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 ProQuest Number: 10027568 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest 10027568 Published by ProQuest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 © by Clark Henson Vangilder, 2016 All rights reserved. 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. vi 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. vii 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. viii 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 ix 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 x 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 xi 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 xii 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 xiii 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 xiv 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 xv 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 - 1 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 2 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. 3 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 4 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 domaingeneral 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. 5 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 6 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 Psychoepistemological 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 7 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. 8 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 9 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 problemsolving 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 10 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 2030 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 semistructured 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 11 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? 12 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— 13 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 14 epistemology of students and their learning in general (Lising & Elby, 2005; SchommerAikins & 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 15 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, GoodsonEspy, & Jeong-Lim, 2010; Kennedy, 2010). Each of these constructs or cognitive functions are communicated through representational systems that students presumably 16 think and reason about along their way to an understanding that shapes their set of personal beliefs. Research that seeks to obtain a deeper understanding of the processes and mechanisms associated with changes along any of those dimensions will have a lasting impact on multiple areas of psychology and learning science in general. The PER community has promoted, created, and uncovered a vast array of IE methods that have surely improved learning outcomes in IP classrooms (Coletta & Phillips, 2010; Coletta et al., 2007a; Hake, 1998; Hestenes, 2010)—and therefore some sort of cognitive behavior. So while there is little doubt that some sort of thinking and/or reasoning is going on while students are learning any topic, it is not clear in the literature what the specific qualities of thinking and reasoning are when it comes to learning in IP. Given the deep connections that exist between metacognition and epistemological frameworks (Barzilai & Zohar, 2014), the effort to obtain the factors of epistemological change in terms of the tools that are instrumental to that effect present a grand opportunity to the teaching and learning enterprise. Rationale for Methodology A qualitative approach was used in this study. The foundations of qualitative research rest on the inductive analysis that makes developing an understanding of the phenomena from the viewpoint of the participants possible (Merriam, 2010) in a manner that respects how the meaning is constructed in social settings (Yin, 2011) where the researcher is the primary data collection instrument responsible for producing a richly descriptive account of the outcomes (Merriam, 2010). Given the nature of the study on personal epistemology—beliefs about knowledge and its acquisition—and how students obtain advances in personal epistemology, qualitative methods lend themselves best to 17 the project described herein because they provide a richer description (Schommer-Aikins, 2012), of the lived experience of the study participants (Charmaz, 2006; Glaser & Strauss, 2009). Moreover, given that the research design was grounded theory, the necessity of qualitative methodology for data collection and analysis is properly constrained within this methodology by virtue of its underlying logic and interpretive framework (Charmaz, 2006). Nature of the Research Design for the Study A grounded theory approach (Charmaz, 2006) was used in designing this qualitative study in order to produce a substantive theory capable of describing the complex interactions that comprise the phenomena of thinking and reasoning with MRS, and its influence on epistemological change within the context of a community college IP classroom. Grounded theory is a qualitative design that allows a researcher to form an abstract theory of processes or interactions that are grounded in the views of the participants (Charmaz, 2006; Glaser & Strauss, 2009). Given the fact that personal epistemology is entirely about personal beliefs and viewpoints, a grounded theory exploration of the underlying mechanisms and processes of epistemological change is entirely consistent with the research questions probing how students think and reason their way towards epistemological change using MRS. Approximately 30 students comprise the study population from which archived data will be drawn at Central Arizona College—which is consistent with the 20-30 study participants recommended for grounded theory research by Creswell (2013), and the 3050 participants suggested by Morse (2000). Charmaz (2006) suggested that 25 interviews are sufficient for grounded theory designs on small projects. Given the current study is 18 using interviews, written journals, and electronic polls, a group of slightly more than 30 student participants should be more than adequate for obtaining the level of theoretical saturation which is the ultimate criterion for sample size in grounded theory designs (Corbin & Strauss, 2008). The archived data in this study will include