A Grounded Theory Investigation of Thinking and Reasoning with Multiple

A Grounded Theory Investigation of Thinking and Reasoning with Multiple

Representational Systems for Epistemological Change in Introductory Physics

Submitted by

Clark Henson Vangilder

 

 

 

 

 

 

 

A Dissertation Presented in Partial Fulfillment

of the Requirements for the Degree

Doctor of Philosophy in Psychology

 

 

 

 

 

 

Grand Canyon University

Phoenix, Arizona

February 23, 2016

 

 

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GRAND CANYON UNIVERSITY

 

A Grounded Theory Investigation of Thinking and Reasoning with Multiple

Representational Systems for Epistemological Change in Introductory Physics

 

I verify that my dissertation represents original research, is not falsified or plagiarized,

and that I have accurately reported, cited, and referenced all sources within this

manuscript in strict compliance with APA and Grand Canyon University (GCU)

guidelines. I also verify my dissertation complies with the approval(s) granted for this

research investigation by GCU Institutional Review Board (IRB).

 

__________________________________________February 8, 2016 Clark Henson Vangilder Date

 

 

 

 

 

 

Abstract

Conceptual and epistemological change work in concert under the influence of

representational systems, and are employed by introductory physics (IP) students in the

thinking and reasoning that they demonstrate in various modelling and problem-solving

processes. A grounded theory design was used to qualitatively assess how students used

multiple representational systems (MRS) in their own thinking and reasoning along the

way to personal epistemological change. This study was framed by the work of Piaget and

other cognitive theorists and conducted in a college in Arizona; the sample size was 44.

The findings herein suggest that thinking and reasoning are distinct processes that handle

concepts and conceptual frameworks in different ways, and thus a new theory for the

conceptual framework of thinking and reasoning is proposed. Thinking is defined as the

ability to construct a concept, whereas reasoning is the ability to construct a conceptual

framework (build a model). A taxonomy of conceptual frameworks encompasses thinking

as a construct dependent on building a model, and relies on the interaction of at least four

different types of concepts during model construction. Thinking is synonymous with the

construction of conceptual frameworks, whereas reasoning is synonymous with the

coordination of concepts. A new definition for understanding as the ability to relate

conceptual frameworks (models) was also created as an extension of the core elements of

thinking and reasoning about the empirically familiar regularizes (laws) that are part of

Physics.

Keywords: thinking, reasoning, understanding, concept, conceptual framework,

personal epistemology, epistemological change, conceptual change, representational

system, introductory physics, model, modeling, physics.

 

 

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Dedication

This work is dedicated to my marvelous wife, Gia Nina Vangilder. Above all

others, she has sacrificed much during the journey to my Ph.D. Her unwavering love and

loyalty transcend the practical benefits of her proofreading assistance over the years, as

well as other logistical maneuverings pertaining to our family enduring the time

commitment that such an endeavor requires of me personally.

You are amazing Gia, and I love you more than mere words can describe!

Most importantly, I thank God Himself for putting my mind in a wonderful

universe so rich with things to explore.

 

 

 

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Acknowledgments

I am exceptionally pleased to have worked with the committee that has approved

this document—Dr. Racheal Stimpson (Chair), Dr. Pat D’Urso (Methodologist), and Dr.

Rob MacDuff (Content Expert). Each one of you has contributed to my success in your

own special way, and with your own particular talents.

I am blessed to have walked this path under your guidance.

Honorable mention is given Dr. Rob MacDuff, whose influence and collaboration

over the years is valuable beyond measure or words. Neither of us would be where we are

at without the partnership of theory and practice that has defined our collaboration for

more than a decade now. I am truly blessed to know you and work with you.

 

 

 

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Table of Contents

List of Tables ……………………………………………………………………………………………………. xiii

List of Figures …………………………………………………………………………………………………… xiv

Chapter 1: Introduction to the Study …………………………………………………………………………1

Introduction ……………………………………………………………………………………………………..1

Background of the Study …………………………………………………………………………………..3

Personal epistemology. ……………………………………………………………………………..5

Representational Systems. …………………………………………………………………………6

Problem Statement ……………………………………………………………………………………………8

Purpose of the Study …………………………………………………………………………………………9

Research Questions and Phenomenon ……………………………………………………………….10

Qualitative Research Questions ………………………………………………………………………..11

Advancing Scientific Knowledge ……………………………………………………………………..12

Significance of the Study …………………………………………………………………………………14

Rationale for Methodology ………………………………………………………………………………16

Nature of the Research Design for the Study ………………………………………………………17

Definition of Terms…………………………………………………………………………………………19

Assumptions, Limitations, Delimitations …………………………………………………………..20

Summary and Organization of the Remainder of the Study ………………………………….21

Chapter 2: Literature Review …………………………………………………………………………………23

Introduction to the Chapter and Background to the Problem ………………………………..23

Theoretical Foundations and Conceptual Framework ………………………………………….29

Personal epistemology …………………………………………………………………………….29

 

