NONABSOLUTE/ RELATIVISTIC (N/R) THINKING:A POSSIBLE UNIFYING COMMONALITYUNDERLYING MODELS OF POSTFORMAL REASONINGbyBERNICE LAI-TING YANB.A., Central Missouri State University, 1971M.Sc., Central Missouri State University, 1973A THESIS SUMMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIES(Department of Educational Psychology and Special Education)We accept this thesis as conformingto the r quired standardTHE UNIVERSITY OF BRITISH COLUMBIAMarch 1995©Bernice Lai-Ting Yan, 1995In presenting this thesis inpartial fulfilment of therequirements for an advanceddegree at the University of BritishColumbia, I agree that the libraryshall make itfreely available for reference andstudy. I further agree that permissionfor extensivecopying of this thesis for scholarlypurposes may be grantedby the head of mydepartment or by his or herrepresentatives. It is understood thatcopying orpublication of this thesis forfinancial gain shall not be allowed withoutmy writtenpermission.(Signature)_____________________________Department of Educational Psychology and Special EducationThe University of BritishColumbiaVancouver, CanadaDateMci-1c%1 /79SDE-6 (2188)IIABSTRACTThis dissertation identified and addressed four of the unresolved issues pertainingto the proposition that nonabsolute/ relativistic (N/R) thinking is one of the possibleunifying commonalities underlying the selected models of postformal reasoning, namelyProblem Finding, Dialectical Reasoning, Relativistic Operations and ReflectiveJudgment.A total of 254 participants aged 10 to 48 and attending Grade 5 to doctoral studieswere involved. Each participant was administered eight tests in pencil-and-paper formatto measure eight different constructs of thinking. Different specific hypotheses wereevaluated through different statistical approaches.The four identified issues were addressed as follows:Firstly, nonabsolute! relativistic thinking was reconceptualized and operationallydefined as a multidimensional and multilevel construct. Two dimensions were proposed:the basic form and the epistemic view. Within the basic form dimension, two levels wereproposed: the formal and the postformal forms.Secondly, a battery of three tests was specifically designed by Arlin and theauthor to measure the different dimensions and levels of nonabsolute/ relativisticthinking.Thirdly, strong empirical evidence was obtained supporting the generalhypothesis that nonabsolute! relativistic thinking is a possible unifying commonalityunderlying the four selected postformal models. Within the construct of nonabsolute/relativistic thinking, two dimensions, the basic form and the epistemic view, can bedifferentiated as hypothesized.Fourthly, empirical evidence was also obtained supporting the general hypothesisthat nonabsolute/ relativistic thinking is an instance of both formal and postformalreasoning. Specifically within the basic form dimension, two qualitatively differentforms, the formal and the postformal, can be differentiated as hypothesized. FindingsIIIalso suggested that the development of a nonabsolute epistemic view might play a crucialrole in the development of the postformal form. Therefore, the emergence of thepostformal form can be explained by a paradigm shift from an absolute to a nonabsoluteepistemic view. Performances in the tests of the postformal form and of the epistemicview in combination were found to be good predictors of performances in the selectedpostformal tests.Significant implications of the findings are that nonabsolute/ relativistic thinkingrepresents a form of metamorphosis from closed-system to open-system thinking and itmight serve as a potential springboard in the development of higher order thinking.IvTABLE OF CONTENTSABSTRACT/IlTABLE OF CONTENTS / IVLIST OF TABLES / VILIST OF FIGURES / VIIACKNOWLEDGEMENTS / IXDEDICATION / XCHAPTER I: INTRODUCTION I 1A. BACKGROUND OF THE STUDY / 1B. PROBLEM STATEMENTS /3C. RESEARCH QUESTIONS /5D. SIGNIFICANCE OF THE STUDY /7E. DEFINITION OF TERMS / 8CHAPTER II: LITERATURE REVIEW /11A. FORMAL REASONING--A FINAL STAGE? /111. Overview/ 112. Criticisms / 13B. POSTFORMAL REASONING--BEYOND FORMAL THINKING /151. Overview/ 152. Diversity / 163. In Search of Unifying Commonalities / 18C. NONABSOLUTE/RELATIVISTIC (N/R) THINKING--A PROPOSEDUNIFYING COMMONALITY UNDERLYING POSTFORMAL MODELS /191. Overview / 192. Unresolved issues /213. Models associated with Nonabsolute/ relativistic (N/R) Thinking / 244. Reconceptualizing the Construct of Nonabsolute/ relativistic (N/R) Thinking /31D. SUMMARY AND DISCUSSION /39CHAPTER III: RESEARCH QUESTIONS & METHODOLOGY /43A. RESEARCH QUESTIONS /43B. METHODOLOGY /451. Operational Definitions of Nonabsolute/ relativistic (N/R) Thinking(Addressing Research Question 1)! 45V2. Tests of Nonabsolute/ relativistic (N/R) Thinking (Addressing ResearchQuestion 2)/473. Pilot Study (Exploring the Relationships among the 3 Tests of Nonabsolute/relativistic (N/R) Thinking) / 584. Design and Proposed Analyses (Addressing Research Question 3 and 4) /66CHAPTER IV: ANALYSES AND RESULTS /89A. DATA COLLECTION /89B. PRELIMINARY STATISTICS /92C. ANALYSES AND RESULTS OF THE MAIN STUDY / 101CHAPTER V: DISCUSSION / 152A. SUMMARY AND INTERPRETATION OF FINDINGS / 152B. IMPLICATIONS OF FINDINGS AND SUGGESTIONS FOR FUTURERESEARCH! 1611. Nonabsolute! relativistic (N/R) Thinking as a Commonality underlyingPostformal Models / 1612. Nonabsolute! relativistic (N/R) Thinking as a Multidimensional and MultilevelConstruct / 1623. Nonabsolute! relativistic (N/R) Thinking as a Form of Metamorphosis fromClosed-System to Open-System Thinking / 1634. Nonabsolute! relativistic (N/R) Thinking as a Potential Springboard in theDevelopment of Higher Order Thinking / 165C. CONCLUDING REMARKS / 167REFERENCES / 169APPENDIXES I 178Appendix A: Test Items of Test of Formal Form of Nonabsolute! relativistic (N/R)thinking / 178Appendix B: Test of Minimal Formal Reasoning (FR) / 180Appendix C: Test of Problem Finding (PF) / 186Appendix D: Test of Dialectical Reasoning (DR) / 191Appendix E: Test of Relativistic Operations (RO) / 193Appendix F: Test of Reflective Judgement (RJ) / 196Appendix G: A Sample of the Complete Set of Tests / 199Appendix H: Glossary of Abbreviations and Symbols / 215Appendix I: Explanation of Fit Indices in Confirmatory Factor Analysis /216VILIST OF TABLESTable 1: Pilot Study: Correlation Matrix of Item Scores of the 3 N/R Tests / 60Table 2: Pilot Study: Correlation Matrix of Test Scores of the 3 N/R Tests / 61Table 3: List of Constructs and Corresponding Tests / 69Table 4: Summary of Interpretation of Test Scores / 72Table 5: Inter-rater Reliability Indices / 93Table 6: Means and Standard Deviations of Item Scores of the 3 N/R Tests / 94Table 7: Means and Standard Deviations of Test Scores of the 8 Tests / 95Table 8: Correlation Matrix of Item Scores of the 3 N/R Tests / 96Table 9: Correlation Matrix of Test Scores of the 8 Tests / 98Table 10: Variance-Covariance Matrix of Item Scores of the 3 N/R Tests / 99Table 11: Variance-Covariance Matrix of Test Scores of the 8 Tests / 100Table 12: Summary of Research Questions and Corresponding Methods of Analysis / 102Table 13: Summary of Fit Indices of Models Al and A2 / 110Table 14: Summary of Fit Indices of Models Bl - B3 / 119Table 15: Results of Exploratory Factor Analysis / 145VIILIST OF FIGURESFigure 1: Dimensions and Levels of Nonabsolute/ relativistic (N/R) Thinking / 32Figure 2: Definition Criteria for the Two Forms of Nonabsolute/ relativistic (N/R)Thinking /36Figure 3: Pilot Study: Contingency Tables /63Figure 4: Model Al of Confirmatory Factor Analysis / 75Figure 5: Model A2 of Confirmatory Factor Analysis /76Figure 6: Model Bl of Confirmatory Factor Analysis /78Figure 7: Model B2 of Confirmatory Factor Analysis /79Figure 8: Model B3 of Confirmatory Factor Analysis / 80Figure 9: Model B4 of Confirmatory Factor Analysis / 82Figure 10: Model Cl of Confirmatory Factor Analysis / 86Figure 11: Model Al: Results of Confirmatory Factor Analysis / 104Figure 12: Model A2: Results of Confirmatory Factor Analysis / 108Figure 13: Model B 1: Results of Confirmatory Factor Analysis / 112Figure 14: Model B2: Results of Confirmatory Factor Analysis / 116Figure 15: Model B3: Results of Confirmatory Factor Analysis / 118Figure 16: Model B4: Results of Confirmatory Factor Analysis / 121Figure 17: Order of Task Difficulty according to Percentage of Task Mastery / 126Figure 18: Contingency Tables: FR (Minimal Formal Reasoning) x 3 N/R Tests / 129Figure 19: Contingency Tables: N/R-F (formal form) x 2 postformal level N/R Tests /130Figure 20: Contingency Tables: N/R-EV (epistemic view) x N/R-PF (postformal form) /131Figure 21: Contingency Tables: N/R-PF (postformal form) x 4 Postformal Tests / 132Figure 22: Contingency Tables: N/R-EV (epistemic view) x 4 Postformal Tests / 134Figure 23: Contingency Tables: Transitional Development of N/R-PF (postformal form)x 4 Postformal Tests / 136Figure 24: Contingency Tables: Transitional Development of N/R-EV (epistemic view) x4 Postformal Tests / 138Figure 25: Order of the 8 Tests according to Ages of Onset of Task Mastery I 142Figure 26: Model Cl: Results of Confirmatory Factor Analysis I 147VIIIIxACKNOWLEDGEMENTSFirst of all, I would like to thank the three advisors on my dissertation advisorycommittee. My gratitude goes to Dr. Patricia K. Arlin who is the major inspiration forthis dissertation. Her support throughout the study from inceptionto fruition isappreciated beyond words. My sincere thanks also go to Dr. MarionPorath for herstimulating ideas and fresh perspectives. I am also extremely gratefulto Dr. NandKishor for his expert advice in all the statistical analyses of my study, particularly inconfirmatory factor analysis.I would like to express my gratitude to the following persons for their specialpermission to cite or use their work:Dr. Patricia K. Arlin for her permission to use her Problem Finding Task, to adaptthe Arlin Test of Formal Reasoning, and to use her adaptation of the scoring criteria ofthe tests of Dialectical Reasoning and of Reflective Judgment. Her joint authorship inthe designing of the battery of the three tests of nonabsolute! relativistic thinking is alsomuch appreciated.Dr. Karen Kitchener and her colleagues for the permission to use and adapt thetest of Reflective Judgment Interview copyrighted by King and Kitchener in 1978.Dr. Deirdre A. Kramer for all the information she had generously shared with me.Dr. Jan Sinnott for her permission to use her test of Relativistic Operations andfor her advice on the scoring criteria.Dr. Marylou F. Worthen for sharing with me her unpublished papers and herPreformal, Formal, Postformal-Relativistic Test (PFPR Test) of Cognitive Development.I would like to thank the following persons for their generous help in therecruitment of participants: Dr. Patricia K. Arlin, Heesoon Bai, Dr. Elizabeth Jordan,Ophelia Kan, Dr. Nand Kishor, Dr. William McKee, Joyce Poon, Dr. Marion Porath, andBarbara Turnboll. I am equally thankful to all the participants without whoseparticipation, this study would not be realized.I would like to express my appreciation to the principal of Selkirk SecondarySchool, Mr. J.P. Harrington, and his staff and the principal of Killarney SecondarySchool, Mr. G. May, and his staff who had been very helpful in the process ofrecruitment of participants.My gratitude also goes to Ophelia Kan for her very professional andindispensable help in serving as the second rater in the scoring of all the test protocolsand in editing the manuscript.My appreciation goes to the faculty, staff and fellow students of the Departmentof Educational Psychology and Special Education who have been extremely supportivein many ways. My appreciation also goes to the staff of the Education ComputingServices for their invaluable assistance.As my study spans a period of time throughout which innumerable persons havegiven me their support, I am unable to list all of them but my thanks go to each and everyone of them.Last but not least, my deepest gratitude goes to my mother for her patience andstanding by me all these years.DEDICATIONThis dissertation is dedicated to my parents and all my teachers with deep gratitude.x1CHAPTER I: INTRODUCTIONThe purpose of this study is to explore nonabsolute/ relativistic (N/R) thinking asone of the possible unifying commonalities underlying the models of postformalreasoning. There has been speculation that nonabsolute/ relativistic (N/R) thinking mightbe required for the performance of higher order thinking, specifically in postformalreasoning (see Arlin, 1974, 1975/6; Basseches, 1980; King, Kitchener, Davidson, Parker& Wood, 1983; Kitchener & King, 1981; Kramer, 1983a; Riegel, 1973; Sinnott, 1981,1989). In this light, better understanding about nonabsolute/ relativistic (NIR) thinkingcould be of benefit to the field of cognitive development and education, be it formal orinformal. However, the specific nature of nonabsolute/ relativistic (N/R) thinking is stillan open question if not a question unexplored. Thus in this study, an attempt is made toexplore nonabsolute/ relativistic (N/R) thinking in the context of both formal andpostformal reasoning from a developmental perspective.A. BACKGROUND OF THE STUDYPiaget’s interdisciplinary research was historically the dominant theory ofcognitive development for several decades. However, in the past decade or so, Piaget’stheory of cognitive development, particularly his structural stage model has beenseriously questioned or even dismissed by some researchers (e.g. Brainerd, 1978;Broughton, 1984; Siegler, 1981).Particularly as a reaction to Piaget’s claim that formal reasoning/ operationsrepresent the final stage of cognitive development, a number of models of postformalreasoning and adult cognition has been proposed. Most of these proposed models sharethe conviction that, by ending the stages of cognitive development in adolescence, Piaget2truncated developmental concepts of both adulthood and cognition (Arlin, 1975;Commons, Armon, Kohlberg, Richards, Grotzer & Sinnott, 1990; Commons, Richards &Armon, 1984; Commons, Sinnott, Richards & Armon, 1989; Mines & Kitchener, 1986).During the first decade of research on postformal reasoning! operations,researchers focused on creating models and developing measures. Thus postformalreasoning has grown to become a collective label for a wide range of models describinglate adolescent and adult thinking. Some of these models might be considered ascontinuations or extensions of the formal stage, and as such they represent one facet ofthe neo-Piagetian movement. On the other hand, other models represent entirelydifferent forms or views of adult cognition. The models of postformal reasoningextended into very diverse domains and were formulated through very differentapproaches.Recently, there seems to be a growing interest in unifying models and organizingdata across domains and measures. In the attempt to unify the diversity in the field, oneapproach is to interrelate empirically the different postformal sequences through “crossmeasures” and “cross domains” studies (e.g. Cavanaugh & Stafford, 1989; Commons etal., 1984; Commons et al., 1989; Hoyer et al., 1989; Kitchener & King, 1985). Asrevealed in these studies, the line of transition from formal to postformal thinking is byno means clear cut. For example, Cavanaugh and Stafford (1989) found that a personmay be identified as functioning at the postformal level using a test developed byLabouvie-Vief and colleagues (Labouvie-Vief, Adams, Hakim-Larson & Hayden, 1983),but not necessarily so using a test developed by Commons and colleagues (Commons,Richards & Kuhn, 1982). Such kind of intra-individual discrepancies might reflectproblems associated with measurement, or level of task difficulty, or domain specificity,or a combination of these factors.However, before entertaining the above mentioned possibilities which might bean explanation for the intra-individual discrepancies regarding the performances with3postformal reasoning tests, I would argue that a more fundamental issue needs to beaddressed, that is, do the postformal reasoning tests in question share any basiccommonalities at all? This fundamental issue is precisely the concern of anotherapproach by which attempts were made to unify the field of postformal research throughtheoretically analyzing the forms or structures of certain postformal models in order toidentify their commonalities (Kramer, 1983; Kitchener, 1983; Arlin, 1984; Commons &Richards, 1984).There has been speculation that nonabsolute/ relativistic (N/R) thinking may beone of the possible unifying commonalities underlying a cluster of postformal modelsand measures. A number of researchers has independently suggested that nonabsolute!relativistic (N/R) thinking is required for postformal reasoning (e.g. Arlin, 1975, 1975/6;Basseches, 1980; King, Kitchener, Davidson, Parker & Wood, 1983; Kitchener & King,1981; Riegel, 1973; Sinnott, 1981, 1989). In a similar vein, Kramer (1983a) proposedthat nonabsolute/ relativistic (‘N/R) thinking may be one of the core features underlyingthe models of postformal reasoning. However, I would argue that the proposition thatnonabsolute/ relativistic (N/R) thinking as one of the commonalities underlying themodels of postformal reasoning contains unresolved issues. Research is needed toexplore and possibly resolve these issues.B. PROBLEM STATEMENTSFour of the unresolved issues pertaining to the proposition that nonabsolute/relativistic (N/R) thinking is one of the commonalities underlying the models ofpostformal reasoning are identified and addressed in this study.The first unresolved issue concerns the lack of empirical evidence in support ofthe proposition that nonabsolute/ relativistic (N/R) thinking is one of the possible4unifying commonalities underlying the models of postformal reasoning.It appears thatsuch a proposition has yet to be tested empirically. However, before submitting such aproposition to empirical testing, there are other basic issues to be addressed.The second unresolved issue is whether nonabsolute! relativistic (N/R) thinking isformal or postformal in nature. An implicit assumption held by some of the researchersis that in order for nonabsolute! relativistic (N/R) thinking to be qualified as a commonfeature of postformal reasoning, it is necessary to demonstrate that it possesses a form orstructure that is postformal in nature (Cavanaugh, Kramer, Sinnott, Camp & Markley,1985; Kramer, 1 983b). While some researchers suggested that some kind of relativisticthinking is required for postformal reasoning (e.g. Arlin, 1984, 1990; Kramer, 1983a;Sinnott, 1981, 1989), other researchers questioned whether nonabsolute! relativistic(N/R) thinking is really postformal (Cavanaugh et al., 1985; Kramer, 1983b). Thecounter-argument as primarily advanced by Kramer (1983b, 1986) contended that theawareness of relativity, contrary to prediction, was found to be necessary but notsufficient for formal operations. Therefore, it is debatable whether nonabsolute/relativistic (N/R) thinking is an instance of formal or postformal reasoning.The discussion of both the first and second unresolved issues would necessarilyextend to the third and the fourth unresolved issues. The third unresolved issue concernsthe need for an operational definition of nonabsolute/ relativistic (N/R) thinking. Thefourth unresolved issue concerns the need for the design of a measure of this veryconstruct. As suggested in the relevant literature, there is really no consensus among theresearchers regarding the specific nature of nonabsolute/ relativistic (N/R) thinking, letalone the definition and measurement of such a construct (Arlin, 1974, 1975/6;Basseches, 1980; Cavanaugh et al., 1985; Kitchener, 1986; Kitchener & King, 1981;Kramer, 1983a; Riegel, 1973; Sinnott, 1981). I would argue that both the first andsecond unresolved issues are hinged upon and eventually have to be related to the thirdand the fourth unresolved issues. The reason is that without an operational definition and5measurement of the construct of nonabsolute/ relativistic (N/R) thinking, there is reallyno basis for 1) testing empirically the proposition that nonabsolute/ relativistic (N/R)thinking is one of the commonalities underlying the selected models of postformalreasoning, and for 2) determining the structural stage status of nonabsolute/ relativistic(N/R) thinking.The focus of this study is to address these four unresolved issues pertaining to theproposition that nonabsolute! relativistic (N/R) thinking is one of the possible unifyingcomnionalities underlying the several models of postformal reasoning.C. RESEARCH QUESTIONSResearch Question 1:How can nonabsolute/ relativistic (NIR) thinking be operationallydefined?This research question is designed to address the third unresolved issue concerning theneed for an operational definition of nonabsolute/ relativistic (N/R) thinking. To addressthis question, nonabsolute/ relativistic (N/R) thinking would be defined as amultidimensional and multilevel construct. Two of the dimensions to be explored are thebasic form dimension and the epistemic view dimension associated with nonabsolute/relativistic (N/R) thinking. Within the dimension of basic form, nonabsolute/ relativistic(N/R) thinking would be defined at both the formal and postformal level.Research Question 2:How can nonabsolute/ relativistic (NJR) thinking be measured?This research question is designed to address the fourth unresolved issue concerning theneed for the design of a measure of nonabsolute! relativistic (N/R) thinking. To address6this question, nonabsolute/ relativistic (N/R) thinking wouldbe measured as amultidimensional and multilevel construct. A battery of three tests of nonabsolute/relativistic (N/R) thinking are proposed in this study to measure 1) the formal form, 2)the postformal form, and 3) the epistemic view of nonabsolute/ relativistic (N/R)thinking.Research Question 3:Is nonabsolute/ relativistic (NJR) thinking a common factorunderlying the selected models of postformal reasoning?This research question is designed to address the first unresolved issue concerning thelack of empirical evidence in support of the proposition that nonabsolute/ relativistic(N/R) thinking is one of the commonalities underlying the models of postformalreasoning. To address this question, the inter-relationships among the tests of postformalreasoning and of nonabsolute/ relativistic (N/R) thinicing would be explored.Research Question 4:Is nonabsolute/ relativistic (NIR) thinking an instance of formal orpostformal reasoning or of both?This research question is designed to address the second unresolved issue concerningwhether nonabsolute! relativistic (N/R) thinking is formal or postformal in nature. Toaddress this question, the relationship among nonabsolute/ relativistic (N/R) thinking,formal reasoning and the selected models of postformal reasoning wouldbe empiricallyexplored. The different dimensions and levels of nonabsolute! relativistic (N/R) thinkingwould also be employed for prediction purposes.7D. SIGNIFICANCE OF THE STUDYThe focus of this study is the exploration of whether nonabsolute/ relativistic(N/R) thinking is one of the possible unifying commonalities underlying the models ofpostformal reasoning. The search for conimonalities underlying the selected postformalmodels would serve two purposes: 1) to unify the diversity in the field of postformalresearch; and 2) to differentiate some of the qualities of postformal reasoning from thoseof formal reasoning.From a theoretical perspective, this study deals with a specific segment within abroader context of problems, namely the search for possible connections among thedifferent models of postformal reasoning and between formal and postformal reasoning.As Arlin (1989) pointed out, the logic and mechanism of the transition betweenformal and postformal operations have yet to be discovered. Thus I would argue that abetter understanding about the possible commonalities underlying a specific cluster ofpostformal models might help shed some light on the transition from formal topostformal reasoning in specific, and from lower to higher order thinking in general.At an empirical level, attempts are made to define operationally, and to measurequantitatively the construct of nonabsolute/ relativistic (N/R) thinking, as well as to relateempirically such a construct with formal and postformal reasoning. Thus such attemptsmight represent an alternative approach to the work done on relativistic thinking bySinnott (1981, 1989) and Kramer (Cavanaugh et al., 1985; Kramer, 1983a) amongothers.From an applications perspective, I would argue that the framework ofnonabsolute! relativistic (N/R) thinking could be applied to operate on a wide variety ofdomains such as issues in science, humanities, laws, politics, religion, and morality oftoday as well as real life problems of everyday living. In a clinical and educationalsense, the framework of nonabsolute/ relativistic (N/R) thinking could be used to8diagnose the presence or absence of the basic forms and theepistemic views associatedwith such types of thinking. The framework of nonabsolute! relativistic(N/R) thinkingcould also provide suggestions for the development of more powerfulforms of datamanipulation so as to facilitate more effective means of problem finding and problemsolving.As findings of this study support the proposition that nonabsolute! relativistic(N/R) thinking is one of the possible unifying commonalities underlying the selectedmodels of postformal reasoning, further research is called for to investigate both thetheoretical and applied implications of such findings. Since one of the prime concerns ofeducation is the development of cognitive potentials, the findings of this study could beof particular interest. Future research would be desirable to explore possible ways ofpromoting and facilitating the development of nonabsolute/ relativistic (N/R) thinkingwhich in turn might serve as a springboard for the development of higher order thinkingwithin and across domains.E. DEFINITION OF TERMSFormal reasoning:Formal reasoning or formal operations are postulated by Piaget to represent thefinal stage of cognitive development (Inhelder & Piaget, 1958). The major characteristicof formal reasoning is the ability to engage in “abstract thinking” which permits thereversibility between reality and possibility. Its essential features include hypotheticaldeductive reasoning, propositional thinking and construction of all possible combinations(see Arlin, 1975; Byrnes, 1988; King, 1986; Neimark, 1975, 1979, 1982).9Nonabsolute/ relativistic (NJR) thinking:Nonabsolute/ relativistic (N/R) thinking has beenproposed to be one of thepossible unifying commonalities underlying the modelsof postformal reasoning. Thistype of thinking is often contrasted with the kind of relatively moreabsolute and rigidthinking associated with formal reasoning. There is no consensusamong researchersregarding the specific nature of nonabsolute/ relativistic(N/R) thinking. The terms“nonabsolute” and “relativistic” are often used interchangeably. The connotation ofsuchterms is often vague and open for interpretation.According to the classical definition of relativity by Irihelder and Piaget (1958),asimple form of relativity can be defined as the coordination of two or more frames orsystems of reference, which is one of the eight formal operational schemataor concepts.Arlin (1984a) argued that this schema might represent the pivotal concept that marks thetransition from high-formal to postformal reasoning.Taking Arlin’s (1984a) argument one step further, it is proposed in this study thatnonabsolute/ relativistic (N/R) thinking can be defmed as a multidimensional andmultilevel construct.Postformal reasoning:Postformal reasoning or postformal operations are defined through a wide rangeof models which have been designed to describe late adolescent and adult thinking,specifically thinking beyond formal reasoning (see Commons et al., 1984). The proposalof postformal reasoning can be viewed as the result of dissatisfactions regardingtheclaim made by Inhelder and Piaget (1985) that formal reasoning represents the finalstageof cognitive development. Researchers in the field of postformal reasoning generallyclaim that adult thinking contains the framework of formal reasoningand otherframeworks as well. This kind of development results in multipleframeworks under10which formal operations are used within a higher-stage system of operations. Theseframeworks provide the means to transcend the limitations of formal reasoning.Models of postformal reasoning associated with nonabsolute/ relativistic (NIR)thinking:The models of postformal reasoning postulated to be associated with nonabsolute/relativistic (N/R) thinking include: problem fmding (Arlin, 1974, 1975/6), dialecticalreasoning (Basseches, 1980), relativistic operations (Sinnott, 1981, 1989), and reflectivejudgment (King, Kitchener, Davidson, Parker & Wood, 1983; Kitchener & King, 1981).More detailed discussion on the terms mentioned above is presented in theliterature review in chapter IL11CHAPTER II. LITERATURE REVIEWA review of the pertinent theoretical and empirical literature related to postformalreasoning is provided in this chapter. This chapter is composed of four parts: A) Formalreasoning--a fmal stage?; B) Postformal reasoning--beyond formal reasoning; C)Nonabsolute! relativistic (N/R) thinking--a proposed unifying commonality underlyingpostformal models; D) Summary and discussion.Part A (Formal reasoning) serves as a background for the discussion of part B(Postformal reasoning) which in turn provides a context for the discussion of part C(Nonabsolute/ relativistic (N/R) thinking). Finally, a summary of the literature review isprovided that leads to the development of research questions.A. FORMAL REASONING--A FINAL STAGE?1. OverviewPiaget described cognitive development as a process of acquisitions of generalstructures that are related to each other in a logical and hierarchical sequence. Withinthis framework of the developmental process, he posited four structural stages: 1)sensorimotor (0-2 years), 2) pre-operational (2-7 years), 3) concrete operational (7-11years), and 4) formal operational (11 years and above).The focus of part A is to provide a brief introduction to the formal operationalstage (see Inhelder & Piaget, 1958). The formal operational stage as considered byInhelder and Piaget (1958) is unique. It is the “fmal equilibrium” in cognitivedevelopment. This claim was made despite the fact that the oldest subject’s protocolreported was 16 years 10 months (Inhelder & Piaget, 1958, p.60).12The major characteristic of formal reasoning! operations is the abilityto engage in“abstract thinking” which contrasts with concrete thinking of the previous stageandwhich permits the reversibility between reality and possibility. Associated with thismajor characteristic of formal reasoning are several essential features that include: 1)hypothetic-deductive reasoning which involves the ability to generate hypotheses andsubject them to empirical investigation; 2) propositional thinking which involves theability to think in terms of propositions and to make logical inferences and 3)construction of all possible combinations which involves the ability to generate allpossible combinations of variables systematically. This strategy ensures a completelisting of “the possible” from which “the real” may be identified. (see Arlin, 1975;Byrnes, 1988; King, 1986; Neimark, 1975, 1979, 1982).According to Piaget (Inhelder & Piaget, 1958, 1969), formal operations areassociated with two logical-mathematical models, namely 1) the combinatorial system,and 2) the INRC group of transformation. The first model, the combinatorial system, isalso known as the 16 binary combinations. Through this model one can generate thelisting of possibilities of elements and their relations. The second model, the INRCgroup, is a representation of the Klein 4-group which is borrowed intact from abstractalgebra (Brainerd, 1978a, 1978b). The four groups of transformation are: Identity (I),Negation (N), Reciprocity (R), and Correlative (C). In this model the relationshipsamong sets of propositions are described. (see Brainerd, 1978a, 1978b; Brynes, 1988;Inhelder & Piaget, 1958, 1969; King, 1986 for more detailed discussion on the twological-mathematical models.)Inhelder and Piaget (1958) identified eight formal operational schemata orconcepts which are dependent not only upon the logical-mathematical operations but alsoon “appropriate data” and “experience” (see p.308). These eight concepts are: 1)multiplicative compensations, 2) correlations, 3) probability, 4) combinations, 5)proportions, 6) forms of conservation beyond direct verification, 7) mechanical13equilibrium, and 8) co-ordination of two or more frames or systemsof reference which issaid to require a simple type of relativistic thinking (Arlin, 1980, 1984a, 1984b,1986a;Inhelder & Piaget, 1958).2. CriticismsPiaget’s model of formal operations has