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M.S. Physics and Astronomy, University of Pittsburgh, 2005 REFLECTION ON PROBLEM SOLVING IN INTRODUCTORY AND ADVANCED PHYSICS by Andrew J. Mason B.S. Physics, State University of New York at Buffalo, 2004 M.S. Physics and Astronomy, University of Pittsburgh, 2005 Submitted to the Graduate Faculty of the Department of Physics and Astronomy in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2009 UNIVERSITY OF PITTSBURGH SCHOOL OF ARTS AND SCIENCES DEPARTMENT OF PHYSICS AND ASTRONOMY This dissertation was presented by Andrew J. Mason It was defended on July 7, 2009 and approved by Dissertation Advisor: Dr. Chandralekha Singh, Associate Professor, Department of Physics and Astronomy Dr. Peter F. M. Koehler, Professor, Department of Physics and Astronomy Dr. Adam Leibovich, Associate Professor, Department of Physics and Astronomy Dr. Robert P. Devaty, Associate Professor, Department of Physics and Astronomy Dr. Christian Schunn, Associate Professor, Department of Psychology ii Copyright © by Andrew J. Mason 2009 iii REFLECTION ON PROBLEM SOLVING IN INTRODUCTORY AND ADVANCED PHYSICS Andrew J. Mason, PhD University of Pittsburgh, 2009 Reflection is essential in order to learn from problem solving. This thesis explores issues related to how reflective students are and how we can improve their capacity for reflection on problem solving. We investigate how students naturally reflect in their physics courses about problem solving and evaluate strategies that may teach them reflection as an integral component of problem-solving. Problem categorization based upon similarity of solution is a strategy to help them reflect about the deep features of the problems related to the physics principles involved. We find that there is a large overlap between the introductory and graduate students in their ability to categorize. Moreover, introductory students in the calculus-based courses performed better categorization than those in the algebra-based courses even though the categorization task is conceptual. Other investigations involved exploring if reflection could be taught as a skill on individual and group levels. Explicit self-diagnosis in recitation investigated how effectively students could diagnose their own errors on difficult problems, how much scaffolding was necessary for this purpose, and how effective transfer was to other problems employing similar principles. Difficulty in applying physical principles and difference between the self-diagnosed and transfer problems affected performance. We concluded that a sustained intervention is required to learn effective problem-solving strategies. Another study involving reflection on problem solving with peers suggests that those who reflected with peers drew more diagrams and had a larger gain from the midterm to final exam. Another study in quantum mechanics involved iv giving common problems in midterm and final exams and suggested that advanced students do not automatically reflect on their mistakes. Interviews revealed that even advanced students often focus mostly on exams rather than learning and building a robust knowledge structure. A survey was developed to further evaluate students’ attitudes and approaches towards problem solving. The survey responses suggest that introductory students and even graduate students have different attitudes and approaches to problem solving on several important measures compared to physics faculty members. Furthermore, responses to individual survey questions suggest that expert and novice attitudes and approaches to problem solving may be more complex than naively considered. v TABLE OF CONTENTS PREFACE - ACKNOWLEDGMENTS ............................................................................... XXII 1.0 INTRODUCTION ........................................................................................................ 1 1.1 PROBLEM SOLVING: DEFINITION ............................................................. 2 1.2 INFLUENCE FROM COGNITIVE SCIENCE: THE CONCEPT OF MEMORY ............................................................................................................................. 3 1.2.1 Schemata........................................................................................................... 4 1.2.2 Chunking and Cognitive Load during Problem Solving ............................. 4 1.3 METACOGNITION ............................................................................................ 7 1.3.1 Metacognition, heuristics, and the problem-solving process ....................... 7 1.4 PHYSICIST’S PERSPECTIVE: AN OVERVIEW OF PROBLEM SOLVING IN PER ............................................................................................................... 9 1.5 REFLECTION ON PROBLEM SOLVING ................................................... 13 1.5.1 The Cognitive Apprenticeship Model .......................................................... 14 1.6 A STUDY OF REFLECTION IN THE CONTEXT OF PROBLEM SOLVING ............................................................................................................................ 16 1.7 CHAPTER REFERENCES .............................................................................. 18 2.0 CATEGORIZATION REVISITED: ASSESSING STUDENT ENTERPRISE IN INTRODUCTORY PHYSICS ................................................................................................... 25 vi 2.1 ABSTRACT ........................................................................................................ 25 2.2 INTRODUCTION ............................................................................................. 26 2.2.1 Goals and Motivation .................................................................................... 27 2.3 CATEGORIZATION TASK AND DETERMINATION OF GOOD CATEGORIES ................................................................................................................... 28 2.4 RESULTS ........................................................................................................... 35 2.4.1 Dependence of Categorization on the Nature of Problems ........................ 36 2.4.2 Comparison between the Algebra-Based and Calculus-Based Introductory Physics Classes .................................................................................... 40 2.4.3 Comparison of Calculus-Based Introductory Students with Physics Graduate Students ..................................................................................................... 51 2.4.4 Correlation between Categorization and Course Grade ........................... 56 2.4.5 Interviews with Individual Students ............................................................ 56 2.5 SUMMARY AND CONCLUSIONS ................................................................ 63 2.6 ACKNOWLEDGMENTS ................................................................................. 67 2.7 REFERENCES .................................................................................................. 67 3.0 SELF-DIAGNOSIS IN INTRODUCTORY PHYSICS .......................................... 70 3.1 ABSTRACT ........................................................................................................ 70 3.2 STUDY 1: SELF-DIAGNOSIS AND TRANSFER FOR AN ATYPICAL QUIZ 71 3.2.1 Introduction ................................................................................................... 71 3.2.2 Rationale for Self-Diagnosis Tasks .............................................................. 74 3.2.3 Experimental Setup ....................................................................................... 79 vii 3.2.3.1 Sample .................................................................................................. 79 3.2.3.2 Interventions and Control .................................................................. 80 3.2.4 Analysis Tools ................................................................................................ 81 3.2.4.1 Structure of the rubric ........................................................................ 81 3.2.4.2 Scoring rubric for quiz 6 .................................................................... 84 3.2.5 Results ............................................................................................................. 88 3.2.5.1 Self-diagnosis - Physics ....................................................................... 88 3.2.5.2 Self-diagnosis - Presentation .............................................................. 90 3.2.5.3 Self-diagnosis and Prior Knowledge ................................................. 93 3.2.6 The Midterm Problem................................................................................... 94 3.2.6.1 Midterm Physics Scores ...................................................................... 95 3.2.6.2 Physics Self-Diagnosis vs. Midterm Performance ............................ 98 3.2.6.3 Midterm Presentation Scores ............................................................. 98 3.3 PART 2 OF THE STUDY: A MORE CONVENTIONAL QUIZ PROBLEM 100 3.3.1 Introduction ................................................................................................. 100 3.3.2 Sample Problem: Quiz Problem Used for Self-Diagnosis ........................ 102 3.3.3 The Rubric Adapted .................................................................................... 103 3.3.3.1 Specific Knowledge: Categories and Subcategories ...................... 103 3.3.3.2 Scoring ...............................................................................................
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