 

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Thinking and reasoning ……………………………………………………………………………30

Building a conceptual model for this study ………………………………………………..34

Representational systems …………………………………………………………………………36

Self-efficacy, self-regulation, and journaling ……………………………………………..38

Convergence of conceptual and theoretical foundations ………………………………39

Review of the Literature ………………………………………………………………………………….40

A brief history of personal epistemology research ………………………………………40

A brief history of assessment on personal epistemology ………………………………43

Connections between conceptual change and personal epistemology …………….48

Conceptual change in introductory physics ………………………………………………..51

Personal epistemologies and learning physics …………………………………………….55

Thinking and reasoning in introductory physics ………………………………………….64

Study methodology …………………………………………………………………………………68

Study instruments and measures ……………………………………………………………….71

Summary ……………………………………………………………………………………………………….72

Chapter 3: Methodology ……………………………………………………………………………………….76

Introduction ……………………………………………………………………………………………………76

Statement of the Problem …………………………………………………………………………………77

Research Questions …………………………………………………………………………………………78

Research Methodology ……………………………………………………………………………………80

Research Design……………………………………………………………………………………………..81

Population and Sample Selection………………………………………………………………………83

Instrumentation and Sources of Data …………………………………………………………………84

 

 

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Classroom activities and assessment instrument …………………………………………86

Validity …………………………………………………………………………………………………………91

Reliability ………………………………………………………………………………………………………93

Data Collection and Management ……………………………………………………………………..94

Data Analysis Procedures ………………………………………………………………………………..97

Preparation of data ………………………………………………………………………………….97

Data analysis ………………………………………………………………………………………….98

Ethical Considerations …………………………………………………………………………………….99

Limitations and Delimitations …………………………………………………………………………100

Summary ……………………………………………………………………………………………………..101

Chapter 4: Data Analysis and Results ……………………………………………………………………105

Introduction ………………………………………………………………………………………………….105

Descriptive Data……………………………………………………………………………………………106

Data Analysis Procedures ………………………………………………………………………………109

Coding schemes ……………………………………………………………………………………110

Triangulation of data ……………………………………………………………………………..113

Results …………………………………………………………………………………………………………116

PEP Analysis. ……………………………………………………………………………………….116

Qualitative analysis. ………………………………………………………………………………121

Analysis of the physics and reality activity journals…………………………………..135

Consideration of research questions with current results. ……………………………136

Combined analysis of the remaining study activities ………………………………….137

Other assessments. ………………………………………………………………………………..143

 

 

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Summary ……………………………………………………………………………………………………..144

Chapter 5: Summary, Conclusions, and Recommendations ……………………………………..147

Introduction ………………………………………………………………………………………………….147

Summary of the Study …………………………………………………………………………………..149

Summary of Findings and Conclusion ……………………………………………………………..151

Research Question 1………………………………………………………………………………152

Research Question 2………………………………………………………………………………162

Definitions ……………………………………………………………………………………………164

Predictions. …………………………………………………………………………………………..171

Suggestions for TRU Learning Theory use ………………………………………………171

Implications………………………………………………………………………………………………….172

Theoretical implications. ………………………………………………………………………..172

Practical implications …………………………………………………………………………….174

Future implications ……………………………………………………………………………….175

Strengths and weaknesses ………………………………………………………………………176

Recommendations …………………………………………………………………………………………177

Recommendations for future research. …………………………………………………….177

Recommendations for future practice. ……………………………………………………..178

References …………………………………………………………………………………………………………181

Appendix A. Site Authorization Form …………………………………………………………………..203

Appendix B. Student Consent Form ……………………………………………………………………..204

Appendix C. GCU D-50 IRB Approval to Conduct Research ………………………………….205

Appendix D. Psycho-Epistemological Profile (PEP)……………………………………………….206

 

 

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Appendix E. What is Physics? What is Reality? Is Physics Reality? …………………………209

