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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.
Published January 1, 1999
Last Modified December 17, 2006
This file is included in the full-text index.
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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
This file is included in the full-text index.
This file has previous versions.
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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
This file is included in the full-text index.
This file has previous versions.
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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
This file is included in the full-text index.
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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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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Chapter 9: Summary and Speculations
This chapter summarizes the new theory of student models and the numerical methods developed.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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Appendix A: FCI and FMCE test
The appendix provides two standard concept tests used in this research.
Published January 1, 1999
Last Modified February 24, 2016
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Appendix B: Supplemental Calculations and Simulations for the Concentration Factor
This appendix provides examples of the student model analysis.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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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.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
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Bibliography
Bibliography for the research work.
Released under a © Lei Bao
Published January 1, 1999
Last Modified February 24, 2016
This file has previous versions.