<p>Student learning in upper-division physics courses is a growing area of research in the field of Physics Education. Developing effective new curricular materials and pedagogical techniques to improve student learning in upper-division courses requires knowledge of both what material students struggle with and what curricular approaches help to overcome these struggles. To facilitate the course transformation process for one specific content area -- upper-division electrostatics -- this thesis presents two new methodological tools: (1) an analytical framework designed to investigate students' struggles with the advanced physics content and mathematically sophisticated tools/techniques required at the junior and senior level, and (2) a new multiple-response conceptual assessment designed to measure student learning and assess the effectiveness of different curricular approaches. We first describe the development and theoretical grounding of a new analytical framework designed to characterize how students use mathematical tools and techniques during physics problem solving. We apply this framework to investigate student difficulties with three specific mathematical tools used in upper-division electrostatics: multivariable integration in the context of Coulomb's law, the Dirac delta function in the context of expressing volume charge densities, and separation of variables as a technique to solve Laplace's equation. We find a number of common themes in students' difficulties around these mathematical tools including: recognizing when a particular mathematical tool is appropriate for a given physics problem, mapping between the specific physical context and the formal mathematical structures, and reflecting spontaneously on the solution to a physics problem to gain physical insight or ensure consistency with expected results. We then describe the development of a novel, multiple-response version of an existing conceptual assessment in upper-division electrostatics courses. The goal of this new version is to provide an easily-graded electrostatics assessment that can potentially be implemented to investigate student learning on a large scale. We show that student performance on the new multiple-response version exhibits a significant degree of consistency with performance on the free-response version, and that it continues to provide significant insight into student reasoning and student difficulties. Moreover, we demonstrate that the new assessment is both valid and reliable using data from upper-division physics students at multiple institutions. Overall, the work described in this thesis represents a significant contribution to the methodological tools available to researchers and instructors interested in improving student learning at the upper-division level.

<p> This study seeks to extend the work done by Brasell and Beichner on the effect of the Microcomputer-Based Laboratory (MBL) on the quality of instruction in kinematics.</p><p> In this thesis, we investigate the idea that the automatic graphing process involved in a typical kinematics MBL has a black box effect on student understanding. In order to make students focus on the values that create the graph, a group of students first experienced kinematic graphs by drawing by hand before performing the MBL as normal. After testing this treatment with 246 students (141 received treatment, 105 were kept as a control), the results showed that there was a slightly positive but insignificant difference in gains between the two groups (<i>p</i> = 0.362), as measured by Beichner's Test for Understanding Graphs in Kinematics (TUG-K).</p>

<p>The role of autonomy in the student experience in a large-enrollment undergraduate introductory physics course was studied from a Self-Determination Theory perspective with two studies. Study I, a correlational study, investigated whether certain aspects of the student experience correlated with how autonomy supportive (vs. controlling) students perceived their instructors to be. An autonomy supportive instructor acknowledges students' perspectives, feelings, and perceptions and provides students with information and opportunities for choice, while minimizing external pressures. It was found that the degree to which students perceived their instructors as autonomy supportive was positively correlated with student interest and enjoyment in learning physics (beta=0.31***) and negatively correlated with student anxiety about taking physics (beta=-0.23**). It was also positively correlated with how autonomous (vs. controlled) students' reasons for studying physics became over the duration of the course (i.e., studying physics more because they wanted to vs. had to; beta=0.24***). This change in autonomous reasons for studying physics was in turn positively correlated with student performance in the course (beta=0.17*). Additionally, the degree to which students perceived their instructors as autonomy supportive was directly correlated with performance for those students entering the course with relatively autonomous reasons for studying physics (beta=0.25**). In summary, students who perceived their instructors as more autonomy supportive tended to have a more favorable experience in the course. If greater autonomy support was in fact the cause of a more favorable student experience, as suggested by Self-determination Theory and experimental studies in other contexts, these results would have implications for instruction and instructor professional development in similar contexts. I discuss these implications. Study II, an experimental study, investigated the effect, on the student experience, of the number of opportunities for choice built into the course format. This was done by comparing two sets of classes. In one set of classes, students spent each class period working through a required series of activities. In the other set of classes, with additional choice, students were free to choose what to work on during nearly half of each class. It was found that the effect of additional choice on student interest and enjoyment in learning physics was significantly different for men vs. women, with a Cohen's d of 0.62 (0.16-1.08; 95% CI). Men became somewhat more interested with additional choice and women became less interested. This gender difference in interest and enjoyment as a result of additional choice could not be accounted for by differences in performance. It was also found that only in classes with additional choice did performance in the course correlate with the degree to which students reasons for studying physics became more autonomous during the quarter (beta=0.30*). I discuss the implications that these effects of additional choice have for instruction and course design in similar contexts.