been the subject of much criticism. Themore common types of criticism are as follows and they are by no means mutuallyexclusive:1) The first criticism is that the model lacks parsimony (cf. Brainerd, 1978) andempirical fit (cf. Bynum, Thomas & Weitz, 1972). It has been pointed out that thelogical competency as described by Piaget’s model of formal operations cannot bedetected in the performance of adolescent subjects. Thus, a less elaborate model wouldalready be sufficient to explain adolescent thinking (see Commons, Richards & Armon,1984).2) The second criticism represents a radical rejection of the stage model ingeneral and of the model of formal operations in particular (cf. Broughton, 1984; Riegel,1973). This type of criticism challenges the entire theoretical foundation of the model.It argues that the centrality of logic in the model of formal operations precludes all otherdimensions of cognition, and has taken cognitive development completely out of thecontext of reality. Broughton (1984), in his criticism of Piaget’s theory, argued that thereare at least 15 major problems with the formal operational model. Each is taken as arefutation of Piaget’s assumptions. All are taken to comprise a critical mass necessitatinga replacement of Piaget’s theory. According to Broughton (1984), “the issue is not one ofthe stage ‘beyond formal operations’, it is one of the stages ‘beyond Piaget” (p.411).14I would argue that this type of criticism might be right in that the model of formaloperations cannot adequately represent the multidimensional character of cognitivedevelopment. However, this does not necessarily mean that the study of cognitivedevelopment should exclude the dimension of formal operations completely. Rather thestudy of cognitive development might be expanded to include other dimensions besidesthose associated with formal operations.3) The third criticism is a challenge to the universality of Piaget’s theory,especially the stage of formal operations (Broughton, 1984; Buck-Morss, 1975;Laboratory of Comparative Human Cognition (LCHC), 1982). Piaget’s theory has beencriticized as being ethnocentric and socioeconomically biased because formal thinking isfound to be absent in many world cultures, and is not even universally present in thepopulation of Western cultures (Buck-Morss, 1975). Piaget (1972) revised his positionregarding the stage of formal operations even within Western culture. He recognized thatthe first results had been “based on a somewhat privileged population”. Nevertheless, hemaintained that all individuals reach the stage of formal operations, if not between 11and 15 years, at least between 15 and 20. Piaget (1972) suggested that they reach thisstage in different domains according to their professional specializations. Dasen (1977)referred to this limitation as a source of paradox: the formal operations, which weresupposed to be context-free, are in fact context-bound or at least domain-specific.According to Chapman (1988), what seems necessary is a model of development-in-context that would do justice to two intuitions: a) that variation in forms of cognitionexists as a function of socio-cultural context, but b) that some forms of cognition maynevertheless be judged as more “advanced” than others in some restricted sense.Chapman pointed out that Piaget’s stage theory is limited in the sense that it isunidirectional (with only one stage sequence) and teleological (with a fixed end point).He proposed to reconceptualize cognitive development as being multi-directional andnon-teleological. The notion of multidirectional development implies that there could be15more than one developmental pathway. That means that there could wellbe otherdevelopmental sequences other than that proposed by Piaget. The notionof non-teleological development implies that it is not exactly necessary to establish a fixed endpoint of development. Developmental progress do not have to be measured in terms ofthe decreasing distance towards the end point, but can be traced in terms of the increasingdistance away from the identified source of error.4) The fourth criticism is that the model of formal operations is too limited tocapture the richness and complexity of adolescent and adult thinking. It is suggested thatthere are other forms of thinking which might develop parallel to formal thinking andsupplement it (e.g. Riegel, 1973). These other forms of thinking might also develop afterformal thinking and might even replace it (cf. Arlin, 1975; Commons, Richards et al.1984). In fact I would argue that this type of criticism is not incompatible withChapman’s (1988) proposal that cognitive development can be reconceptualized as beingmulti-directional and non-teleological.This fourth criticism provides the basis to explore potential development beyondformal reasoning. As a result, more sophisticated types of thinking have been proposedand they are generally grouped under the collective label of “postformal” reasoning (seeCommons, Richards et al, 1984).B. POSTFORMAL REASONING--BEYOND FORMAL REASONING1. OverviewPostformal reasoning is a collective label for a wide range of models ofadultthinking, specifically thinking beyond formal operations.16As mentioned in the previous section, some researchers in the mid-i 970’s beganto challenge Piaget’s claim about fonnal operations being the finalstage of cognitivedevelopment. Riegel (1973) proposed dialectical operations to be the final period ofcognitive development. Arlin (1975) was among the first to point out that formaloperational thinking is not necessarily the final equilibrium and suggested a possible fifthstage or postformal stage of cognitive development.In general, the researchers espousing this perspective considered that formalreasoning cannot capture the richness, complexity and creative power of the maturehuman mind as exemplified by achievements in arts, humanities, contemporary sciences,spiritual traditions and everyday living (cf. Commons, Armon, Kohlberg et al., 1990;Commons, Armon, Richards et al., 1989; Commons, Richards & Armon, 1984; Mines &Kitchener, 1986; Sinnott, 1989). Most of these researchers shared the conviction that byending the stages of cognitive development in adolescence, Piaget truncateddevelopmental concepts of both adulthood and cognition. As a result there is a growinginterest in the study of adolescent and adult cognitive development. More specifically, inthis type of research, attempts are made to explore the potential development beyondformal reasoning. More sophisticated types of thinking have been proposed. They aregrouped under the collective label of “postformal reasoning” though not all of thesecharacterizations of postformal reasoning presuppose formal operations.2. DiversityUnder the collective label of “postformal” reasoning is a wide range of models ofadult thinking extended into very diverse domains such as problem fmding and problemsolving (Arlin, 1975, 1989), moral reasoning (Armon, 1984, 1989; Erdynast, 1990;Tappan, 1990), social reasoning (Benack, 1984; Blanchard-Fields, 1989; Powell, 1980,171984; Sinnott, 1984), life-span psychology (Labouvie-Vief, 1984, 1990; Smith, Dix &Baltes, 1989), and epistemic cognition (Kitchener & King, 1978).According to Commons, Richards et al. (1984), there are two general approachesto the formulation of postformal reasoning.1) One approach is to locate limitations in formal operations and then to describea kind of thinking that enables the individual to transcend those limitations. Researchersborrow examples of thinking already developed in other contexts such as dialecticaltraditions (Basseches, 1980), philosophy of science (Linn & Siegel, 1984), generalsystem theory and Buddhism (Koplowitz, 1984), relativity theory (Sinnott, 1981), andmoral philosophy (Armon, 1984) as models for postformal reasoning. In these models,the proposition that formal operations are sufficient for adults to solve all problems isquestioned. For other models, an argument is made as to whether formal operations areeven necessary.2) Another approach is to analyze the nature of cognitive developmentalprocesses rather than the limitations inherent in formal operations. Instead of focusingon a demonstration that change does occur, this approach attempts to show how changeoccurs. For example, Fischer, Hand and Russell (1984) relate postformal reasoning tothe development of abstractions; Sternberg (1982, 1984) to higher-order relationalthinking; Commons and Richards (1984) to the increase in levels of complexity; andPascual-Leone (1984) to the development of attentional capacity.Researchers from either of the above two approaches generally claim that adultthinking contains the formal operational framework but encompasses other frameworksas well. This kind of development results in multiple frameworks under which formaloperations are used within a higher-stage system of operations and transcend thelimitations of formal operations. There may well be other approaches in which theformal operational framework is simply ignored and alternate models of cognitive18development are proposed. An example of these approaches would be Vedic psychology(see Alexander, Davies et al., 1990).3. In Search of Unifying CommonalitiesDuring the first decade of research on postformal reasoning, the tasks thatoccupied most researchers were those of developing models and validating measures.Recently, there appears to be an increasing interest in organizing or unifying the diversityin the field of postformal research. According to Benack and Basseches (1989), there aretwo approaches in the attempt to organize or unify the field of postformal research. Oneapproach is to interrelate empirically the different postformal sequences through “crossdomains” and “cross measures” studies (e.g.Cavanaugh & Stafford, 1989; Commons &Richards, 1984; Commons, Sinnott et al., 1989; Hoyer et al. 1989; Kitchener & King,1985; Schrader et al., 1989). These studies showed that the line of transition from formalto postformal reasoning is by no means clear cut. For example, Cavanaugh and Stafford(1989) found that a person may be identified as functioning at the postformal level usinga test developed by Labouvie-Vief and colleagues (Labouvie-Vief, Adams, HakimLarson & Hayden, 1983), but not necessarily so using the test developed by Commonsand colleagues (Commons, Richards & Kuhn, 1982). Such kind of intra-individualdiscrepancies might reflect problems associated with measurement, level of taskdifficulty and/or domain specificity. However, before entertaining these possibilities, Iwould argue that a more fundamental issue needs to be addressed, namely, do thesepostformal models in question share any basic commonalities at all? This fundamentalissue is precisely the concern of another approach which attempts to unify the diversity inthe field of postformal reasoning. In this approach, the forms or structures of certainpostformal models would be analyzed theoretically in order to identify their common19features (e.g. Arlin, 1984; Commons & Richards, 1984; Kitchener, 1983; Kramer,1983a). The aim of such theoretical work is to reduce the conceptual complexity of thefield by making clear the logical relationships among the various models of postformalreasoning. One of the proposed unifying commonalities underlying the models ofpostformal reasoning is nonabsolute/ relativistic (N/R) thinking which is the main topicof this study (see Kramer, 1983a).C. NONABSOLUTE/RELATIVISTIC (NIR) THINKING--A PROPOSED COMMONALITY UNDERLYING POSTFORMAL MODELS1. OverviewThere has been speculation that nonabsolute/ relativistic (N/R) thinking might beone of the possible unifying commonalities underlying a cluster of postformal models. Anumber of researchers has independently suggested that nonabsolute/ relativistic (N/R)thinking is required for the operations of postformal reasoning (e.g. Arlin, 1974, 1975/6;Basseches, 1980; Cavanaugh, Kramer, Simiott, Camp & Markley, 1985; King, Kitchener,Davidson, Parker & Wood, 1983; Kitchener & King, 1981; Riegel, 1973; Sinnott, 1981,1989).In a similar vein, Kramer (1983a) proposed that nonabsolute/ relativistic (N/R)thinking might be one of the core features of postformal reasoning. Kramer (1983a,p.91) identified three “core” features shared by most of the postformal models: 1) therealization of the nonabsolute, relativistic nature of knowledge; 2) an acceptance ofcontradiction; and 3) the integration of contraction into an overriding whole. (Thesecond and third features are characteristics of dialectical thinking as well.) However, inthe literature there is no consensus regarding the specific nature of nonabsolute/20relativistic (N/R) thinking (feature 1). The terms “nonabsolute” thinking and“relativistic” thinking are often used interchangeably. The connotation of such terms isoften vague and open to interpretation. I would suggest that, in order to be more explicit,the term “nonabsolute” thinking can be used to imply the general construct whereas theterm “relativistic” thinking can be used to imply a specific type of “nonabsolute” thinkingthough there could well be other types of “nonabsolute” thinking besides that of“relativistic” thinking. According to Inhelder and Piaget (1958, p.317), a simple form ofrelativity can be defined as the coordination of two or more frames or systems ofreference, which is one of the eight concepts or schemata of formal operations. Arlin(1984a) argued that this schema might represent the pivotal concept that marks thetransition from high-formal to postformal operations.Based on hihelder and Piaget’s (1958) definition that a simple form of relativitycan be defined as the coordination of two or more frames or systems of reference, Iwould further argue that nonabsolute/ relativistic (N/R) thinking (feature 1) is a generalcase of features 2 and 3 mentioned in the above in that feature 2 (i.e. the acceptance ofcontradiction) can be considered as the acceptance of the specific nature of therelationship among the parts or frames to be coordinated and similarly, feature 3 (i.e.integration of contradiction) can be considered as the specific type of coordination thatrelates and synthesizes the parts or frames into a dialectical whole. Thus features 2 and3, which are characteristics of dialectical thinking, can be regarded as specific cases offeature 1, that is, nonabsolute/ relativistic (N/R) thinking.In this light, nonabsolute! relativistic (N/R) thinking indeed seems to represent abasic common feature among postformal models. However, the proposition thatnonabsolute! relativistic (N/R) thinking is one of the commonalities underlying themodels of postformal reasoning is yet to be empirically tested. There are a number ofunresolved issues pertaining to such a proposition. They are discussed in the nextsection.212. Unresolved IssuesFour of the unresolved issues pertaining to the proposition that nonabsolute/relativistic (N/R) thinking is one of the possible unifying commonalities underlying theselected postformal models are identified and addressed in this study.The first unresolved issue concerns the lack of empirical evidence to support theproposition that nonabsolute/ relativistic (N/R) thinking is one of the possible unifyingcommonalities underlying the selected postformal models. These postformal modelsinclude : problem finding (Arlin, 1974, 1975/6), dialectical reasoning (Basseches, 1980;Benack & Basseches, 1989), relativistic operations (Cavanaugh et al., 1985; Sinnott,1981, 1989), and reflective judgment (King et a!., 1983; Kitchener, 1986; Kitchener &King, 1981). It is important to point out that empirical work has yet to be done to testthis proposition. However, before submitting such a proposition to empirical testing,there are several other issues to be examined.The second unresolved issue is whether nonabsolute/ relativistic (N/R) thinking isformal or postformal in nature. An implicit assumption held by some of the postformalresearchers is that in order for nonabsolute/ relativistic (N/R) thinking to be qualified as acommon feature underlying the models of postformal reasoning, it is necessary todemonstrate that it possesses a form or structure that is postformal in nature (Cavanaughet al., 1985; Kramer, 1983b). While a number of researchers (e.g. Arlin, 1984, 1990;Kramer, 1983a; Sinnott, 1981, 1989) have suggested that some kind of relativisticthinking is required for postformal operations, others have questioned whether theawareness of relativity is really postformal at all (Cavanaugh et al., 1985). Thus it isdebatable whether nonabsolute/ relativistic (N/R) thinking is an instance of formal orpostformal reasoning.Although Kramer (1983a) proposed in her earlier work that nonabsolute/relativistic (N/R) thinking is one of the core features of postformal operations, later she,22as well as others, queried the postformal status of relativistic thinking (Cavanaugh et al.,1985; Kramer, 1983b, 1986). Their query was based on the findings that the awarenessof relativity was necessary but not sufficient for formal thinking, and formal thinkingwas in turn found to be necessary but not sufficient for “acceptance of contradiction” and“integration of contradiction” into the dialectical whole. Such findings seem to castdoubt on the proposition that awareness of relativity itself is postformal. However, Iwould argue that such findings were contingent upon the definition of relativisticthinking as well as the nature of the specific tasks used in Kramer’s work and their levelof difficulty.Firstly, I would relate to Kramer’s definition of relativity. In Kramer’s studies(1 983b, 1986), relativistic and dialectical reasoning were assessed by two tasks bothpresenting a dilemma. The tasks were coded for the following four categories: a)formism-mechanism, b) awareness of relativity, c) acceptance of contradiction, and d)integration of contradiction into the dialectical whole. Pepper’s (1942) synthetic worldviews were used to guide the coding process. Under this coding system, relativity wasdefined as the awareness of the relativistic nature of knowledge. Four subcategorieswere used for coding the presence of relativity: a) pragmatism, b) change as basic toreality, c) contextualism, and d) uniqueness-indeterminacy. I would argue that the abovedefinition of relativity represents only a rudimentary notion of the relativistic nature ofknowledge.Secondly, I would relate to Kramer’s definition of formal reasoning. In Kramer’s(1983b, 1986) studies, formal reasoning was defined by four tasks: a) the Plant Taskwhich measures the ability to separate variables; b) the Snail Task which measures theability to coordinate two frames of reference, a simple form of relativity (Arlin (1984)suggested that such form might represent a pivotal concept that marks the transition fromhigh formal to postformal reasoning.); and c) the Grade Inflation Task and d) thePolitical Climate Task which were designed by Kramer to measure the ability to23coordinate multiple frames of reference. In fact three of the four formal tasks measureacertain form of relativity but with varying degrees of difficulty. In this light, Kramer’sfinding that the awareness of relativity was necessary but not sufficient for formalreasoning could in fact be re-interpreted as that the awareness of relativity was necessarybut not sufficient for the operations of relativity at the high-formal level. At thisjuncture, I would argue further that Kramer’s findings do not necessarily preclude thepossibility that relativity could operate at both the formal and postformal levels.Therefore, the definition and measurement of relativistic thinking operating at both theformal and postformal levels are yet to be reconceptualized.The discussion of both the first and second unresolved issues would necessarilyextend to the third and the fourth unresolved issues. The third unresolved issue concernsthe need for an operational definition of nonabsolute/ relativistic (N/R) thinking. Thefourth unresolved issue concerns the need for the design of a measure of such a construct.Although a number of researchers have suggested that nonabsolute/ relativistic (N/R)thinking seems to be required for the operations of postformal reasoning, there is reallyno consensus regarding the specific nature of nonabsolute/ relativistic (N/R) thinking, letalone the definition and measurement of the construct(Arlin, 1974, 1975/6; Basseches,1980; Kitchener, 1986; Kitchener & King, 1981; Kramer, 1983a; Riegel, 1973; Sinnott,1981, 1989).I would argue that both the first and the second unresolved issues in fact arehinged upon and eventually have to be related to the third and the fourth unresolvedissues. The reason for this argument is that without an operational definition andmeasurement of the construct of nonabsolute/ relativistic (N/R) thinking, there is reallyno basis for 1) testing empirically the proposition that nonabsolute/ relativistic (N/R)thinking is one of the commonalities underlying the selected postformal models, and for2) determining the structural stage status of nonabsolute/ relativistic (N/R) thinking.24Thus it seems that, in order to address the above stated unresolved issues, theformulation of a definition of nonabsolute/ relativistic (N/R) thinking would be of utmostimportance. However, before formulating a definition of such a construct, it would seemlogical to examine some of the postformal models which have been postulated to requirenonabsolute/ relativistic (N/R) thinking.3. Models associated withNonabsolute/ relativistic (NJR) ThinkingThe models of postformal reasoning which have been postulated to requirenonabsolute/ relativistic (N/R) thinking include:a) Problem Finding (Arlin, 1974, 1975/76);b) Dialectical Reasoning (Riegel, 1973; Basseches, 1980);c) Relativistic Operations (Cavanaugh, Kramer, Sinnott, Camp & Markley, 1985;Sinnott, 1981, 1989) andd) Reflective Judgement (King, Kitchener, Davidson, Parker & Wood, 1983;Kitchener & King, 1981).The above four models of postformal reasoning are selected for discussion fortwo reasons: 1) the authors of these models have independently suggested thatnonabsolute/ relativistic (N/R) thinking is required for their respective models ofreasoning; and 2) the nature of postformal reasoning could be considered as bestcharacterized by the kind of reasoning described by these four models (Arlin, 1990).Through examining these selected models of postformal reasoning, one might beable to extract from them some common essentials which could provide ingredients forthe conceptualization and definition of nonabsolute/ relativistic (N/R) thinking.25In order to provide an advance organizer to the following review of thepostformal models, I would point out that there are different aspects of nonabsolute!relativistic (N/R) thinking embedded in these selected models of postformal reasoning.These different aspects of nonabsolute! relativistic (N/R) thinking could be viewed as thedifferent dimensions of the very construct. Two of the more important dimensions ofnonabsolute/ relativistic (N/R) thinking proposed to be explored are: 1) the basic formdimension and 2) the epistemic view dimension.Regarding the basic form dimension, I would argue that a basic form ofnonabsolute/ relativistic (N/R) thinking could in fact be identified throughout the selectedpostformal models and therefore, propose that such a “postformal” form of nonabsolute!relativistic (NIR) thinking could be defined as “multiple-frame operations on ill-definedproblems”. The definition proposed will be expanded in the later part of this chapter.However, at this point, this proposed definition could serve as a frame of reference forthe review of these models.Regarding the epistemic view dimension, I would argue that the epistemic viewassociated with nonabsolute/ relativistic (N/R) thinking could be reflected primarily inone of the postformal models, namely the Reflective Judgment model, although theepistemic view has also been mentioned sporadically in the rest of the selected models.In the following, the selected models of postformal reasoning will be brieflyintroduced and discussed in terms of their relationship with nonabsolute/ relativistic(N/R) thinking.a) Problem FindingThe concept of problem-finding (cf. Arlin, 1975, 1989) can be traced back tostudies concerning creative thought vis-a-vis “discovered problems” (Getzels, 1964;Getzels & Csikszentimihalyi, 1970); the formulation of generic problems (Taylor, 1972);26the raising of general questions from ill-defined problems (Mackworth,1965); and theslow cognitive growth represented in the development of significant scientificthought(Gruber, 1973). Mackworth’s (1965) work on the development of scientificbreakthroughs characterized the work of the technician as problem-solving andthat ofthe scientist as problem-finding. He used information processing terms to describe the“outcome” of problem-finding as “the generation of many general (or generic) questionsfrom many ill-defined problems”. Mackworth considered that the ability to engageinproblem-finding is precisely what distinguished the scientist from the highly competenttechnician. A similar view is contained in Einstein’s (Infeld & Einstein, 1938)observation that “the formulation of a problem is often more essential than its solution,which may be merely a function of mathematical or experimental skill. To raise newquestions, new possibilities, to regard old questions from a new angle requires creativeimagination and marks real advance in science” (p. 92).In relation to postformal reasoning, problem-fmding (Arlin, 1975) was initiallyhypothesized to be the fifth stage of cognitive development. Later it wasreconceptualized as one of the important forms of reasoning associated withpostformal/fifth stage thinking. The model of problem-finding has been subjected tocontinuous revision (Arlin, 1984, 1986, 1989). Findings (Arlin, 1975, 1989) revealedthat problem-finding and problem-solving are two distinct processes and suggested thatone has to be a good problem solver before one can be a good problem finder.Such anidea corresponds with Smilansky’s (1985) argument. The logic for such a proposition isas follows. Formal operations involve problem-solving processes associated with welldefined problems. By definition, each well-defined problem has one or a limited numberof correct solutions. In contrast, problem-finding processes are associatedwith illdefined problems. By definition, ill-defined problems have no known methodof solutionand no criteria for judging the correctness of the solution(s). Thus Arlin (1975,1989)argued that formal thinking, being problem-solving in nature, is a necessarybut not27sufficient condition for problem-finding. Problem-finding was found to be highlycorrelated with other postformal measures including dialectical and relativistic thinking.In the context of this review, problem-finding, as a specialized form ofpostformal reasoning, can be viewed as operating at a metacognitive level providingorientation to problem-formulation and problem-solving processes. As Arlin (1975)pointed out, the situation of problem finding is typically ill-defined in nature. I wouldfurther argue that the ill-defined nature of problem finding requires a person to generatedifferent frames of reference which can then be developed into different ways oforganizing the data and asking questions about the situation presented. In addition, suchprocesses of problem finding would also allow a person to question or challengeassumptions upon which knowledge is based. In this light, I would argue that problemfinding would necessarily involve “multiple-frame operations on ill-defined problems”,which is proposed to be the postformal form of nonabsolute/ relativistic (N/R) thinking.Such a form is argued to be one of the commonalities underlying the selected postformalmodels.b) Dialectical ThinkingThe dialectical philosophical perspective comprises a family of world views aboutthe nature of existence and knowledge. These world views while differing from eachother in many aspects, share three common features: the common emphasis on change,wholeness, and internal relations. A dialectical world view can be contrasted with astatic world view.From the dialectical perspective, what might otherwise be viewed asfundamental elements of existence are instead viewed as temporary formswhich existence takes, and what might otherwise be viewed as interactions28of fundamental elements are instead viewed as fundamental processes ofchange through which these forms of existence emerge. (Basseches, 1980,p.404)Both Riegel (1973) and Basseches (1980) proposed dialectical thinking as formsof thinking beyond formal operations. However, Riegel’s model and Basseches’ modeldiffer considerably from each other. Riegel’s model did not assume formal operations.He emphasized the dialectical nature of non-alienated thought at all ages (primitivedialectics as differentiated from scientific dialectics). Riegel did use Piaget’s notion offormal operations as “final equilibrium” as a springboard for his own theory.Basseches describes dialectical thinking as a metasystemic form of cognitiveorganization operating at a postformal stage of cognitive development. Dialecticalthinking, according to this model, is organized by the concept of dialectic, in which theprocess of transformation of forms is understood in terms of interactive and constitutiverelationships. Dialectical thinking is operationalized in the Dialectical SchemataFramework. The framework consists of 24 schemata or “moves in thought” thatdialectical thinkers tend to make. The schemata represent motion, relations, forms, andintegration of motion, relations and forms in a model of dialectical evolution. Each ofthese schemata is not necessarily dialectical thinking in itself. Rather, dialecticalthinking is an organization of these schemata into a structure equilibrated by the idea ofdialectic. Thus one may use many of these schemata or “moves of thought” withoutengaging any organized structures of dialectical thinking.In the context of this review, I would suggest that dialectical thinking can beregarded as a metasystemic form of cognitive organization in a qualitative sense asdifferentiated from a quantitative sense. Thus dialectical thinking as such could be saidto require the coordination and/or integration of multiple frames or systems in the contextof ill-defined problems. In this light, I would argue that dialectical thinking would29necessarily involve “multiple-frame operations on ill-defined problems” whichisproposed to be the postformal form of nonabsolute/ relativistic (N/R) thinking. Suchaform is argued to be one of the commonalities underlying the selected postformalmodels.ci Relativistic OperationsA number of researchers have suggested that some kind of relativistic logic isrequired for postformal thinking (e.g. Arlin, 1984, 1990; Kramer, 1983a; Sinnott, 1981,1989).According to Simiott (1989), relativistic thought can come into play only whenthe problem is seen as ill-structured. Relativistic operations may be defined as logicaloperations which can be used as a system to relate, order and select the more useful ofmany mutually contradictory but ‘true’ formal-operational systems (Cavanaugh, Kramer,Sinnott, Camp & Markley, 1985).In Sinnott’s model (1989), there are two main characteristics of relativisticpostformal operations: 1) self-reference and 2) the ordering of formal operations. Theessential notions of self-reference are that all knowledge has a subjective component andso is, of necessity, incomplete. Thus any logic one uses is self-referential. As for theordering of formal operations, the postformal system of self-referential truth ordersformal truth systems, one of which is somewhat subjectively chosen and imposed ondata. These two characteristics are considered to be qualitatively different fromcharacteristics of other developmental stages and are not part of any other postformalsystems proposed thus far.These two characteristics can in fact be viewed as special features of nonabsolute/relativistic (N/R) thinking in the context of this review. I would suggest that the firstcharacteristic of ‘self-reference’ is meant to emphasize the subjectivity which might be30involved in the coordination of thoughts; and that the second characteristic of ‘theordering of formal operations’ is meant to emphasize the form of thinking which involvesmultiple-frame operations. In this light, I would argue that relativistic operations wouldalso necessarily involve “multiple-frame operations on ill-defined problems”, which isproposed to be the postformal form of nonabsolute! relativistic (N/R) thinking. Such aform is argued to be one of the commonalities underlying the selected postformalmodels.d Reflective JudgmentIn the model of reflective judgment, seven stages or levels of epistemic cognitionare postulated (Kitchener, 1986; Kitchener & King, 1981). The model is used to describe“an individual’s assumptions about what can be known and what cannot (e.g. ourknowledge of some things is ultimately uncertain), how we can know (e.g. by observingevents