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Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics
A good understanding of how students understand physics is of great importance for developing and delivering effective instructions. This research is an attempt to develop a coherent theoretical and mathematical framework to model the student learning of physics. The theoretical foundation is based on useful ideas from theories in cognitive science, education, and physics education. The emphasis of this research is made on the development of a mathematical representation to model the important mental elements and the dynamics of these elements, and on numerical algorithms that allow quantitative evaluations of conceptual learning in physics.
Model analysis is used to determine common student models. The theory is applied to student understanding of quantum mechanics. Multiple-choice instruments to probe student models and a set of quantum tutorials are developed.
University:
University of Maryland
Academic Department: Department of Physics Pages 260 
16 supplemental documents are available
Chapter 1: Physics Education: the Physics of Education in Education of PhysicsChapter 1 provides a context for this research study within Physics Education Research. download 46kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Chapter 2: Student Models of PhysicsChapter 2 introduces the model of student learning of physics. A mathematical representation is developed for the physical models and student model states. download 235kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Chapter 3: Model Analysis Algorithms I: The Concentration FactorThis chapter presents a method to study the structure of student responses in a multiple-choice test, providing information on the distribution of student responses. The results are used to analyze the state of student mental models. Sample applications with FCI data confirm the method. download 302kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Chapter 4: Model Analysis Algorithms II: Model EstimationThis chapter presents an algorithm for quantitative evaluations of student mental models that goes beyond simple scores. This algorithm can provide better information about student understandings and how to improve instructions. A great deal of information can be … download 426kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Chapter 5: Refinements and ExtensionsThis chapter contains examples of student model analysis that require modifcations and additions to the algorithms presented previously. Mixed model states, coherence of responses, and model triggers are explored. download 512kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Chapter 6: Model Based Research on Student Difficulties with Quantum MechanicsThis chapter introduces studies on student difficulties in learning Quantum Mechanics. The model evaluation process is used to investigate student understanding of classical pre-requisites for quantum mechanics and important quantum concepts. download 89kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Chapter 7: Student Difficulties with Classical Pre-requisitesThis chapter presents results of studies of student understanding of potential energy diagrams, total energy, and probability in classical mechanics. This background is important for the quantum mechanics. Tutorials are presented to help students with these topics, although they remain difficult. download 173kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Chapter 8: Student Models of Quantum MechanicsThis chapter presents research on several common student models in quantum mechanics. Instructional approaches and a multiple choice test to test them are described. download 226kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Chapter 9: Summary and SpeculationsThis chapter summarizes the new theory of student models and the numerical methods developed. download 120kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Appendix A: FCI and FMCE testThe appendix provides two standard concept tests used in this research. download 189kb .pdf Published: January 1, 1999
Appendix B: Supplemental Calculations and Simulations for the Concentration FactorThis appendix provides examples of the student model analysis. download 138kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Appendix C: Supplemental Calculations for Model Evaluations and a New Multiple-Choice Instrument on Newton III with Isolated Physical FeaturesThis appendix gives an example calculation involving multi-model states. A concept survey on Newton's Third Law is also provided. download 247kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Appendix D: Questions to Probe the Student Understandings on Classical Pre-requisites of Quantum MechanicsThis appendix contains concept questions on classical and quantum mechanics. download 63kb .pdf Published: January 1, 1999 Rights: © Lei Bao
Appendix E: Quantum TutorialsThis appendix contains three tutorials on quantum mechanics and classical pre-requisites for quantum mechanics. Topics include Potential Energy Diagrams, Classical Probability, and LED's - Energy Band Structure. download 139kb .pdf Published: January 1, 1999 Rights: © Lei Bao
BibliographyBibliography for the research work. download 33kb .pdf Published: January 1, 1999 Rights: © Lei Bao
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<a href="https://www.compadre.org/portal/items/detail.cfm?ID=4760">Bao, Lei. "Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics." University of Maryland, 1999.</a>
AIP Format
L. Bao, , University of Maryland, 1999, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=4760&DocID=188).
AJP/PRST-PER
L. Bao, Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics, University of Maryland, 1999, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=4760&DocID=188>.
APA Format
Bao, L. (1999, January 1). Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics (University of Maryland, 1999). Retrieved November 12, 2025, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=4760&DocID=188
Chicago Format
Bao, Lei. "Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics." University of Maryland, 1999. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=4760&DocID=188 (accessed 12 November 2025).
MLA Format
Bao, Lei. "Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics." 1 Jan. 1999. University of Maryland, 1999. 12 Nov. 2025 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=4760&DocID=188>.
BibTeX Export Format
@phdthesis{
Author = "Lei Bao",
Title = {Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics},
School = {University of Maryland},
Month = {January},
Year = {1999}
}
Refer Export Format
%A Lei Bao %T Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics %D January 1, 1999 %P 260 %I University of Maryland %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=4760&DocID=188 %O Department of Physics %O application/pdf
EndNote Export Format
%0 Thesis %A Bao, Lei %D January 1, 1999 %T Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics %B Department of Physics %I University of Maryland %P 260 %8 January 1, 1999 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=4760&DocID=188 Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.
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The AIP Style presented is based on information from the AIP Style Manual. The APA Style presented is based on information from APA Style.org: Electronic References. The Chicago Style presented is based on information from Examples of Chicago-Style Documentation. The MLA Style presented is based on information from the MLA FAQ. |
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