Appendix F. Numbers Do Not Add ………………………………………………………………………213

Appendix G. The Law of the Circle………………………………………………………………………214

Appendix H. The Zeroth Laws of Motion ……………………………………………………………..215

Appendix I. End of Term Interview ………………………………………………………………………218

 

 

 

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List of Tables

Table 1. Literature Review Search Pattern 1 …………………………………………………………. 26

Table 2. Literature Review Search Pattern 2 …………………………………………………………. 27

Table 3. Study Population Demographics …………………………………………………………… 107

Table 4. Interview Transcript Data …………………………………………………………………….. 109

Table 5. PEP Dimension Scores ………………………………………………………………………… 117

Table 6. Basic PEP Composite Descriptive Statistics …………………………………………… 117

Table 7. Basic PEP Dimension Descriptive Statistics …………………………………………… 118

Table 8. Primary PEP Dimension Changes …………………………………………………………. 119

Table 9. Secondary PEP Dimension Changes ……………………………………………………… 120

Table 10. Tertiary PEP Dimension Changes ……………………………………………………….. 120

Table 11. PEP Score Distributions Normality Tests ……………………………………………… 121

Table 12. Overall Coding Results ………………………………………………………………………. 122

Table 13. Coding Results for the Elements of Thought (EoT) ……………………………….. 123

Table 14. Jaccard Indices for Distinction and EoT Code Comparison …………………….. 125

Table 15. Examples of Concept Coordination ……………………………………………………… 130

Table 16. Examples of Belief Development Claims About Thinking ……………………… 139

Table 17. Examples of EoT Belief Development …………………………………………………. 140

Table 18. Examples of Belief Development ………………………………………………………… 141

Table 19. Examples of Belief Development ………………………………………………………… 143

Table 20. Force Concept Inventory (FCI) Results ………………………………………………… 144

Table 21. Mechanics Baseline Test (MBT) Results ……………………………………………… 144

Table 22. Cognitive Modeling Approach to Axiom Development………………………….. 167

 

 

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List of Figures

Figure 1.The eight elements of thought. ………………………………………………………………… 33

Figure 2. The eight elements of scientific thought. …………………………………………………. 34

Figure 3. Typiscal classroom activity life cycle. …………………………………………………….. 86

Figure 4. Cluster analysis circle graph for EoT and distinctions. …………………………….. 124

Figure 5. Cluster analysis dendrogram. ……………………………………………………………….. 126

Figure 6. Distinctions and coordinations vs. EoT node matrix. ………………………………. 128

Figure 7. Concepts and individual POV node matrix. ……………………………………………. 129

Figure 8. Distinctions and coordinations vs. EoT node matrix. ……………………………….. 131

Figure 9. MSPR group discussions distinctions-coordinations EoT node matrix. ……… 132

Figure 10. MSPR journals distinctions-coordinations EoT node matrix. ………………….. 132

Figure 11. MSPR math EoT node matrix. ……………………………………………………………. 133

Figure 12. MSPR science EoT node matrix………………………………………………………….. 134

Figure 13. MSPR physics EoT node matrix. ………………………………………………………… 134

Figure 14. Distinctions vs. EoT node matrix. ……………………………………………………….. 135

Figure 15. Coordinations vs. EoT node matrix. …………………………………………………….. 136

Figure 16. Belief development with TRU claims node matrix. ……………………………….. 138

Figure 17. Node matrix comparing beliefs with EoT. ……………………………………………. 140

Figure 18. Node matrix comparing true claims with EoT. …………………………………….. 142

Figure 19. Cognitive Modeling Taxonomy of Conceptual Frameworks – Processes. … 158

Figure 20. Cognitive Modeling Taxonomy of Conceptual Frameworks – Collections. . 165

Figure 21. CMTCF example 1: first zeroth law of motion. …………………………………….. 166

Figure 22. Vector diagrammatic model of the First Zeroth Law. …………………………….. 168

 

 

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Figure 23. Graphical model of the First Zeroth Law. …………………………………………….. 169

Figure 24. CMTCF Example 2: Second Zeroth Law of Motion………………………………. 169

Figure 25. CMTCF example 3: Second Zeroth Law axiom. …………………………………… 169

 

 

 

 

 

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Chapter 1: Introduction to the Study

Introduction

The cumulative history of physics education research (PER) for the last 34 years

has led to a reform in science teaching that has fundamentally changed the nature of

physics instruction in many places around the world (Modeling Instruction Project, 2013;