directly, via authority), and how certain we can be in our knowing (e.g.absolutely, probabilistically). Corresponding to each stage of knowing is a description ofhow beliefs are justified in light of the certainty or lack of certainty of knowledge. Eachstage of justification appears to be a logical outgrowth of a set of epistemic assumptions(p.219).”The seven stages of epistemic cognition postulated in this model are ordered insequence. For example, an individual who uses Stage 7 reasoning would typically haveshown evidence of the other six stages of epistemic cognition at earlier ages. Theepistemic assumptions of the early stages (i.e. Stages 1-3) do not acknowledge that realuncertainty exists. Rather, they assume that, ultimately, uncertainty can be translated tocertainty, for example, by consulting an authority or by waiting until the truth is knownsometime in the future. Stages 4-7 acknowledge the uncertainty of knowing although31there are subtle differences in the understanding of the causes of uncertainty.Whatappears to mature in the later stages is the understanding of how judgmentscan be madein the face of this uncertainty.The main concern of the model of reflective judgment is the detection ofthechanges in epistemic view from an absolute to a nonabsolute!relativistic view of theknowledge of reality. Although Kitchener and Kitchener (1981)considered that logicand epistemology are different domains, I wouldstill argue that these two domains arerelated because it is probable that a certain formof thinking or logic could be contingentupon certain types of epistemic view. Formaloperations, according to Kitchener andBrenner (1990), when defined as the ability to operateon propositions inductively anddeductively, do not account for differences inepistemic assumptions. However, I wouldargue that this might in fact suggest that some kindof postformal logic is associated witha more sophisticated epistemic view.The tasks of reflective judgment basicallyinvolve dialectical thinking, aspecialized form of postformal operations. Again, I wouldargue that the form ofthinking required for reflective judgment is alsocompatible with “multiple-frameoperations on ill-defined problems”,which is proposed to be the postformal form ofnonabsolute! relativistic (N/R) thinking. Sucha form is argued to be one of theconimonalities underlying the selected postformalmodels.4. Reconceptualizing the Construct ofNonabsolute/ relativistic (N[R) ThinkingBased on the above review of the postformal models, I would argue thatthe“formal” form of relativity, which was defined by Inhelder and Piaget (1958)as the32coordination of two or more frames or systems of reference, cannot adequately representthe kind of nonabsolute/ relativistic (N/R) thinking underlying these selected postformalmodels. In order to formulate a definition of nonabsolute/ relativistic (N/R) thinking thatcould characterize both its formal and postformal qualities, I would argue that areconceptualization of the construct of nonabsolute/ relativistic (N/R) thinking would benecessary.In this context, I would argue that nonabsolute/ relativistic (N/R) thinking couldbe conceptualized and defined as a multidimensional and multilevel construct. Two ofthe more important dimensions of nonabsolute! relativistic (N/R) thinking are proposed:1) the basic form dimension, and 2) the epistemic view dimension. Within the basicform dimension, two levels are proposed: 1) the formal form, and 2) the postformalform. (See Figure 1.)Figure 1Dimensions and Levels of Nonabsolute/ Relativistic (N/R)ThinkingDIMENSIONSBasic Form Epistemic ViewL Formal Formal FormEVEL Post- Postformal Form Epistemic ViewS formalThe conception of nonabsolute/ relativistic (N/R) thinking beingmultidimensional is in fact compatible with Kitchener’s (1983) three-level model ofcognitive processing which represents an account of the complex monitoring done by33individuals when faced with ill-defined problems. In Kitchener’s three-level model ofcognitive processing, the first level is “cognition”. Individuals, at this level, compute,memorize, perceive, solve problems, etc.. The second level is “metacognition”.Individuals, at this level, monitor their own cognitive processes when they are engaged inthe first level tasks. The third level is “epistemic cognition”. Individuals, at this level,reflect on the limits of knowing, the certainty of knowing, and the criteria of knowing.According to Kitchener (1983), epistemic assumptions influence how individualsunderstand the nature of problems and the strategies they use for problem solving.Current research suggests that, while cognitive and metacognitive processes appear todevelop in childhood and are used throughout the life span, epistemic cognition developsin the late adolescent and adult years.With reference to Kitchener’s (1983) model of cognitive processing, I wouldargue that each dimension of nonabsolute/ relativistic (NIR) thinking corresponds to aspecific aspect of a particular level in Kitchener’s model. Specifically, the basic formdimension of nonabsolute/ relativistic (N/R) thinking can be viewed as a specific aspectof the second level or the metacognitive level processing in Kitchener’s model.Similarly, the epistemic view dimension of nonabsolute/ relativistic (N/R) thinking canbe considered as a specific aspect of the third level or the epistemic level of processing inKitchener’s model.a The Basic Form Dimensionof Nonabsolute/ relativistic (NJR) ThinkingThe basic form of nonabsolute! relativistic (N/R) thinking can be construed as acertain form of knowing or thinking associated with a nonabsolute! relativisticrepresentation of reality. Within the basic form dimension of nonabsolute/ relativistic(N/R) thinking, two levels are proposed: 1) the formal form, and 2) the postformal form.34I have argued earlier in this chapter that “relativistic” thinking can be regarded asa specific type of “nonabsolute” thinking. Within this type of “nonabsolute” thinking, itis crucial to distinguish between two forms of relativity, namely the formal form and thepostformal form (Kramer, 1983a). If such forms can be distinguished, it is alsoimportant to explain why the formal and the postformal forms are structurally and/orqualitatively different. Here, a similar if not parallel case can be made with the transitionfrom the concept of compensation in concrete operations to the concept of multiplicativecompensations and mechanical equilibrium in formal operations (see Arlin,1984b,1 986a).In the concrete operational stage, the conception of compensation wouldgenerally involve two dimensions as exemplified in the conservation tasks. (e.g. Theconservation of liquid would involve compensation between the height of water levelsand the width of the containers. Similarly, the conservation of substance would involvecompensation between the length and the thickness of the clay dough.)However, in the formal operational stage, the concept of compensation isexpanded to become that of multiplicative compensations in which multiple dimensionswould be involved. (e.g. The conservation of volume would involve compensationsamong the dimensions of length, height and width.)In the high-formal operational stage, the concept of compensation is furtherexpanded to become that of mechanical equilibrium in which multiple sets ofcompensation would be involved, so that a balance or equilibrium would be maintained(e.g. the piston task).I would argue that the example of the development of the concept ofcompensation could be used to demonstrate how a certain concept can evolve acrossstages through its structural elaboration and transformation.In the case of relativistic thinking, at the formal level, Inhelder and Piaget (1958)defined a simple form of relativity as the coordination of two or more frames or systems35of reference. This is one of the eight concepts of formal operations. Arlin (1984) arguedthat the coordination of two or more frames or systems of reference might represent apivotal concept that marks the transition from high-formal to postformal reasoning. Thequestion is whether such a form can adequately represent the common form ofnonabsolute! relativistic (N/R) thinking underlying the models of postformal reasoning.In relation to this issue, Arlin (1980) suggested that the coordination of multiple framesor abstract frames might represent a basis for the postformal form of relativity. Based onthe concept of multiple-frame coordination, Kramer (1984) designed a task (called“political climate”) to assess the ability to coordinate three frames of reference.However, Kramer (1985) reported that the coordination of two frames of reference wasnot found to be a “necessary but not sufficient” condition for the coordination of threeframes of reference. Thus Kramer argued against the coordination of multiple frames ofreference as well as against relativistic thinking as postformal reasoning. Thus whetherrelativity is formal or postformal in nature remains an open question.I would argue that Arlin’s (1980) suggestion of “coordination of multiple frames”represents a major step towards the conceptualization and definition of relativisticthinking. Following this line of argument, I propose to take Arlin’s suggestion one stepfurther. That is, I propose to define the forms of nonabsolute/ relativistic (N/R) thinkingin terms of two criteria: 1) the quantity of the frames of reference, and 2) the quality ofthe task involved. (See Figure 2.)From such a perspective, the formal tasks, regardless of the number of frames ofreference involved, are well-defined problems. This also applies to the task assessing thecoordination of three frames of reference designed by Kramer (1984). On the contrary,the postformal tasks are life-like tasks involving not only multiple frames of referencebut also ill-defined problems. In this light, I would argue that one of the majordifferences between formal and postformal forms is that between well-defined and illdefined problems.36Figure 2Definition Criteria for the Two Forms of Nonabsolute/Relativistic (N/R) ThinkingQUANTITY OF FRAMES OF REFERENCESingle MultipleQ0 Well- Not Postformal FormalU F definedAL TIAT S Ill- Not Postformal PostformalY K definedA brief contrast between well-defined and ill-defined problems is as follows. Forwell-defined problems all the information necessary to produce a solution is given, thus itis possible to derive objective answers to the problems. For ill-defined problems, theinformation given is not complete, thus it is not possible to derive any objective answers.(For discussion on similar concepts of well-structured problems and ill-structuredproblems, see Wood, 1990; Brabeck & Wood, 1990).Following this line of argument, I propose to define the basic forms ofnonabsolute/ relativistic (N/R) thinking at two levels namely, the formal form and thepostformal form:1) The formal form of nonabsolute/ relativistic (N/R) thinking can be defined as“multiple-frame operations on well-defined problems”.2) The postformal form of nonabsolute/ relativistic (N/R) thinking can be definedas “multiple-frame operations on ill-defined problems”.Moreover, I would argue that these two forms of nonabsolute/ relativistic (N/R)thinking are qualitatively different though structurally similar.37Structurally speaking, both forms involve multiple-frame operations. In thiscontext, a “frame” can be defined as a system or organization of relationships amongelements. For example, in the Piagetian task of “Co-ordination of two or more frames orsystems of reference”, the relationship between the turtle and the paper strip wouldconstitute one frame or system of reference, and the relationship between the paper stripand the desk would constitute another frame or system of reference. In this sense,multiple-frame operations refer to the operations on or the co-ordinations of multiplesystems or organizations of relationships among elements.Qualitatively speaking, I would argue that the kinds of problem involved with thetwo forms of nonabsolute/ relativistic (N/R) thinking are different in nature.The formal form operates on well-defmed problems which can be represented byclosed systems. For well-defmed problems, all the information necessary to produce asolution is given or can be derived from what is given. In this case, it is possible toderive one or a few solutions.By contrast, the postformal form operates on ill-defined problems which can berepresented by self-constructed as well as open systems (see Koplowitz, 1984). For ill-defined problems, the information given is not complete. Thus it is crucial to point outthat, for ill-defined problems, because the systems for operations have yet to beconstructed and defined, one is often required to generate information beyond that whichis given or known. That is to say, a person’s knowledge or experience about the contentand context of the problems concerned would be called for. Such quality of postformalform would be in contrast with that of the formal form which is content/context-freeaccording to Inhelder and Piaget (1958). Another crucial difference is that, since thepostformal form typically deals with self-constructed and open systems, it is not possibleto expect any absolute or objective solutions. Thus I would further argue that postformaloperations would necessarily imply uncertainty, indeterminacy, subjectivity and perhapseven creativity.38With reference to the above mentioned qualitative differences, it is possible tosuggest that the formal form of relativity is confined to solving arbitrary or contrivedproblems, whereas the postformal form of relativity is meant to deal with life-likeproblems in a more flexible and creative manner. In this study, it is hypothesized that ashift from an absolute to a nonabsolute epistemic view might have a crucial role to playin the development of the postformal form.b) The Epistemic View Dimensionof Nonabsolute/ relativistic (N/RI ThinkingThe epistemic view of nonabsolute/ relativistic (N/R) thinking can be construedas certain theories of knowing or theories of knowledge of reality associated with anonabsolute/ relativistic world view. The epistemic view dimension of nonabsolute!relativistic (N/R) thinking is theoretically hypothesized to be associated with thepostformal” form of nonabsolute/ relativistic (N/R) thinking. However, this hypothesisis yet to be empirically tested. In a similar vein, Kitchener (1983) considered epistemiccognition as the highest level of cognitive processing in her three-level model ofcognition.During the course of cognitive development, individuals do tend to shift from anabsolute to a nonabsolute/ relativistic view about the nature of knowledge of reality. Iwould propose that several specific aspects pertinent to the nature of knowledge of realitycan be identified. The following are four of these specific aspects which are extractedand modified from the work of Kitchener and colleagues (Kitchener, 1981; Kitchener &Brenner, 1990; Kitchener & King, 1986). They concern:1) The means of knowledge: a nonabsolute/ relativistic view would be implied bythe recognition that all means involved in the construction of knowledge are ultimatelysubjective.392) The limits of knowledge: a nonabsolute/ relativistic view would be implied bythe recognition that the ultimate nature of reality can only be approximated but can neverbe completely in grasp. Thus the limits of knowledge are ever unfolding but neverreached.3) The criteria of knowledge: a nonabsolute/ relativistic view would be impliedby the recognition that there is no absolute criterion for judging any solution, because allcriteria are always relative to certain sets of assumptions.4) The nature of reality: a nonabsolute/ relativistic view would be implied by therecognition that reality is in constant flux (i.e. the notion of a dynamic world view versusa static world view).These four specific aspects are by no means exhaustive, but are argued to be vitalpoints for tapping a person’s epistemic view. It is hypothesized that a shift from anabsolute to a nonabsolute epistemic view could be crucial to the development of thepostformal form of nonabsolute/ relativistic (N/R) thinking. This would be analogous toKuhn’s (1970/72) “paradigm shift” in the revolution of scientific reasoning. Therelationship between one’s epistemic view and one’s form(s) of thinking is explored inone of the specific research questions in chapter III.The above mentioned characteristics of nonabsolute/ relativistic (N/R) thinkingare used in chapter III as a basis for formulating an operational definition as well as fordesigning a battery of tests of nonabsolute/ relativistic (N/R) thinking.E. SUMMARY & DISCUSSIONOne of the attempts to unify the diversity in the field of postformal research is tosearch for commonalities underlying the models of postformal reasoning. Nonabsolute/40relativistic (N/R) thinking has been proposed to be one of the possible unifyingcommonalities underlying the postformal models (Kramer, 1983a). However, such aproposition is inconclusive. Four of the unresolved issues pertaining to such aproposition are identified and addressed in this study.Briefly speaking, the first unresolved issue concerns the lack of empiricalevidence to support the proposition that nonabsolute/ relativistic (N/R) thinking is one ofthe commonalities underlying the selected models of postformal reasoning. An empiricaltesting of this proposition is called for. However, before submitting such a proposition toempirical testing, there are other basic issues to be addressed.The second unresolved issue is whether nonabsolute/ relativistic (N/R) thinking isformal or postformal in nature. An implicit assumption held by some of the postformalresearchers is that in order for nonabsolute! relativistic (N/R) thinking to be qualified as acommon feature underlying the postformal models, it is necessary to demonstrate that itpossesses a form or structure that is postformal in nature (Cavanaugh et al., 1985;Kramer, 1983b). While a number of researchers (e.g. Arlin, 1984, 1990; Kramer, 1983a;Sinnott, 1981) suggested that some kind of relativistic thinking is required for postformaloperations, others questioned the postformal stage status of relativistic thinking(Cavanaugh et al., 1985). Thus the postformal stage status of relativistic thinking hasbeen a debatable issue.The discussion of both the first and the second issues would necessarily extend tothe third and the fourth issues. The third unresolved issue concerns the need for anoperational definition of nonabsolute/ relativistic (N/R) thinking. The fourth unresolvedissue concerns the need for the design of a measure of such a construct. As revealed inrelevant literature, there is really no consensus regarding the specific nature ofnonabsolute! relativistic (N/R) thinking, let alone the definition and measurement of sucha construct.41I would argue that both the first and second unresolved issues actually are hingedupon and eventually have to be related to the third and the fourth unresolved issues. Thereason is that without the definition and measurement of nonabsolute/ relativistic (N/R)thinking, there is no basis for 1) testing empirically the proposition that nonabsolute/relativistic (N/R) thinking is one of the commonalities underlying the selected postformalmodels; and for 2) determining the structural stage status of nonabsolute! relativistic(N/R) thinking. In order to address the above stated unresolved issues, the formulationof a definition of nonabsolute/ relativistic (N/R) thinking would seem to be of utmostimportance.In order to define nonabsolute/ relativistic (N/R) thinking, four selectedpostformal models which are postulated to require nonabsolute/ relativistic (N/R)thinking are reviewed in this study. They are: 1) Problem Finding (Arlin, 1974, 1975/76,1989); 2) Dialectical Reasoning (Basseches, 1980; Benack & Basseches, 1989); 3)Relativistic Operations (Sinnott, 1981, 1989); and 4) Reflective Judgment (Kitchener,1986; Kitchener & King, 1981). The aim of reviewing these models is to extract fromthem some common essentials which could provide ingredients for the conceptualizationand definition of nonabsolute/ relativistic (N/R) thinking.Based on the review of the selected postformal models, I would argue that the“formal” form of relativity, defined by Inhelder and Piaget (1985) as the coordination oftwo or more frames or systems of reference, cannot adequately represent the kind ofnonabsolute/ relativistic (N/R) thinking underlying the selected postformal models. Inorder to formulate a definition of nonabsolute/ relativistic (N/R) thinking that couldcharacterize both its formal and postformal qualities, a reconceptualization of theconstruct of nonabsolute/ relativistic (N/R) thinking would be necessary.In this context, I propose that nonabsolute/ relativistic (N/R) thinking could beconceptualized and defined as a multidimensional and multilevel construct. Two of the42more important dimensions of nonabsolute! relativistic (N/R) thinking proposed are: 1)the basic form dimension and 2) the epistemic view dimension.Within the basic form dimension of nonabsolute/ relativistic (N/R) thinking, twolevels are proposed: 1) the formal form, and 2) the postformal form. I propose that thesetwo forms can be defined according to two criteria: 1) the quantity of the frames ofreference and 2) the quality of the tasks involved.Regarding the epistemic view dimension of nonabsolute/ relativistic (N/R)thinking, I would argue that four specific aspects pertinent to the nature of knowledge ofreality can be identified. They concern: 1) the means of knowledge, 2) the limits ofknowledge, 3) the criteria of knowledge, and 4) the nature of reality.The above characteristics are used as a basis for the formulation of an operationaldefinition and the design of a battery of tests of nonabsolute/ relativistic (N/R) thinkingwhich are described in chapter III.To conclude, the main focus of this study is to address four of the unresolvedissues pertaining to the proposition that nonabsolute! relativistic (NIR) thinking is one ofthe possible unifying commonalities underlying the selected models of postformalreasoning. In order to address the four unresolved issues presented above, four generalresearch questions as well as some related specific questions are raised. These questionsare discussed and addressed in the next chapter.43CHAPTER III: RESEARCH QUESTIONS & METHODOLOGYIn this chapter, there are two parts. Part A contains research questions and part Bcontains methodology. Under part A, four general research questions are listed. Underpart B are four sections: 1) Operational defmitions of nonabsolute/ relativistic (N/R)thinking (addressing Research Question 1), 2) Tests of nonabsolute! relativistic (N/R)thinking (addressing Research Question 2), 3) Pilot study (initially exploring therelationships among the 3 tests of nonabsolute/ relativistic (N/R) thinking), and 4) Designand proposed analyses (addressing Research Questions 3 and 4).A. RESEARCH QUESTIONSFour of the unresolved issues pertaining to the proposition that nonabsolute!relativistic (N/R) thinking is one of the possible unifying commonalities underlyingcertain selected models of postformal reasoning were identified in chapter II. Torecapitulate, the first issue concerns the lack of empirical evidence to support such aproposition. The second issue concerns whether nonabsolute/ relativistic (N/R) thinkingis formal or postformal in nature. The third issue concerns the need for an operationaldefinition of nonabsolute/ relativistic (N/R) thinking. The fourth issue concerns the needfor a design of a measure of nonabsolute/ relativistic (N/R) thinking. I would argue thatboth the first and second issues are hinged upon and would eventually have to be relatedto the third and the fourth issues. In order to address these four unresolved issues, fourgeneral research questions are raised and are addressed in this chapter. These fourgeneral research questions are as follows:441. How can nonabsolute/ relativistic (N/R) thinking be operationally defined?(This research question is designed to address the third unresolved issue concerning theneed for an operational definition of nonabsolute/ relativistic (N/R) thinking.)2. How can nonabsolute/ relativistic (NIR) thinking be measured?(This research question is designed to address the fourth unresolved issue concerning theneed for a design of a measure of nonabsolute/relativistic (N/R) thinking.)3. Is nonabsolute/ relativistic (NIR) thinking a common factor underlying theselected models of postformal reasoning?(This research question is designed to address the first unresolved issue concerning thelack of empirical evidence in support of the proposition that nonabsolute/ relativistic(NIR) thinking is one of the possible unifying commonalities underlying the models ofpostformal reasoning.)4. Is nonabsolute/ relativistic (N/R) thinking an instance of formal or postformalreasoning or of both?(This research question is designed to address the second unresolved issue concerningwhether nonabsolute/ relativistic (N/R) thinking is formal or postformal in nature.)45B. METHODOLOGY1. Operational Definition ofNonabsolute/ relativistic (NJR) ThinkingIn this section, the first research question namely, “How can nonabsolute/relativistic (NIR) thinking be operationally defined?” is addressed.I propose to use the term “nonabsolute thinking” to imply the general constructand the term “relativistic thinking” to imply a specific type of nonabsolute thinking,though there could well be other types of nonabsolute thinking besides relativisticthinking. In this light, the whole term “nonabsolute/ relativistic (NIR) thinking” refersto a specific type of nonabsolute thinking that involves the use of relativistic thinking asa form of cognitive operations.As proposed in the previous chapter, nonabsolute! relativistic (N/R) thinkingcould be conceptualized and defined as a multidimensional and multilevel construct (seefigure 1). Two of the more important dimensions of nonabsolute! relativistic (N/R)thinking proposed are: a) the basic form dimension and b) the epistemic view dimension.Within the dimension of the basic form, two levels are proposed: 1) the formal form, and2) the postformal form.a) The operational definition of the basic form dimension of nonabsolute!relativistic (N/R) thinking is as follows:1) The formal form of nonabsolute! relativistic (N/R) thinking is operationallydefined as “multiple-frame operations on well-defined problems” which require theability to coordinate two or more frames or systems of reference within a well-definedand closed system as a whole. For well-defined problems, all information necessary to46produce a solution is given or can be derived from what is given. Thus it is possibletoderive one or a few objective solutions.2) The postformal form of nonabsolute! relativistic (N/R) thinking isoperationally defined as “multiple-frame operations on ill-defmed problems”whichrequire the ability to think flexibly in terms of multiple frames within self-constructedaswell as open systems. For ill-defined problems, the information given is not complete.The systems for operations have yet to be constructed and defined, and are open tointeractions. The person is often required to generate information beyond that which isgiven or known. Thus it is not possible to expect any absolute or objective solutions.Such operations would necessarily imply uncertainty and indeterminacy.b) The operational definition of the epistemic view dimension of nonabsolute!relativistic (N/R) thinking is as follows:The epistemic view associated with nonabsolute! relativistic (N/R) thinking isoperationally defined in terms of four specific aspects pertinent to the nature ofknowledge of reality. These four specific aspects are extracted and modified from theinformation derived from the Reflective Judgment model which concerns the changes inepistemic view from an absolute to a nonabsolute view of the knowledge of reality(Kitchener, 1986; Kitchener & King, 1981). These four specific aspects concern:1) The means of knowledge: a nonabsolute! relativistic view would be impliedby the recognition that all means involved in the construction of knowledge areultimately subjective.2) The limits of knowledge: a nonabsolute! relativistic view would be implied bythe recognition that the ultimate nature of reality can only be approximated but can neverbe completely in grasp. Thus the limits of knowledge are ever unfolding but neverreached.473) The criteria of knowledge: a nonabsolute! relativistic view would be impliedby the recognition that there is no absolute criterion for judging any solution, because allcriteria are always relative to certain sets of assumptions.4) The nature of reality: a nonabsolute/ relativistic view would be implied bythe recogntion that reality is in constant flux (i.e. the notion of a dynamic world viewversus a static world view).The above definition of nonabsolute/ relativistic (N/R) thinking was used as abasis for the design of a battery of 3 tests of nonabsolute/ relativistic (N/R) thinking.2. Tests of Nonabsolute/ relativistic (NJR) ThinkingIn this section, the second research question namely, “How can nonabsolute/relativistic (N/R) thinking be measured?” is addressed. A battery of 3 tests ofnonabsolute! relativistic (N/R) thinking was specifically designed to measure theconstruct of nonabsolute! relativistic (N/R) thinking. These 3 tests of nonabsolute!relativistic (N/R) thinking are: 1) The test of the formal form of N/R thinking (N/R-F), 2)The test of the postformal form of N/R thinking (N/R-PF), and 3) The test of theepistemic view of N/R thinking (N/R-EV). The first 2 tests were designed to measurethe 2 levels of the basic form dimension and the last test was designed to measure theepistemic view dimension of nonabsolute/ relativistic (NIR) thinking.48a) The Test of the Formal Form of N/R Thinking (N/R-F)Test DescriptionThe purpose of this test is to assess the presence of the formal form ofnonabsolute/ relativistic (N/R) thinking. Such form of thinking is operationally definedas “multiple-frame operations on well-defined problems”. This test adopts a subtest ofthe Arlin Test of Formal Reasoning (ATFR) (Arlin, 1984b), specifically the subtest ofthe coordination of two or more frames or systems of reference which makes up part ofthe third (or the highest) tier of the ATFR. This subtest is designed to test the ability tocoordinate two or more frames or systems of reference. Inhelder and Piaget (1958)demonstrated that a simple form of relativity can be defmed as the coordination of two ormore frames or systems of reference, which is one of the eight concepts or schemata offormal operations. Arlin (1984) argued that this schema might represent a pivotalconcept that marks the transition from high-formal to postformal operations.This test is a pencil-and-paper test made up of 4 multiple-choice questions. The 4questions are organized into 2 pairs. Each pair of questions is related to a problem whichis accompanied with a drawing (see Appendix A). The test items are as follows.Test itemsA small toy wind-up turtle is placed on a shaded strip of paper.The paper strip is lined up along the edge of a board as shown in thepicture. The turtle can be moved along the paper strip. The paper stripcan also be moved along the board. Both the toy and the paper strip canbe moved forward or backward. The toy, the end of the paper strip, andthe starting point on the board are all lined up as shown.491. If the turtle moves forward at the same speed that the paper strip moves backward,how far will the turtle be from the starting point after a short time (as long as theturtle is still on the strip of paper)?A. It would be at the starting point.B. One-fourth the distance of the paper strip from the starting point.C. Double the distance of the paper strip from the starting point.D. It would be behind the starting point.2. If the turtle moves forward at 1/3 the speed that the paper strip moves backward,where would the turtle be after a short period of time (as long as the turtle is still onthe strip of paper)?A. Three times as far forward as the paper strip is backward from the starting point.B. One-third the distance in front of the starting point as the paper strip is behind thestarting point.C. It would be behind the starting point.D. As far in front of the starting point as the end of the paper strip is in back of it.Two people are sitting on this train as it passes through a longtunnel in the side of a mountain. Mr. Red (R) is sitting at the front of thetrain and Mr. Blue (B) is sitting at the back of the train. For the followingtwo situations, decide whether Mr. R and Mr. B will stay in the tunnel forthe same amount of time.3. SITUATION 1: After the train enters the tunnel, Mr. R gets up from his seat in thefront, and walks back to sit with Mr. B. How much time altogether will Mr. R spendin the tunnel?50A. Less time in the tunnel than Mr. B.B. Twice the time in the tunnel as Mr. B.C. The same amount of time in the tunnel as