<p>This dissertation presents the results of an experiment that measured the learning outcomes associated with three different pedagogical approaches to introductory physics labs. These three pedagogical approaches presented students with the same apparatus and covered the same physics content, but used different lab manuals to guide students through distinct cognitive processes in conducting their laboratory investigations. We administered post-tests containing multiple-choice conceptual questions and free-response quantitative problems one week after students completed these laboratory investigations. In addition, we collected data from the laboratory practical exam taken by students at the end of the semester. Using these data sets, we compared the learning outcomes for the three curricula in three dimensions of ability: conceptual understanding, quantitative problem-solving skill, and laboratory skills. </p><p> Our three pedagogical approaches are as follows. Guided labs lead students through their investigations via a combination of Socratic-style questioning and direct instruction, while students record their data and answers to written questions in the manual during the experiment. Traditional labs provide detailed written instructions, which students follow to complete the lab objectives. Open labs provide students with a set of apparatus and a question to be answered, and leave students to devise and execute an experiment to answer the question. In general, we find that students performing Guided labs perform better on some conceptual assessment items, and that students performing Open labs perform significantly better on experimental tasks. Combining a classical test theory analysis of post-test results with in-lab classroom observations allows us to identify individual components of the laboratory manuals and investigations that are likely to have influenced the observed differences in learning outcomes associated with the different pedagogical approaches. Due to the novel nature of this research and the large number of item-level results we produced, we recommend additional research to determine the reproducibility of our results. </p><p> Analyzing the data with item response theory yields additional information about the performance of our students on both conceptual questions and quantitative problems. We find that performing lab activities on a topic does lead to better-than-expected performance on some conceptual questions regardless of pedagogical approach, but that this acquired conceptual understanding is strongly context-dependent. The results also suggest that a single &ldquo;Newtonian reasoning ability&rdquo; is inadequate to explain student response patterns to items from the Force Concept Inventory. We develop a framework for applying polytomous item response theory to the analysis of quantitative free-response problems and for analyzing how features of student solutions are influenced by problem-solving ability. Patterns in how students at different abilities approach our post-test problems are revealed, and we find hints as to how features of a free-response problem influence its item parameters. The item-response theory framework we develop provides a foundation for future development of quantitative free-response research instruments. </p><p> Chapter 1 of the dissertation presents a brief history of physics education research and motivates the present study. Chapter 2 describes our experimental methodology and discusses the treatments applied to students and the instruments used to measure their learning. Chapter 3 provides an introduction to the statistical and analytical methods used in our data analysis. Chapter 4 presents the full data set, analyzed using both classical test theory and item response theory. Chapter 5 contains a discussion of the implications of our results and a data-driven analysis of our experimental methods. Chapter 6 describes the importance of this work to the field and discusses the relevance of our research to curriculum development and to future work in physics education research. </p>

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008. / Source: Dissertation Abstracts International, Volume: 69-05, Section: B, page: 3041. Adviser: Douglas H. Beck. Includes bibliographical references (leaves 182-185) Available on microfilm from Pro Quest Information and Learning.

<p> Although a large part the Physics Education Research (PER) literature investigates students' conceptual understanding in physics, these investigations focus on qualitative, conceptual reasoning. Even in modeling expert problem solving, attention to conceptual understanding means a focus on initial qualitative analysis of the problem; the equations are typically conceived of as tools for "plug-and-chug" calculations. In this dissertation, I explore the ways that undergraduate physics students make conceptual sense <i>of physics equations</i> and the factors that support this type of reasoning through three separate studies.</p><p> In the first study, I investigate how students' can understand physics equations intuitively through use of a particular class of cognitive elements, <i> symbolic forms</i> (Sherin, 2001). Additionally, I show how students leverage this intuitive, conceptual meaning of equations in problem solving. By doing so, these students avoid algorithmic manipulations, instead using a heuristic approach that leverages the equation in a conceptual argument. </p><p> The second study asks the question why some students use symbolic forms and others don't. Although it is possible that students simply lack the knowledge required, I argue that this is not the only explanation. Rather, symbolic forms use is connected to particular <i>epistemological stances,</i> in-the-moment views on what kinds of knowledge and reasoning are appropriate in physics. Specifically, stances that value <i>coherence</i> between formal, mathematical knowledge and intuitive, conceptual knowledge are likely to support symbolic forms use. Through the case study of one student, I argue that both reasoning with equations and epistemological stances are dynamic, and that shifts in epistemological stance can produce shifts in whether symbolic forms are used to reason with equations. </p><p> The third study expands the focus to what influences how students reason with equations across disciplinary problem contexts. In seeking to understand differences in how the same student reasons on two similar problems in calculus and physics, I show two factors, beyond the content or structure of the problems, that can help explain why reasoning on these two problems would be so different. This contributes to an understanding of what can support or impede transfer of content knowledge across disciplinary boundaries.</p>