ISLE, 2014). Historical developments in PER have highlighted the connection that exists

between conceptual change and the way that students come to learn (Hake, 2007;

Hestenes, 2010), the difficulties that impede their learning (Lising & Elby, 2005), the

connection between personal epistemology and learning physics (Brewe, Traxler, de la

Garza & Kramer, 2013; Ding, 2014; Zhang & Ding, 2013), and theoretical developments

that inform pedagogical reform (Hake, 1998; Hestenes, 2010). To date, little research has

been done exploring the particular mechanisms of general epistemological change

(Bendixen, 2012), with PER pioneers such as Redish (2013) suggesting the need for a

basis in psychological theory for how physics students think and believe when it comes to

learning and knowledge acquisition. There is still no definitive answer about general

epistemological change within the literature (Hofer, 2012; Hofer & Sinatra, 2010), and

many of the leading researchers have been studying that with the context of mathematics

and/or physics (see Hammer & Elby, 2012; Schommer-Aikins & Duell, 2013).

The central goal of this research was to determine how students encode meaning

through the deployment of multiple representational systems (MRS)—such as words,

symbols, diagrams, and graphs—in an effort towards thinking and reasoning their way

through epistemological change in an Introductory Physics (IP) classroom. Specifically,

this study positions MRS as tools for thinking and reasoning that are capable of

 

 

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producing epistemological change. Among other things, the study sought to find the types

and numbers of MRS that are the most useful in producing epistemological change. Such

findings would then inform the PER community concerning the capacity that MRS have

for encoding meaning during the scientific thinking and reasoning process. Moreover, the

relative importance of personal epistemology in the process of conceptual change—either

as a barrier or a promoter—is the kind of information needed for continued progress in

the PER reform effort, as well as learning theory in general. The PER Community has a

number of peer-reviewed journals such as the American Journal of Physics (see Hake

1998, 2007; Lising & Elby, 2005; Redish 2013) and the Physical Review Special Topics –

Physics Education Research (see Bing & Redish, 2012; Bodin, 2012; Brewe, 2011; De

Cock, 2012; Ding, 2014), where much of the research is reported.

The multi-decade findings of both the PER community and the researchers

involved with personal epistemology, indicate a deep connection between learning

physics and beliefs about the world, as well as how those epistemic views correspond to

conceptual change. It is impossible to do Physics without the aid of conventional

representational systems such as natural language and mathematics; hence the inherent

capacity for those representational systems to influence both conceptual and epistemic

knowledge (Plotnitsky, 2012) is a legitimate point of inquiry that has gone largely

unnoticed. The usage of one or more representational systems should inform researchers

of what the students is thinking or reasoning about—specifically, the ontology, and

therefore the beliefs that such a learner has concerning what has been encoded by MRS.

Beliefs about reality and the correspondence to Physics are inextricably linked through

MRS.

 

 

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According to Pintrich (2012), it is unclear at this time how representational

systems influence epistemological change when deployed in learning environments of

any type. Historically, the lessons learned from the advance of the learning sciences have

shown that personal choices in representational systems are critical to the metacognitive

strategies that lead to increased learning and knowledge transfer (Kafai, 2007) when

situated in learning environments that are collaborative and individually reflective against

the backdrop of prior knowledge (Bransford, Brown, Cocking, & National Research

Council, 1999). The central goal of this research was to determine how thinking and

reasoning with multiple representational systems (MRS)—such as diagrams, symbols,

and natural language—influences epistemological change within the setting of an IP

classroom. The study described herein positions adult community college students in a

learning environment rich with conceptual and representational tools, along with a set of

challenges to their prior knowledge and beliefs. This study answers a long-standing

deficit in the literature on epistemological change (Bendixen, 2012; Pintrich, 2012) by

providing a deeper understanding of the processes and mechanisms of epistemological

change as they pertain to context (domain of knowledge) and representational systems in

terms of the psychological constructs of thinking and reasoning. This chapter will setup

the background for the study research questions based on the current and historical

findings within the fields of personal epistemology research, and the multi-decade

findings of the PER community.

