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
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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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Chapter 1 provides a context for this research study within Physics Education Research.

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Chapter 2 introduces the model of student learning of physics. A mathematical representation is developed for the physical models and student model states.

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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.

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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.

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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.

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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.

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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.

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This chapter presents research on several common student models in quantum mechanics. Instructional approaches and a multiple choice test to test them are described.

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This chapter summarizes the new theory of student models and the numerical methods developed.

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The appendix provides two standard concept tests used in this research.

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This appendix provides examples of the student model analysis.

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This appendix gives an example calculation involving multi-model states. A concept survey on Newton's Third Law is also provided.

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This appendix contains concept questions on classical and quantum mechanics.

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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.

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Bibliography for the research work.

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