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«ABSTRACT Title of Dissertation: THE DYNAMICS OF VARIABILITY IN INTRODUCTORY PHYSICS STUDENTS’ THINKING: EXAMPLES FROM KINEMATICS Brian W. Frank, ...»

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ABSTRACT

Title of Dissertation: THE DYNAMICS OF VARIABILITY IN INTRODUCTORY

PHYSICS STUDENTS’ THINKING: EXAMPLES FROM

KINEMATICS

Brian W. Frank, Doctor of Philosophy, 2009

Directed By: Research Assistant Professor, Rachel E. Scherr, Department of

Physics

Professor, David Hammer, Departments of Physics and

Curriculum & Instruction

Physics education research has long emphasized the need for physics instruction to address students’ existing intuitions about the physical world as an integral part of learning physics. Researchers, however, have not reached a consensus-view concerning the nature of this intuitive knowledge or the specific role that it does (or might) play in physics learning. While many early characterizations of student misconceptions cast students’ intuitive thinking as largely static, unitary in structure, and counter-productive for the purpose of learning correct physics, much of contemporary research supports a conceptualization of intuitive thought as dynamic, manifold in structure, and generative in the development of expertise. This dissertation contributes to ongoing inquiry into the nature of students’ intuitive thought and its role in learning physics through the pursuit of dynamic systems characterizations of student reasoning, with a particular focus on how students settle into and shift among multiple patterns of reasoning about motion.

In one thread of this research, simple experimental designs are used to demonstrate how individual students can be predictably biased toward and away from different ways of thinking about the same physical situation when specific parameters of questions posed to students are varied. I qualitatively model students’ thinking in terms of the activations and interactions among fine-grained intuitive knowledge and static features of the context. In a second thread of this research, case studies of more dynamic shifts in students’ conceptual reasoning are developed from videos of student discussions during collaborative classroom activities. These show multiple local stabilities of students’ thinking as well, with evidence of group-level dynamics shifting on the time scale of minutes.

This work contributes to existing research paradigms that aim to characterize student thinking in physics education in two important ways: (1) through the use of methods that allow for forms of empirical accountability that connect descriptive models of student thinking to experimental data, and (2) through the theoretical development of explanatory mechanisms that account for patterns in students’ reasoning at multiple levels of analysis.

THE DYNAMICS OF VARIABILITY IN INTRODUCTORY PHYSICS

STUDENTS’ THINKING: EXAMPLES FROM KINEMATICS

–  –  –

Advisory Committee:

Professor David Hammer, Chair Research Assistant Professor Rachel E. Scherr, Advisor Professor Edward F. Redish Professor Michael S. Fuhrer Professor Todd J. Cooke © Copyright by Brian Wallace Frank Acknowledgements This research discussed in this document has been funded in part by the National Science Foundation under Grants No. DUE 05-24987, No. DUE 03-41289, No. DUE 03-41333, and No. REC 0440113. Any opinions, conclusions, or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

Foremost, I would like to thank my advisors, Rachel Scherr and David Hammer, for not only providing me with the tremendous opportunity to join the Physics Education Research Group at the University of Maryland, but for providing me with the time and space to both pursue and struggle with my own intellectual pursuits.

Their patience, restraint, and compassion throughout all of this have been invaluable.

I would like to also thank the following people at Maryland and beyond who have all made substantial contributions to my intellectual development and emotional well-being: Andy Elby, Steve Kanim, Luanna Gomez, Joe Redish, Ayush Gupta, Luke Conlin, Renee Michelle Goertzen, Matty Lau, and Rosemary Russ.

Special thank goes to my entire family: Bethany, Biddy & Jan, Dave & Andrea, Goo & Kelly, Kapil, and Wizzy. Their support and encouragement is always there.