Mr. B.D. More time in the tunnel than Mr. B.4. SITUATION 2: After the train has entered the tunnel, Mr. B gets up from his seat inthe back. He walks forward to sit with Mr. R. Halfway on his trip forward, hedecides to go back to his seat for his paper. He gets his paper and then goes forwardagain and joins Mr. R while the train is still in the tunnel. How much time did Mr. Bspend in the tunnel?A. Less time in the tunnel than Mr. R.B. More time in the tunnel than Mr. R.C. One-and-one-half as much time in the tunnel as Mr.R.D. The same amount of time in the tunnel as Mr. R.Scoring CriteriaThe correct answers for the test items are follows.l.A 2.C 3.D 4.AScore 1 point for each correct answer to an item. An individual test score is thesum of the 4 item scores.51InterpretationA score of 0 to 1 would be interpreted as the absence of the formal form ofnonabsolute/ relativistic (N/R) thinking. A score of 2 represents a transitionaldevelopment of such a form. A score of 3 represents the presence of a partiallydeveloped formal form of nonabsolute/ relativistic (N/R) thinking. A score of 4represents the presence of a fully developed formal form of nonabsolute! relativistic(N/R) thinking.Technical information about ATFR:In a multi-trait, multi-method validity study of the ATFR, the test-retestreliabilities yielded were of the order of .76 to .89 (Arlin, 1982). For the total test theHoyt estimates of reliability ranged from .71 to .89. The Cronbach Alphas for the totaltest composites ranged from .60 to .73. (Arlin, 1984b)b) The Test of the Postformal Form of NJR Thinking (N/R-PF)Test descriptionThis test is specifically designed by Arlin and the author for this study to assessthe presence of the postformal form of nonabsolute/ relativistic (N/R) thinking. Thisform of thinking is operationally defined as “multiple-frame operations on ill-definedproblems” which require the ability to think flexibly in terms of multiple frames withinself-constructed as well as open systems. This test differs from N/R-F (formal form) inthat it involves ill-defined problems for which examinees are required to generateinformation beyond that which is given including relevant frames of reference. Also thistest does not require accuracy in mental computation. Since absolute answers cannot be52expected for this test, the recognition of uncertainty and indeterminacy is necessarilyimplied.This test is a pencil-and-paper test made up of 4 open-ended questions. The 4 testitems are presented in the following.Test Items1. “A” grows 1 cm per month. “B” grows 2 cm per month.Who is taller?ANSWER:_________________________Why? Explain your answer.2. City “A” is120C. City “B” is100C.Which city is warmer?ANSWER:_________________________Why? Explain your answer.3. “A” can run at 15 k.p.h. “B” can run at 12 k.p.h.Who would arrive earlier?ANSWER:_________________________Why? Explain your answer.4. “A” weighed 8 kg. “B” weighed 9 kg.Which one is heavier?ANSWER:_______________Why? Explain your answer.53Scoring CriteriaA typical absolute answer would be a forced choice between A and B. A typicalnonabsolute answer would be exemplified by not choosing between A and B. However,there could be exceptions to the above defmitions of an absolute and a nonabsoluteanswer. Scoring would be based primarily on the quality of the reasons given ratherthanmerely on the choices made. A general guideline is as follows.Score 1 for an absolute answer in which there was only one frame or system ofreference involved in the explanation. (e.g. A is taller than B because A grows faster.)Score 2 for a nonabsolute answer without relevant explanation. (e.g. Don’t know.Unable to decide.).Score 3 for a nonabsolute answer with a partially relevant explanation. Theexaminee showed partial awareness of the multiple-frame operations. (e.g. Unable todecide because of insufficient information. There is no information on how tall A and Bare in the first place.)Score 4 for a nonabsolute answer with a general and/or comprehensiveexplanation. The examinee showed full awareness of the multiple-frame operations inaddition to the ability to generate the relevant frames of reference. Ideally, the examineecould point out the problematic assumptions underlying the questions. (e.g. Unabletodecide because faster growth rate does not necessarily imply greater height/length. Thereis other information to be considered such as...).An individual test score is the average of the 4 item scores. If there is more thanone rater, the final test score would be the average of the individual test scores providedby the different raters.InterpretationA score of 1 to less than 2 would be interpreted as the absence of N/R-PF, thepostformal form of nonabsolute/ relativistic (N/R) thinking. A score of 2 to less than354represents the transitional development of such a form. A score of 3 to less than 4represents the presence of a partially developed postformal form of nonabsolute/relativistic (N/R) thinking. A score of 4 represents the presence ofa fully developedformal form of nonabsolute! relativistic (N/R) thinking.c) The Test of the Epistemic View of NJR Thinking (NJR-EV)Test descriptionThis test is specifically designed by Arlin and the author for this study to assessthe level of the epistemic view (or the theories of knowledge of reality) associated withnonabsolute/ relativistic (N/R) thinking. The epistemic view of nonabsolute! relativistic(N/R) thinking is operationally defined in terms of four specific aspects pertinent to thenature of knowledge of reality. These four specific aspects concern: 1) the means ofknowledge, 2) the limits of knowledge, 3) the criteria of knowledge, and 4) the nature ofreality. They are modified extractions from the Reflective Judgment model whichconcerns the detection of the changes in epistemic view from an absolute to anonabsolute view of the knowledge of reality (Kitchener, 1986, Kitchener & King,1981).This test is a pencil-and-paper test made up of 4 items, each of which containsboth a multiple-choice and an open-ended question. Each item correspondsto one of thefour specific aspects of the epistemic view. The 4 test items are presented in thefollowing.55Test Items1. How do you know about the world around you?a. through your senses (eyes, ears, nose, etc.)b. through your own interpretation (thinking).c. othersWhy? Explain your chosen answer.2. It is possible for you to understand something completely without doubt.a. agreeb. disagreec. othersWhy? Explain your chosen answer.3. When three persons have three different solutions to the same problem, at leastone of them must be wrong.a. agreeb. disagreec. othersWhy? Explain your chosen answer.4. Some things will never change.a. agree (What are they?__________)b. disagreec. othersWhy? Explain your chosen answer.56Scoring CriteriaFirst of all, the rater would have to determine whether an answer is an absolute ornonabsolute one. A general guideline for determining the absolute or nonabsolute natureof an answer for each of the four items are provided in the following.Item 1 examines the epistemic view concerning the means of knowledge. Anonabsolute/ relativistic view would be implied by the recognition that all meansinvolved in the construction of knowledge are ultimately subjective.A typical absolute answer would exclude answer (b).A typical nonabsolute answer would include answer (b).If answer (c) was chosen, scoring would be based on the quality of theexplanation as to whether the answer is absolute or nonabsolute according to the aboveguideline in relation to a nonabsolute/ relativistic view.Item 2 examines the epistemic view concerning the limits of knowledge. Anonabsolute/ relativistic view would be implied by the recognition that the ultimatenature of reality can only be approximated but can never be completely in grasp. Thusthe limits of knowledge are ever unfolding but never reached.A typical absolute answer would be answer (a).A typical nonabsolute answer would be answer (b).If answer (c) was chosen, scoring would be based on the quality of theexplanation as to whether the answer is absolute or nonabsolute according to the aboveguideline in relation to a nonabsolute! relativisitic view.Item 3 examines the epistemic view concerning the criteria of knowledge. Anonabsolute! relativistic view would be implied by the recognition that there is noabsolute criterion for judging any solution, because all criteria are always relative tocertain sets of assumptions.A typical absolute answer would be answer (a).A typical nonabsolute answer would be answer (b).57If answer (c) was chosen, scoring would be based on the qualityof theexplanation as to whether the answer is absolute or nonabsolute accordingto the aboveguideline in relation to a nonabsolute! relativistic view.Item 4 examines the epistemic view concerning the nature of reality. Anonabsolute/ relativistic view would be implied by the recognition that reality isaconstant flux of existence (i.e. the notion of a dynamic world view versus a staticworldview).A typical absolute answer would be answer (a).A typical nonabsolute answer would be answer (b).If answer (c) was chosen, scoring would be based on the quality of theexplanation as to whether the answer is absolute or nonabsolute according to the aboveguideline in relation to a nonabsolute/ relativistic view.All in all, scoring would be based primarily on the quality of the explanationgiven rather than merely on the choices made. Once the absolute or nonabsolute natureof an answer is determined, each item can then be scored according to the followingcriteria:Score 1 for an absolute answer with an explanation adhering to an absolute viewwith regard to the content of the test item. (e.g. Item 4: The fact that I am a human beingwill never change.)Score 2 for a nonabsolute answer without relevant explanation.Score 3 for a nonabsolute answer with a partially relevant explanation. (e.g. Item4: Life is a cycle of birth and death.)Score 4 for a nonabsolute answer with a general or comprehensive explanationrelevant to the test item. (e.g. Item 4: Change is the only constant” in the world.)An individual test score is the average of the 4 item scores. If there is morethanone rater, the final test score would be the average of the individual test scoresprovidedby the different raters.58InterpretationA score of 1 to less than 2 would be interpreted as the absence of the epistemicview associated with nonabsolute/ relativistic (N/R) thinking.A score of 2 to less than 3represents a transitional development of such kind of epistemic view.A score of 3 toless than 4 represents the presence of a partially developed epistemicview ofnonabsolute/ relativistic (N/R) thinking. A score of 4 represents the presence ofa fullydeveloped epistemic view of nonabsolute/ relativistic (N/R) thinking.3. Pilot StudyObjectiveThe objective of this pilot study was to explore initially the relationships amongthe 3 tests of nonabsolute/ relativistic (N/R) thinking which are specifically designed forthis study: 1) the test of the formal form of NIR thinking (N/R-F), 2) the test of thepostformal form of N/R thinking (N/R-PF), and 3) the test of the epistemic view of N/Rthinking (N/R-EV).Related questions include:a. What, if any, commonalities exist among the item scores of the 3 tests of nonabsolute/relativistic (N/R) thinking?b. What, if any, commonalities exist among the individual test scores of the 3 testsofnonabsolute! relativistic (N/R) thinking?c. Is the mastery of N/R-F (formal form) a necessary but not sufficient condition forthemastery of N/R-PF (postfonnal form) and N/R-EV (epistemic view)?d. Is the mastery of N/R-EV (epistemic view) a necessary but not sufficient conditionforthe mastery of N/R-PF (postformal form)?59e. How internally consistent are the item scores of the tests of N/R-PF (postformal form)and of N/R-EV (epistemic view) (i.e. the two tests designed by Arlin and the authorfor this study)?ParticiDantsThe participants were 22 volunteers comprising 14 males and 8 females rangingfrom age 7 years to 44 years and above. They were residents of Vancouver, B.C. andhad been recruited through friends and through faculty members and students ofUniversity of British Columbia. Of the 22 participants, only the scores of 17 participants(aged 12 and above) were entered for data analysis, because the other 5 participants wereall aged below 12 and were only administered one test, namely N/R-PF (postformalform).Procedures & MeasuresThe 3 N/R tests -- N/R-F (formal form), N/R-PF (postformal form), and N/R-EV(epistemic view) -- were in pencil-and-paper format. The N/R-F (formal form) wasadministered in its original form of four items; the N/R-PF (postformal form) wasrevised for administration by dropping two redundant items from the original form of sixitems; and the N/R-EV (epistemic view) was revised for administration by dropping oneredundant item from the original form of five items.All three tests were administered to 14 of the 22 participants. Due to situationalconstraints, other 3 participants were not administered the N/R-F (formal form). Theirmissing scores for N/R-F (formal form) were replaced by the variable means. Theremaining 5 participants (aged 7 to 12) were administered only the N/R-PF (postformalform). Thus their scores were not used for data analysis, but for reference only.60Two testers were involved in the test administration and data collection.Clarification of vague answers and feedback on the participants opinions about the testswere elicited whenever a follow-up discussion was possible.Analysis, Results & InterpretationTo address Questions (a) and (b), exploratory factor analyses using SPSS:Xcomputer programme were conducted to see if the scores of the 3 N/R tests share anycommonalities. The method of factor extraction was principal axis factoring (PAF).For Question (a), an exploratory factor analysis was conducted based on thecorrelations among the item scores of the 3 N/R tests obtained from the 17 participants.In the revised version of the 3 N/R tests, there were 4 items in each test. Therefore, atotal of 12 items were involved. (The correlation matrix is presented in Table 1.)Table 1Pilot Study: Correlation Matrix of Item Scores of the 3 N/RTestsFl F2 F3 F4 P1 P2 P3 P4 El E2 E3 E4Fl 1F2 .09 1F3 .35 .26 1F4 .04 .47 .12 1P1 .51 .11 .44 -.07 1P2 .32 .32 .27 - .08 .86 1P3 .49 .11 .42 - .07 .98 .86 1P4 .33 .48 .15 .28 .74 .81 .75 1El .44 .25 .26 .27 .76 .68 .79 .89 1E2 .28 .36 .21 .17 .75 .80 .80 .94 .91 1E3 .41 .22 .35 .16 .74 .74 .78 .87 .82 .84 1E4 .24 .65 .20 .42 .48 .54 .49 .79 .75 .73 .57 1Note. Fl-4 = items of Test of Formal Form of Nonabsolute/relativistic (N/R) Thinking. P1-4 = items of Test ofPostformal Form of N/R Thinking. E1-4 = items of Test ofEpistemic View of N/R Thinking.61Results indicate that three eigenvalues greater than 1.0 were obtained(eigenvalues = 6.90, 1.82, 1.15). However, extraction was terminated in 2 iterationsdueto communality exceeding 1.As an alternative, another exploratory factor analysis was conducted based on theitem scores of only the 2 postformal level N/R tests -- N/R-PF (postformal form) andN/R-EV (epistemic view). A total of 8 variables (4 items x 2 tests) were involved. Oneeigenvalue greater than 1.0 was obtained. The eigenvalue was 6.40, accounting for 80%of the variance. One factor was extracted. Items of both tests yielded high loadings onone factor. For N/R-PF (postformal form), the loadings ranged from 0.86 to 0.95. ForN/R-EV (epistemic view), the loadings ranged from 0.69 to 0.95.For Question (b), an exploratory factor analysis was conducted based on thecorrelations among the individual test scores of the 3 tests obtained from the 17participants. (See Table 2 for the correlation matrix.)Table 2Pilot study: Correlation Matrix of Test Scores of the 3 N/RTestsN/R-F N/R-PF N/R-EVN/R-F 1N/R-PF .41 1N/R-EV .52 .87 1Note. N/R-F=Test of Formal Form of Nonabsolute/ relativistic(N/R) Thinking. N/R-PF=Test of Postformal Form of N/RThinking. N/R-EV=Test of Epistemic View of N/R Thinking.62A total of 3 sets of test scores were involved in the analysis. One eigenvaluegreater than 1.0 was obtained (eigenvalue=2.23). Similar to the analysis conducted onthe items of all 3 tests of nonabsolute! relativistic (N/R) thinking, extraction wasterminated in 7 iterations due to communality exceeding 1.Again as an alternative, another exploratory factor analysis was conducted on thetest scores of only the 2 postformal level N/R tests -- N/R-PF (postformal form) andN/R-EV (epistemic view). A total of 2 variables (2 sets of test scores) were involved.One eigenvalue greater 1.0 was obtained. The eigenvalue was 1.87, accounting for93.7% of the variance. One factor was extracted. Both tests yielded equally highloadings (0.93) on this factor.Results of the above exploratory factor analyses seem to suggest that the scores ofthe 2 postformal level NIR tests -- N/R-PF (postformal form) and N/R-EV (epistemicview) -- tended to load on a common factor. However, when the scores of all 3 N/R testswere analyzed together, they did not converge on a common factor. This seem to suggestthat the formal form of nonabsolute! relativistic (N/R) thinking is indeed qualitativelydistinct from the postformal form and the epistemic view of nonabsolute/ relativistic(N/R) thinking as hypothesized in this study. However, such preliminary results whichwere based on a very small sample need to be validated with a full data set based on alarger sample in the main study.To address Questions (c) and (d), contingency tables were constructed to evaluatethe certain specific relationships among the 3 N/R tests as to the primacy of one test overthe other (that is the mastery of one test is a necessary but not sufficient condition for thatof the other). The contingency tables of the forms: N/R-F (formal form) x N/R-PF(postformal form), N/R-F (formal form) x N/R-EV (epistemic view),and N/R-EV(epistemic view) x N/R-PF (postformal form) are displayed in Figure3.To establish that mastery of one test is a necessary but notsufficient condition forthat of another, logically the contingency table involved should contain one empty cell63Figure 3Pilot Study: Contingency TablesN/R-F (formal form) x N/R-PF (postformalform)N/R-PF (postformalform)non-mastery mastery(1,2) (3,4)non-mastery 8 0(1,2)N/R-Fmastery(3,4) 4 2N/R—F (formal form) x N/R-EV (epistemic view)N/R-EV (epistemic view)non-mastery mastery(1,2) (3,4)non-mastery 7 1(1,2)N/R - Fmastery(3,4) 4 2N/R-EV (epistemic view) x N/R-PF (postformal form)N/R-PF (postformal form)non-mastery mastery(1,2) (3,4)non-mastery 11 0(1,2)N/R-EVmastery(3,4) 2 464(target cell). This target cell is the intersection of the non-mastery of an easier test andthe mastery of a more difficult test and therefore, there should be no entry for the targetcell. Therefore, there should be no entries for cell N/R-F (1,2) by N/R-PF (3,4); cellN/R-F (1,2) by NIR-EV (3,4); and cell N/R-EV (1,2) by N/R-PF (3,4). However,exceptional cases would not be unexpected. If these exceptional cases are few innumber, the model would not be threatened.Tentatively, the results of the contingency tables appear to support the hypothesesthat the mastery of N/R-F (formal form) is a necessary but not sufficient condition forthat of N/R-PF (postformal form) and NIR-EV (epistemic view), and that the mastery ofN/R-EV (epistemic view) is a necessary but not sufficient condition for that of NIR-PF(postformal form). Again, these results need to be validated with a full data set in themain study.To address Question (e), the internal consistency among the test items of the 2postformal level N/R tests -- N/R-PF (postformal form) and N/R-EV (epistemic view) --was explored. The Cronbach Alphas obtained for N/R-PF (postformal form) was 0.95and for N/R-EV was 0.93. These results suggest that the item scores of both tests werequite internally consistent though not necessarily implying unidimensionality within thetests.Other observationsIn the data obtained from the scores of all 22 participants, it was observed that thetransitional development of the postformal form of nonabsolute/ relativistic (N/R)thinking does not appear until the approximate age of 13 years. Regarding the 5participants who were administered only the N/R-PF (postformal form), their agesranged from 7 years to 12 years. Their scores did not contradict the above observation inthat the transitional development of the postformal form of nonabsolute! relativistic(N/R) thinking also did not appear in all 5 participants.65Follow upInformation obtained from this pilot study in conjunction with participantfeedback on the tests were used as input for item revision. Some items on both tests wererephrased for clarity and simplicity. For the NIR-PF (postformal form), 2 items weredeleted from the original 6 items, and for the N/R-EV (epistemic view), 1 item wasdeleted from the original 5 items because of redundancy. Only the items selected for therevised version of the tests were used for analyses in this pilot study.Different item orders were tried for the presentation of N/R-PF (postformal form)and N/R-EV (epistemic view) and did not seem to yield significant differences in theresponse patterns. Tester bias had not been observed.664. Design and Proposed AnalysisThis is the last section of part B (Methodology). To recapitulate, insections 1and 2, Research Question 1 (How can nonabsolute/ relativistic(NIR) thinking beoperationally defined?) and Research Question 2 (How can nonabsolute! relativistic(N/R) thinking be measured?) were addressed respectively. In section3, a pilot studywas conducted to explore initially the relationships among the 3 tests of nonabsolute/relativistic (N/R) thinking which are specifically designed for this study.In this section,Research Questions 3 and 4 which are related to the main study are addressed. Theresearch questions to be addressed are as follows:Research Question 3:Is nonabsolute/ relativistic (NIR) thinking a possible unifyingcommonality underlying the selected models of postformal reasoning?Research Question 4:Is nonabsolute/ relativistc (NIR) thinking an instance of formal orpostformal reasoning or both?The design and proposed analysis for the main study are discussed in thesubsections: 1) Participants; 2) Procedures;3) Instruments; and 4) Research questions,hypotheses, and statistics.ParticipantsThe participants would be about 250 persons with ages rangingfrom 10 to above40. The participants would be categorized into 3 agegroups: 1)10 to 15; 2)16 to 20;and 3) 21 and above. The participants would be recruitedon an individual basis as well67as from the public schools in Vancouver, B.C. and outlying areas and University ofBritish Columbia.The reasons for deciding on the sample size of about 250 are as follows. Firstly,the major method of statistical analysis employed in this study would be confirmatoryfactor analysis. According to Comrey (1992), a sample size of 200 would be consideredas fair, and 300 as good, for factor analysis in general. Thus a sample of about 250would be adequate to demonstrate the general patterns of relationships among variables ifthere are any. Secondly, from a statistical standpoint, when factors are strong anddistinct and the number of variables is not too large, a relatively small sample size wouldbe acceptable. As a general rule of thumb, a minimum of 5 cases for each observedvariable would be considered adequate (Tabachnich & Fidell, 1989). In this study, amaximum of 12 variables (a maximum of 8 individual test scores or 12 item scores)would be involved in each analysis. Thus about 250 cases would more than satisfy theminimum requirement.The rationale for selecting the age range of 10 to above 40 years is that this agerange would probably identify the onsets of minimal formal reasoning,nonabsolute/relativistic (N/R) thinking and minimal postformal reasoning as well as theirmaturing phases.According to Piaget (1972), all individuals reach the stage of formal operations, ifnot between 11 and 15 years, at least between 15 and 20, though some researcherssuggested that up to 50 percent of adults never reach the formal reasoning stage (seeKing, 1986). Correspondingly, as revealed in the tentative findings of the pilot study, theage of onset of nonabsolute/ relativistic (N/R) thinking is around 15. Thus group 1 (ages10 to 15) is set up to identify the onsets of both minimal formal reasoning andnonabsolute/ relativistic (N/R) thinking.68It is speculated that the development of postformal reasoning begins in lateadolescence and early adulthood (see Commons, Richards & Armon, 1984). Thus group2 (ages 16 to 20) is set up to identify the onset of the minimal postformal reasoning.Finally, group 3 (ages 21 and above) is set up to identify the maturing phases ofall three types of thinking (formal reasoning, nonabsolute! relativistc (N/R) thinking andpostformal reasoning).Students currently enrolled in English as a Second Language (ESL) Program andspecial programs would be screened out so as not to confound the findings.ProceduresThe participants would be administered a battery of tests in pencil-and-paperformat. The tests would be administered individually or in groups. These tests wereeither designed or adapted to measure three types of thinking, namely nonabsolute/relativistic (N/R) thinking, minimal formal reasoning and the minimal postformalreasoning specific to the selected postformal models. A table containing the constructsbeing measured and the list of corresponding tests is presented in the next section underthe topic of Instruments.All the tests would be scored by two raters. The final test scores for each testentered for statistical analyses would be based on inter-rater agreement which was theaverage of the individual test scores provided by the two raters.To minimize intra-rater bias in the scoring of any age group or educational level,all the protocols would be shuffled before scoring. Also, to minimize intra-rater bias inthe sôoring of any individual protocol, the raters would score the protocols of all theparticipants on one test before proceeding to the next test in the battery.69Table 3.InstrumentsThe constructs being measured and the tests which measure them are contained inTable 3List of Constructs and Corresponding TestsFormal Formof N/R Thinking(N/R-F)2. Postformal Formof N/R Thinking(N/R-PF)N/R-F(ATFR subtest:Coordination of 2or more frames ofreference)N/R-PF Designed byArlin & theauthor (1993)3. Epistemic Viewof N/R Thinking(N/R-EV)N/R-EV Designed byArlin & theauthor (1993)4. Minimal FormalReasoningFR (ATFR subtests:Multiplicativecompensations;probabilities;correlations.)Arlin (1984b)5. Problem Finding(minimal presence)PF(CognitiveProblem Finding)Arlin (1974)6. DialecticalReasoning(minimal presence)DR(Structuredquestions)Adapted byArlin & theauthor fromBasseches (1980)7. RelativisticOperations(Minimal presence)RO(Bedroom problem)Adapted by theauthor fromSinnott (1984)8. ReflectiveJudgment(minimal presence)RJ(Food Additives)Adapted byArlin & theauthor fromKing et al.(1983)Construct being Test Sourcemeasured1. - Arlin (1984b)Note. N/R=Nonabsolute/ relativistic.70Eight tests are selected for use in this study. They can be divided into3 groups oftests. These tests were either designed or adapted to measure 3 types of thinking, namelynonabsolute! relativistic (N/R) thinking, minimal formal reasoning and minimalpostformal reasoning. Below is a brief overview of these groups of tests.The first group of tests includes the 3 tests of nonabsolute/ relativistic (N/R)thinking:1) The Test of the Formal Form of N/R Thinking (N/R-F) which aims at measuring thebasic form of nonabsolute/ relativistic (N/R) thinking operating at the formal level.In this test, a subtest of the Arlin Test of Formal Reasoning (ATFR) (1984) wasadopted to assess the presence of a simple form of relativistic thinking.2) The Test of the Postformal Form of N/R Thinking (N/R-PF) which aims at measuringthe basic form of nonabsolute! relativistic (N/R) thinking operating at the postformallevel.3) The Test of the Epistemic View of N/R Thinking (N/R-EV) which aims at measuringthe level of epistemic beliefs associated with nonabsolute/ relativistic (N/R) thinking.(Both the N/R-PF and the N/R-EV are specifically designed by Arlin and the authorfor this study to measure nonabsolute/ relativistic (N/R) thinking operating at thepostformal level.)The second group of test(s) includes:4) The test of Minimal Formal Reasoning (FR) which aims at measuring the minimallevel of ability for the performance of formal operations. Three subtests of theATFR (1984) are used representing the first tier of the ATFR which is originallycomposed of three tiers.The third group of tests includes the 4 postformal tests:5) The test of Problem Finding (PF),6) The test of Dialectical Reasoning (DR),7) The test of Relativistic Operations (RO), and718) The test of Reflective Judgment (RJ).For both Relativistic Operations and Reflective Judgment, one subtest wasadopted from the original tests. The rationale for the selection of the particular subtestsis stated in their respective test descriptions (see Appendixes B - F). For this study, thescoring criteria of the 4 postformal tests are adapted to tap the minimal presence ofpostformal reasoning specific to each model.The descriptions of the 3 tests of nonabsolute/ relativistic (N/R) thinking (tests 1 -3) were already presented in section 3 of this chapter. The descriptions of the rest of thetests (Tests 4 - 8) as well as their relevant statistical information are provided in theAppendixes.A summary of the interpretation of test scores of these 8 tests is presented inTable 4.A sample of the complete set of tests to be administered to the participants isprovided in Appendix G. The set of tests is presented in two forms (A and B). Thepurpose of having two forms of the same set of tests is to counterbalance the test ordereffect of 1) multiple choice questions (of well-defined problems) and 2) open-endedquestions (of ill-defined problems). In Form A, the multiple choice questions -- MinimalFormal Reasoning (FR) and NIR-F (formal form) precede the open-ended questions --N/R-PF (postformal form), NIR-EV (epistemic view), Problem Finding (PF), DialecticalReasoning (DR), Relativistic Operations (RO) and Reflective Judgment (Ri) -- in theorder as stated. In Form B, the open-ended questions (N/R-PF, N/R-EV, PF, DR, ROand RJ) precede the multiple choice questions (FR and N/R-F) in the order as stated.Each participant would be assigned either Form A or Form B on a random basis.72Table 4Summary of Interpretation of Test ScoresTests Scores1 2 3 4N/R-F Absence Transitional Partial Full(formal development development developmentform)N/R-PF Absence Transitional Partial Full(postformal development development developmentform)N/R-EV Absence Transitional Partial Full(epistemic development development developmentview)FR Absence Transitional Partial Full(Minimal development Mastery MasteryFormalReasoning)1 2 3PF Absence Transitional Minimal presence of(Problem development postformal reasoningFinding) specific to PFDR Absence Transitional Minimal presence of(Dialectical development postformal reasoningReasoning) specific to DRRO Absence Transitional Minimal presence of(Relativistic development postformal reasoningOperations) specific to RORJ Absence Transitional Minimal presence of(Reflective development postformal reasoningJudgment) specific to RJNote. N/R=Nonabsolute/ relativistic.73Research Ouestions, Hypotheses & StatisticsThis is the last subsection in section 4 (Design and Proposed Analysis). In thissubsection, research questions of the main study, namely Research Questions 3 and 4, arestated together with the proposed statistics and with the hypotheses to be tested.Analyses and results of these two research questions are presented in the next chapter(chapter IV).Research Question 3:Is nonabsolute/ relativistic (NJR) thinking a common factorunderlying the selected models of postformal reasoning?Specific questions, proposed statistics and hypotheses related to ResearchQuestion 3 are stated below:3a. What, if any, commonalities exist among the items of the 3 tests of nonabsolute/relativistic (NIR) thinking --NIR-F (formal form), NIR-PF (postformal form)and NIR-EV (epistemic view)?The purpose of this question is to explore the nature of and the relationshipsamong the items of the 3 N/R tests using confirmatory factor analysis.From a measurement perspective, the application of factor analysis on item scoresrepresents one approach of internal structure analysis in the context of constructvalidation (Pedhazur & Schmelkin, 1991). Both internal and external structure analysescontribute to part of the ever-ongoing process of construct validation.Althoughconstruct validation is not the main focus of this study, the results of the confirmatoryfactor analyses conducted on the test items could serve as a foundation for the analyses to74be conducted at the next level using test scores instead of item scores of the three N/Rtests.The proposed statistics would involve confirmatory factor analysis using theLISREL 8 computer program. The method of estimation would be MaximumLikelihood (ML). The analysis would be based on the covariances rather than thecorrelations among the item scores of the 3 N/R tests. The rationale is that the analysisof correlation matrices is problematic in several ways. Such an analysis may a) modifythe model being analyzed, b) produce incorrect Chi-square and other goodness-of-fitmeasures, and c) give incorrect standard errors (Cudeck, 1989; Joreskog & Sorbom,1993). Therefore, all the subsequent confirmatory factor analyses in this study would bebased on covariance matrices.Two models (Models Al and A2) would be constructed and tested.Model Al would evaluate the following hypotheses:Hypothesis 3a(l): Three test factors, namely N/R-F (formal form), N/R-PF(postformal form) and N/R-EV (epistemic view), would underlie the 12 test items.Hypothesis 3a(2): The 3 test factors would be correlated. (The implication ofthis hypothesis is that these 3 test factors tap three different aspects of the same construct,hypothesized to be the nonabsolute! relativistic thinking (N/R) test factor.)