Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics Documents
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Dynamics of Student Modeling: A Theory, Algorithms, and Application to Quantum Mechanics
written by
Lei Bao
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.
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Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Primary Documents (16)
Table of Contents
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.
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© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Chapter 1: Physics Education: the Physics of Education in Education of Physics
Chapter 1 provides a context for this research study within Physics Education Research.
- Download 1_chapter1.pdf - 46kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Chapter 2: Student Models of Physics
Chapter 2 introduces the model of student learning of physics. A mathematical representation is developed for the physical models and student model states.
- Download 2_chapter2.pdf - 235kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Chapter 3: Model Analysis Algorithms I: The Concentration Factor
This 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 3_chapter3.pdf - 302kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Chapter 4: Model Analysis Algorithms II: Model Estimation
This 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 retained for easy extraction and use. Graphic representations make the results much easier to understand.
- Download 4_chapter4.pdf - 426kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Chapter 5: Refinements and Extensions
This 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 5_chapter5.pdf - 512kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Chapter 6: Model Based Research on Student Difficulties with Quantum Mechanics
This 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 6_chapter6.pdf - 89kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Chapter 7: Student Difficulties with Classical Pre-requisites
This 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 7_chapter7.pdf - 173kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Chapter 8: Student Models of Quantum Mechanics
This chapter presents research on several common student models in quantum mechanics. Instructional approaches and a multiple choice test to test them are described.
- Download 8_chapter8.pdf - 226kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Chapter 9: Summary and Speculations
This chapter summarizes the new theory of student models and the numerical methods developed.
- Download 9_chapter9.pdf - 120kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
Appendix A: FCI and FMCE test
The appendix provides two standard concept tests used in this research.
- Download Appendix_A.pdf - 189kb Adobe PDF Document
Published January 1, 1999
Last Modified December 17, 2006
Appendix B: Supplemental Calculations and Simulations for the Concentration Factor
This appendix provides examples of the student model analysis.
- Download Appendix_B.pdf - 138kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
Appendix C: Supplemental Calculations for Model Evaluations and a New Multiple-Choice Instrument on Newton III with Isolated Physical Features
This appendix gives an example calculation involving multi-model states. A concept survey on Newton's Third Law is also provided.
- Download Appendix_C.pdf - 247kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
Appendix D: Questions to Probe the Student Understandings on Classical Pre-requisites of Quantum Mechanics
This appendix contains concept questions on classical and quantum mechanics.
- Download Appendix_D.pdf - 63kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
Appendix E: Quantum Tutorials
This 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 Appendix_E.pdf - 139kb Adobe PDF Document
© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
Bibliography
Bibliography for the research work.
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© Lei Bao
Published January 1, 1999
Last Modified December 17, 2006