ii Table of Contents Acknowledgements

Table of Contents

List of Tables

List of Figures

Chapter 1: Introduction and Dissertation Overview

HISTORICAL AND CURRENT DIRECTIONS IN PHYSICS EDUCATION

The Substance of Student Thinking

Basic Research on Student Thinking

Curricular Orientations to Student Thinking

The Paradigm of Pre-Post Testing

Written Assessments in Physics Education

Reflections on Measurement

DISSERTATION OVERVIEW

Chapter 2: Review of Literature

ISSUES OF BOUNDARY AND CONSTITUENCY

CATCHING FLY BALLS: COGNITION IN TIME AND SPACE

COGNITIVE ASSEMBLIES IN TIME

Cognitive Assemblies in the Past

Structural Achievements and Acquisitions in Cognitive Development

Knowledge Frameworks and Misconceptions in Conceptual Change

Characteristics of Accounts Focusing on Past Assemblies

Cognitive Assemblies in Real Time





Dynamic Systems Approaches to Cognitive Development

Complex Knowledge Systems Approaches in Science Education

Characteristics of Accounts focusing on Real-time Assembly

Brief Summary

COGNITIVE ASSEMBLIES IN SPACE

Cognitive Assemblies in the Mind

Cognitive Assemblies in the World

Distributed Accounts of Socio-technological Systems

Situated Accounts of Participant Activity in Setting

Brief Summary

FOOTHOLD IDEAS FOR COGNITIVE ONTOLOGY

Cognitive Attributions of the Individual Mind

Structures and Processes

Methods of Identification

Cognitive Attributions in the World

Structures and Processes in the World

CHAPTER SUMMARY

Chapter 3: Models of Student Thinking about Motion

CHAPTER INTRODUCTION

RESEARCH ON STUDENT THINKING ABOUT MOTION

Evidence for and Accounts of Coherence

Existence of Naïve Theories of Motion

Development of Naïve Theories of Motion

Evidence for Variability and Context-dependence

Phenomenology of Variability

An Ontology for Variability and Systematicity

iii A SIMPLE MODEL FOR STUDENT THINKING ABOUT MOTION

Cognitive Elements and their Properties

More Distance Implies More Time

More Speed Implies Less Time

More Speed implies More Distance

Combining and Coordinating Intuitions

Applying the Model: Student Thinking about Oscillators

THEORETICAL APPLICATIONS OF THE MODEL

Exploratory Investigation

Designing a More Rigorous Study

Chapter 4: Experimental Measures of Variability

EXPERIMENTAL DESIGN AND MODEL-BASED PREDICTIONS

Experimental Design and Description of Surveys

The Horizontal Launch Question

The Vertical Toss Question

Model-based Predictions

Context for Research

PRIMARY ANALYSIS: STUDENT RESPONSES ACROSS CUES

Categorization of Student Answers

Across-Cue Analysis of Student Answers

Answers to Horizontal Launch Task

Answers to Vertical Toss Task

Summary of Primary Analysis

SECONDARY ANALYSIS: STUDENT EXPLANATIONS

Categorization of Written Explanations

Explanations on the Horizontal Launch Task

Explanations for Experiment 3 takes the Most Time

Explanations for Experiment 3 takes the Least Time

Explanations for All Experiments Take The Same Time

Other Student Explanations

Summary of Explanations for Horizontal Launch Task

Explanations on the Vertical Toss Task

Explanations for Second Toss Takes Less Time

Explanations for Second Toss Takes Most Time

Explanations for Second Toss Takes Same Time

Summary of Explanations to Vertical Toss Task

Summary of Secondary Analysis

TERTIARY ANALYSES: CONSISTENCY AND VARIABILITY

Across-Task Analysis of Student Answers

Newtonian Consistency

Naïve Theory Consistency

Within-Task Analysis of Student Explanations

Student Erasures and Scratched out Answers

Multiple Answers from Students

Summary of Tertiary Analysis

REFINEMENTS AND REFLECTIONS UPON THE MODEL

Student Reasoning about Speed and Gravity

Plausible Cognitive Structures

Cognitive Assemblies of Multiple Elements

Suggestions for Further Experimentation

Further Exploration of Conceptual Dynamics

Dynamics in Diverse Settings and Populations

Exploring Other Dynamics

CHAPTER SUMMARY

Chapter 5: Student Thinking in the Classroom

CHAPTER INTRODUCTION

iv ACCOUNTING FOR VARIABILITY AND STABILITY

Explanations in terms of the Structure of Knowledge

Explanations in terms of the Contexts that Support them

Brief summary

CONTEXT AND SETTING FOR RESEARCH

Instructional Setting

Tutorials as Instructional Setting

The Meaning of Speed Tutorial

Collection and Selection of Data

ANALYSIS OF FINE-GRAINED INTUITIONS

Intuitive Thinking about Time Ranking

More Distance Implies More Time

More Speed Implies Less time