(For specifications of Model Al, see Figure 4.)Model A2 would evaluate the following hypothesis:Hypothesis 3a(3): A second order factor, hypothesized to be the nonabsolute/relativistic thinking (N/R) test factor, would underlie the 3 test factors.(For specifications of Model A2, see Figure 5.)75Figure 4Model Al Of Confirmatory Factor Analysise—NRF2_______e — RFlN/R - F_____________(FORMAL FORM)e-+NRF3e--NRF4TEST FACTORe-NRPF1e-.NRPF2 - PF________OSTFORMAL FORM)e—NRPF3 TEST FACTORe— [NRPF4e—NREV1e—, ENREV2- EVPISTEMIC VIEW)e-÷[_NREV3 TEST FACTORe-.I_NREV4Note. NRF1-4 = items of Test of Formal Form of Nonabsolute/relativistic (N/R) Thinking. NRPF1-4 = items of Test ofPostformal Form of N/R Thinking. NREV1-4 = items of Test ofEpistemic View of N/R Thinking. e = error! unique variance.76Figure 5Model A2 of Confirmatory Factor Analysis_______/Ze—_NRF2N/R-F(FORMAL FORM)1e NRF3 TEST FACTORe NRF4: ::::: N/RPF________(POSTFORMAL FORM))ITESTIe .—.[NRPF3 TEST FACTOJJ____e-.,{NRPF4e NREV1ze NREV2 N/R-EV(EPISTEMIC VIEW)e—_NREV3TEST FACTORe NREV4Note. NRF1-4 = items of Testof Formal Form of Nonabsolute/relativistic (N/R) Thinking. NRPF1-4= items of Test ofPostformal Form of N/R Thinking.NREV1-4 = items of TestofEpistemic View of N/R Thinking.e = first order error!unique variance. z = secondorder error! unique variance.773b. What, if any, commonalities exist among the 3 tests of nonabsolute/ relativistic(NIR) thinking and the 4 tests of postformal reasoning (Problem Finding (PF),Dialectical Reasoning (DR), Relativistic Operations (RO) and ReflectiveJudgment (RJ))?The purpose of this question is to explore nonabsolute/relativistic (N/R) thinkingas a possible unifying commonality underlying the selected models of postformalreasoning.The proposed statistics would involve confirmatory factor analysis using theLISREL 8 computer program. The method of estimation would be MaximumLikelihood (ML). The analysis would be based on the covariances among the test scoresof the 3 N/R tests and the 4 postformal tests.Four models (Models Bi to B4) would be constructed and tested.Model Bi would evaluate the following hypotheses:Hypothesis 3b(1): A common factor, namely the nonabsolute/ relativisticthinking (N/R) test factor, would underlie the 3 N/R tests.Hypothesis 3b(2): A common factor, namely the postformal test factor, wouldunderlie the 4 postformal tests.Hypothesis 3b(3): The nonabsolute/ relativistic thinking (N/R) test factor and thepostformal test factor would be correlated. (The implication of this hypothesis is that thetwo test factors would represent two different aspects of the same construct, hypothesizedto be nonabsolute/ relativistic (N/R) thinking.)(For specifications of Model Bi, see Figure 6.)Models B2 and B3 would evaluate the following hypothesis:Hypothesis 3b(4): nonabsolute/ relativistic (N/R) thinking is a possible unifyingcommonality underlying the 3 N/R tests and the 4 postformal tests.(For specifications of Models B2 and B3, see Figures 7 and 8.)78TESTFACTORTESTPOSTFORMALFACTORFigure 6Model Bi of Confirmatory Factor AnalysisN/R-F(formal form)N/R-PF[(postformal form)N/R-EV(epistemic view)e —e—e —e —e —PF( ProblemFinding)DR(DialecticalReasoning)RO(RelativisticOperations)RJ(ReflectiveJudgment)Note. N/R=Nonabsolute/ relativistic. e = error! uniquevariance.79Figure 7Model B2 of Confirmatory Factor Analysise N/R-F[(formal form)e—)I N/R-PF N/RI(postformalform) TESTFACTORe— N/R-EV(epistemic view)_________________N/RPF THINKINGe .— (Problem[Finding)DRe —a (DialecticalReasoning) POSTFORMAL__________________TESTRO FACTORe— (Relativistic[Operations)_____________________zRJe— (ReflectiveIJudgment)Note. N/R=Nonabsolute/ relativistic.e = first order error!unique variance. z = second order error! unique variance.80Figure 8Model B3 of Confirmatory Factor Analysise N/R-F(formal form)e N/R-PFI(postformal form)e N/R-EVI_(epistemicview)N/RTHINKINGPFe-_ (ProblemI.Finding)DRe—j (Dialectical[Reasoning)ROe— (RelativisticOperations)RJe-— (ReflectiveJudgment)Note. N/R=Nonabsolute/ relativistic.e = error! uniquevariance.81Model B4 would evaluate the following hypotheses:Hypothesis 3b(5): A common factor, namely the basic form dimension, wouldunderlie the 4 tests -- N/R-PF (postformal form), PF (Problem Finding), DR (DialecticalReasoning), and RO (Relativistic Operations).Hypothesis 3b(6): A common factor, namely the epistemic view dimension,would underlie the 2 tests -- N/R-EV (epistemic view) and RJ (Reflective Judgment).Hypothesis 3b(7): The two factors, namely the basic form dimension and theepistemic view dimension, would be correlated. (The implication of this hypothesis isthat two dimensions could be differentiated within the same construct, hypothesized to bethe postformal level of nonabsolute/ relativistic (N/R) thinking.)(For specifications of Model B4, see Figure 9.)82Figure 9Model B4 of ConfirmatoryFactor Analysise N/R-PF(Postformal form)e__>PF(ProblemFinding)BASICFORMe_{DRDIMENSION(DialecticalReasoning)e__RO(RelativisticOperations)N/R-EV(Epistemic view)e_>{RJ(ReflectiveDIMENS IONJudgment)Note. 1/R=Nonabsolute/relativistic.e = error! uniquevariance.83Research Question 4:Is nonabsolute/ relativistic (NJR) thinking an instance of formal orpostformal reasoning or of both?Specific questions, proposed statistics and hypotheses related to ResearchQuestion 4 are stated below:4a. What is the order of difficulty among the 8 tests -- Minimal Formal Reasoning(FR), NIR-F (formal form), NJR-PF (postformal form), NIR-EV (epistemicview), Problem Finding (PF), Dialectical Reasoning (DR), RelativisticOperations (RO), and Reflective Judgment (RJ))?The first approach to this question would be to rank order the 8 tests according tothe percentage of task mastery.The following hypothesis would be evaluated.Hypothesis 4a(1): The hypothesized order of task difficulty from the least to themost difficult would be as follows -- the test of Minimal Formal Reasoning (FR); theN/R test at the formal level (N/R-F (formal form)); the 2 N/R tests at the postformal level(N/R-PF (postformal form) and N/R-EV (epistemic view)); and the 4 postformal tests(Problem Finding (PF), Dialectical Reasoning (DR), Relativistic Operations (RO) andReflective Judgment (RJ)).The rationale for this hypothesized rank order is that N/R-F (formal form) iscloser to formal reasoning whereas N/R-PF (postformal form) and N/R-EV (epistemicview) are closer to postformal reasoning. This hypothesis is based on the assumption thatthe relationships among the tests can be described in a linear model.The second approach to this question would be to construct contingency tables toevaluate the certain specific relationships among the 8 tests as to the primacy of one test84over the other (that is the mastery of one test is a necessary but not sufficient conditionfor that of the other).The following hypotheses would be evaluated.Hypothesis 4a(2): Minimal Formal Reasoning (FR) << (is a necessary but notsufficient condition for) each of the 3 N/R tests.Hypothesis 4a(3): N/R-F (formal form) << each of the 2 postformal N/R tests(N/R-PF (postformal form) and N/R-EV (epistemic view)).Hypothesis 4a(4): N/R-EV (epistemic view) <<N/R-PF (postformal form).Hypothesis 4a(5): N/R-PF (postformal form) <<each of the 4 postformal tests.Hypothesis 4a(6): N/R-EV (epistemic view) <<each of the 4 postformal tests.Hypothesis 4a(7): The transitional development of N/R-PF (postformal form) <<each of the 4 postformal tests.Hypothesis 4a(8): The transitional development of N/R-EV (epistemic view) <<each of the 4 postformal tests.4b. What is the order of the 8 tests according to their ages of onset of task mastery?To address this question, the 8 tests were rank ordered according to the age ofonset at which the task of each test is mastered. The age of onset is defined as the basalage at and above which age level there is a minimum of at least one incidence of taskmastery. For example, in a particular test, if at least one incidence of task masteryappeared at ages 10, 11, 12 and so forth, age 10 would be taken as the age of onset; but ifat least one incidence of task mastery of the test appeared at ages 10, 12, 13, 14 and soforth, then age 12 rather than age 10 would be taken as the age of onset. It is notnecessary for all the participants of the age of onset thus defined to master the test inquestion. However, the definition is conditional on an adequate representation ofparticipants at each different age level.The following hypothesis would be evaluated.85Hypothesis 4b(1): The hypothesized order of the 8 tests accordingto their agesof onset of task mastery would be as follows -- the test of Minimal Formal Reasoning(FR); the N/R test at the formal level (N/R-F (formal form)); the 2 N/R tests at thepostformal level (N/R-PF (postfonnal form) and N/R-EV (epistemic view)); and the 4postformal tests (Problem Finding (PF), Dialectical Reasoning (DR), RelativisticOperations (RO) and Reflective Judgment (RI)).The rationale for this hypothesized rank order is that NIR-F (formal form) iscloser to formal reasoning whereas N/R-PF (postformal form) and N/R-EV (epistemicview) are closer to postformal reasoning. This hypothesis is based on the assumption thatthe relationships among the tests can be described in a linear model.4c. How do the 3 N/R tests correlate with the factors of formal level reasoning andof postformal level reasoning?The following hypotheses would be evaluated.Hypothesis 4c(1): N/R-F (formal form)would load primarily on the factor offormal level reasoning.Hypothesis 4c(2): N/R-PF (postformal form) and N/R-EV (epistemic view)would load primarily on the factor of postformal level reasoning.The first approach to this question would involve exploratory factor analysisusing SPSS:X computer programme. The analysis would be based on the correlationsamong the scores of the 8 tests, namely the 3 N/R tests, the 4 postformal test and the testof Minimal Formal Reasoning (FR). The method of factor extraction wouldbe PrincipalAxis Factoring (PAF).The second approach to this question would involve confirmatory factoranalysisusing LISREL 8 computer programme. The method of estimation would be MaximumLikelihood (ML). The analysis would be based on the covariances among the scores ofthe 8 tests. (For specifications of Model Cl, see Figure 10.)86IIFORMALLEVELNINGPOSTFORMALLEVELREASONINGNote. N/R=Nonabsolute/ relativistic. e = error! uniquevariance.Figure 10Model Cl of Confirmatory Factor AnalysisFR(Minimal FormalReasoning)N/R-F(formal form)N/R-PF(postformal form)e —e —eee—)e .—eeN/R-EV(epistemic view)PF(ProblemFinding)DR(DialecticalReasoning)RO(RelativisticOperations)RJ(ReflectiveJudgment)874d. Which of the performances in the 3 NJR tests would singly or in combinationbest predict the performances in each of the 4 postformal tests?To address this question, the following hypothesis would be evaluated.Hypothesis 4d(1): Performances in N/R-PF (postformal form) and in N/R-EV(epistemic view) rather than that in N/R-F (formal form) would be better predictors ofthe performances in the 4 postformal tests.Proposed statistics would involve four separate multiple regression analyses. Thepredictors in each of the 4 analyses would be the performances in the 3 N/R tests. Thecriterion variable in each analysis would be the performance in Problem Finding (PF),Dialectical Reasoning (DR), Relativistic Operations (RO) and Reflective Judgment (RJ)respectively.The analyses and results are presented in chapter IV.4e. Between the performances in NIR-F (formal form) and in N/R-PF (postformalform), which would be better predicted by the performance in NIR-EV(epistemic view)?To address this question, the following hypothesis would be evaluated.Hypothesis 4e(1): Performance in N/R-PF (postformal form) rather than that inN/R-F (formal form) would be better predicted by performance in N/R-EV (epistemicview).The rationale of this hypothesis is that the performances in both N/R-PF(postformal form) and N/R-EV (epistemic view) are hypothesized to represent thepostformal level of nonabsolute! relativistic (N/R) thinking, and that a shift from anabsolute to a non-absolute epistemic view is crucial to the development of the postformalform of nonabsolute! relativistic (N/R) thinking.Proposed statistics would involve 2 separate simple regression analyses. Thepredictor in each analysis would be the performance in N/R-EV (epistemic view). The88criterion variable in each analysis would be the performance in N/R-F (formalform) andin NIR-PF (postformal form) respectively.The analyses and results are presented in chapter IV.89CHAPTER IV: ANALYSES AND RESULTSIn this chapter the analyses and results of the main study are presented. There arethree parts in this chapter. Part A contains the information on data collection. Part Bcontains the preliminary statistics pertinent to the main analyses. Part C contains theanalyses and results of the main study which is specifically designed to address ResearchQuestions 3 and 4 of this study.In order to evaluate the different research hypotheses of this study, differentstatistical approaches were applied. The computer software LISREL 8 (Joreskog &Sorbom, 1993) was used for the confirmatory factor analyses conducted in this study.The computer programme SPSS:X was used for the rest of the statistical analyses.For a glossary of the abbreviations and symbols used in this chapter, seeAppendix H.A. DATA COLLECTIONA total of 254 participants who had completed the paper-and-pencil task wereinvolved in this study. There were 25 participants who did not complete the pencil-and-paper task, and their protocols were excluded from the analysis. The participants wereencouraged to attempt and complete all the test items; but they were also given thefreedom to discontinue at any point. Upon examining the 25 incomplete protocols, itwas revealed that based on the performance on other test items, the unanswered questionsreflected the participants’ test attitude rather than their inability to understand or answerthe questions.Of the 254 participants whose protocols were analyzed, their ages ranged from 10to 48. They were categorized into 3 general groups. Group 1 comprising participants90aged 10 to 15 was meant to identify the onsets of both formal reasoning and nonabsolute!relativistic (N/R) thinking. This group made up 44.1% of the sample. Group 2comprising participants aged 16 to 20 was meant to identify the onsets of postformalreasoning. This group made up 3 3.9% of the sample. Group 3 comprising participantsaged 21 and above was meant to identify the maturing phases of all 3 types of thinking,namely formal reasoning, nonabsolute/ relativistic (N/R) thinking and postformalreasoning. This group made up the remaining 22% of the sample.Of the sample, 38.6% was male and 61.4% was female.The educational levels of the participants ranged from Grade 5 to the doctorallevel.The primary school students were recruited on an individual basis. The pencil-and-paper task was administered in small group sessions with the help of a volunteerresearch assistant. In view of the students’ age and educational levels, special effortswere taken to ensure that they understood all the test questions. Forty completedprotocols (15.7% of the total sample) were obtained from students of Grades 5 to 7.The secondary school students were recruited from two sources. Students ofGrades 9 to 12 were contacted through the school authorities of Selkirk SecondarySchool, Kimberly, British Columbia. The pencil-and-paper task was administered inclass sessions through the help of the principal advisor of this study. Fifty-threecompleted protocols (20.9% of the total sample) were obtained from these students.Another group of secondary school students residing in Vancouver, British Columbiawas contacted on an individual basis. The pencil-and-paper task was given as a takehome assignment. Eighty-five completed protocols (33.5% of the total sample) wereobtained from students of Grades 8 to 12.Participants of post-secondary levels were recruited on an individual basis as wellas through the help of course instructors at the University of British Columbia. Thepencil-and-paper task was given as a take-home assignment.Seventy-six completed91protocols (29.9% of the total sample) were thus obtained from individuals, andundergraduate and graduate students of the University of British Columbia. Theeducational levels of these 76 participants ranged from first year university to doctorallevel. Their major fields of study encompassed Arts, Commerce, Education, Science andSocial Sciences.These 254 participants were administered a pencil-and-paper task either in groupsessions or as individual take-home assignments. There are two forms, Form A andForm B, to the pencil-and-paper task, and each participant was assigned one of eitherform on a random basis. The pencil-and-paper task was composed of 8 tests eachmeasuring a construct of reasoning. A brief overview of these tests was presented inchapter III. For quick reference, these 8 tests are listed below:1) Test of the Formal Form of N/R thinking (NIR-F)2) Test of the Postformal Form of N/R thinking (N/R-PF)3) Test of the Epistemic View of N/R thinking (N/R-EV)4) Test of Minimal Formal Reasoning (FR)5) Test of Problem Finding (PF)6) Test of Dialectical Reasoning (DR)7) Test of Relativistic Operations (RO)8) Test of Reflective Judgment (RJ)A summary of the interpretation of test scores of the 8 tests was presented inTable 4.For the 3 N/R tests -- N/R-F (formal form), N/R-PF (postformal form) and N/REV (epistemic view) -- and the test of Minimal Formal Reasoning (FR), the maximumscore of each test is 4. For the 4 postformal tests (Problem Finding, DialecticalReasoning, Relativistic Operations and Reflective Judgment), the maximum score ofeach test is 3. It is important to note that the scoring criteria of the 4 postformal testswere adapted from their original scoring criteria in order to tap the minimal presence92rather than the fully developed forms of postformal reasoning specific to the selectedpostformal models.B. PRELIMINARY STATISTICSIn part B, the preliminary statistics pertinent to the main analysis of this study arepresented. There are 4 sections. Section 1 contains the inter-rater reliability indices;section 2 the means and standard deviations; section 3 the correlation matrices; andsection 4 the covariance matrices.1. Inter-rater Reliability IndicesAll the test protocols were scored by two raters. The final test scores entered forstatistical analyses in part B were based on inter-rater agreement which was the averageof the individual test scores provided by the two raters.The inter-rater reliabilities of the test scores except for those in the multiplechoice tests of Minimal Formal Reasoning (FR) and of N/R-F (formal form) arepresented in Table 5. Also presented in this table are the reliability indices of the itemscores of two N/R tests, namely N/R-PF (postformal form) and N/R-EV (epistemicview), which were specifically designed for this study.The inter-rater reliabilities for the scores of each test and of each item of the twoN/R tests were computed by Pearson Product-moment Correlations on the two sets ofscores provided by the two raters. The inter-rater reliabilities of the test scores rangedfrom 0.82 to 0.99, and those of the item scores ranged from 0.93 to 0.99. Based on theconventional criterion of 0.80 as an indication of high correlation, these reliabilityindices would be considered very high.93Table 5Inter-rater Reliability IndicesTests rN/R-PF (postformal form) 0.99N/R-EV (epistemic view) 0.98PF (Problem Finding) 0.90DR (Dialectical Reasoning) 0.82RO (Relativistic Operations) 0.98RJ (Reflective Judgment) 0.92Items of N/R-PF (postforrnal form) rNRPF1 0.99NRPF2 0.99NRPF3 0.99NRPF4 0.99Items of N/R-EV (epistemic view) rNREV1 0.98NREV2 0.96NREV4 0.93NREV4 0.96Note. r = Pearson Product-moment Correlations.2. Means and Standard DeviationsThe means and standard deviations of all the 12 item scores of the 3 N/R tests --N/R-F (formal form), N/R-PF (postformal form) and N/R-EV (epistemic view) -- arepresented in Table 6.As items of N/R-F (formal form) are in multiple choice format, the item scoresyielded are either 1 or 0. The means of the item scores of this test range from 0.28 to0.59. The standard deviations of the items scores of this test range from 0.45 to 0.50.94Table 6Means and Standard Deviations of Item Scores of the 3 N/RTestsItems Means Standard DeviationsN/R-F (formal form)NRF1 0.54 0.50NRF2 0.28 0.45NRF3 0.59 0.49NRF4 0.30 0.46N/R-PF (postformal form)NRPF1 1.87 0.94NRPF2 1.24 0.59NRPF3 1.84 0.93NRPF4 1.37 0.75N/R-EV (epistemic view)NREV1 1.92 1.04NREV2 1.63 0.82NREV3 2.68 0.78NREV4 2.13 1.05As items of both N/R-PF (postformal form) and NIR-EV (epistemic view) are inopen-ended questions format, the item scores yielded range from 1 to 4. For the itemscores of N/R-PF (postformal form), the means range from 1.24 to 1.87 and the standarddeviations range from 0.59 to 0.94. For the item scores of N/R-EV (epistemic view), themeans range from 1.63 to 2.68 and the standard deviations range from 0.78 to 1.05. Incomparison, the means of N/R-EV (epistemic view) fall within a higher range and thestandard deviations of N/R-EV (epistemic view) are shown to have a wider spread.The means and standard deviations of the individual test scores of the 8 tests --Minimal Formal Reasoning (FR), N/R-F (formal form), N/R-PF (postformal form), N/REV (epistemic view), Problem Finding (PF), Dialectical Reasoning (DR), RelativisticOperations (RO)and Reflective Judgment (RJ) -- are presented in Table 7.95The means of the individual test scores of FR (Minimal Formal Reasoning), N/RF (formal form), N/R-PF (postformal form) and N/R-EV (epistemic view) range from1.57 to 2.77 out of a maximum score of 4 with the test scores of FR (Minimal FormalReasoning) yielding the highest means. The standard deviations of the individual testscores of these 4 tests range from 0.61 to 1.00 with the test scores of N/R-F (formalform) showing the widest spread.Table 7Means and Standard Deviations of Test Scores of the 8 TestsTest Means Standard DeviationsFR 2.77 0.84(Minimal FormalReasoning)N/R-F 1.70 1.00(formal form)N/R-PF 1.57 0.64(postformal form)N/R-EV 2.09 0.61(epistemic view)PF 1.52 0.66(ProblemFinding)DR 1.60 0.85(DialecticalReasoning)RO 1.97 0.80(RelativisticOperations)RJ 1.51 0.67(ReflectiveJudgment)The means of the individual test scores of PF (Problem Finding), DR (DialecticalReasoning), RO (Relativistic Operations) and RJ (Reflective Judgment) range from 1.5196to 1.97 out of a maximum of 3 with the test scores of RO (Relativistic Operations)yielding the highest means. The standard deviations of the individual test scoresof these4 tests range from 0.66 to 0.85 with the test scores of DR (Dialectical Reasoning)showing the widest spread.3. Correlation MatricesThe correlation matrix of all the 12 item scores of the 3 N/R tests is presented inTable 8.Table 8Correlation Matrix of Item Scores of the 3 N/R TestsFl F2 F3 F4 P1 P2 P3 P4 El E2 E3 E4Fl 1F2 - .25 1F3 .19 - .08 1F4 .11 - .06 .26 1P1 .08 -.03 .27 .26 1P2 .07 -.06 .05 .03 .33 1P3 .08 -.07 .30 .25 .79 .39 1P4 .09 - .05 .15 .12 .44 .40 .51 1El .15 - .02 .33 .05 .46 .24 .45 .36 1E2 - .03 - .01 .05 .11 .26 .21 .27 .18 .23 1E3 .14 - .10 .27 .07 .42 .24 .42 .32 .46 .22 1E4 .14 .01 .05 - .05 .04 .00 .12 .11 .13 .19 .11 1Note. F1-4 = items of Test of Formal Form of Nonabsolute/relativistic (N/R) Thinking. P1-4 = items of Test ofPostformal Form of N/R Thinking. E1-4 = items of Test ofEpistemic View of N/R Thinking.The correlations among all the 12 item scores range from -0.25 to 0.79.The correlations among the item scores of N/R-F (fonnal form) range from -0.25to 0.26.97The correlations among the item scores of the 2 postformal level N/R tests,namely N/R-PF (postformal form) and of N/R-EV (epistemic view), range from 0 to0.79.The correlations among the item scores of N/R-F (formal form) and of the 2postformal level N/R tests which range from -0.10 to 0.33 are relatively low. As twodifferent levels of test are involved, such a pattern of correlations is not unexpected.As suggested in some literature on statistics, (see Tabachnich & Fidell, 1989,p.604), a matrix that is factorable should include several sizable correlations. Theexpected size depends, to some extent, on the sample size. Larger sample sizes tend toproduce smaller correlations. If none of the correlations in the matrix exceeds 0.3, theuse of factor analysis is questionable because there is probably nothing to factor analyze.In view of this criterion of factorability, the correlation matrix presented in Table 8 couldbe considered as factorable because it includes several sizable correlations exceeding 0.3.However, instead of subjecting this correlation matrix to confirmatory factor analysis, itsassociated variance-covariance matrix presented in Table 10 is used in order to avoidproblems related to the application of confirmatory factor analysis on correlations asstated in chapter III.The correlation matrix of the individual test scores of the 8 tests are presented inTable 9.The correlations among the individual test scores of all the 8 tests range from0.12 to 0.64.The correlation between the individual tests scores of the 2 formal level tests,namely FR (Minimal Formal Reasoning) and N/R-F (formal form), is 0.28.The correlations among the individual test scores of the 6 postformal level tests,namely N/R-PF (postformal form), N/R-EV (epistemic view), PF (Problem Finding), DR98(Dialectical Reasoning), RO (Relativistic Operations), and RJ (Reflective Judgment),range from 0.33 to 0.64.Table 9Correlation Matrix of Test Scores of the 8 TestsFR NRF NRPF NREV PF DR RD RJ1FRNRF .28NRPF .36 .25NREV .29 .23 .51PF .15 .12 .39 .42DR .28 .22 .50 .55 .45 1RD .27 .24 .44 .45 .33 .42 1RJ .36 .26 .61 .62 .47 .64 .48 1Note. FR=Test of Minimal Formal Reasoning. N/R-F=Test ofFormal Form of Nonabsolute/ relativistic (N/R) Thinking.N/R-PF=Test of Postformal Form of N/R Thinking. N/R-EV=Testof Epistemic View of N/R Thinking. PF=Test of ProblemFinding. DR=Test of Dialectical Reasoning. RO=Test ofRelativistic Operations. RJ=Test of Reflective Judgment.1111The correlations among the individual test scores of the 2 formal level tests andthose of 6 postformal level tests range from 0.12 to 0.36. As two different levels of testare involved, such a pattern of correlations is not unexpected.Except for 3 N/R tests, namely N/R-F (formal form), N/R-PF (postformal form)and N/R-EV (epistemic form), which are specifically designed for this study, the othertests have been adapted in terms of their scoring criteria to tap the minimal presence ofthe forms of thinking specific to the tests adapted. Therefore, the pattern of thecorrelations might differ from that generated from the scores obtained by using theunadapted scoring criteria.On the whole, this correlation matrix could be considered as factorable because itincludes several sizable correlations exceeding 0.3.994. Variance-Covariance MatricesThe variance-covariance matrix of all the 12 item scores of the 3 N/R tests ispresented in Table 10.The covariances among all the 12 item scores range from -0.06 to 0.69.The covariances among the item scores of N/R-F (formal form) range from -0.06to 0.06.The covariances among the item scores of the 2 postformal level N/R tests,namely N/R-PF (postformal form) and N/R-EV (epistemic view), range from 0 to 0.69.The covariances among the item scores of N/R-F (formal form) and of the 2postformal level N/R tests which range from -0.04 to 0.17 are relatively low. As twodifferent levels of test are involved, such a pattern of covariances is not unexpected.Table 10Variance-Covariance Matrix of Item Scores of the 3 N/R TestsFl F2 F3 F4 P1 P2 P3 P4 El E2 E3 E4Fl .25F2- .06 .20F3 .05 -.02 .24F4 .03 -.01 .06 .21P1 .04 - .01 .12 .11 .88P2 .02 - .02 .01 .01 .19 .35P3 .04 - .03 .13 .11 .69 .21 .86P4 .03 - .02 .05 .04 .31 .18 .36 .56El .08 - .01 .17 .03 .45 .15 .44 .28 1.08E2- .01 - .00 .02 .04 .20 .10 .21 .11 .19 .67E3 .05 - .04 .10 .03 .31 .11 .30 .19 .37 .14 .61E4 .08 .00 .02 -.02 .04 .00 .12 .09 .14 .16 .09 1.1Note. Fl-4 = items of Test of Formal Form of Nonabsolute/relativistic (N/R) Thinking. P1-4 = items of Test ofPostformal Form of N/R Thinking. E1-4 = items of Test ofEpistemic View of N/R Thinking.100Interpretation of a variance-covariance matrix is more complicated than that ofacorrelation matrix because the magnitude of the variances and covariances are affectedby the units of measurement. However, based on its associated correlation matrixpresented in Table 8 which includes several sizable correlations exceeding 0.3, thisvariance-covariance matrix could be considered factorable and could be subjected toconfirmatory factor analysis.The variance-covariance matrix of the individual test scores of the 8 tests arepresented in Table 11.Table 11Variance-Covariance Matrix of Test Scores of the 8 TestsFR NRF NRPF NREV PF DR RO RJFR .71NRF .24 1.00NRPF .20 .16 .41NREV .15 .14 .20 .37PF .08 .08 .17 .17 .44DR .20 .19 .27 .28 .25 .72RO .18 .19 .23 .22 .18 .28 .64RJ .20 .17 .26 .25 .21 .37 .25 .45Note. FR=Test of Minimal Formal Reasoning. N/R-F=Test ofFormal Form of Nonabsolute/ relativistic (N/R) Thinking.N/R-PF=Test of Postformal Form of N/R Thinking. N/R-EV=Testof Epistemic View of N/R Thinking. PF=Test of ProblemFinding. DR=Test of Dialectical Reasoning. RO=Test ofRelativistic Operations. RJ=Test of Reflective Judgment.The covariances among the individual test scores of all the 8 tests range from0.08 to 0.37.101The covariance between the individual tests scores of the 2 formal level tests,namely FR (Minimal Formal Reasoning) and N/R-F (formal form), is 0.24.The covariances among the individual test scores of the 6 postformal level tests,namely N/R-PF (postformal form), N/R-EV (epistemic view), PF (Problem Finding), DR(Dialectical Reasoning), RO (Relativistic Operations), and RJ (Reflective Judgment),range from 0.17 to 0.37.The covariances among the individual test scores of the 2 formal level tests andthose of 6 postformal level tests range from 0.08 to 0.20. As two different levels of testare involved, such a pattern of covariances is not unexpected.Similarly, as some of the tests are adapted in terms of their scoring criteria, thepattern of the correlations might differ from that generated from the scores obtained byusing the unadapted scoring criteria.Based on its associated correlation matrix presented in Table 9 which includesseveral sizable correlations exceeding 0.3, this variance-covariance matrix could beconsidered factorable and could be subjected to confirmatory factor analysis.C. ANALYSES & RESULTS OF THE MAIN STUDYPart C contains the analyses and results of the main study which is specificallydesigned to address Research Questions 3 and 4. For reference, a chart containing thespecific research questions and the corresponding methods of analysis is presented inTable 12.102Table 12Summary of Research Questions and Corresponding Methods ofAnalysisResearch Questions3. Is N/R thinking a possibleunifying commonality underlying the selected modelsof postforxnal reasoning?Methods of Analysis3a. What, if any, commonalitiesexist among the items of the3 tests of N/R thinking(N/R-F, N/R-PF & N/R-EV)?3b. What, if any, commonalitiesexist among the 3 tests ofN/R thinking and the 4 testsof postformal reasoning (PF,DR, RO & RJ)?4. Is N/R thinking an instanceof formal or postforiualreasoning or of both?4a. What is the order ofdifficulty among the 8tests (FR, N/R-F, N/R-PF,N/R-EV, PF, DR, RO & RJ)?4b. What is the order of the 8tests according to theirages of onset of taskmastery?4c. How do the 3 N/R testscorrelate with the factorsof formal level reasoningand of postformal levelreasoning?4d. Which of the performances inthe 3 N/R tests would singlyor in combination bestpredict the performances inthe 4 postformal tests?4e. Between the performances inN/R-F and N/R-PF, whichwould be better predicted bythe performance in N/R-EV?