numerous student journals throughout the IP curriculum, group discussion transcripts, and miscellaneous assessment results—such as Force Concept Inventory (FCI), and the Psychoepistemological Profile (PEP)—that are all part of the normal classroom experience of IP students at Central Arizona College, which were selected purposively due to their suitability for the study and amount of data available for the researcher. In order to eliminate as much researcher bias as possible, archived data was used. Grounded theory design was selected because of its capacity to capture in theory the ‘how’ of structure and process within a social setting, versus a phenomenological ‘what’ of the events (Birks & Mills, 2011). The research questions proposed for this study ask how MRS are used in the processes of thinking and reasoning within epistemological change, and thus fall under the heading of grounded theory by virtue of the research question itself—which seeks an answer to a how type of question. In order to make the connection to epistemological change in these terms though, a certain amount of discourse analysis is required. However, discourse analysis alone cannot answer the ‘how’ questions because such a design is methodologically constrained to the meaning that is negotiated in the ‘what’ of language rather than the process of negotiating meaning with language itself (Yin, 2011). Though phenomenology, discourse analysis, and grounded theory come from different historical and philosophical traditions, the boundaries between them are somewhat porous in terms of the methodology required for 19 a particular kind of research question (Yin, 2011), as well as the fact that the elements of one type of question—such as a ‘how’ question—often entail elements of another type of research question, such as the ‘what’ type (Starks & Trinidad, 2007). Since the nature of this study’s research questions probe how students use MRS in their thinking and reasoning for epistemological change, the importance of using grounded theory as a tool for grounding the theory in the particular viewpoints of the participants (Charmaz, 2006; Glaser & Strauss, 2009) further solidifies the primacy of grounded theory over other designs—such as discourse analysis. Personal epistemology obviously pertains to personal viewpoints, which must be expressed in language. The language used by IP students is situated in social contexts constrained by the MRS that are conventionally used within Physics—such as graphs, equation, pictures, and words (Plotnitsky, 2012). In this case, the viewpoints that are the central focus of personal epistemological change are developing within a context that can only be described using a limited set of representational systems. The connection between the personal and social aspects of the learning environment for this study, in parallel with the particular uses of MRS (language), was far too intimate to ignore. Definition of Terms Conceptual change. In order to define conceptual change, one must first define a concept. In general, it is the internal representation that learners construct for themselves based on the external representations of others (Nersessian, 2010). Conceptual change is measured on many levels from the taxonomic and semantic aspects of how symbols are related to referents, as well as how those representations correspond to more complex conceptual structures such as an event (Hestenes, 2010). 20 Multiple representational systems (MRS). The use of words, symbols, and pictures to in order to communicate an idea or present a model is described as multiple representations (Fyfe, McNeil, Son, & Goldstone, 2014; Harr et al., 2014), multiple external representations (Fyfe et al, 2014; Wu & Puntambekar, 2012), and multiple representational systems (Ainsworth, Bibby, & Wood, 2002) in the literature. Personal epistemology. The psychological construct of personal epistemology is used to describe how personal beliefs convey to what knowledge is, how it is obtained, what it is used for, and how useful it is in any context (Hofer & Pintrich, 2012). Assumptions, Limitations, Delimitations The following assumptions are given with respect to this study. 1. It was assumed that survey participants in this study were not be deceptive with their answers, and that the participants answered questions honestly and to the best of their ability. The course and curriculum under study was the regular curriculum for Physics students at Central Arizona College, and therefore part of the normal experience that counts for a grade. 2. It is assumed that this study was an accurate representation of what is typical in IE IP classrooms. The instructor (the author) has been trained in IE methods for the last decade and has based his research on the best practices of the PER community. The following limitations/delimitations apply to this study. The generalizability of the findings that emerge from this study are limited to the IE class of IP classrooms typically studied by the PER community. According to Merriam (2010), generalizability in qualitative research must be thought of differently than it is in quantitative designs. External validity is the qualitative equivalent of generalizability, and is constrained by the perception that users of the research have with regard to the transferability to another context or domain of knowledge. The author makes no claims with regard to generalizability in this study aside from the likelihood that this design could produce 21 similar results in other IE IP classrooms. This limitation is consistent with the theoretical and pedagogical norms that persist in that category of instructional practice. One longterm goal of this dissertation is preparatory towards the development of a learning theory requiring a great deal more than is typically contained in just one dissertation. 1. The student body was not randomly selected. This qualitative study depends on purposive sampling of qualified students, which was obtained by identifying students who meet the pre-requisites for taking physics for university transfer purposes. 