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.

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.

© 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.

© 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.

© 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.

© 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.

© 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.

© 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.

© 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.

© 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.

© 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.

© 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.

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.

© 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.

© 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.

© 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.

© Lei Bao

Published January 1, 1999
Last Modified December 17, 2006

Bibliography 

Bibliography for the research work.

© Lei Bao

Published January 1, 1999
Last Modified December 17, 2006