- Confirmatory factoranalysis (CFA)Models Al & A2(see Figs. 11 & 12)- CFA: (Set 1)Models B1-B3(see Figs. 13-15)- CFA: (Set 2)Model 34 (see Fig. 16)- Rank ordering accordingto percentage of taskmastery (see Fig. 17)- Contingency tables(see Figs. 18-24)- Rank ordering accordingto ages of onset of taskmastery (see Fig. 25)- EFA- CFA: Model Cl(see Fig. 26)Multiple regressionanalyses- Simple regressionanalyses103Research Question 3:Is nonabsolute/ relativistic (NIR) thinking a common factorunderlying the selected models of postformal reasoning?Related to this research question are 2 specific questions, Questions 3a and 3b.The analyses and results of Question 3a are presented in the following.3a. What, if any, commonalities exist among the items of the 3 tests of nonabsolute/relativistic (NIR) thinking -- NJR-F (formal form), N/R-PF (postformal form),NIR-EV (epistemic view)?The purpose of this question is to explore the nature of and the relationshipsamong the items of the 3 NIR tests using confirmatory factor analysis on the item scores.The results could serve as a foundation for the analyses to be conducted at the next levelusing test scores instead of item scores of the 3 N/R tests.To address Question 3a, confirmatory factor analysis was conducted usingLISREL 8. The method of estimation was Maximum Likelihood (ML). The analyseswere based on the covariances among the item scores of the 3 N/R tests and the resultsreported were based on completely standardized solutions.Two models were constructed and tested and they are presented below.Model Al (see Figure 11)The purpose of testing this model is to evaluate the following two hypotheses:Hypothesis 3a(l): Three test factors, namely N/R-F (formal form), N/R-PF(postformal form), and N/R-EV (epistemic view) would underlie the 12 test items.Hypothesis 3a(2): The 3 test factors would be correlated. (The implication ofthis hypothesis is that these 3 test factors tap three different aspects of the same construct,hypothesized to be the nonabsolute! relativistic thinking (N/R) test factor).104Figure 11Model Al: Results ofConfirmatory FactorAnalysis—. 92- LF1ç2 7- .22 I________98-NRF2_‘ON/R- F________RMAL FORM7”.85 ; [NRF4TEST FACTO.53-.*[_NRF369.49.27 —_______N/R - PF.83 NRPF2 .41TFORMAL FORM).57.18 .15L.70—.j_NRPF474_____N/R-EV.51 NREV1 .70_____________.88—.f_NREV2.35ISTEMIC VIEW)_______—_NREV364.97 NREV4 .18TEST FACTO7Note. NRF1-4 = itemsof Test of Formal Formof Nonabsolute/relativistic (N/R)Thinking. NRPF1-4= items of Test ofPostformal Form of N/R Thinking.NREV1-4 = items of TestofEpistemic View 9f N/R Thinking.Fit-indices: X =64.87,df=49, p=.064, Q=1.32,RMR=.025,SRMR=.045, GFI=.96,AGFI=.94, NFI=.91, NNFI=.97(seeAppendix I for explanationof fit-indices).105In this model, the variables were all 12 items of the 3 N/R tests. The 4 items ofeach test were specified to load on their corresponding test factor. The 3 test factorswere: N!R-F (formal form), N/R-PF (postformal form), and N!R-EV (epistemic view).They were specified to correlate with each other. Furthermore, the error! uniquevariances of two pairs of items (NRF 1 & 2 and NRPF2 & 4) were respecified to correlatewith each other, because of the following reasons. NRF 1 and NRF2, which belonged tothe same subtest, yielded the highest negative covariance (-0.06) and the highest negativecorrelation (-0.25) among all the test items; and NRPF2 and NRPF4 represented the twomost difficult items in the respective tests as reflected in the relatively low percentage oftask mastery.The following fit-indices are obtained:The Chi-Square is 64.87 with 49 Degrees of Freedom(dOand a probability (p) of0.064. The Chi-Square!df Ratio(Q)is 1.32. The Root Mean Square Residual (RMR)and the Standardized RMR (SRMR) are 0.025 and 0.045 respectively. The Goodness ofFit Index (GFI) and the Adjusted Goodness of Fit Index (AGFI) are 0.96 and 0.94respectively. The Normed Fit Index (NFl) and the Non-normed Fit Index (NNFI) are0.91 and 0.97 respectively.(For a brief explanation of the fit indices, see Appendix I. In confirmatory factoranalysis, contrary to conventional interpretation of Chi-square statistics, a small Chisquare value and high probability (p) level would indicate a good fit. The degrees offreedom (df) serve as a standard for judging the size of a Chi-Square value. Someresearchers proposed a Chi-Square!df ratio(Q)of below 2 or 3 as a criterion of fit(Carmines & Mclver, 1981). In this study, a significance level of pO.O5 is used. A Chisquare value associated with a probability level greater than 0.05 would be consideredsignificant.)As shown in the above results, the model provides an acceptable fit to the data.The results could, therefore, lend support to Hypothesis 3a( 1).106Furthermore, the fact that the 3 test factors were shown tobe correlated couldalso lend support to Hypothesis 3a(2). The correlations between N!R-F (formal form)test factor and the other two postformal level test factors --N!R-PF (postformal form)and N/R-EV (epistemic view) -- being 0.49 and 0.57 respectively, were only moderate.The correlation between the two postformal level test factors which was 0.74 wasrelatively higher. Such a pattern of correlations among test factors is due to the fact that,at the item level, correlations! covariances between the items of N!R-F (formal form) andthe 2 postformal level NIR tests were relatively low (correlations ranging from -0.10 to0.33 and covariances ranging from 0 to 0.17); whereas correlations! covariance betweenthe items of the 2 postformal level N!R tests were relatively higher (correlations rangingfrom 0 to 0.79 and covariances ranging from 0 to 0.69).The conventional cut-off point for the acceptability of a factor loading is set at0.30 (Tabachnick & Fidell, 1989). Factor loadings of 0.30 or above would be consideredacceptable for completely standardized solutions. Except for 3 test items, namely NRF 1,NRF2 and NREV4, which yielded low factor loadings of 0.27, -0.13 and 0.18respectively, all the other test items which yielded higher factor loadings ranging from0.35 to 0.92 could be considered as fairly valid indicators of their correspondingconstructs (test factors).For completely standardized solutions, the error or unique variance of eachindicator (test item) is derived from the formula of one minus the variance which is thesquared factor loading of that particular indicator. As the conventional cut-off point forthe acceptability of a factor loading is 0.30, the conventional cut-off point for an error orunique variance is automatically 0.91 as derived from (1- 0.32).Error or uniquevariances of 0.91 or below would be considered acceptable.Except for 3 test items, namely NRF 1, NRF2 and NREV4, which yielded higherror or unique variances of 0.92, 0.98 and 0.97 respectively, all the other test items107which yielded lower error or unique variances ranging from 0.88 to 0.15 fell within theacceptable range.As specified in the model, the unique variances of the two pairs of items (NRF1& 2 and NRPF2 & 4) were relaxed to correlate with each other. The correlation betweenthe unique variances of NRF1 & 2 was -0.22 and that between the unique variances ofNRPF2&4was0.18.In conclusion, findings of Model Al tend to support Hypotheses 3a(1) and (2).Model A2 (see Figure 12)The purpose of testing this model is to evaluate Hypothesis 3a(3): A secondorder factor hypothesized to be the nonabsolute! relativistic thinking (N/R) test factorwould underlie the 3 test factors.In this model all the 12 items were specified to load on their corresponding testfactors. The 3 test factors were further specified to load on a second order factor whichwas hypothesized to be the nonabsolute/ relativistic thinking (N/R) test factor. In orderto standardize the test factors, a value of 1 was assigned to one of the loadings on thesecond order factor.The following fit indices are obtained:The Chi-Square is 31.41 with 51 Degrees of Freedom (df) and a probability (p) of0.99. The Chi-Square/df Ratio(Q)is 0.62. The Root Mean Square Residual (RMR) andthe Standardized RMR (SRMR) are 0.032 and 0.10 respectively. The Goodness of FitIndex (GFI) and the Adjusted Goodness of Fit Index (AGFI) are 0.89 and 0.83respectively. The Normed Fit Index (NFl) and the Non-normed Fit Index (NNFI) are0.99 and 1.0 respectively.108Figure 12Model A2: Results of ConfirmatoryFactor Analysis.90— rNRF1.31_________.62.97— [NRF2 - .18 N/R-F_______(FORMAL FORM).56—NRF3 .66 TESTFACTOR.85 -. [RF4 .39.62.27— LNRPF1 .86___________.36____.82LNRPF2.43 N/R-PFN/R(POSTFORMAL FORM)J TEST.15 —*[NRPF3 . 2 TESTFACTO,/ .80 FACTOR.69 .-* NRPF4 .56• 51 — [NREV1 . 70 .14.88—, [NREV2 .35 N/R-EV(EPISTEMIC VIEW) .93.58—‘ LEV3.65 TEST FACTORNREV4 .18Note. NRF1-4 = items of Test of Formal Formof Nonabsolute/relativistic (N/R) Thinking.NRPF1-4 = items of Test ofPostformal Form of N/R Thinking. NREV1-4 = itemsof Test ofEpistemic View of N/R Thinking.Fit-indices: X2=31.41, df=51, p=.99,Q=.62, RMR=.032,SRNR=.100, GFI=.89, AGFI=.83, NFI=.99, NNFI=1.0(seeAppendix I for explanation offit-indices).109As shown in the above results, the smallQratio of 0.62 and the high NFl andNNFI of 0.99 and 1.0 respectively indicate a good fit; but the GFI of 0.89 and the AGFIof 0.83 which are slightly below the suggested threshold of 0.9 do not indicate aparticularly good fit. When the overall fit-indices are considered, Model A2 couldrepresent a plausible model. The results would, therefore, still lend support toHypothesis 3a(3) and further support to the implication of Hypothesis 3a(2).Based on the conventional criterion of 0.30 and above for the acceptability of afactor loading, except for 2 test items, namely NRF2 and NREV4, which yielded lowfactor loadings of -0.18 and 0.18 respectively, all the other test items which yieldedhigher factor loadings ranging from 0.31 to 0.92 could be considered as fairly validindicators of their corresponding test factors.As stated earlier, the criterion of 0.91 and below for the acceptability of an erroror unique variance is automatically derived from the conventional criterion of 0.3 andabove for the acceptability of a factor loading. Based on this criterion, except for 2 testitems, namely NRF2 and NREV4, both of which yielded a high error or unique varianceof 0.97, all the other test items which yielded lower error or unique variances rangingfrom 0.90 to 0.15 fell within the acceptable range.Based on the same criterion mentioned above, the 3 factor loadings on the secondorder factor (N/R test factor) ranging from 0.62 to 0.93 fell within acceptable range.Correspondingly, the second order error or unique variances ranging from 0.14 to 0.62also fell within the acceptable range.The two test items, NRF2 and NREV4, despite their low factor loadings, wereretained in the test due to their uniqueness. Subsequently, the item scores of each testcould be combined into a single composite score to reflect the corresponding test factor.A summary of the fit indices of both Models Al and A2 is presented in Table 13.110Table 13Summary of Fit Indices of Models Al and A2Model df pQRNR SRMR GFI AGFI NFl NNFIAl 64.87 49 .06 1.32 .025 .045 .96 .94 .91 .97A2 31.41 51 .99 .62 .032 .100 .89 .83 .99 1.0Note. X2=Chi-Square, df=degree of freedom, p=probabilitylevel, Q=X/df ratio, RMR=Root Mean Square Residual, SRMS=Standardized RMR, GFI=Goodness of Fit Index, AGFI=AdjustedGoodness of Fit Index, NFI=Normed Fit Index, NNFI=Non-normedFit Index.To conclude, hypotheses 3a(l) through (4) were generally supported by findingsof Question 3a.Hypothesis 3a(1) -- 3 test factors, namely N/R-F (formal form), N/R-PF(postformal form), and N/R-EV (epistemic view) would underlie the 12 items -- wassupported by findings in Model Al. The implication of such findings is that the testitems could be considered as fairly valid indicators of their corresponding test factors.Hypothesis 3a(2) -- the 3 test factors would be correlated -- was also supportedby findings in Model Al. The implication of such findings is that the 3 N/R testsmeasure three different aspects of the same construct, namely nonabsolute/ relativisticthinking (N/R) test factor.Hypothesis 3a(3) -- a second order factor would underlie the 3 test factors -- wassupported by findings in Model A2. Such findings also supported the implications ofHypothesis 3a(2).Here ends the analyses and results of Question 3 a.The analyses and results of Question 3b are presented in the following.1113b. What, if any, commonalities exist among the 3 tests of nonabsolute/ relativistic(NLR) thinking and the 4 tests of postformal reasoning (Problem Finding (PF),Dialectical Reasoning (DR), Relativistic Operations (RO), ReflectiveJudgment (RJ))?The purpose of this question is to explore nonabsolute/ relativistc (N/R) thinkingas a possible unifying commonality underlying the selected models of postformalreasoning.To address Question 3b, several confirmatory factor analyses were conductedusing LISREL 8. The method of estimation was Maximum Likelihood (ML). Theanalyses were based on the covariances among test scores of the 3 N/R tests and the 4postformal tests. The results reported were based on completely standardized solutions.Two sets of models were constructed and tested. The first set (Models B 1 to B3)was designed to explore if nonabsolute! relativistic (N/R) thinking would underlie the 3N/R tests and the 4 postformal tests. The second set (Model B4) was designed to exploreif the 2 dimensions (the basic form and the epistemic view) could be differentiated withinthe postformal level of nonabsolute! relativistic (N/R) thinking. These models arepresented below.Model Bi (see Figure 13)The purpose of testing this model is to evaluate the following hypotheses.Hypothesis 3b(1): A common factor, namely the nonabsolute/ relativisticthinking (N/R) test factor would underlie the 3 N/R tests.Hypothesis 3b(2): A common factor, namely the postformal test factor wouldunderlie the 4 postformal tests.112Figure 13Model Bl:90 —.51 —.46 •-*Results ofConfirmatory Factor Analysis_________________CTOR.741.0.56.74POSTFORMALTESTFACTOR.59.85Note. N/R=Nonabsolute/ relativistic.Fit-indices: X2=7.75,df13, p=.86,SRMR=. 021, GFI=. 99, AGFI=.98, NFI=. 99,Appendix I for explanationof fit-indices).Q=.60, RMR=.014,NNFI=1.0 (seeN/R-F(formal form)N/R-PF(postformalform)N/R-EV(epistemicview)PF(ProblemFinding).68 —..45 .-.66 —+.28DR(DialecticalReasoning)RO(RelativisticOperations)RJ(ReflectiveJudgment)113Hypothesis 3b(3): The N/R test factor and the postformal test factor would becorrelated. (The implication of this hypothesis is that the two test factors wouldrepresent two different aspects of the same construct, hypothesized to be nonabsolute!relativistic (N/R) thinking.)In this model, the 3 N/R tests were specified to load on the N/R test factor; the 4postformal tests were specified to load on the postformal test factor; and these 2 testfactors were specified to correlate with each other.The following fit indices are obtained:The Chi-Square is 7.75 with 13 Degrees of Freedom (df) and a probability (p) of0.86. The Chi-Square/df Ratio(Q)is 0.60. The Root Mean Square Residual (RMR) andthe Standardized RMR (SRMR) are 0.014 and 0.021 respectively. The Goodness of FitIndex (GFI) and the Adjusted Goodness of Fit Index (AGFI) are 0.99 and 0.98respectively. The Normed Fit Index (NFl) and the Non-normed Fit Index (NNFI) are0.99 and 1.0 respectively.As shown in the above results, the model provides an extremely good fit to thedata. The good fit is evidenced in the smallQratio, the high p level, the small RMR andSRMR, and the high GFI, AGFI, NFl and NNFI. Thus the results lend support toHypotheses 3b(1) to (3).Based on the conventional criterion of 0.30 and above for the acceptability of afactor loading, the factor loadings of all the tests which ranged from 0.31 to 0.85 fellwithin the acceptable range.Based on the conventional criterion of 0.91 and below for the acceptability of anerror or unique variance, the unique variances of all the tests which ranged from 0.90 to0.28 fell within the acceptable range.The difference in magnitude of factor loadings on the N/R test factor suggestedthat the formal and the postformal levels of nonabsolute/ relativistic (N/R) thinking couldbe differentiated. The relatively low factor loading of 0.31 for NIR-F (formal form)114could be interpreted to reflect the formal level of nonabsolute! relativistic (N/R) thinking.On the other hand, the relatively high factor loadings of 0.70 for N/R-PF (postformalform) and 0.74 for N/R-EV (epistemic view) could be interpreted to reflect thepostformal level of nonabsolute! relativistic (N/R) thinking.The difference in magnitude of factor loadings on the postformal test factorranging from 0.56 to 0.85 could be interpreted to reflect differences in the level of taskdifficulty among the 4 postformal tests.Two tests yielded relatively low factor loadings. PF (Problem Finding) whichyielded a factor loading of 0.56 represents the most difficult (8.2% of task mastery)among the 4 postformal tests whereas RO (Relativistic Operations) which yielded afactor loading of 0.59 represents the least difficult (29.5% of task mastery). Therefore,low factor loadings in this model seem to reflect both extremes in the level of taskdifficulty.Of the other two tests, DR (Dialectical Reasoning) and RJ (Reflective Judgment)yielded relatively high factor loadings of 0.74 and 0.85 respectively. They represent themoderately difficult among the 4 postformal tests, with DR yielding 23.6% of taskmastery and RJ yielding 9.4% of task mastery.As revealed in the findings, the N/R test factor and the postformal test factor wereshown to be perfectly correlated (r=1 .0). (The exact value obtained for this correlationwas 1.01 which had been rounded to 1.0 as advised by the technical consultant ofLISREL 8 in a personal communication.) This correlation could be interpreted tosuggest that a commonality would probably underlie the two test factors.In order to explore further the relationships among the constructs described inModel B1, another two models were respecified to evaluate Hypothesis 3b(4) --nonabsolute/ relativistic (N/R) thinking is a possible unifring commonality underlyingthe 3 N/R tests and the 4 postformal tests. In one model, Model B2, the two test factors115were specified to load on a second order factor. In the other model, Model B3, the twotest factors were replaced by one first order factor. These models are presented below.Model B2 (see Figure 14)The purpose of testing this model is to evaluate Hypothesis 3b(4): nonabsolute/relativistic (N/R) thinking is a possible unifying commonality underlying the 3 N/R testsand the 4 postformal tests.In this model, the 3 N/R tests were specified to load on the N/R test factor; the 4postformal tests were specified to load on the postformal test factor; and the two testfactors were specified to further load on a second order factor, namely nonabsolute!relativistic (N/R) thinking.The following fit indices are obtained:The Chi-Square is 7.80 with 12 Degrees of Freedom (df) and a probability (p) of0.80. The Chi-Square/df Ratio(Q)is 0.65. The Root Mean Square Residual (RMR) andthe Standardized RMR (SRMR) are 0.0 14 and 0.021 respectively. The Goodness of FitIndex (GFI) and the Adjusted Goodness of Fit Index (AGFI) are 0.99 and 0.98respectively. The Normed Fit Index (NFl) and the Non-normed Fit Index (NNFI) are0.99 and 1.0 respectively.As shown in the above results, the model provides an extremely good fit to thedata. In the comparison of Models B1 and B2, it was shown that their corresponding fitindices yielded the same values except for an insignificant increase in the Chi-squarevalue by 0.05 and in theQratio by 0.05 in Model B2. Although Model B2 did notprovide an improved fit over Model B1 which already provides an extremely good fit tothe data, Model B2 is still a plausible model. Therefore, the findings could still lendsupport to Hypothesis 3b(4).116.31.70 N/RTEST___________________FACTOR1.0• 74_________________N/R.56THINKING.741.0POSTFORMALTESTFACTOR.59.85Note. N/R=Nonabsolute/relativistic.Fit-indices:X2=7.80, df=12,p=.80,Q=.65, RMR=.014,.SRMR=.021, GFI=.99,AGFI=.98 NFI=.99,NNFI=1.0(seeResults of ConfirmatoryFactor AnalysisN/R-F(formal form)N/R-PF(postformalform)Figure 14Model B2:.90 —.50 .-+.46 —.68 .-..45 —.66 —+.28 ..-*N/R-EV(epistemic view)PF( ProblemFinding)DR(DialecticalReasoning)RO(RelativisticOperations)RJ(ReflectiveJudgment)Appendix I forexplanation offit-indices).117The factor loadings of this model ranging from 0.31 to 0.85 are identical to thoseof Model B 1. Similarly both the factor loadings and the error or unique variances fellwithin the acceptable range.The 2 factor loadings on the second order factor are both 1.0. Correspondingly,the second order error or unique variances would both be 0. Such results are reflective ofthe perfect correlation (r=l .0) between the 2 test factors.The alternative model, Model B3, which is more parsimonious, is presented in thefollowing.Model B3 (See Figure 15)The purpose of testing this model is also to evaluate Hypothesis 3b(4):nonabsolute/ relativistic (N/R) thinking is a possible unifying commonality underlyingthe 3 N/R tests and the 4 postformal tests.In this model, the 3 N/R tests and the 4 postformal tests were specified to load ononly one first order factor.The following fit indices are obtained:The Chi-Square is 7.80 with 14 Degrees of Freedom (df) and a probability (p) of0.90. The Chi-Square/df Ratio(Q)is 0.56. The Root Mean Square Residual (RMR) andthe Standardized RIvIR (SRMR) are 0.0 14 and 0.02 1 respectively. The Goodness of FitIndex (GFI) and the Adjusted Goodness of Fit Index (AGFI) are 0.99 and 0.98respectively. The Normed Fit Index (NFl) and the Non-normed Fit Index (NNFI) are0.99 and 1.0 respectively.118.31.70.74_________________THINKING.56.74.59.85Note. N/R=Nonabsolute/ relativistic.Fit-indices: X2=7.80, df=14,p=.90, Q=.56, RMR=.014,SRMR=.021, GFI=.99, AGFI=.98, NFI=.99, NNFI=1.O(seeAppendix I for explanation of fit-indices).Figure 15Model B3: Results of Confirmatory Factor AnalysisN/R-F(formal form)N/R-PF(postformalform)N/R-EV(epistemic view).90 -..50 •-..46 —..68.45 —.66 —.28 —,PF(ProblemFinding)DR(DialecticalReasoning)RO(RelativisticOperations)RJ(ReflectiveJudgment)119As shown in the above results, the model also provides an extremely good fit tothe data. In the comparison of Models Bi and B3, it was also shown that theircorresponding fit indices yielded the same values except for an insignificant decrease inthe Chi-square value by 0.05 and in theQratio by 0.04 in Model B3, suggesting thatModel B3 represents a slightly improved fit over Model B 1. Therefore, findings alsolend support to Hypothesis 3b(4).The factor loadings of this model ranging from 0.31 to 0.85 are also identical tothose of Models Bi and B2. Similarly both the factor loadings and the error or uniquevariances fell within the acceptable range.A summary of the fit indices of Models Bl to B3 is presented in Table 14.Table 14Summary of Fit Indices of Models Bi - B3Model df pQRMR SRMR GFI AGFI NFl NNFIBi 7.75 13 .86 .60 .014 .021 .99 .98 .99 1.0B2 7.80 12 .80 .65 .014 .021 .99 .98 .99 1.0B3 7.80 14 .90 .56 .014 .021 .99 .98 .99 1.0Note. X2=Chi-Square, df=degree of freedom, p=probabilitylevel, Q=X/df ratio, RMR=Root Mean Square Residual, SRMSStandardized RMR, GFI=Goodness of Fit Index, AGFI=AdjustedGoodness of Fit Index, NFI=Normed Fit Index, NNFI=Non-normedFit Index.In comparing these three models, it was found that the differences among themwere insignificant. Of the two models (Models B2 and B3) both designed to explorefurther the relationships among the constructs described in Model B 1, for parsimony,Model B3 (one first order factor model) would be the model of choice and for a moreelaborate description of the relationships among the constructs, Model B2 (second order120factor model) would be the model of choice. However, since all 3 models (B1 to B3)implied nonabsolute/ relativistic (N/R) thinking as a possible unifying commonalityunderlying the 3 N/R tests and the 4 postformal tests and since all of them provided anextremely good fit to the data, any one of the 3 models could be used to lend support tothe general hypothesis that nonabsolute/ relativistic (N/R) thinking is a possible unifyingcommonality underlying the selected models of postformal reasoning.The model of the second set (Model B4) was designed to explore if the twodimensions (the basic form dimension and the epistemic view dimension) could bedifferentiated within the postformal level of nonabsolute! relativistic (N/R) thinking.This model is presented below.Model B4 (see Figure 16)The purpose of testing this model is to evaluate the following hypotheses.Hypothesis 3b(5): A common factor, namely the basic form dimension, wouldunderlie the 4 tests -- N/R-PF (postformal form), PF (Problem Finding), DR (DialecticalReasoning), and RO (Relativistic Operations).Hypothesis 3b(6): A common factor, namely the epistemic view dimension,would underlie the 2 tests -- N/R-EV (epistemic view) and RJ (Reflective Judgment).Hypothesis 3b(7): The two factors, namely the basic form dimension and theepistemic view dimension, would be correlated. (The implication of this hypothesis isthat two dimensions could be differentiated within the same construct, hypothesized to bethe postformal level of nonabsolute! relativistic (N/R) thinking.)In this model, N/R-PF (postformal form), Problem Finding, DialecticalReasoning and Relativistic Operations were specified to load on the factor of the basicform dimension; N/R-EV (epistemic view) and Reflective Judgment were specified toload on the factor of the epistemic view dimension; and the two factors were specified tocorrelate with each other.121.70.57FORMDIMENSION.58N/R-EV(Epistemic view)RJ(ReflectiveJudgment)Note. N/R=Nonabs,lute/relativistic.Fit-indices: X’=4.43,df=8, p=.82, Q=.55, RMR=.008,SRMR=.015, GFI=.99,AGFI=.98, NFI=.99, NNFI=1.O(seeAppendix I for explanationof fit-indices).Figure 16Model B4: Resultsof ConfirmatoryFactor AnalysisN/R-PF(Postformal form)PF(ProblemFinding)DR(DialecticalReasoning).51 -.+.68 •.-.45 -..66 —.46 —.29 —RO(RelativisticOperations)1.0122The following fit indices are obtained:The Chi-Square is 4.43 with 8 Degrees of Freedom (df) and a probability(p) of0.82. The Chi-Square/df Ratio(Q)is 0.55. The Root Mean Square Residual (RMR) andthe Standardized RMR (SRMR) are 0.008 and 0.015 respectively. The Goodness of FitIndex (GFI) and the Adjusted Goodness of Fit Index (AGFI) are 0.99 and 0.98respectively. The Normed Fit Index (NFl) and the Non-normed Fit Index (NNFI) are0.99 and 1.0 respectively.As shown in the above results, the model provides an extremely good fit to thedata. The good fit is evidenced in the smallQratio, the high p level, the small RMR andSRMR, and the high GFI, AGFI, NFl and NNFI. Thus the results lend support toHypotheses 3b(5) to (7).As revealed in the findings, the factors of the basic form dimension and of theepistemic view dimension were shown to be perfectly correlated (r=l .0). (The exactvalue obtained for this correlation was 1.01 which had been rounded to 1.0 as advised bythe technical consultant of LISREL 8 in a personal communication.) This correlationcould be interpreted to suggest that these two factors represent two dimensions of thesame construct, hypothesized to be the postformal level of nonabsolute! relativistic (N/R)thinking.Based on the conventional criterion of 0.30 and above for the acceptability of afactor loading, the factor loadings of this model which ranged from 0.57 to 0.85 fellwithin the acceptable range.Based on the conventional criterion of 0.91 and below for the acceptability of anerror or unique variance, the unique variances of this model which ranged from 0.68 to0.29 fell within the acceptable range.For the factor of “basic form dimension”, the factor loadings of the 4 tests rangedfrom 0.57 to 0.74. For the factor of “epistemic view dimension”, the factor loadings of123the 2 tests were 0.73 and 0.85. Therefore, all the tests could be considered as quite goodindicators of their corresponding factors.To conclude findings of question 3b, Hypotheses 3b(1) through (7) weresupported by findings of the above analyses.Hypothesis 3b(1) -- a common factor, namely the nonabsolute/ relativisticthinking (N/R) test factor would underlie the 3 N/R tests -- was supported by findings ofModel B 1. The implication of such findings is that the 3 N/R tests measure threedifferent aspects of the same construct, namely nonabsolute/ relativistic (N!R) thinking.The formal and the postformal levels of nonabsolute/ relativistic (N/R) thinking couldalso be differentiated as suggested in the difference in magnitude of factor loadings.Hypothesis 3b(2) -- a common factor, namely the postformal test factor wouldunderlie the 4 postformal tests -- was also supported by findings of Model B 1. Theimplication of such findings is that commonality exists among the 4 selected models ofpostformal reasoning as hypothesized in this study.Hypothesis 3b(3) -- the nonabsolute! relativistic thinking (N/R) test factor andthe postformal test factor would be correlated -- was also supported by findings of ModelB 1. The implication of such findings is that a commonality, which is hypothesized to benonabsolute! relativistic (N/R) thinking, would probably underlie these two test factors.Hypothesis 3b(4) -- a common factor, namely nonabsolute/ relativistic (N/R)thinking, would underlie the 3 N/R tests and the 4 postformal tests -- was supported byfindings of both Models B2 and B3. The implication of such findings is thatnonabsolute/ relativistic (N/R) thinking is a possible unifying commonality underlyingthe selected models of postformal reasoning.Hypothesis 3b(5) -- a common factor, namely the factor of the basic formdimension, would underlie the 4 tests: N/R-PF (postformal form), Problem Finding,Dialectical Reasoning and Relativistic Operations -- was supported by findings of ModelB4.124Hypothesis 3b(6) -- a common factor, namely the factor of the epistemic viewdimension, would underlie the 2 tests: N/R-EV (epistemic view)and Reflective Judgment-- was also supported by findings of Model B4.Hypothesis 3b(7) -- the factors of the two dimensions, namely the basic form andthe epistemic view, would be correlated -- was also supported by findings of Model B4.The implication of the findings of Model B4 is that two dimensions, namely the basicform and the epistemic view, could be differentiated within the postformal level ofnonabsolute! relativistic (N/R) thinking.In the context of construct validation, the analysis in Model B 1 could serve as anexample of the internal structure analysis of the nonabsolute/ relativistic thinking (N/R)test factor. The analyses in Models B2, B3 and B4 could also serve as examples of theexternal structure analyses of the N/R tests using four other postformal tests as externalreferences.Here ends the analyses and results of Question 3b.All in all, all the above findings related to Research Question 3 could lendsupport to the general hypothesis that nonabsolute! relativistic (N/R) thinking is apossible unifying commonality underlying the models of postformal reasoning.Research Question 4:Is nonabsolute/ relativistic (NIR) thinking an instance of formal orpostformal reasoning or of both?Related to this research question are 5 specific questions, 4a to 4e.The analyses and results of Question 4a are presented below.1254a. What is the order of difficulty among the 8 tests -- FR (Minimal FormalReasoning), NIR-F (formal form), NIR-PF (postformal form), NJR-EV(epistemic view), PF (Problem Finding), DR (Dialectical Reasoning), RO(Relativistic Operations), and RJ (Reflective Judgment)?The first approach to this question was to rank order the 8 tests according to thepercentage of task mastery. The following hypothesis was evaluated.Hypothesis 4a(1): The hypothesized order of task difficulty from the least to themost difficult would be as follows -- the test of Minimal Formal Reasoning (FR); theN/R test at the formal level (N/R-F (formal form); the 2 N/R tests at the postformal level(N/R-PF (postformal form) and N/R-EV (epistemic view)); and the 4 postformal tests(Problem Finding, Dialectical Reasoning, Relativistic Operations and ReflectiveJudgment).The rationale for this rank ordering is that N/R-F (formal form) is closer toformal reasoning whereas N/R-PF (postformal form) and N/R-EV (epistemic view) arecloser to postformal reasoning. This hypothesis is based on the assumption that therelationships among tasks can be described in a linear model. That is to say that theorder of the tests could be presented one after another in a straight line.The results are presented in Figure 17.From the perspective of a linear model, the tests can be classified into 3 levels.Level 1 which is the least difficult includes Minimal Formal Reasoning (yielding 50.8%of task mastery). Level 2 which is the moderately difficult includes RelativisticOperations, Dialectical Reasoning, and N/R-F (formal form) (yielding 29.5%, 23.6% and23.2% of task mastery respectively). Level 3 which is the most difficult includes N/REV (epistemic view), Reflective Judgment, Problem Finding, and N/R-PF (postformalform) (yielding 9.4%, 9.4%, 8.2% and 