2. The study population was limited to two Physics courses at one community college. The author-researcher has no other access to students. Summary and Organization of the Remainder of the Study Conceptual change and epistemological change are connected by the representational systems used by learners when deploying them in contexts that require modeling (Hestenes, 2010, Nersessian, 2010). Learning physics requires thinking and reasoning within a context for problem solving where beliefs about the world are regularly challenged (Lising & Elby, 2005). However, there is no clear definition of the terms thinking and reasoning (Nimon, 2013; Peters, 2007) even though scores of types of thinking are well attested within the literature—specifically with respect to this study: scientific thinking and reasoning within the context of learning physics (Coletta et al., 2007a, 2007b; Hake, 1998; Hestenes, 2010). Chapter 2 presents a review of current and historical research on the connections that exist between thinking, reasoning, representational systems, conceptual change and epistemological change, as well as the theoretical foundations underlying the present study. Chapter 3 describes the methodology and research design for a generic qualitative design, and the data collection and analysis procedures for this investigation. Chapter 4 22 delivers the actual data analysis with written and graphic summaries of the results, which lead into an interpretation and discussion of the results, as they relate to the existing body of research related to the dissertation topic. The timeline for completing this dissertation consists of three primary stages. In stage one, the proposal is completed and approved by August 13, 2014—the end of PSY955 Dissertation 1, and subsequently approved in PSY960 Dissertation 2. Data collection begins immediately in PSY960 Dissertation 2 in conjunction with the start of the courses being studied at Central Arizona College that begin on August 18th. The analysis phase began subsequent to the approved Proposal in July 2015, and the data analysis was completed during PSY969 Research Continuation 4. The remainder of the dissertation was completed during PSY970 Research Continuation 5 in January 2016. 23 Chapter 2: Literature Review Introduction to the Chapter and Background to the Problem The basic premise of this research was that the use of MRS is the fundamental feature of the kinds of thinking and reasoning that promote both conceptual and epistemological change; however, this study was concerned with just the connections that exist between thinking and reasoning with MRS and personal epistemological change. Specifically, that the resources for conceptual change are contingent on the resources for epistemic change, if not entirely the same. Moreover, the inherent need of representational systems for communicating meaning is central to conceptual change as well as the set of personal beliefs that accompany personal epistemology. The extent to which epistemological change is connected to the deployment of MRS, is the central research focus that is capable of better informing all PER initiatives concerning the foundations of thinking and reasoning required for this sort of change. The current state of research on the personal epistemology of learners situated within different contexts, domains of inquiry, and developmental stages, has not produced a clear understanding of how those learners (a) develop conceptual knowledge about the world with respect to (b) their personal beliefs about the world as it (c) relates to physics (Hofer, 2012). However, there is evidence showing that when the science pedagogy matches the science practice, then students are more likely to obtain positive conceptual change based on the features of instruction and curricular content upon which student beliefs about the world are formed (Lee & Chin-Chung, 2012). Conceptual change research has also failed to produce clear understanding of how learners develop conceptual knowledge about the world, and suffers from a punctuated view of conceptual 24 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. 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. The general call for studies probing the connections that exist between conceptual and epistemological change, as well as the processes and mechanisms that are productive for those changes, is clearly warranted by these findings. Moreover, the PER literature also includes studies into the connection between personal epistemology and conceptual change in terms of representational systems (Brewe et al., 2013; Lising & Elby, 2005), lending further warrant to the study proposed herein. Though the particular research questions for this study were focused on epistemological change, the findings cited thus far warrant a discussion of conceptual change in this literature review. Wiser and Smith (2010) describe 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 (perceptions influenced by prior knowledge) and bottom-up (perceptions influenced by new data) 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 25 nature. The student’s transition from naïve to expert theories is by means of representational systems that serve in part as epistemic resources for modeling real-world phenomena (Bing & Redish, 2012; Hestenes, 2010; 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 and its assessment (Nersessian, 2010). 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 was to identify some of the most basic representational tools that are instrumental for epistemological change. The Physics Education Research (PER) community has claimed significant gains in student thinking and reasoning (Coletta & Phillips, 2010; Coletta et al., 2007a; Hake, 2007) through conceptual change (Hake, 1998), without ever defining what is meant by the terms thinking and reasoning. As shown in the forthcoming review of the literature, thinking and reasoning are poorly defined and often conflated (Mulnix, 2012; Nimon, 2013; Peters, 2007). 