Background of the Study

The current state of research on personal epistemology is one of theoretical

competition (Hofer, 2012: Pintrich, 2012), concerning how learners situated within

 

 

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different contexts, domains of inquiry, and developmental stages obtain epistemological

advancement, as well as whether or not to include the nature of learning alongside the

nature of knowledge and knowing in the definition of personal epistemology (Hammer &

Elby, 2012). The term epistemology deals with the origin, nature, and usage of

knowledge (Hofer, 2012), and thus epistemological change addresses how individual

beliefs are adjusted and for what reasons. Moreover, the field has not produced a clear

understanding of how those learners develop conceptual knowledge about the world with

respect to their personal beliefs about the world (Hofer, 2012). Conceptual change

research has not faired much better, and suffers from a punctuated view of conceptual

change that has been dominated by pre-post testing strategies rather than process studies

(diSessa, 2010). According to Hofer (2012), future research needs to find relations

between psychological constructs and epistemological frameworks in order to improve

methodology and terminology such that comparable studies can be conducted—thus

unifying the construct of personal epistemology within the fields of education and

developmental psychology. Bendixen (2012) suggested that little research on the

processes and mechanisms of epistemological change have been done, and echo the call

by Hofer and Pintrich (1997) for more qualitative studies examining the contextual

factors that can constrain or facilitate the process of personal epistemological theory

change. Moore (2012) cited the need for research addressing the debate over domain-

general versus domain-specific epistemic cognition in terms of the features of learning

environments that influence learning and produce qualitative changes in the complexity

of student thinking.

 

 

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Wiser and Smith (2010) described some of the deep connections that exist

between concept formation, ontology, and personal epistemology, within a framework of

metacognitive control that is central to modeling phenomena through both top-down and

bottom-up mental processes. These sorts of cognitive developments depend on the ability

to use representational systems that are rational (mathematics) and/or metaphorical

(natural language), within a methodological context that is empirical (measurement) in

nature. The student’s transition from holding a naïve theory—such as objects possess a

force property—to holding a more sophisticated or expert theory—that forces act on

objects (Hammer & Elby, 2012)—is by means of representational systems that serve in

part as epistemic resources for modeling real-world phenomena (Bing & Redish, 2012;

Moore et al., 2013). Moreover, it is the coupling of internal representations (mental

models) with the external representations that we call models, which is critical to the

reasoning process (Nersessian, 2010) and its assessment. These findings suggest an

intimate connection between personal epistemology and representational systems as they

function in concert with thinking, reasoning, and conceptual change; however, they do so

without specifying any particular tools. The central aim of this research is to describe

how MRS are used in the thinking and reasoning that accompanies epistemological

change.

Personal epistemology. Personal Epistemology (PE) has been an expanding field

of inquiry for at least 40 years, with a coalescence of a handful of models and theories

emerging in the late 1990s to early 2000s—such as process and developmental models,

and at least four different assessment instruments for judging the epistemic state of

learners at most any age (Herrón, 2010; Hofer & Pintrich, 2012). While the current

 

 

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models and theories agree on the relationships to variables such as gender, prior

knowledge, beliefs about learning, and critical thinking (Herrón, 2010), it is not clear at

this time whether or not a unitary construct for personal epistemology applies in all

cases—suggesting a number of domain-specific (knowledge area such as science) gaps

that need further research.

The content of physics is neither purely rational nor empirical, but also depends

on metaphorical representations—such as the term flow for energy transfer, light is a

particle/wave, and electrons tunneling through quantum spaces—in order to foster the

understanding of complex phenomena and their underlying theories (Brewe, 2011;

Lancor, 2012; Scherr, Close, McKagan, & Vokos, 2012; Scherr, Close, Close, & Vokos,

2012). One of the earliest attempts to measure personal epistemology was the Psycho-

epistemological Profile (PEP) (Royce & Mos, 1980), which measures personal

epistemology on three dimensions: Rational, Empirical, and Metaphorical, and is

therefore an ideal assessment tool for scientific domains of epistemology. The rational

dimension of PEP assumes that knowledge is obtained through reason and logic, whereas

the empirical dimension derives and justifies knowledge through direct observation. The

metaphorical dimension of PEP defines knowledge as derived intuitively with a view to

subsequent verification of its universality.