3.5% of task mastery respectively).126Figure 17Order of Task Difficulty according to Percentage of TaskMasteryLINEAR MODEL NON-LINEAR MODELCategory 1 Category 2Percentage PercentageLeast 50.8 FR 50.8 FRDifficultModerately 29.5 RO 29.5 RODifficult23.6 DR 23.6 DR23.2 N/R-F 23.2 N/R-FMost 9.4 N/R-EV, RJ 9.4 N/R-EV RJDifficult 8.2 PF 8.2 PF3.5 N/R-PF 3.5 N/R-PFNote. FR=Test of Minimal Formal Reasoning. N/R-F=Test ofFormal Form of Nonabsolulte/ relativistic (N/R) Thinking.N/R-PF=Test of Postformal Form of N/R Thinking. N/R-EV=Testof Epistemic View of N/R Thinking. PF=Test of ProblemFinding. DR=Test of Dialectical Reasoning. RO=Test ofRelativistic Operations. RJ=Test of Reflective Judgment.127The above results, however, do not correspond strictly to the hypothesized order.As the order of the tests could not be presented one after another in a straight line, theywould rather suggest that a non-linear model might be more appropriate in describing therelationships among these tests. (see Figure 17).From the perspective of a non-linear model, the tests could be rearranged into twocategories. Under category 1 are Minimal Formal Reasoning and the 3 N/R tests yieldingthe following percentage of task mastery: Minimal Formal Reasoning (50.8%), N/R-F(formal form) (23.2%), N/R-EV (epistemic view) (9.4%), and N/R-PF (postformal form)(3.5%). The results for category 1 correspond precisely with the hypothesized order oftask difficulty.Under category 2 are the 4 postformal tests yielding the following percentage oftask mastery: Relativistic Operations (29.5%), Dialectical Reasoning (23.6%), ReflectiveJudgment (9.4%), and PF (8.2%). When the two categories were cross-referenced tocompare their relative levels of difficulty, Relativistic Operations and DialecticalReasoning were shown to be closely associated with N/R-F (formal form); and N/R-F(formal form) was hypothesized to represent a transition from high formal to postformalreasoning (Arlin, 1984). On the other hand, Reflective Judgment and Problem Findingwere shown to be closely associated with N/R-EV (epistemic view) and N/R-PF(postformal form); N/R-EV (epistemic view) and N/R-PF (postformal form) werehypothesized in this study to represent the postformal level of nonabsolute/ relativistic(N/R) thinking.This pattern suggested that the relationships among the 3 N/R tests and the 4postformal tests were not linear but non-linear. When only Minimal Formal Reasoningand the 3 N/R tests were considered, the assumption of a linear model could still beapplied. However, when the 4 postformal tests were also taken into consideration, theassumption of a non-linear model would be more appropriate in describing therelationships among the 8 tests.128All in all, the findings that the 2 postformal level N/R tests (N/R-PF (postformalform) and N/R-EV (epistemic view)) were more difficult than N/R-F (formal form)suggested that the formal and the postformal level could be differentiated withinnonabsolute/ relativistic (N/R) thinking.The second approach to Question 4a was to construct contingency tables toevaluate the certain specific relationships among the 8 tests as to the primacy of one testover the other (that is the mastery of one test is a necessary but not sufficient conditionfor that of the other). The primacy of one test over the other is based on the assumptionthat the relationships among these tests could be described in a linear model.To establish that mastery of one test is a necessary but not sufficient condition forthat of another, logically the contingency table involved should contain one empty cell(target cell). This target cell is the intersection of the non-mastery of an easier test andthe mastery of a more difficult test and therefore, there should be no entry for the targetcell. However, a few exceptional cases would not be unexpected. If these exceptionalcases are few in number, the model would not be threatened. For this study, an arbitrarycut-off point was set at 5% which is roughly 13 out of the total of 254 participants.For evaluation of Hypothesis 4a(2) -- Minimal Formal reasoning (FR) <<(is anecessary but not sufficient condition for) each of the 3 N/R tests -- contingency tablesare presented in Figure 18.For the contingency table Minimal Formal Reasoning (FR) x N/R-F (formalform), the entry in the target cell was 16 (6.3% of 254, the total number of participants)which would not lend a strong support the hypothesis that FR is a necessary but notsufficient condition for N/R-F. However, this result was not unexpected, because bothFR and N/R-F fall within formal reasoning though with N/R-F being more difficult asshown in the entry of 86 (33.9%) in cell FR (mastery) by NIR-F (non-mastery).129Figure 18Contingency Tables: FR (Minimal Formal Reasoning) x 3 N/RTestsN/R-F (formal form)non-mastery mastery(1,2) (3,4)non-mastery 109 16(1,2) 42% 6.3%FRmastery 86 43(3,4) 33.9% 16.9%N/R-PF (postformal form)non-mastery mastery(<3) (3,4)non-mastery 123 2(1,2) 48.4% 0.8%FRmastery 122 7(3,4) 48% 2.8%N/R-EV (episteinic view)non-mastery mastery(<3) (3,4)non-mastery 121 4(1,2) 47.6% 1.6%FRmastery 109 20(3,4) 42.9% 7.9%For the contingency table Minimal Formal Reasoning (FR) x N/R-EV (epistemicview), the entry in the target cell was 4 (1.6%) which could be considered as exceptionalcases and should not, therefore, threaten the model. Thus the results could support thehypothesis that FR is a necessary but not sufficient condition for N/R-EV.For the contingency table Minimal Formal Reasoning (FR) x N/R-PF (postformalform), the entry in the target cell was 2 (0.8%) which could also be considered as130exceptional cases. Thus the results could support the hypothesis that FR is a necessarybut not sufficient condition for N/R-PF.For evaluation of Hypothesis 4a(3) -- N/R-F (formal form) << each of the 2postformal N/R tests (N/R-PF (postformal form) and N/R-EV (epistemic view)) --contingency tables are presented in Figure 19.Figure 19Contingency Tables: N/R-F (formal form) x 2 postformal levelN/R TestsN/R-PF (postformal form)non-mastery mastery(<3) (3,4)non-mastery 191 4(1,2) 75.2% 1.6%N/R-Fmastery 54 5(3,4) 21.3% 2%N/R-EV (epistemic view)non-mastery mastery(<3) (3,4)non-mastery 180 15(1,2) 70.9% 5.9%N/R-Fmastery 50 9(3,4) 19.7% 3.5%For the contingency table N/R-F (formal form) x N/R-EV (epistemic view), theentry in the target cell was 15 (5.9%). According to the arbitrary cut-off point of 13(5%), this result would not support the hypothesis that N/R-F is a necessary but notsufficient condition for N/R-EV. Nevertheless, as the entry is only an excess of 2 cases(0.9%) over the arbitrary cut-off point, the hypothesis could still be considered plausible.131For the contingency table N/R-F (formal form) x N/F-PF (postformal form), theentry in the target cell was 4 (1.6%) which could be considered as exceptional cases.Thus the results could support the hypothesis that N/R-F is a necessary but not sufficientcondition for N/R-PF.For evaluation of Hypothesis 4a(4) -- N/R-EV (epistemic view) << N/R-PF(postformal form) -- the contingency table is presented in Figure 20.Figure 20Contingency Table: N/R-EV (epistemic view) x N/R-PF(postformal form)N/R-PFnon-mastery mastery(<3) (3,4)non-mastery 223 7(<3) 87.8% 2.8%N/R-EVmastery 22 2(3,4) 8.7% 0.8%For the contingency table N/R-EV (epistemic view) x N/R-PF (postformal form),the entry in the target cell was 7 (2.8%) which could be considered as exceptional cases.Thus the results could support the hypothesis that N/R-EV is a necessary but notsufficient condition for N/R-PF.For evaluation of Hypothesis 4a(5) -- N/R-PF (postformal form) <<each of the 4postformal tests (PF (Problem Finding), DR (Dialectical Reasoning), RO (RelativisticOperations) and RJ (Reflective Judgment)) -- contingency tables are presented in Figure21.132Figure 21Contingency Tables: N/R-PF (postformalform) x 4 PostformalTestsPF (Problem Finding)non-mastery mastery(<3) (3)non-mastery 228 17(<3) 89.8% 6.7%N/R-PFmastery 5 4(3,4) 2% 1.6%DR (Dialectical Reasoning)non-mastery mastery(<3) (3)non-mastery 189 56(<3) 74.4% 22%N/R - PFmastery 5 4(3,4) 2% 1.6%RO (Relativistic Operations)non-mastery mastery(<3) (3)non-mastery 174 71(<3) 68.5% 28%N/R-PFmastery 5 4(3,4) 2% 1.6%RJ (Reflective Judgnent)non-mastery mastery(<3) (3)non-mastery 224 21(<3) 88.2% 8.3%N/R-PFmastery 6 3(3,4) 2.4% 1.2%133The entries in the target cell for the contingency tables N/R-PF x the 4 postformaltests are as follows:N/R-PF x PF: 17 (6.7%)N/R-PF x DR: 56(22%)N/R-PF x RO: 71(28%)N/R-PF x RJ: 21(8.3%)All the above entries in the target cell were too high to support the hypothesis thatN/R-PF is a necessary but not sufficient condition for the 4 postformal tests.When the hypothesis was reversed to state that each of the 4 postformal tests is anecessary but not sufficient condition for N/R-PF, the entries in the new target cellsuggested that each of the 4 postformal tests is a necessary but not sufficient conditionfor N/R-PF. The entries in the new target cell for the contingency tables are as follows:N/R-PF x PF: 5 (2%)N/R-PF x DR: 5 (2%)N/R-PF x RO: 5 (2%)N/R-PF x RJ: 6 (2.4%)These results were in fact in line with the findings concerning the order of task difficultyin which N/R-PF was shown to be the most difficult among all 8 tests.For evaluation of Hypothesis 4a(6) -- N/R-EV (epistemic view) <<each of the 4postformal tests (PF (Problem Finding), DR (Dialectical Reasoning), RO (RelativisticOperations) and RJ (Reflective Judgment)) -- contingency tables are presented in Figure22.The entries in the target cell for the contingency tables N/R-EV x the 4postformal tests are as follows:N/R-EV x PF: 14 (5.5%)N/R-EV x DR: 42(16.5%)N/R-EV x RO: 58(22.8%)134Figure 22Contingency Tables: N/R-EV (epistemic view) x 4 PostformalTestsPF (Problem Finding)non-mastery mastery(<3) (3)non-mastery 216 14(<3) 85% 5.5%N/R - EVmastery 17 7(3,4) 6.7% 2.8%DR (Dialectical Reasoning)non-mastery mastery(<3) (3)non-mastery 188 42(<3) 74% 16.5%N/R-EVmastery 6 18(3,4) 2.4% 7.1%RO (Relativistic Operations)non-mastery mastery(<3) (3)non-mastery 172 58(<3) 67.7% 22.8%N/R-EVmastery 7 17(3,4) 2.8% 6.7%RJ (Reflective Judgment)non-mastery mastery(<3) (3)non-mastery 218 12(<3) 85.8% 4.7%N/R-EVmastery 12 12(3,4) 4.7% 4.7%135N/R-EVxRJ: 12 (4.7%)All the above entries in the target cell were too high to support the hypothesis that N/REV is a necessary but not sufficient condition for the 4 postformal tests.When the hypothesis was reversed to state that each of the 4 postformal tests is anecessary but not sufficient condition for N/R-EV, the entries in the new target cellsuggested that only DR and RO are necessary but not sufficient conditions for N/R-EV.The entries in the new target cell for the contingency tables N/R-EV x DR and N/R-EV xRO are 6 (2.4%) and 7 (2.8%) respectively.That Hypotheses 4a(5) and 4a(6) were not supported was not unexpected in lightof the fact that the 4 postformal tests were adapted to tap the minimal presence ofpostformal reasoning specific to the selected postformal models. In view of the nonlinear relationships among N/R-PF (postformal form) and N/R-EV (epistemic view) andthe 4 postformal tests in terms of level of difficulty, two additional sets of contingencytables were constructed.The first set of contingency tables which was constructed to evaluate Hypothesis4a(7) -- the transitional development of N/R-PF (postformal form) << each of the 4postformal tests (Problem Finding (PF), Dialectical Reasoning (DR), RelativisticOperations (RO) and Reflective Judgment (RJ)) -- is presented in Figure 23.For this set of contingency tables, the “non-mastery of N/R-PF (postformalform)” was changed to “pre-transitional development of N/R-PF (postformal form)”,defined as below the score of 2 (<2); and “mastery of N/R-PF (postformal form)” waschanged to “transitional development of mastery of N/R-PF (postformal form)”, definedas the scores from 2 to 4 (2-4).136Figure 23Contingency Tables: Transitional Development of N/R-PF(postformal form) x 4 Postformal TestsPF (Problem Finding)non-mastery mastery(<3) (3)pre-transitional 156 5development (<2) 61.4% 2%N/R-PFtransitional 77 16development to 30.3% 6.3%mastery (2-4)DR (Dialetical Reasoning)non-mastery mastery(<3) (3)pre-transitional 145 16development (<2) 57.1% 6.3%N/R-PFtransitional 49 44development to 19.3% 17.3%mastery (2-4)RO (Relativistic Operations)non-mastery mastery(<3) (3)pre-transitional 134 27development (<2) 52.8% 10.6%N/R-PFtransitional 45 48development to 17.7% 18.9%mastery (2-4)RJ (Reflective Judgement)non-mastery mastery(<3) (3)pre-transitional 157 4development (<2) 61.8% 1.6%N/R-PFtransitional 73 20development to 28.7% 7.9%mastery (2-4)137The entries in the target cell for this set of contingency tables are as follows:N/R-PF x PF: 5 (2%)N/R-PF x DR: 16 (6.3%)N/R-PF x RU : 27 (10.6%)N/R-PF x RJ : 4 (1.6%)The entries in the target cells suggested that only PF (Problem Finding) and RJ(Reflective Judgment) are necessary but not sufficient conditions for the transitionaldevelopment of N/R-PF (postformal form).The second set of contingency tables which was constructed to evaluateHypothesis 4a(8) -- the transitional development of N/R-EV (epistemic view) <<each ofthe 4 postformal tests (Problem Finding (PF), Dialectical Reasoning (DR), RelativisticOperations (RU) and Reflective Judgment (RJ)) -- is presented Figure 24.For this set of contingency tables, the “non-mastery of N/R-EV (epistemic view)”was changed to “pre-transitional development of N/R-EV (epistemic view)”, defined asbelow the score of 2 (<2); and “mastery of N/R-EV (epistemic view)” was changed to“transitional development of mastery of N/R-EV (epistemic view)”, defined as the scoresfrom 2 to 4 (2-4).The entries in the target cell for this set of contingency tables are as follows:N/R-EV x PF : 0 (0%)N/R-EV x DR: 4(1.6%)N/R-EV x RU: 10(3.9%)N/R-EV x RJ: 0 (0%)All the above entries in the target cell could lend support to the hypothesis that thetransitional development of N/R-EV (epistemic view) is a necessary but not sufficientcondition for each of the 4 postformal tests.138Figure 24Contingency Tables: Transitional Development of N/R-EV(epistemic view) x 4 Postformal TestsPF (Problem Finding)non-mastery mastery(<3) (3)pre-transitional 102 0development (<2) 40.2% 0%N/R-EVtransitional 131 21development to 51.6% 8.3%mastery (2-4)DR (Dialetical Reasoning)non-mastery mastery(<3) (3)pre-transitional 98 4development (<2) 38.6% 1.6%N/R-EVtransitional 96 56development to 37.8% 22%mastery (2-4)RO (Relativistic Operations)non-mastery mastery(<3) (3)pre-transitional 92 10development (<2) 36.2% 3.9%N/R-EVtransitional 87 65development to 34.3% 25.6%mastery (2-4)RJ (Reflective Judgement)non-mastery mastery(<3) (3)pre-transitional 102 0development (<2) 40.2% 0%N/R-EVtransitional 128 24development to 50.4% 9.4%mastery (2-4)139A summary of the results of all the contingency tables are presented below.Hypothesis 4a(2) -- Minimal Formal Reasoning (FR) << each of the 3 N/R tests -- was partly supported, because results suggested that Minimal Formal Reasoning (FR) isa necessary but not sufficient condition for the two postformal N/R tests, namely N/R-EV(epistemic view) and NIR-PF (postformal form) but not for N/R-F (formal form) thoughNIR-F (formal form) was shown to be more difficult than Minimal Formal Reasoning(FR). The implication of such findings is that N/R-F (formal form) represents the formallevel of nonabsolute! relativistic (N/R) thinking whereas N/R-PF (postformal form) andN/R-EV (epistemic view) represents the postformal level of nonabsolute/ relativistic(N/R) thinking.Hypothesis 4a(3) -- N/R-F (formal form) <<each of the 2 postformal N/R tests -- was partly supported.The hypothesis that N/R-F (formal form) is a necessary but not sufficientcondition for N/R-PF (postformal form) was supported and in turn provided crucialsupport to the general hypothesis that two qualitatively distinct levels could bedifferentiated within the dimension of the basic form of nonabsolute/ relativistic (NIR)thinking.The hypothesis that N/R-F (formal form) is a necessary but not sufficientcondition for N/R-EV (epistemic view) was not supported by virtue of the entry in thetarget cell exceeding the arbitrary cut-off point of 13 (5%). As the excess was only 2cases (0.9%) over the arbitrary cut-off point, the hypothesis though not supported couldstill be considered plausible.Hypothesis 4a(4) -- N!R-EV (epistemic view) <<N/R-PF (postformal form) --was supported. The implication of this result is that the development of the epistemicview of nonabsolute! relativistic (N/R) thinking is a crucial antecedent to thedevelopment of N/R-PF, the postformal form of nonabsolute/ relativistic (N/R) thinking,and this was hypothesized in the study.140Hypothesis 4a(5) -- NIR-PF (postformal form) <<each of the 4 postformal tests -- was not supported. Instead, the reverse conditions that each of the 4 postformal testswas a necessary but not sufficient condition for N/R-PF (postformal form) weresupported by findings. These results were consistent with findings concerning the orderof task difficulty. The implication of such findings is that a non-linear model rather thana linear model would be more appropriate in describing the relationships among the 3N/R tests and the 4 postformal tests.Hypothesis 4a(6) -- N/R-EV (epistemic view) <<each of the 4 postformal tests -- was also not supported. When the hypothesis was stated in reverse that each of the 4postformal tests << N/R-EV (epistemic view), Dialectical Reasoning and RelativisticOperations were found to be necessary but not sufficient conditions for N/R-EV(epistemic view). A non-linear model is also implied in such findings.Hypothesis 4a(7) -- the transitional development of N/R-PF (postformal form)<<each of the 4 postformal tests -- was partly supported by findings that the transitionaldevelopment of N/R-PF (postformal form) was a necessary but not sufficient conditionfor only Problem Finding and Reflective Judgment.Hypothesis 4a(8) -- the transitional development of N/R-EV (epistemic view) <<each of the 4 postformal tests -- was supported. The implication of such findings is thatthe transitional development of N/R-EV (epistemic view) also plays a crucial role in thedevelopment of postformal reasoning.To conclude, results derived from all the above contingency tables wereconsistent with findings concerning the order of task difficulty and suggested a nonlinear model for a more appropriate description of the relationships among the 8 testsespecially when the 4 postformal tests were also taken in consideration.All in all, the findings also showed that the 2 postformal N/R tests (N/R-PF(postformal form) and N/R-EV (epistemic view)) were more difficult than N/R-F (formalform). Moreover, the mastery of N/R-F (formal form) was found to be a necessary but141not sufficient condition for the mastery of N/R-PF (postformal form). Therefore, it couldbe suggested that the formal and the postformal levels could be differentiated withinnonabsolute/ relativistic (N/R) thinking.The analyses and results of Question 4b are presented in the following.4b. What is the order of the 8 tests according to their ages of onset of task mastery?To address this question, the 8 tests were rank ordered according to the age ofonset at which the task of each test is mastered. The age of onset is defined as the basalage at and above which age level there is a minimum of at least one incidence of taskmastery. It is not necessary for all the participants of the age of onset thus defined tomaster the test in question. However, the definition is conditional on an adequaterepresentation of participants at each different age level. (Of the participants recruitedfor this study, the numbers of participants at each consecutive age level from age 10 toage 20 vary from 4 to 36.)The following hypothesis would be evaluated.Hypothesis 4b(1): The hypothesized order of the 8 tests according to their agesof onset of task mastery would be as follows -- the test of Minimal Formal Reasoning(FR); the N/R test at the formal level (N/R-F (formal form)); the 2 N/R tests at thepostformal level (N/R-PF (postformal form) and N/R-EV (epistemic view)); and the 4postformal tests (Problem Finding (PF), Dialectical Reasoning (DR), RelativisticOperations (RO) and Reflective Judgment (RJ)).The rationale for this hypothesized rank order is that N/R-F (formal form) iscloser to formal reasoning whereas N/R-PF (postformal form) and N/R-EV (epistemicview) are closer to postformal reasoning. This hypothesis is based on the assumption thatthe relationships among the tests can be described in a linear model.142The rank order derived from the results was as follows:FR (age 10); RO (age 13); N/R-F (age 14); NIR-EV, N/R-PF, DR and PF (age 15); andRJ (age 17). (See Figure 25.)Figure 25Order of the 8 Tests according to Ages of Onset of TaskMasteryLINEAR MODEL NON-LINEAR MODELCategory 1 Category 2Age Age10 FR 10 FR11 1112 1213 RO 13 RO14 N/R-F 14 N/R-F15 N/R-EV, N/R-PF 15 N/R-EV, N/R-PF DR, PFDR, PF16 1617 RJ 17 RJNote. N/R-F=Test of Formal Form of Nonabsolulte/relativistic (N/R) Thinking. N/R-PF=Test of Postformal Formof N/R Thinking. N/R-EV=Test of Epistemic View of N/RThinking. FR=Test of Minimal Formal Reasoning. PF=Test ofProblem Finding. DR=Test of Dialectical Reasoning. RO=Testof Relativistic Operations. RJ=Test of Reflective Judgment.From the perspective of a linear model, the above results did not correspondstrictly to the hypothesized rank order. Similar to findings in Question 4a, theysuggested that a non-linear model would be more appropriate in describing therelationships among the 8 tests (see Figure 25).143From the perspective of a non-linear model, the tests could be re-arranged into 2categories. Under category 1 are Minimal Formal Reasoning (FR) and the 3 NIR tests,the rank order of which according to the age of onset was as follows: FR (age 10),N/R-F (age 14), N/R-EV and N/R-PF (age 16). The rank order in this categorycorresponds precisely with the hypothesized order.Under category 2 are the 4 postformal tests, the rank order of which according tothe age of onset was as follows: RO (age 13), DR (age 15), PF (age 15), and RJ (age 17).The rank order in this category approximates to that of task difficulty in category 2 ofQuestion 4a, Hypothesis 4a(1) with a reversal in the order of PF and RJ.When the categories 1 and 2 are cross referenced to compare the ages of onset,Relativistic Operations (RO) was shown to be more closely associated with N/R-F(formal form) than with N/R-EV (epistemic view) and N/R-PF (formal form); and N/R-F(formal form) was hypothesized to represent a transition from high formal to postformalreasoning (Arlin, 1984). On the other hand, the other 3 postformal tests, namelyDialectical Reasoning (DR), Problem Finding (PF) and Reflective Judgment (RJ), wereshown to be more closely associated with N/R-EV (epistemic view) and N/R-PF(postformal form) than with N/R-F (formal form); and N/R-EV (epistemic view) andN/R-PF (postformal form) were hypothesized in this study to represent the postformallevel of nonabsolute/ relativistic (N/R) thinking.Again, this pattern suggested that the relationships among the 8 tests were notlinear but non-linear. Similar to findings in Question 4a, the above results seem tosuggest that when only Minimal Formal Reasoning (FR) and the 3 N/R tests wereconsidered, the assumption of a linear model could still be applied. However, when the 4postformal tests were also taken into consideration, the assumption of a non-linear modelwould be more appropriate in describing the relationships among the 8 tests.To conclude, the findings that the mastery of N/R-F (formal form) precedes thatof the two postformal N/R tests (N/R-PF (postformal form) and N/R-EV (epistemic144view)) suggested that the formal and the postformal levels could be differentiated withinnonabsolute/ relativistic (N/R) thinking.The analyses and results of Question 4c are presented in the following.4c. How do the 3 NIR tests correlate with the factors of formal level reasoning andof postformal level reasoning?Related to this question, the following hypotheses were evaluated.Hypothesis 4c(1): N/R-F (formal form) would load primarily on the factor offormal level reasoning.Hypothesis 4c(2): NIR-PF (postformal form) and N/R-EV (epistemic view)would load primarily on the factor of postformal level reasoning.The first approach to Question 4c was to conduct exploratory factor analysisusing SPSS:X computer programme. The analysis was based on the correlations amongthe test scores of the 8 tests, namely the 3 N/R tests, the 4 postformal tests and the test ofMinimal Formal Reasoning (FR). The correlation matrix was presented in Table 9. Themethod of extraction was Principal Axis Factoring (PAF). The method of rotation wasOblimin due to the assumption that the factors were correlated. Two eigenvalues (3.77and 1.03) were obtained accounting for 47.1% and 12.8% of the variance respectively,which together total 59.9% of the variance. Two factors were extracted. The first factorwas hypothesized to be the factor of postformal level reasoning and the second to be thefactor of formal level reasoning. Relevant information concerning the findings arepresented in Table 15.145Table 15Results of Exploratory Factor AnalysisFACTOR MATRIXFACTOR 1 FACTOR 2RJ 0.84 -0.07DR 0.73 -0.14N/R-EV 0.73 -0.09N/R-PF 0.72 0.07RO 0.60 0.04PF 0.56 -0.24FR 0.45 0.42N/R-F 0.35 0.30Oblimin rotation converged in 5 iterations.PATTERN MATRIXFACTOR 1 FACTOR 2RJ 0.77 0.11DR 0.75 0.00N/R-EV 0.70 0.06PF 0.68 —0.15N/R-PF 0.54 0.25RO 0.47 0.19FR 0.02 0.61N/R-F 0.03 0.43STRUCTURE MATRIXFACTOR 1 FACTOR 2RJ 0.84 0.55DR 0.75 0.43N/R-EV 0.73 0.46N/R-PF 0.69 0.56PF 0.59 0.23RO 0.58 0.46FR 0.36 0.62N/R-F 0.28 0.45FACTOR CORRELATION MATRIXFACTOR 1 FACTOR 2FACTOR 1 1.00FACTOR 2 0.57 1.00Note. FR=Test of Minimal Formal Reasoning. N/R-F=Test ofFormal Form of Nonabsolute/ relativistic (N/R) Thinking.N/R-PF=Test of Postformal Form of N/R Thinking. N/R-EV=Testof Epistemic View of N/R Thinking. PF=Test of ProblemFinding. DR=Test of Dialectical Reasoning. RO=Test ofRelativistic Operations. RJ=Test of Reflective Judgment.146As revealed in the pattern matrix, all the 6 postformal level tests (N/R-PF(postformal form), NIR-EV (epistemic view), PF (Problem Finding), DR (DialecticalReasoning), RO (Relativistic Operations) and RJ (Reflective Judgment)) yielded mediumto high loadings (0.47 to 0.77) on the factor of postformal level reasoning whereasthe 2formal level tests (N/R-F (formal form) and FR (Minimal Formal Reasoning))yieldedextremely low loadings (0.02 to 0.03) on the factor of postformal level reasoning.On the other hand, all the 6 postformal level tests yielded very low loadings(-0.15 to 0.25) on the factor of formal level reasoning whereas the2 formal level testsyielded medium to moderately high loadings (0.43 to 0.61) onthe factor of formal levelreasoning.The above results lend support to both Hypotheses 4c(1) and (2).The second approach to Question 4c was to conductconfirmatory factor analysisusing LISREL 8. The method of estimation was MaximumLikelihood (ML). Theanalysis was based on the covariances among the scores of the 8 tests. Theresultsreported were based on completely standardized solutions.Model Cl (see Figure 26)This model was based on 8 tests. N/R-F (formal form) and FR (Minimal FormalReasoning) were specified to load on the factor of formal level reasoning;and N/R-PF(postformal form), N/R-EV (epistemic view) and the 4 postformaltests (PF (ProblemFinding), DR (Dialectical Reasoning), RO (Relativistic Operations)and RJ (ReflectiveJudgment)) were specified to load on the factor of postformal levelreasoning. These twofactors were specified to correlate with each other.The following fit indices are obtained:147Figure 26Model Cl: Results ofConfirmatory FactorAnalysis.63 —.79 —.50 —.46 —.69 —.45 -+.66 —p,.28 -.DR(DialecticalReasoning)RO(RelativisticOperations)RJ(ReflectiveJudgment).61FORMALLEVEL.46REASONING.71.6873.56POSTFORMALLEVELREASONING• 85Note. N/R=Nonabsolute/ relativistic.Fit-indices: X2=13.56,df=19, p=.81,SRMR=.027, GFI=.99,AGFI=.97, NFI=.98,Appendix I for explanationof fit-indices).Q=.71, RMR=.016,NNFI=l.0(seeFR(Minimal FormalReasoning)N/R-F(formal form)N/R-PF(postformalform)N/R-EV(epistemic view)PF(ProblemFinding)148The Chi-Square is 13.56 with 19 Degrees of Freedom (df) and a probability (p)of0.81. The Chi-Square/df Ratio(Q)is 0.71. The Root Mean Square Residual (RMR) andthe Standardized RMR (SRMR) are 0.0 16 and 0.027 respectively. The Goodness of FitIndex (GFI) and the Adjusted Goodness of Fit Index (AGFI) are 0.99 and0.97respectively. The Normed Fit Index (NFl) and the Non-normed Fit Index (NNFI) are0.98 and 1.0 respectively.As shown in the above results, the model provides a very good fit to the data.The good fit is evidenced in the smallQratio, the high p level, the small RIVIR andSRMR, and the high GFI, AGFI, NFl and NNFI. Besides, the two factors were found tobe correlated as specified in the model (r=0.68). The results lend support to Hypotheses4c(1) and (2).Based on the conventional criterion of 0.30 and above for the acceptability of afactor loading, the factor loadings of this model which ranged from 0.46 to 0.85 fellwithin the acceptable range.Based on the conventional criterion of 0.91 and below for the acceptability of anerror or unique variance, the unique variances of this model which ranged from 0.79 to0.28 fell within the acceptable range.For the factor of “formal level reasoning”, the factor loadings of the 2 tests were0.61 and 0.46. For the factor of “postformal level reasoning”, the factor loadings of the6tests ranged from 0.56 to 0.85. Therefore, all the tests could be considered as quite goodindicators of their corresponding factors.To conclude, results of both the exploratory and the confirmatory factoranalysessuggested that the formal and the postformal levels could be differentiated withinnonabsolute! relativistic (NIR) thinking.The analyses and results of Question 4d are presented in the following.1494d. Which of the performances in the 3 NIR tests would singly or in combinationbest predict the performances in each of the 4 postformal tests?In relation to this question, the following hypothesis was evaluated.Hypothesis 4d(1): Performances in N/R-PF (postformal form) and in N/R-EV(epistemic view) rather than that in N/R-F (formal form) would be better predictors ofthe performances in the 4 postformal tests.To address this question, 4 separate multiple regression analyses were conducted.The predictors in each of the 4 analyses were the performances in the 3 N/R tests. Thecriterion variable in each analysis was the performance in Problem Finding (PF),Dialectical Reasoning (DR), Relativistic Operations (RO) and Reflective Judgment (RJ)respectively. When the 3 predictors (performances in N/R-F (formal form), N/R-PF(postformal form) and N/R-EV (epistemic view)) were entered using a stepwiseregression method, results showed that N/R-F (formal form) did not make an additionalcontribution to the prediction equations for each of the criterion variables. This isprobably due to the fact that N/R-F (formal form) represents formal reasoning.The four prediction equations are presented below:The prediction equation for PF (Problem Finding) was PF=0.44 + 0.33 (N/R-EV)+ 0.25 (NIR-PF). Standard errors associated with the betas were 0.14, 0.07, 0.07. Themultiple R was 0.47 (F=35.83, p=O.0000, df(2, 251)).The prediction equation for DR (Dialectical Reasoning) was DR= -0.19 + 0.56(N/R-EV) + 0.40 (N/R-PF). The standard errors of the betas were 0.16, 0.08, 0.08. Themultiple R was 0.61 (F=72.48, p=O.0000, df(2, 251)).The prediction equation for RO (Relativistic Operations) was RO=0.57 + 0.40(N/R-EV) + 0.36 (N/R-PF). The standard errors of the betas were 0.16, 0.08, 0.08. Themultiple R was 0.51 (F=45.22, p=O.0000, df(2, 251)).150The prediction equation for RJ (Reflective Judgment) was RJ= -0.12 + 0.47 (N/REV) + 0.41 (N/R-PF). The standard errors of the betas were 0.11, 0.06, 0.05. Themultiple Rwas 0.71 (F=126.31, p=O.0000, df(2. 