of Differential Element In Non-Cartesian Coordinate Systems, Benjamin Schermerhorn

##### Electronic Theses and Dissertations

Differential length, area, and volume elements appear ubiquitously over the course of upper-division electricity and magnetism (E&M), used to sum the effects of or determine expressions for electric or magnetic fields. Given the plethora of tasks with spherical and cylindrical symmetry, non-Cartesian coordinates are commonly used, which include scaling factors as coefficients for the differential terms to account for the curvature of space. Furthermore, the application to vector fields means differential lengths and areas are vector quantities. So far, little of the education research in E&M has explored student understanding and construction of the non-Cartesian differential elements used in applications of vector calculus. This study contributes to the research base on the learning and teaching of these quantities.

Following course observations of junior-level E&M, targeted investigations were conducted to categorize student understanding of the properties of these differentials as they are constructed in a coordinate system without a physics context and as they are determined within common physics tasks. In general, students did not have a strong understanding of the geometry of non-Cartesian coordinate systems. However, students who were able to construct differential area and volume elements as a product of differential lengths within a given coordinate system were more successful when applying vector calculus. The results of this study were used to develop preliminary instructional resources to aid in the teaching of this material.

Lastly, this dissertation presents a theoretical model developed within the context of this study to describe students’ construction and interpretation of equations. The model joins existing theoretical frameworks: symbolic forms, used to describe students’ representational understanding of the structure of the constructed equation; and conceptual blending, which has been used to describe the ways in which students combine mathematics and physics knowledge when problem solving. In addition to providing a coherent picture for how the students in this study connect contextual information to symbolic representations, this model is broadly applicable as an analytical lens and allows for a detailed reinterpretation of similar analyses using these frameworks.

Echoes Of The Past: The Effect Of Background Experience On Far Transfer, Graham H. Hummel-Hall May 2018

#### Echoes Of The Past: The Effect Of Background Experience On Far Transfer, Graham H. Hummel-Hall

##### Electronic Theses and Dissertations

Far transfer is the application of knowledge learned in one setting to a problem in a very different setting. This multi-method study looked at far transfer in humans and whether it could be facilitated, inhibited, or remain unaffected by the number of courses or years a student at a university spent learning about the subject matter of the knowledge being transferred. Through quantitative and qualitative analysis of pretest and post-test data from an introductory undergraduate earth science course, I found that students with more physical science background experience more frequently engaged in successful and accurate transfer of physics information to ...

Aug 2014

#### Student Application Of The Fundamental Theorem Of Calculus With Graphical Representations In Mathematics And Physics, Rabindra R. Bajracharya

##### Electronic Theses and Dissertations

One mathematical concept frequently applied in physics is the Fundamental Theorem of Calculus (FTC). Mathematics education research on student understanding of the FTC indicates student difficulties with the FTC. Similarly, a few studies in physics education have implicitly indicated student difficulties with various facets of the FTC, such as with the definite integral and the area under the curve representation, in physics contexts. There has been no research on how students apply the FTC in graphically-based physics questions.

This study investigated student understanding of the FTC and its application to graphically-based problems. Our interest spans several aspects of the FTC ...

Identifying Productive Resources In Secondary School Students' Discourse About Energy, Benedikt Walter Harrer Dec 2013

#### Identifying Productive Resources In Secondary School Students' Discourse About Energy, Benedikt Walter Harrer

##### Electronic Theses and Dissertations

A growing program of research in science education acknowledges the beginnings of disciplinary reasoning in students’ ideas and seeks to inform instruction that responds productively to these disciplinary progenitors in the moment to foster their development into sophisticated scientific practice. This dissertation examines secondary school students’ ideas about energy for progenitors of disciplinary knowledge and practice. Previously, researchers argued that students’ ideas about energy were constrained by stable and coherent conceptual structures that conflicted with an assumed unified scientific conception and therefore needed to be replaced. These researchers did not attend to the productive elements in students’ ideas about energy ...