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 (1) flexible enough to encompass any representational system, (2) straightforward enough to permit the kinds of frequency distributions and classification schemes that enable direct measurement of this cognitive behavior, and is (3) 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— 26 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. Though the reform movement as studied in the PER literature has obtained notable success (Coletta et al., 2007a, 2007b; Hake, 1998), one question that emerges from the gaps in this body of literature, as well as the persistent conflation of the terms thinking and reasoning that are common to both the literature and the discourse of math and science education research (Glevey, 2006), is what exactly do we mean by thinking and reasoning? The search terms “definition of thinking” OR “thinking is defined” in scholarly journals whose names include psycholog* OR cogn* OR educ* yielded only 118 peerreviewed articles from 1963 to 2014 in EBSCO Academic Search Complete (EBSCO), and 47 articles from 1991 – 2014 in ProQuest—as illustrated below in Table 1. Table 1 Literature Review Search Pattern 1 Date Range 1963 - 2014 Type of thinking Critical Other Hits in EBSCO 27 91 Hits in ProQuest — — 1991 - 2014 Critical Other — — 23 24 These initial search results indicate dominance on the field of research by critical thinking that has remained stable over the years since 1963, yet waning in recent years. In both databases, the table entry for “other” is predominantly filled with n = 1 tallies, while the remainder are n = 2. In other words, somewhere between one-half and three-quarters 27 of published research on thinking is scattered among scores of types of thinking distinct from critical thinking, or types of thinking such as schizophrenic thinking, that are not applicable to this study. Table 2 below illustrates a more recent tally for the search terms given above. Table 2 Literature Review Search Pattern 2 Date Range 2004 - 2014 Type of thinking Critical Other Hits in EBSCO 16 70 Hits in ProQuest 5 15 2009 - 2014 Critical Other 8 31 3 8 Applying the same search criteria for a definition of reasoning yielded only 31 articles in EBSCO for the years 1981 – 2014, and 6 articles in ProQuest for the years 1996 – 2014. Restricting the years to 2004 – 2014 produced on 4 ProQuest and 21 EBSCO articles, whereas a 2009 – 2014 search obtained only 3 ProQuest and 9 EBSCO articles. Changing the search constraints in both databases to just the term “thinking” produced 946 EBSCO and 652 ProQuest articles for the years 2004 – 2014. This means that at best, roughly 9% of all research making claims about thinking in the last 10 years operated with a clear definition of the term. An identical search for the term “reasoning” produced 601 EBSCO and 152 ProQuest articles—indicating that approximately 3% of research articles in the last 10 years made claims about reasoning without the aid of a basic definition. This review of the literature was structured in terms of how the theories and the histories of conceptual and epistemological change correspond to the progress of learning in general, and physics in particular. Though the study was particularly focused on 28 epistemological change, thinking and reasoning within the context of IP has been historically concerned with conceptual change. However, a great deal of research in personal epistemology has occurred within IP classrooms; hence the need to give attention to both conceptual and epistemological change in this literature review. Additionally, the constructs of thinking and reasoning were considered in general psychological terms as well as the particulars of Physics education. Self-regulated learning, self-efficacy, metacognition, and student journaling converge on the aforementioned theoretical aspects of this study in terms of conceptual and epistemological change, as well as classroom management and the curriculum used by the study sample. The foundations of this study were both theoretical and conceptual, consisting of the constructs of personal epistemology, thinking and reasoning, and representational systems—as well as the connections that exist between them and conceptual change, metacognition, self-efficacy, self-regulated learning, and locus of control. Though the study was focused on personal epistemology, the entailments listed herein are given treatment in this chapter in accord with how they influence the study and research questions. Personal epistemology, thinking and reasoning, and representational systems were the central focus of the two research questions that are given in the so-named subsections of the section titled theoretical and conceptual foundations. Metacognition, self-efficacy, self-regulated learning, and locus of control were factors of the study environment by virtue of research demonstrating that particular pedagogical and curricular interventions—such as journaling—convey to changes in these same constructs, and are covered in the subsection titled self-efficacy, self-regulation, and 29 journaling. In this way, they served as conceptual foundations for the study in terms of what to expect in the data analysis phase. The literature review section of chapter two builds on the theoretical and conceptual foundations as they apply first to epistemological and conceptual change in general, and second to how thinking and reasoning within the context of IP conveys to personal epistemological change within that domain, and perhaps in general. This section begins with brief histories of personal epistemology research and the attempts to assess this construct, followed by a discussion of how personal epistemology and conceptual change intersect as fields of research. The remainder of the literature review consists of subsections addressing conceptual change in IP, personal epistemology in IP, and thinking and reasoning in IP classroom settings. Theoretical Foundations and Conceptual Framework Personal epistemology. Piaget’s cognitive developmental process of equilibration (Piaget, 1970) is—from a historical perspective—central to the theoretical underpinnings of what personal epistemology researchers call epistemological advancement (Bendixen, 2012). Hofer (2004) suggested the concept of epistemic metacognition as a way to understand how students shift beliefs through reflection, while epistemic beliefs also constrain and/or advance conceptual change. In either case, the domain of knowledge and the educational context determine the direction and magnitude of such transitions in personal epistemology, as well as its overall advancement for the student. Scientific reasoning is naturally recursive by virtue of the fact that empirical investigations challenge the models and hypotheses put forward by scientists—thus forcing the type of declarative metacognition (Hofer & Sinatra, 2010) 30 that influences personal beliefs. IE physics classrooms attempt to simulate the behavior of a scientific community by virtue of a discourse that is based on inquiry, collaboration, and consensus building (Bruun & Brewe, 2013; Hestenes, 2010; Irving & Sayre, 2014). Moreover, the very nature of an IE physics classroom relies on leveraging representational systems in order to produce a change in beliefs about the real world through conceptual change. However, in practice, conceptual change interventions differ from epistemological change interventions by virtue of the fact that conceptual change instruction seeks to merely confront and change existing beliefs, whereas epistemological change instruction seeks to influence how beliefs direct learning and the enactment of epistemology in the classroom (Ding, 2014). Epistemic recursion is therefore a key factor in scientific advance, and is one way to understand Hofer’s conceptual model of epistemic metacognition—which served as the conceptual framework of this study. Thinking and reasoning. In the new paradigm for the psychology of reasoning, probability rather than logic, is the rational basis for understanding all human inference (Pfeifer, 2013). Moreover, thinking and reasoning are coupled through the new paradigm in dual-process theories by virtue of the fact that Type 2 (reflective process) thinking is defined as enabling “us to reason by supposition, engaging in hypothetical thinking and mental simulation decoupled from some of our actual beliefs” (Evans & Over, 2013), whereas Type 1 intuitive thinking is fast and automatic concerning the feeling of confidence that accompany answers or decisions (Evans, 2012). Common definitions of the term thinking refer to particular cognitive processes such as transformations of mental representations (Holyoak & Morrison; 2012; Sinatra & Chinn, 2011), or even cognition as a general process (Nimon, 2013), whereas reasoning has become synonymous with 31 cognitive processing in general (Evans, 2012) via memory and reasoning for decision making in social habitats (Rai, 2012). Mulnix (2012, p. 477) conflates the terms thinking and reasoning by stating, “Critical thinking is the same as thinking rationally or reasoning well.” Such definitions are clearly circular, and therefore do nothing in the effort to clarify what is meant by the psychological construct, much less the neuropsychological reality in terms of neurons and various regions of the brain. Piaget operationalized the construct of thinking in terms of developmental stages, whereas more modern cognitivists adopted an information-theoretic approach based on brain waves, and connectionist notions of neural systems (Peters, 2007). Vygotsky defined it simply as dialog (Fernyhough, 2011). In describing the conceptions of philosophers such as Hegel, Heidegger, Kant, and Wittgenstein, Peters (2007) listed thinking as representation, opinion-making, scientific problem-solving, revealing what is concealed, and concept-making—thereby covering most of psychology in the broadest sense of the term, while giving little by way of specific mechanisms. These assertions made within the literature suggested a need for greater clarity in defining both thinking and reasoning before any progress can be made in measuring these constructs. However, according to Elder and Paul (2007b), all thinking consists of the following eight elements: the generation of purpose(s), raising questions, using information, utilization of concepts, inference-making, assumption-making, it generates implications, and embodies a point of view. Elder and Paul affirm the common treatment of thinking and reasoning as virtually synonymous terms in their assertion that “whenever we think, we reason” (Elder & Paul, 2007b, “All Humans Use Their Thinking”, para. 2). In other words, thinking is merely a stage of reasoning in the model put forward by Elder 32 and Paul. Reasoning is then defined as a sense-making and conclusion-making process conducted by the mind, based on reasons—implying an “ability to engage in a set of interrelated intellectual processes” (Elder & Paul, 2007b, “All Humans Use Their Thinking”, para. 5), such as the eight elements of thinking already given herein. One distinguishing factor of thinking relative to reasoning in the model offered by Elder and Paul, is that thinking is what agents do when making sense of the world, whereas reasoning is how agents are able to come to decisions about the elements of their thought. In an attempt to explain how the human mind learns, Elder and Paul (2007a) define thinking in even more general terms as the process by which we take control of the mind in an effort to figure things out. Moreover, these thoughts influence our feelings, and thus the way that we interpret and come to believe various things—in other words, thinking informs our viewpoints. Given the consistency of this model with the general scope of personal epistemology, the models and definitions for thinking and reasoning by Elder and Paul described herein, will serve as a conceptual foundation for what is meant in this study by constructs of thinking and/or reasoning. The model put forward by Elder and Paul (2007b) contains 35 dimensions of critical thought consisting of 9 affective dimensions, and 26 cognitive dimensions broken into 17 macro-abilities, and 9 micro-skills. Point of view, questioning, assumption making, and using information are four of the eight elements of thought that also appear within the cognitive dimension macro-abilities. Of the remaining four elements of thought, only inference making appears in cognitive dimension micro-skills set. No other elements of thought are clearly listed within the 35 dimensions, although each of the key 33 terms are—for example, the exploration of implications is listed as a cognitive microskill, but the ability to generate implications is specified in the eight elements of thought. Figure 1.The eight elements of thought. All thought, according to Paul and Elder (2008) consists of eight unique elements that are situated within particular context. Mulnix (2012) affirms the equivalence of thinking and reasoning that Elder and Paul (2007a) assert, whereas Evans (2012) places thinking at the heart of decisionmaking and reasoning, as Elder and Paul suggest—in particular, that the process of thinking generates the reasons that the process of reasoning then bases its conclusions on. Holyoak and Morrison (2012, p. 1) define thinking as “the systematic transformation of mental representations of knowledge to characterize actual or possible states of the world, often in service of goals,” which is essentially goal-directed modeling as defined herein. These convergences in definitions for the constructs of thinking and reasoning suggest a recent emergence of coherence in the field that is useful for the purposes of this study. 