Intuitive Thinking about Speed Ranking

More Speed implies more Distance

Other Students Responses for Speed Ranking

Brief Summary

ANALYSIS OF LOCAL STABILITIES IN STUDENT THINKING

Case Study 1, Part 1: Nora’s Initial Understanding

Case Study 2, Part 1: A Group’s Initial Understanding

Case Study 3, Part 1: Another Group’s Initial Understanding

Characterizing Students’ Initial Thinking

Similarities Across the Case Studies

A Plausible Account

A Finer-grained Account

Case Study 1, part 2: Nora’s Groupmates Disagree

The Other Students’ Thinking

Nora’s Continued Thinking

Case Study 2, part 2: Mark’s New Thinking

Features of their New Thinking

Case Study 3, Part 2: Rita Changes her Mind

Revisiting our Cognitive Accounts

Accounts of Students’ Initial Thinking

Accounting for Students’ Correct Thinking

Brief Summary

MECHANISMS CONTRIBUTING TO STABILITY

Knowledge Structure Mechanisms

Contextual Mechanisms

Implications

Implications of Polysemy as Stabilizing Students’ Thinking

Testable Implications for How Context Stabilizes Students’ Thinking

CHAPTER SUMMARY

Chapter 6: Dynamics Shifts Among Multiple Stabilities

CHAPTER INTRODUCTION

ANALYZING PATTERNS OF STUDENT BEHAVIOR

Brief Motivation

Brief Introduction to Case Study

Methodology for Identifying Patterns of Student Behavior

Underlying Methodological Framework

Categorizing Patterns of Student Behavior

Emerging Patterns of Behavior

Sources of Change and Couplings among Students’ Orientation

Sources of Change in Students’ Orientation

Coupling Among Students’ Behavior

Putting the Tool to Use for Analyzing Student Thinking

SCENE 1: THE DYNAMICS OF STUDENTS’ INITIAL THINKING

Presentation of Data

v Scene 1, Part 1: Moving the Strips to the Center

Scene 1, Part 2: More Distance Implies More Time

Scene 1, Part 3: Attention to the Physical Features

Scene 1, Part 4: Shifts and Recognition of Attention

Scene1, Part 5: Shorter Papers are Faster

Analysis of Students’ Thinking

Consistency with the Fine-grained Cognitive Account

Consistency with Account of Contextual Mechanisms

Dynamics of the Extended Cognitive System

Brief Summary

SCENE 2: THE DYNAMICS OF STUDENTS’ NEW THINKING

Presentation of Data

Scene 2, Part 1: Deconstructing the Side-by-Side Arrangement

Scene 2, Part 2: A New Pattern of Orientation

Analysis of Students’ Thinking

Consistency with the Fine-grained Cognitive Account

Dynamics of the Extended Cognitive System

Reasons to be Skeptical of Stable Change

SCENE 3: THE PERSISTING INFLUENCE OF CONTEXT

Presentation of Data

Scene 3, Part 1: The Impact of a New Object

Scene 3, Part 2: Reorienting to Prior Written Artifacts

Analysis of Students’ Thinking

Variability in Individual Students’ Thinking

Dynamics of the Extended Cognitive System

SUMMARY AND IMPLICATIONS OF CASE STUDY

Summary of Case Study

Implications for Student Learning and Instruction

CHAPTER SUMMARY

Chapter 7: Dissertation Summary and Future Directions

DISSERTATION SUMMARY

FUTURE DIRECTIONS

Bibliography

–  –  –

vii List of Figures Figure 1: Horizontal Launch Question in Distance-cueing Survey

Figure 2: Horizontal Launch Question in Speed-cueing Survey

Figure 3: Vertical Toss Question in Distance-cueing Survey

Figure 4: Vertical Toss Question in Speed-cueing Survey

Figure 5: Distributions of Incorrect Answers to the Horizontal Launch (N= 318).......... 61 Figure 6: Distribution of Wrong Answers on the Vertical Toss Question (N= 309)........ 62 Figure 7: Difference in the Frequency of Student Answers Across Cuing Conditions.... 63 Figure 8: Locations of Students

Figure 9: Example #1 of Student Behavior

Figure 10: Example #2 of Student Behavior

Figure 11: Example #3 of Student Behavior

Figure 12: Example #4 of Student Behavior

Figure 13: Example of Student Orienting to Other Student Behavior

Figure 14: Example of Students Reorienting after Verbal Statement

Figure 15: Example of Students Orienting to Objects

Figure 16: Students Collectively Oriented to Worksheets

Figure 17: Students Collectively Oriented to the Center of the Table

Figure 18: Students Mutually Oriented to Each Other

Figure 19: Tickertape Strips Located at Center of Table

Figure 20: Tickertape Strips in Side-by-Side Arrangement

Figure 21: Illustration of John Spreading his Fingers over a Strip

Figure 22: Illustration of Paul Indicating a Length between Two Fingers

Figure 23: Illustration of Beth Indicating a Length on a Strip



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