Representational Systems. Schemata theory (Anderson et al., 1977) suggested a

dynamic process of memory storage and retrieval in concert with the use of

representational systems lead to schemata, which serve as interpretive frameworks within

the process of epistemological advancement. Under the Modeling Instruction Theory for

Teaching Physics (Hestenes, 2010) students are taught to use a representational tool

 

 

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known as a system schema that represents an abstraction of a given picture of some

physical situation. Specifically, this diagrammatic tool compels students to represent

various objects and interactions with regard to the system that governs them, and these

relationships are then productive for various aspects of the problem-solving event. One of

its capacities is as an error-checking device that validates (or invalidates) the equation

model of the same system—such as verifying the equation set adequately represents the

superposition of forces. Simply put, you can move forward with a solution (decision)

once you have verified that nothing was (a) left out of the model or (b) included

illegitimately. The use of multiple representational systems within an IE classroom force

the reconciliation of multiple schemata on singular and/or connected phenomena. This

sort of conceptual turbulence challenges the epistemic stance of the learner, and thereby

provides an opportunity to detect epistemological change as a function of MRS.

Hestenes (2010) deployed multiple types of representations for encoding structure

in terms of systemic (links among interacting parts), geometric (configurations and

locations), object (intrinsic properties), interaction (causal), and temporal (changes in the

system) as ways to model and categorize the observation that students of science make in

an effort to mimic the expert view. In these ways, MRS are instrumental for the modeling

the structure of physical phenomena (Plotnitsky, 2012; Scherr et al., 2012), and therefore

serve as evidence of what students believe the varied representational conventions of

mathematics and physics are capable of describing. The status as of MRS as elements of

epistemological change is the primary research question in this study.

 

 

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Problem Statement

It was not known how (a) thinking and reasoning with MRS occurs, and (b) how

that sort of thinking and reasoning affects epistemological change in terms of

mechanisms and processes—whether cognitive, behavioral, or social—in an IP

classroom. Moreover, as shown in the review of the literature herein, it is not clear what

anyone means by the terms thinking and reasoning within any context. The use of

representational systems—such as symbols, diagrams, and narratives—is undoubtedly

central to the progress of science education by virtue of its ubiquitous deployment in the

realm of natural science itself (Plotnitsky, 2012; Scherr, Close, McKagan & Vokos,

2012). Given the cognitive filter that personal epistemology provides for the acquisition

and the application of knowledge (Schommer-Aikins, 2012), it seemed reasonable to

investigate the nature of epistemological change in concert with the thinking and

reasoning that occurs by means of the representational systems associated with a domain

of knowledge—such as IP. The importance of this study hinged on its ability to answer a

long-standing deficit in the literature on epistemological change (Bendixen, 2012;

Pintrich, 2012) by providing a deeper understanding of the processes and mechanisms of

epistemological change as they pertain to context (domain of knowledge) and

representational systems in terms of the psychological constructs of thinking and

reasoning. These findings better inform the Physics Education Research (PER)

community concerning the capacity that MRS have for encoding meaning during the

scientific thinking and reasoning process, while simultaneously clarifying what is meant

by those processes. Moreover, the relative importance of personal epistemology in the

process of conceptual change—either as a barrier or a promoter—is the kind of

 

 

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information needed for continued progress in the PER reform effort, as well as learning

theory in general. The importance of advancing scientific thinking and reasoning,

conceptual change—in terms of epistemological change—lies in the clear evidence from

PER that conceptual change has a positive effect on achievement in terms of problem-

solving skills (Coletta & Phillips, 2010; Coletta, Phillips & Steinert, 2007a; Hake, 2007).

Purpose of the Study

The purpose of this qualitative grounded theory study was to determine how

representational systems deployed in an IP classroom correspond to epistemological

change in accordance with the ways that students therein think and reason, within a study

sample at Central Arizona College—located in Coolidge, Arizona. The collaborative and

writing-intensive nature of the IP curriculum at Central Arizona College lends itself well

to the research questions and methodology of this study. The use of representational

systems—such as symbols, diagrams, and natural language—is undoubtedly central to

the progress of science education by virtue of its ubiquitous deployment in the realm of

natural science itself (Plotnitsky, 2012; Scherr, Close, McKagan & Vokos, 2012). Given

the cognitive filter that personal epistemology provides for the acquisition and the

application of knowledge (Schommer-Aikins, 2012), it seemed reasonable to investigate

the nature of epistemological change in concert with the thinking and reasoning that

occurs by means of the representational systems associated with a domain of

knowledge—such as IP. The researcher identified the mechanisms of epistemological

change (Bendixen, 2012) as they correspond to thinking and reasoning with MRS. The

value of such knowledge to educational reform efforts is significant in terms of (a) the

 

 

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specific mechanisms for epistemological change (Bendixen, 2012), and (b) the

psychological constructs that generate them (Hofer, 2012).