34 Figure 2. The eight elements of scientific thought. The general elements of thought remain unchanged when applied in a particular context—such as natural science. 1 Building a conceptual model for this study. The transition from general thought to scientific thought is in the specificity of context (Paul & Elder, 2008). In an effort to distinguish thinking from reasoning, the author proposed the following definitions of thinking and reasoning as conceptual bases for coding evidence of the same throughout this study. Thinking is hereby defined as the ability to construct a model—which is one of the items within the elements scientific of thought given by Paul and Elder, called concepts. This definition is (1) flexible enough to encompass any representational system, (2) straightforward enough to permit the kinds of frequency distributions and classification schemes that enable direct measurement of this cognitive behavior, and is (3) inspired by the work of PER pioneers cited herein, such as Hestenes, Hake, Redish, 1 From The Miniature Guide for Students and Faculty to Scientific Thinking (Kindle section title Why Scientific Thinking?), by L Elder and R. Paul, 2008, Copyright 2008 by the Foundation for Critical Thinking... Reprinted with permission. 35 and Mazur. The term model is simply any representation of structure (Hestenes, 2010), and structure is a broader term—open to wide interpretation—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. This definition for reasoning is consistent with two of the elements of scientific thought suggested by Paul and Elder: scientific implications and consequences, and scientific point of view. In the model for scientific thought shown in Figure 2 above, axioms are part of the assumption that are made rather than the result of any process, whereas in Physics, axioms are used in order to generate new ones, as well as being part of fundamental assumptions. Moreover, there are implications and consequences associated with axiom development—also an element of scientific thought—that must be accounted for. The right-hand side of Figure 2 is largely empirical in nature, whereas the left-hand side is rational. To the degree that reasons are generated by thinking about scientific information in the form of data and observations, and if decisions about the interrelatedness of those reasons are what comprise reasoning, then the model for scientific thought put forward by Paul and Elder (2008), already has natural divisions for the constructs of thinking and reasoning as defined herein by the author. Given that the authors definitions are primarily for high-level coding that is consistent with the practice of physics in an IP classroom, the fine-grained distinction put forward in the model by Paul and Elder served as additional theoretical codes used in the data analysis. 36 Language is the primary means by which human beings encode for meaning. The academic setting of an Introductory Physics (IP) classroom requires an array of languages—or what this study calls multiple representational systems (MRS). Words, symbols, graphs, and diagrams encode various kinds of meaning depending on the context of student inquiry. The following section addresses this topic with a view to how encoding for meaning with MRS corresponds to thinking and reasoning. Representational systems. Representational tools and systems have the capacity to encode information (Fekete, 2010), promote conceptual change (Johri & Lohani, 2011; Johri & Olds, 2011), as well as direct inquiry (Moore et al., 2013), scaffold learning (Eitel et al., 2013), and facilitate the process of knowledge construction (Kolloffel, Eysink, & Jong, 2011). Fekete (2010) suggested that representations are simply the realization that there exists an isomorphism (one-to-one relationship) between the conceptual/perceptual domain, and the activity space where representation occurs. Activity spaces are technically defined as “spatiotemporal events produced by dynamical systems” (Fekete, 2010, p. 69), and neural systems in the human brain mimic those dynamical systems to some degree. The dynamical systems approach is conceptually equivalent to using most any marker, or token, to describe one thing in terms of another—which is the general practice of Physics (Plotnitsky, 2012; Wu & Puntambekar, 2012). 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 37 an effort to mimic the expert view. In these ways, MRS are instrumental for modeling the structure of physical phenomena, and therefore serve as evidence of what students believe the varied representational conventions of mathematics and physics are capable of describing. Their status as mechanisms of epistemological change is the primary research question at hand. Waldrip and Prain (2012) have qualitatively tested an intervention that relies heavily on representational systems in an effort to promote scientific reasoning as a cognitive activity that involves thinking by means of constructing representations, and subsequently judging them for their efficacy—which under the model for scientific thought proposed by Paul and Elder (2008), is both thinking by representation, and reasoning through judgment of those thoughts. The results they obtained indicate that an interactive environment where observed phenomena are tested and re-tested, represented and re-represented, and evaluated through group collaborations that give opportunities to defend and judge hypotheses, positively influences student confidence and engagement. The distinction that Fekete (2010) offers in terms of how representations relate to their encodings is part of the conceptual basis for thinking and reasoning as defined by Paul and Elder (2008), and described in learning environments by Waldrip and Prain (2012). Moreover, the features of models in Physics—such as systemic, geometric, object, interaction, and temporal (Hestenes, 2010)—serve as very particular and fine-grained conceptual distinctions to be coded for in the qualitative analysis of student artifacts in this study. Prior knowledge influences the top-down thinking and reasoning that students bring to learning habitats where new information found therein is designed to promote 38 bottom-up forms of thinking and reasoning for conceptual, and potentially epistemological change. However, as shown in the next section, epistemic beliefs are strong motivators for and against self-regulated learning. In other words, certain beliefs either promote or stifle the types of thinking and reasoning that are required for learning. Self-efficacy, self-regulation, and journaling. The epistemic beliefs that students have concerning the development of scientific knowledge directly influence the acquisition of that knowledge, and therefore the achievement that shepherd self-concept and self-efficacy when learning in the scientific domain (Mason, Boscolo, Tornatora, & Ronconi, 2012; Sawtelle, Brewe, Goertzen, & Kramer, 2012). Cassidy (2011) points out the fact that academic control is one factor within the complex of self-regulated learning that competes with a student’s self-evaluation—such as the belief that learning is dependent on the amount of struggle involved with academic endeavors and inborn traits such as intelligence (Koksal & Yaman, 2012). Achievement gaps narrow in classrooms where extensive reading and writing are organic to an engaging experience that contributes to enhanced motivation, self-efficacy, and locus of control—which are essential components of active learning and achievement in academic settings (Kennedy, 2010). Moreover, the likelihood that a student will deploy any particular representational medium—journal or otherwise—depends on factors such as motivation, goal orientation, self-regulation, and general interest in the domain of knowledge relevant to the setting (Bodin & Winberg, 2012; Kennedy, 2010). Therefore, providing students with an opportunity to defend their strategies through discussion and written journals is helpful in promoting the kinds of self-advocacy that catalyzes self-regulated learning (Cifarelli, Goodson-Espy, & Jeong-Lim, 2010; Muis & Duffy, 2013). Furthermore, metacognitive 39 monitoring, self-efficacy, and self-regulated learning are optimized when the epistemological domain of a learner and the epistemology of the domain focus are matched—such as a rationalist in a mathematics setting (Muis & Franco, 2010). The aforementioned findings served as a broad conceptual and theoretical foundation for this study by virtue of the fact that data collection and pedagogy within the study environment match the general features described therein. Journaling and collaboration are the central features of the classroom environment where thinking and reasoning with MRS is being deployed. Muis and Franco (2010) linked metacognitive monitoring, self-efficacy, self-regulated learning, and epistemology in ways that are consistent with Hofer’s epistemic metacognition model (Hofer, 2004)—which also served the overarching conceptual framework for this study. The connections that exist between metacognition, epistemology, and self-regulated learning (Barzilai & Zohar, 2014; Greene, Muis, & Pieschl, 2010) are relatively new in the literature (Hofer & Sinatra, 2010), but nonetheless warranted attention in this study given their connections to the primary data collection method of student journals. Convergence of conceptual and theoretical foundations. The expression of epistemic beliefs is typically expressed in the form of language. Within the field of Physics—and thus an IP classroom—MRS serve as the languages by which a learner is able to encode for meaning, and therefore transmit in writing or in narratives their own epistemic stance. Thinking and reasoning are unavoidable cognitive activities for both conceptual and epistemological change, and are necessarily metaphorical, empirical, and rational in the context of Physics. The efficacy of journal activities to generate selfefficacy and self-regulated learning through metacognitive monitoring (Muis & Franco, 40 2010), while simultaneously affording the author-researcher a corpus of student artifacts employing MRS, provides an equally fertile source of data for analysis of student thinking and reasoning. In these ways, the model for scientific thought (Elder & Paul, 2007b) corresponds with the advance of self-efficacy and self-regulation that is consistent with epistemic change in scientific domains of knowledge (Mason et al., 2012; Muis & Duffy, 2013; Sawtelle et al., 2012). Moreover, the use of journals and interviews provides ample opportunity for the kinds of student reflection that reveal the connections between conceptual and epistemological change through what Hofer (2004) described as epistemic metacognition. Review of the Literature A brief history of personal epistemology research. Personal Epistemology (PE) has been an expanding field of inquiry for at least 40 years, with the coalescence of a handful of models and theories emerging in the late 1990’s to early 2000’s—such as process and developmental models (Bendixen, 2012), and at least four different assessment instruments for judging the epistemic state of learners at most any age (Hofer & Pintrich, 2012). Student beliefs about knowledge are multidimensional and multilayered, such that the nature of knowledge itself can be described along the dimensions of certainty and simplicity, whereas the dimensions source of knowledge and its justification describe the nature of knowing (Hofer & Pintrich, 2012; Mason, Boldrin, & Ariasi, 2010). Epistemological beliefs are simply beliefs about what knowledge is and how it is obtained (Richter & Schmid, 2010), and are a form of declarative metacognitive knowledge (Hofer, 2004). Richter and Schmid (2010) distinguish epistemological metacognition from psychological metacognition in terms of their differing content— 41 where psychological metacognition refers to mechanisms of memory and learning, and epistemological metacognition refers to the process by which knowledge is qualified. Multiple lines of research into personal epistemology in student populations