Ongoing PER reform efforts—such as the development of assessment instruments

and pedagogical change—will benefit tremendously from knowing the types and

frequencies of deployment for representational systems that are effective for producing

conceptual and epistemological change in IP. Furthermore, the relative frequency of use

coupled with personal stances about the usefulness of those representational systems will

provide the information needed to reform instruction in topics that tend to confuse

students during their learning trajectory.

Research Questions and Phenomenon

The goal of this qualitative grounded theory study was to determine the influence

that multiple representational systems (MRS) have on the thinking and reasoning of 20-

30 community college IP students at Central Arizona College with respect to their

conceptual frameworks and personal epistemology. Forty-four semi-structured interviews

based on instructional goals, survey response data, and student journal entries were

conducted at regular intervals during the study in order to obtain emergent themes

concerning how students think and reason about symbols and operations in mathematics,

as well as how they monitor their own thinking about the same. Journals and semi-

structured interviews—in the form of group Socratic dialogs—reveal the ways in which

students shift between representational systems (languages) in an effort to model

mathematical systems, while providing ample means for triangulating the data in parallel

with field notes and memos made by the author-researcher. Multiple electronic polls were

 

 

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given throughout the treatment in order to capture opinions about thinking and reasoning,

knowledge acquisition and usage, as well as how concepts and beliefs change as a result.

As shown in the forthcoming review of the literature, thinking and reasoning are

poorly defined and often conflated (Evans, 2012; Evans & Over, 2013; Mulnix, 2012;

Nimon, 2013; Peters, 2007). Given the absence of consensus on the definitions of

thinking and reasoning within the research literature, the author proposed new definitions

for thinking and reasoning as a means for coding, counting, and classifying instances of

student thinking and reasoning with representational systems that were based on the

synthesis of a model for thinking put forward by Paul and Elder (2008). Thinking is

defined as the ability to construct a model, and reasoning is defined as the ability to relate

two or more models. A model is simply any representation of structure, and structure

refers to the way in which relations can be encoded (Hestenes, 2010). The following

research questions were crafted in such a manner as to encompass the gap in the literature

related to the process and mechanisms of epistemological change as they relate to the

psychological constructs of thinking and reasoning within the domain of IP, as well as the

features of Hofer’s epistemic cognition model (Hofer, 2004; Sinatra, Kienhues, & Hofer,

2014) involving the domain of knowledge, the contextual factors of the learning

environment, and how student reflection within the curriculum conveys towards

metacognitive monitoring.

Qualitative Research Questions

R1: How do IP students use representational systems in their thinking and

reasoning?

 

 

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R2: How does the use of MRS in the thinking and reasoning of IP students

promote personal epistemological change?

In order to facilitate an investigation of these research questions, a series of

activities comprising the standard curriculum of IP students at a rural community college

will be studies. Beginning with group discussions, journals and surveys on the nature of

Physics and reality, students then begin to deploy new representational systems designed

to expose and refine conceptions of number and mathematical operations that are critical

to the language of Physics. These advances are then carried forward to an investigation of

motion that serves as the basis of the entire course. Exit interviews at the semesters end

reflected on all that was learned and how the conceptual and representational tools used

throughout the course influence thinking, reasoning, and personal epistemology.

Advancing Scientific Knowledge

As described in the forthcoming literature review, a lack of clarity exists in the

literature concerning the definitions of thinking and reasoning; however, there is an

abundance of claims that all sorts of thinking and reasoning underlie every advance in

human learning. In order to facilitate more efficient data collection, the author introduced

definitions of thinking and reasoning as follows. Thinking is defined as the ability to

construct a model. This definition is (a) flexible enough to encompass any

representational system, (b) straightforward enough to permit the kinds of frequency

distributions and classification schemes that enable direct measurement of this cognitive

behavior, and is (c) inspired by the work of PER pioneers cited herein, such as Hestenes,

Hake, Redish, and Mazur. The term model is simply any representation of structure

(Hestenes, 2010), and structure is a broader term—open to wide interpretation—

 

 

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encompassing the way that interconnectedness between and within systems is articulated.

Furthermore, the term reasoning is defined herein as the ability to relate two or more

models; and therefore, coordinates the terms in a manner that lends consistency and

coherence to the measure of these cognitive behaviors by simply counting attempts.

Little research has been done exploring the particular mechanisms of

epistemological change along developmental trajectories or with respect to the

dimensions of personal epistemology (Bendixen, 2012; Hofer, 2012). Moreover, it was

not known how representational systems influence such change when deployed in

learning environments of any type (Pintrich, 2012). Personal epistemology is linked to

conceptual change (Bendixen, 2012; Hofer, 2012), and representational systems are

required for producing conceptual change (diSessa, 2010). The gap in the literature that

this study addresses is the lack of connections that exists between representational

systems, conceptual change, and epistemological change, and what processes and

mechanisms are productive for such change (Bendixen, 2012; Hofer, 2012; Pintrich,

2012). The persistent question of educational research is ‘what works best and why?’ and

it is the lived experience of learners situated in an IP classroom that should expose their

thoughts and beliefs concerning the representational tools that they use and/or struggle

with when encoding for meaning.

The PER literature speaks extensively to improving the thinking and/or reasoning

skills of students in introductory physics courses (Coletta & Phillips, 2010; Coletta et al.,

2007a; Hake, 2007), without ever providing or relying on a clear definition for thinking

or reasoning in general terms. Thinking and reasoning within the context of problem

solving is part of the functional relationship that exists between the personal

 

 

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epistemology of students and their learning in general (Lising & Elby, 2005; Schommer-

Aikins & Duell, 2013). The use of representational systems—such as symbols, graphs,

diagrams, and narratives—is undoubtedly central to the progress of science education by

virtue of its ubiquitous deployment in the realm of natural science itself. The evidence

cited herein shows a lack of clarity on the mechanisms of conceptual and epistemological

change as they correspond to (1) one another, and (2) towards problem-solving skills.

Moreover, it is not clear what sort of thinking and reasoning is being deployed in an

effort to produce those changes in a knowledge-domain requiring MRS (Plotnitsky,

2012). This study addressed all of these concerns at the focal point of epistemological

change, and thus answered the call for clarity and mechanistic description within the

literature.

Significance of the Study

The role of representational systems is believed to be a factor in promoting

conceptual and epistemological change in settings such as Introductory Physics

classrooms (Brewe et al., 2013), as well as learning in general (Lising & Elby, 2005;

Pintrich, 2012). This research sought to understand (1) what, if any, connection(s) exist

between thinking and reasoning with MRS and epistemological change—as prescribed in

the research questions, and then (2) begin to unravel the types and numbers of

representational systems that are effective for promoting those changes by specifying the

mechanisms (Bendixen, 2012) and processes (Hofer, 2012) found therein. The value of

such knowledge to educational reform efforts is significant, as it identified specific

mechanisms for epistemological change (Bendixen, 2012) in terms of the psychological

constructs that generate them (Hofer, 2012), as well as the epistemic resources for

 

 

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conceptual formation (Bing & Redish, 2012; Wiser & Smith, 2010) and change

(Jonassen, Strobel, & Gottdenker, 2005) within learning environments designed for

epistemic change (Muis & Duffy, 2013).

The importance of epistemological change for this study is evident in its close

connection to the field of conceptual change (diSessa, 2010) and how they are

coordinated in PER through the use of representational systems (Brewe et al., 2013).

Moreover, epistemological change would be better understood in terms of the influence

of representational systems (Pintrich, 2012) and the incremental processes associated

with conceptual change (diSessa, 2010), while also contributing to the lack of theoretical

clarity that persists in defining each of these constructs (Hofer, 2012; Pintrich, 2012). A

secondary goal that is inextricably linked to the primary goal, is to clearly distinguish

thinking and reasoning from one another, and how MRS are used to encode the meaning

evident in those constructs. Such a discovery has the potential for providing a general

metric for the constructs of thinking and reasoning in any domain of knowledge with

respect to the representational systems that accompany it.

Personal epistemology has connections with multiple fields of psychology and

learning science including conceptual change (diSessa, 2010; Jonassen et al., 2005,

Nersessian, 2010), metacognition (Barzilai & Zohar, 2014; Bromme, Pieschl, & Stahl,

2010; Hofer, 2012; Hofer & Sinatra, 2010; Mason & Bromme, 2010; Muis, Kendeou &

Franco, 2011), self-regulated learning (Cassidy, 2011; Greene, Muis & Pieschl, 2010;

Muis & Franco, 2010), and self-efficacy through locus of control (Cifarelli, Goodson-

Espy, & Jeong-Lim, 2010; Kennedy, 2010). Each of these constructs or cognitive

functions are communicated through representational systems that students presumably

 

 

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