indicates that fine-grained cognitive resources better explain the formation of beliefs about learning than do developmental stages, or belief-systems (Hofer & Pintrich, 2012). Naïve epistemologies are proposed to precede sophisticated ones developmentally—such that the natural progression of knowledge as facts justified by authority (naïve) is transformed into a more complex and nuanced network of ideas (sophisticated) that are understood socially and contingently, and subsequently result in higher achievement (Bromme et al., 2010). However, Bråten and Strømsø (2005) found that naïve epistemology produces better results when the topic at hand is unfamiliar and complex— thus compelling the epistemological framework to rely on authority—whereas a more sophisticated epistemology relying on knowledge as a more personal and subjective construction is more likely to misconstrue the textual evidence under analysis. Sophisticated epistemologies as the means by which learning is positively influenced is contingent on the context of the task and the level of expertise that task participants possess (Hammer & Elby, 2012). Both context and skill place particular kinds of demands on the deployment of representational systems in accordance with the epistemic beliefs that students possess with respect to the capacity of those systems to encode meaning. Developmental models such as the epistemological reflection model (Baxter Magolda, 2012) offer a constructivist viewpoint for understanding the mechanism(s) for epistemological change, whereas process-model theorists consider more fine-grained 42 cognitive resources than developmental stages or beliefs (Bendixen, 2012) as a means for explaining epistemological advance. Finer-grained resources include particular views about knowledge in general, acquisition of said knowledge, the kinds of and interrelations of knowledge types, and the sources of that knowledge. Bendixen and Feucht (2010) offer an integrative model that attempts to capture the clear findings of both the developmental and cognitive branches of the field, by framing the mechanism of change as having three distinct components: epistemic doubt, epistemic volition, and resolution strategies. Epistemic doubt (cognitive dissonance related to beliefs) and epistemic volition (the will to change) work in concert towards epistemological advance (Rule & Bendixen, 2010). Resolution strategies are simply reflective, socially interactive, retrospections by which a person analyzes the implications of personal belief (Baxter Magolda, 2012; Bendixen, 2012). Domain-general and domain-specific epistemologies are distinct factors that influence learning (Lee & Chin-Chung, 2012; Schommer-Aikins & Duell, 2013). In a study involving 701 college students in the United States, researchers used path analysis to determine that domain-general beliefs have an indirect effect on performance, whereas domain-specific (mathematics) beliefs have both direct and indirect effect on mathematical problem solving. The beliefs that are formed within the context of a particular domain influence thinking and reasoning more dramatically than do domaingeneral beliefs that apply to all situations. For example, the belief that the average person learns quickly or not at all was strongly correlated with a weak mathematical background due to choices influenced by the belief that mathematics is not useful or accessible. Moreover, the opposite was also found to be true—that a belief that mathematics takes 43 time to learn and is useful is consistent with the practice of taking more mathematics courses and devoting the diligence to them that accompanies successful skill development (Schommer-Aikins & Duell, 2013). While few researchers in the field of personal epistemology doubt the reality of development stages for epistemological advance, the evidence of domain-specific processes and environments is the primary reason that the majority of attention has shifted to the mechanisms of epistemological change in terms of psychological constructs—such as thinking and reasoning (Hofer & Pintrich, 2012). Strategies for resolving epistemic doubt (Bendixen & Feucht, 2010) and the implications of and on personal beliefs (Bendixen, 2012) are metacognitive and epistemological in nature (Barzilai & Zohar, 2014; Hofer, 2004; Richter & Schmid, 2010), and require some level of social interaction and individual analysis, as well as a positive affective backdrop from which motivation leads to concentration and control in problem-solving settings (Bodin & Winberg, 2012; Muis & Duffy, 2013). With respect to this study, the context of epistemological advance is scientific, and therefore the thinking and reasoning is as well (Paul & Elder, 2008). A brief history of assessment on personal epistemology. One of the earliest attempts to psychometrically measure personal epistemology was the Psychoepistemological Profile (PEP), which measures the construct on three dimensions: Rational, Empirical, and Metaphorical (Royce & Mos, 1980). 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 sees knowledge as derived intuitively with a view to subsequent 44 verification of its universality. The PEP instrument has demonstrated concurrent validity based on examination of group scores and their correspondence to the underlying theory (Royce & Mos, 1980). For example, biologists and chemists were typically strongest on the empirical dimension of PEP, whereas persons situated in the performing arts were more metaphorical in nature—just as mathematicians tend to be more rational than any of the other two PEP dimensions. Furthermore, the construct validity of the PEP has obtained moderate to moderately high correlations at the p = 0.05 level for the MyersBriggs Personality Test, and the MMPI (Royce & Mos, 1980). Royce and Mos (1980) also reported positive correlations for each item on the PEP with the total score in its dimension. Split-half reliability coefficients on two forms of the PEP indicate satisfactory homogeneity with correlations of r = .75, .85, and .76 corresponding to the rational, metaphoric, and empirical dimensions, respectively, for a sample of n = 142 students on form V of the test given in 1970, versus correlations of r = .77, .88, and .77 for a sample of n = 95 students on ...
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