251)).The above results show that performances in N/R-PF (postformal form) and N/REV (epistemic view) were better predictors than that in N/R-F (formal form) inpredicting the performance in each of the 4 postformal tests. These results lend supportto Hypothesis 4d(1). The implication of such findings is that the formal and thepostformal levels could be differentiated within nonabsolute! relativistic (N/R) thinking.The analyses and results of Question 4e are presented in the following.4e. Between the performances in NIR-F (formal form) and in NIR-PF (postformalform), which would be better predicted by the performance in N/R-EV(epistemic view)?In relation to this question, the following hypothesis was evaluated.Hypothesis 4e(1): Performance in N/R-PF (postformal form) rather than that inN/R-F (formal form) would be better predicted by performance in N/R-EV (epistemicview).To address this question, 2 separate simple regression analyses were conducted.The predictor in each analysis was the performance in N/R-EV (epistemic view). Thecriterion variable in each analysis was the performances in N/R-F (formal form) and inN/R-PF (postformal form) respectively. The results are presented below.The prediction equation for N/R-F (formal form) was N/R-F=0.90 + 0.38 (N/REV). The standard errors of the betas were 0.22 and 0.10. The multiple R was 0.23(F=14.26, p=O.0002, df (1, 252)).The prediction equation for N/R-PF (postformal form) was N/R-PF=0.46 + 0.53(N/R-EV). The standard errors of the betas were 0.12 and 0.06. The multiple R was0.50 (F86.25, p=O.0000, df(1, 252)).151The above results lend support to Hypotheses 4e(1). The implication of suchfindings is that the formal and the postformal levels could be differentiated withinnonabsolute! relativistic (N/R) thinking.All in all, all the findings of Research Question 4 also consistently suggest thatthe formal and the postformal levels could be differentiated within nonabsolute!relativistic (N/R) thinking, thus supporting the general hypothesis that nonabsolute/relativistic (N/R) thinking is an instance of both formal and postformal reasoning.In summary, chapter IV contains the analyses and results of the main study whichwas specifically designed to address Research Questions 3 and 4 of this study. Findingsof Research Question 3 seem to support the general hypothesis that nonabsolute/relativistic (N/R) thinking is a possible unifying commonality underlying the models ofpostformal reasoning. Findings of Research Question 4 seem to support the generalhypothesis that nonabsolute/ relativistic (N/R) thinking is an instance of both formal andpostformal reasoning.152CHAPTER V: DISCUSSIONThis final chapter consists of two parts. Part A contains a summary of the studyand interpretation of the findings. Part B contains the implications of the findings andsuggestions for future research. Part C contains the concluding remarks.A. SUMMARY AND INTERPRETATION OF FINDINGSIn the recent growing interest in unifying the diverse models of postformalreasoning, there has been speculation that nonabsolute/ relativistic (N/R) thinking is oneof the possible unifying commonalities underlying the selected models of postformalreasoning.In this study, four of the unresolved issues pertaining to this speculation wereidentified. In order to address these four unresolved issues, four general researchquestions were raised and addressed.The first research question, “How can nonabsolute/ relativistic (NIR) thinkingbe operationally defined?”, was designed to address the unresolved issue concerningthe need for an operational definition of nonabsolute/ relativistic (N/R) thinking. Anoperational definition of nonabsolute/ relativistic (N/R) thinking was proposed in chapterIII. To summarize, “nonabsolute! relativistic (N/R) thinking” refers to a specific type ofnonabsolute thinking that involves the use of relativistic thinking as a form of cognitiveoperation. Nonabsolute/ relativistic (N/R) thinking was conceptualized and defined as amultidimensional and multilevel construct (see Figure 1). Two of the more importantdimensions of nonabsolute/ relativistic (N/R) thinking were proposed: a) the basic formdimension and b) the epistemic view dimension. Within the basic form dimension, twolevels were proposed: 1) the formal form and 2) the postformal form.153a) The operational definition of the basic form dimension of nonabsolute/relativistic (N/R) thinking is as follows: 1) The formal form of nonabsolute! relativistic(N/R) thinking is operationally defined as “multiple-frame operations on well-definedproblems”. 2) The postformal form of nonabsolute/ relativistic (N/R) thinking isoperationally defined as “multiple-frame operations on ill-defined problems”.b) The operational definition of the epistemic view dimension of nonabsolute/relativistic (N/R) thinking is as follows. The epistemic view associated withnonabsolute! relativistic (N/R) thinking is operationally defined in terms of four specificaspects pertinent to the nature of knowledge of reality. They concern: 1) the means ofknowledge, 2) the limits of knowledge, 3) the criteria of knowledge, and 4) the nature ofreality.The above definition of nonabsolute/ relativistic (NIR) thinking was used as abasis for the design of a battery of three tests of nonabsolute! relativistic (N/R) thinking.The second research question, “How can nonabsolute/ relativistic (NIR)thinking be measured?”, was designed to address the unresolved issue concerning theneed for a design of a measure of nonabsolute/ relativistic (N/R) thinking. A battery ofthree tests of nonabsolute/ relativistic (N/R) thinking was specifically designed tomeasure the construct of nonabsolute/ relativistic (N/R) thinking. These three tests ofnonabsolute! relativistic (N/R) thinking are: 1) the test of the formal form of nonabsolute/relativistic thinking (N/R-F), 2) the test of the postformal form of nonabsolute/relativistic thinking (N/R-PF), and 3) the test of the epistemic view of nonabsolute!relativistic thinking (N/R-EV). The N/R-F (formal form) was adapted from a subtest ofthe Arlin Test of Formal Reasoning (Arlin, 1984b). The N/R-PF (postformal form) andN/R-EV (epistemic view) were specifically designed by Arlin and the author for thisstudy. The detailed descriptions of these three tests were presented in chapter III.The third research question, “Is nonabsolute/ relativistic (N/R) thinking acommon factor underlying the selected tests of postformal reasoning’?”, was154designed to address the unresolved issue concerning the lack of empirical evidence insupport of the proposition that nonabsolute/ relativistic (N/R) thinking is one of thepossible unifying commonalities underlying the models of postformal reasoning.A number of researchers have independently suggested that nonabsolute/relativistic (N/R) thinking is required for the operations of postformal reasoning (e.g.Arlin, 1974, 1975/6; Basseches, 1980; Cavanaugh, Kramer, Sinnott, Camp & Markley,1985; King, Kitchener, Davidson, Parker & Wood, 1983; Kitchener & King, 1981;Riegel, 1973; Sinnott, 1981, 1989). In a similar vein, Kramer (1983a) proposed thatnonabsolute/ relativistic (N/R) thinking might be one of the core features of postformalreasoning. However, the proposition that nonabsolute/ relativistic (N/R) thinking is oneof the commonalities underlying the models of postformal reasoning was yet to beempirically tested. This unresolved issue was addressed in the third research questionwhich consists of two subquestions, Questions 3a and 3b. The analyses and results ofResearch Question 3 were presented in chapter IV.Question 3a is “What, if any, commonalities exist among the items of the 3NIR tests?”. The purpose of this question was to analyze the test items of the 3 N/Rtests in order to provide a foundation for the analyses conducted at the next level usingtest scores instead of item scores. Confirmatory factor analysis was conducted on theitems of the 3 N/R tests. Three test factors, namely the N/R-F (formal form) test factor,the N/R-PF (postformal form) test factor and the N/R-EV (epistemic view) test factor,are identified. These factors appear to underlie all of the 12 test items. Moreover, the 3test factors are shown to be correlated and a second order factor, namely the N/R testfactor, underlies these 3 test factors. The implication of such findings is that these 3 testfactors measure three different aspects of the same construct, namely nonabsolute/relativistic (N/R) thinking.In the second order factor model, except for 2 test items, namely NRF2 andNREV4, which yielded low factor loadings of -0.18 and 0.18 respectively, the other 10155test items yielded factor loadings ranging from 0.31 to 0.92 which fell within theacceptable range. Despite their low factor loadings, NRF2 and NREV4 were retained inthe test due to their uniqueness. On the whole, the 12 test items could be considered asfairly valid indicators of their respective test factors. Subsequently, the item scores ofeach test could be combined into a single composite score to reflect the correspondingtest factor.Question 3b is “What, if any, commonalities exist among the 3 N/R tests andthe 4 postformal tests?”. Confirmatory factor analysis was conducted on the test scoresof the 3 N/R tests and the 4 postformal tests. As shown in the results of the analysis, anN/R (nonabsolute/ relativistic thinking) test factor underlies the 3 N/R tests and apostformal test factor underlies the 4 postformal tests. Furthermore, these two testfactors are shown to be perfectly correlated (r=1 .0). This relationship between the twotest factors could be explained either by a second order common factor model or by amore parsimonious model. In the more parsimonious model, these two test factors werereplaced by one first order common factor which was hypothesized to be nonabsolute/relativistic (N/R) thinking. Such findings lend support to the general hypothesis thatnonabsolute! relativistic (N/R) thinking is a possible unifying commonality underlyingthe selected models of postformal reasoning as postulated in the literature.As shown in the results of further analysis, a factor of basic form dimensionunderlies the N/R-PF (postformal form) and 3 of the 4 postformal tests (ProblemFinding, Dialectical Reasoning and Relativistic Operations) and a factor of epistemicview dimension underlies the N/R-EV (epistemic view) and the postformal test ofReflective Judgment. Furthermore, these two factors are shown to be perfectly correlated(r=1 .0). The implication of such findings is that two dimensions (basic form andepistemic view) could be differentiated within the postformal level of nonabsolute!relativistic (N/R) thinking. Such findings lend support to the conceptualization thatnonabsolute/ relativistic (N/R) thinking is a multidimensional construct. The hypothesis156that nonabsolute/ relativistic (N/R) thinking is also a multilevel construct wasfurtherexplored in the fourth research question.The fourth research question, “Is nonabsolute/ relativistic (NIR) thinking aninstance of formal or postformal reasoning or of both?”, was designed to address theunresolved issue concerning whether nonabsolute! relativistic (N/R) thinking is formal orpostformal in nature.An implicit assumption held by some postformal researchers is that in order fornonabsolute! relativistic (N/R) thinking to be qualified as a common feature underlyingthe postformal models, it is necessary to demonstrate that it possesses a form or structurethat is postformal in nature (Cavanaugh et al., 1985; Kramer, 1983b). While a number ofresearchers (e.g. Arlin, 1984, 1990; Kramer, 1983a; Sinnott, 1981) suggested that somekind of relativistic thinking is required for postformal operations, others (Cavanaugh etal., 1985) questioned the postformal level status of relativistic thinking. Thus thepostformal level status of relativistic thinking has been a debatable issue. Thisunresolved issue was addressed in the fourth research question which consists of fivesubquestions, Questions 4a to 4e. Analyses and results of Research Question 4 werepresented in chapter IV.Question 4a is “What is the order of difficulty among the 8 tests -- FR(Minimal Formal Reasoning), NIR-F (formal form), N/R-EV (epistemic view), N/RPF (postformal form), PF (Problem Finding), DR (Dialectical Reasoning), RO(Relativistic Operations) and RJ (Reflective Judgment)?”.As a result of the analysis, it appears that a non-linearmodel*might be moreappropriate in describing the relationships among the 8 tests. When only MinimalFormal Reasoning and the 3 N/R tests were rank ordered according to their level ofdifficulty, results show that Minimal Formal Reasoning was less difficult than N/R-F(formal form) and that N/R-F (representing the formal level of nonabsolute/ relativisticthinking) was less difficult than N/R-PF and N/R-EV (representing the postformal level157of nonabsolute/ relativistic thinking). Analysis of contingency table was used to establishthat N/R-F (formal form) was a necessary but not sufficient condition for N/R-PF(postformal form). The hypothesis that NIR-F (formal form) is a necessary but notsufficient condition for NIR-EV (epistemic view) was not supported by virtue of theentry in the target cell exceeding the arbitrary cut-off point of 13 (5%). As the excesswas only 2 cases (0.9%) over the arbitrary cut-off point, the hypothesis though notsupported could still be considered plausible.When the 4 postformal tests were also rank ordered, the level of difficulty ofRelativistic Operations and of Dialectical Reasoning was found to approximate that ofN/R-F (formal form), falling within the moderately difficult range, and that of ReflectiveJudgment and of Problem Finding to approximate that of N/R-EV (epistemic view) andof N/R-PF (postformal form), falling within the most difficult range.Question 4b is “What is the order of the 8 tests according to their ages ofonset of task mastery?”.Similarly, findings suggest that a non-linearmodel*might be more appropriate indescribing the relationships among the 8 tests. When only Minimal Formal Reasoningand the 3 N/R tests were rank ordered according to their respective ages of onset, resultsindicate that Minimal Formal Reasoning preceded N/R-F (formal form) and that N/R-F(formal form) preceded N/R-EV (epistemic view) and N/R-PF (postformal form). Whenthe 4 postformal tests were also taken into consideration, Relativistic Operations wasfound to precede the other 3 postformal tests and Dialectical Reasoning and ProblemFinding to precede Reflective Judgment. Correspondingly, Relativistic Operationsapproximated NIR-F (formal form) and Dialectical Reasoning and Problem Findingapproximated N/R-EV (epistemic view) and N/R-PF (postformal form).Question 4c is “How do the 3 N/R tests correlate with the factors of formallevel reasoning and of postformal level reasoning?”.158Exploratory factor analysis resulted in N/R-F (formal form) loading primarily onthe factor of formal level reasoning, and N/R-PF (postformal form) and N/R-EV(epistemic view) loading primarily on the factor of postformal level reasoning. Suchresults were further supported through confirmatory factor analysis.Question 4d is “Which of the performances in the 3 N/R tests would singly orin combination best predict the performances in each of the 4 postformal tests?”.As shown in the results of multiple regression analysis, performances in N/R-PF(postformal form) and in N/R-EV (epistemic view) were better than that in N/R-F(formal form) as predictors of the performances in the 4 postformal tests (ProblemFinding, Dialectical Reasoning, Relativistic Operations and Reflective Judgment).Question 4e is “Between the performances in NIR-F (formal form) and inN/R-PF (postformal form), which would be better predicted by the performance inNJR-EV (epistemic view)?”.As shown in the results of simple regression analysis, performance in N/R-PF(postformal form) rather than that in N/R-F (formal form) was better predicted byperformance in N/R-EV (epistemic view). The implication of such findings is that N/RPF (postformal form) and N/R-EV (epistemic view) both represent the postformal levelof nonabsolute! relativistic (N/R) thinking.All in all, it was consistently suggested in all the findings of the fourth researchquestion that the formal and the postformal levels could be differentiated withinnonabsolute/ relativistic (N/R) thinking, thus supporting the general hypothesis thatnonabsolute/ relativistic (N/R) thinking is an instance of both formal and postformalreasoning. The implication is that nonabsolute/ relativistic (N/R) thinking is a multilevelconstruct. As a result of these findings, an alternative perspective to the debateconcerning the stage level of nonabsolute/ relativistic (N/R) thinking is available. Thealternative perspective is that it is not necessary to categorize nonabsolute! relativistic159(N/R) thinking strictly into either formal or postformal level as it can be conceptualizedas a multilevel construct.*Non..linearModel of DevelopmentAccording to certain ordering criteria, when the tests could be arranged one afteranother in a straight line, the pattern of the relationships among the tests could bedescribed as a linear model. When the tests could not be arranged one after another in astraight line, the pattern of the relationships among the tests would be described as a nonlinear model.An interesting pattern concerning the relationships among formal reasoning,nonabsolute/ relativistic (N/R) thinking and postformal reasoning appears to emerge fromthe findings. In rank ordering of the 8 tests by their level of difficulty as well as by agesof onset of task mastery, it is consistently shown in the results that when only MinimalFormal Reasoning and the 3 N/R tests -- N/R-F (formal form), N/R-PF (postformal form)and N/R-EV (epistemic view) -- were considered, the assumption of a linear model couldstill be applied. However, when the 4 postformal tests (Problem Finding, DialecticalReasoning, Relativistic Operations and Reflective Judgment) were also taken intoconsideration, the assumption of a non-linear model rather than a linear model would bemore appropriate in describing the relationships among the 8 tests. In other words, the 4postformal tests were found to approximate the 3 N/R tests in terms of their level ofdifficulty as well as of their ages of onset of task mastery. Such findings are contrary tothe assumption of a linear model that all 4 postformal tests would be more difficult thanthe 3 NIR tests and that the ages of onset of task mastery of the 4 postformal tests wouldbe later than those of the 3 N/R tests.A probable explanation for such findings might be related to the scoring criteriaof the 4 postformal tests. The 4 postformal tests used in this study are adapted from the160original tests in order to tap the minimal presence of postformal reasoning specific totheir respective models. The original tests were Problem Finding, Dialectical Reasoning,Relativistic Operations and Reflective Judgment. It is crucial to point out that theminimal presence of these forms of postformal reasoning does not represent the fullydeveloped forms of postformal reasoning but rather some variation of them. As thescoring criteria of the original tests of the selected postformal models are very stringent,it is obvious that the adapted scoring criteria would deflate the level of difficulty of the 4postformal tests. They would probably also be responsible for the relatively lowcorrelations between each of the 4 postformal tests and Minimal Formal Reasoning andbetween each of the 4 postformal tests and N/R-F (formal form). It is speculated that ifthese selected postformal tests were administered and scored in accordance with theiroriginal criteria, they would probably be more difficult than the 3 NIR tests, and theirages of onset of task mastery would probably be later than those of the 3 N/R tests.Furthermore, the correlations between each of the 4 postformal tests and Minimal FormalReasoning and between each of the 4 postformal tests and N/R-F (formal form) wouldprobably increase. However, the interest of this study is on the basic forms or structuresas postulated in the above selected models of postformal reasoning. Therefore, tappingonly the minimal presence of postformal reasoning specific to their respective modelssuffices. The non-linear model suggested by the findings in fact reveals the nature of theinterconnectedness among the development of nonabsolute! relativistic (NIR) thinkingand the emergence of these specialized forms of postformal reasoning.Volatility due to individual differences and sampling errors can be expected onthe ages of onset of task mastery, defined as the basal age at and above which age levelthere is a minimum of at least one incidence of task mastery. The ages of onset of taskmastery should not, therefore, be taken as a conclusive point of reference for therelationships among the 8 tests. They should rather be used as a supplementary referenceto the level of task difficulty according to the percentage of task mastery and the results161of the contingency tables. Therefore, all three sets of information, namely ages of onsetof task mastery, percentage of task mastery and the contingency tables, should beintegrated in order to provide a better and more consolidated representation of therelationships among the 8 tests.As shown in the results, the ages of onset of task mastery of both nonabsolute!relativistic (N/R) thinking and postformal reasoning span from age 13 to 17,concentrating around age 15 particularly. Such findings are not incompatible with thelogic that the emergence of these forms of higher order thinking happens to coincide withthe consolidation period of formal reasoning which was suggested by Piaget (1972) to bearound age 15 though many researchers would hypothesize an age above 15.B. IMPLICATIONS OF FINDINGS ANDSUGGESTIONS FOR FUTURE RESEARCHFindings of this study are discussed in four contexts and suggestions for futureresearch would be made accordingly. These four contexts are: 1) nonabsolute/relativistic (N/R) thinking as a commonality underlying postformal models, 2)nonabsolute/ relativistic (N/R) thinking as a multidimensional and multilevel construct,3) nonabsolute/ relativistic (N/R) thinking as a form of metamorphosis from closedsystem to open-system thinking, and 4) nonabsolute! relativistic (N/R) thinking as apotential springboard in the development of higher order thinking.1. Nonabsolute/ relativistic (NIR) Thinkingas a Commonalityunderlying Postformal Models162Findings in this study supported the proposition that nonabsolute/ relativistic(N/R) thinking is a possible unifying commonality underlying the selected modelsofpostformal reasoning. These findings would shed light to clarify the logical relationshipsexisting among the said models as well as provide a common link unifying these diversemodels. However, the claim is not made that nonabsolute/ relativistic (N/R) thinking isthe sole unifying commonality underlying the selected models nor that it is a possiblecommonality underlying all models of postformal reasoning. The work reported hereserves as an alternative perspective in the attempt to unify the diverse models. Therefore,other possible unifying commonalities warrant exploration.As this study was an initial attempt to provide empirical evidence to support theproposition that nonabsolute! relativistic (N/R) thinking is a possible unifyingcommonality, only the minimal presence of postformal reasoning specific to the selectedmodels was tapped. Though the hypothesis was supported that nonabsolute/ relativistic(N/R) thinking is a possible unifying commonality underlying the selected models ofpostformal reasoning, further studies are called for to explore the relationships betweennonabsolute/ relativistic (N/R) thinking and the fully developed forms of postformalreasoning.2. Nonabsolute/ relativistic (NJR) Thinkingas a Multidimensionaland Multilevel ConstructIn this study, nonabsolute/ relativistic (N/R) thinking was definedas amultidimensional and multilevel construct. Two of the important dimensionsofnonabsolute/ relativistic (N/R) thinking were proposed: 1) basic form dimensionand 2)epistemic view dimension. Within the basic form dimension, two levels were proposed:1631) formal form and 2) postformal form. It is suggested in the findings that the twodimensions and the two levels can be differentiated within the construct of nonabsolute!relativistic (N/R) thinking. As construct validation was not the main focus of this study,this construct as defined needs to be validated by further studies specific to this purpose.Furthermore, other dimensions and other levels of nonabsolute/ relativistic (N/R)thinking have yet to be explored.3. Nonabsolute/ relativistic (N/R) Thinkingas a Form of Metamorphosisfrom Closed-system to Open-system ThinkingA simple form of relativity which is one of the eight concepts of formaloperations was defined by Piaget (1958) as “co-ordination of two or more systems orframes of reference”. Arlin (1984) suggested that this might represent a pivotal conceptthat marks the transition from high formal to postformal reasoning. Based on thissuggestion, two forms of nonabsolute/ relativistic (N/R) thinking, namely formal andpostformal, were proposed in this study.The formal form of nonabsolute! relativistic (N/R) thinking is operationallydefined as “multiple-frame operations on well-defined problems” as measured by N/R-F(formal form) which is adapted from the Piagetian task “Coordinations of two or moresystems or frames of reference”. The task requires the ability to coordinate multipleframes of reference within a well-defined and closed-system as a whole. For welldefined problem, all information necessary to produce a solution is given or can bederived form what is given. On the other hand, the postformal form of nonabsolute/relativistic (N/R) thinking is operationally defined as “multiple-frame operations on illdefined problems” as measured by N/R-PF (postformal form) which is one of the three164N/R tests specifically designed for this study. This test was designed to measuretheability to think flexibly in terms of multiple frames within self-constructed aswell asopen systems. As the task involves ill-defined problems, a person would be required togenerate information beyond that which is given including relevant frames of reference.Since absolute answers cannot be expected for this kind of task, the recognition ofuncertainty and indeterminacy is necessarily implied.In view of the above, one could argue that the postformal form of nonabsolute/relativistic (NIR) thinking, although structurally similar to, is qualitatively moreadvanced than the formal form. Correspondingly, the representation of reality associatedwith the postformal form is more dynamic and allows for uncertainty, and therefore, ismore compatible with the notion of modern science that reality is in a constant flux.It is my argument that the transition from the formal form to the postformal formmight represent a form of metamorphosis from closed-system thinking (associated withwell-defined problems) to open-system thinking (associated with ill-defined problems),and that the transition might be explained by a paradigm shift from an absolute to anonabsolute epistemic view. In this light, Piaget’s formal operations would mark thefinal stage not of cognitive development but of closed-system thinking.At the postformal level, the functions of nonabsolute! relativistic (N/R) thinkingare double-edged. On the side which is more recognized and duly emphasized,nonabsolute/ relativistic (N/R) thinking could function to generate, construct and coordinate complex dynamic systems of thinking which allow for uncertainty,indeterminacy, and subjectivity. On the other side which is less recognized, nonabsolute!relativistic (N/R) thinking could function to free fixed perspectives and to break mentalsets. If reality is the construction of the mind, nonabsolute/ relativistic (N/R) thinkingmight serve to liberate the mind’s construction of reality.At the postformal level, formal reasoning is not necessarily abandoned butincorporated into a higher order system of cognitive operations. In nonabsolute!165relativistic (N/R) thinking, the ability to generate self-constructed open systems involvesin essence the ability to create space for imagination. In this light, the postformal formof nonabsolute/ relativistic (N/R) thinking defined as multiple-frame operations on ill-defined problems represents an interplay between the use of logic and imagination. Thusthe difference between formal and postformal reasoning is not so much in the level ofcomplexity but creativity. In this context, nonabsolute! relativistic (N/R) thinking has aclose affinity to the works on creative intelligence (Sternberg, 1990) and on wisdom asadvanced by researchers such as Arlin (1990, 1993), Baltes and Smith (1990; in press),Chandler and Holliday (1990), and Meacham (1990). Future study is suggested toexplore the possible role of nonabsolute! relativistic (N/R) thinking in these and relateddomains. The basic form and the epistemic view associated with the postformal level ofnonabsolute! relativistic (N/R) thinking as definable and measurable constructs mightprovide an alternative and viable basis for the analysis of higher order thinking withparticular regards to creative intelligence and wisdom.4. Nonabsolute/ relativistic (N/R) Thinkingas a Potential Springboard inthe Development of Higher Order ThinkingAs shown in the four prediction equations generated for the four postformal tests(Problem Finding, Dialectical Reasoning, Relativistic Operations, and ReflectiveJudgment), the performance in the two postformal N/R tests -- N/R-PF (postformalform) and N/R-EV (epistemic view) -- taken in combination could serve as potentiallyuseful predictors of higher order thinking as characterized in the 4 selected postformaltests. This is particularly so with N/R-EV (epistemic view) as a predictor.166In addition, the mastery of N/R-EV (epistemic view) was found to be necessarybut not sufficient for the mastery of N/R-PF (postformal form) as hypothesized in thisstudy. The implication for such findings is that N/R-EV (epistemic view) might beconstrued as a crucial antecedent to the development of N/R-PF (postformal form).The transitional development of N/R-EV (epistemic view) was also found to benecessary but not sufficient for the mastery of each of the 4 postformal tests.Furthermore, the transitional development of N/R-PF (postformal form) was found to benecessary but not sufficient for the mastery of two postformal tests, namely ProblemFinding and Reflective Judgment. Such findings seem to suggest that the transitionaldevelopment of nonabsolute! relativistic (N/R) thinking indeed plays a crucial role in thedevelopment of the basic forms or structures of higher order thinking specificallypostformal reasoning. In view of this role of nonabsolute/ relativistic (N/R) thinking inthe development of higher order thinking, nonabsolute/ relativistic (N/R) thinking couldbe taken as a potential springboard in the development of postformal reasoning and otherforms of higher order thinking. A similar argument was presented in a study yieldingevidence that relativistic thinking can play a major role in identifying exceptionalcognitive ability in adolescents (Worthen, paper presented in 1992). Conversely, theabsence of nonabsolute/ relativistic (N/R) thinking in the course of cognitivedevelopment might have a hindering effect on the development of higher order thinkingor might even reflect difficulties in cognitive functioning. Research in a similar veinsuggested that relativistic thinking was typically absent in groups of psychiatricallyhospitalized youth (Chandler & Boyes, 1990). Thus future research is needed to explorethe specific effects of the presence or absence of nonabsolute! relativistic (N/R) thinkingon the development of higher order thinking as well as of optimal cognitive functioning.167C. CONCLUDING REMARKSSome researchers in the field of cognitive development had associated postformalreasoning with advanced scientific thinking. As observed by Einstein (Infeld & Einstein,1938), “to raise new questions, new possibilities, to regard old questions from a newangle requires creative imagination and marks real advance in science”(p.92). Thisview was taken by Arlin (1989) to be an instance of quality problem-finding which is aspecialized form of postformal reasoning. Sinnott (1989) associated post-Einsteinphysics with postformal reasoning and pre-Einstein physics with formal reasoning. AndOser and Reich (1987) associated postformal reasoning with the concept ofcomplementarity.It could be argued that the theories of relativity and of complementarity onlyepitomize the ingenious application of nonabsolute! relativistic (N/R) thinking in thefield of physics. From a wider perspective, it could be further argued that nonabsolute/relativistic (N/R) thinking could also be applied to other domains with far-rangingbenefits. These domains would include arts and humanities, economics and politics,physical and social sciences, and philosophy and religion as well as real life problems ofeveryday living.The application of nonabsolute! relativistic (N/R) thinking into specific domainsis a challenge and calls for interdisciplinary research.In light of the significant role of nonabsolute! relativistic (N/R) thinking in thedevelopment of higher order thinking, findings of this study have particularly importantimplications for research on cognitive development, clinical and counselling psychology,educational psychology, and education with particular reference to higher education,curriculum and instruction, and teachers’ training.In this age of advanced technology in information and communication,information has never been so readily accessible. For students, the task of obtaining168information has never been so convenient. With such profusion of information, theteacher’s role to provide guidance in the use and integration of information and tostimulate critical and original thinking has never been so important. One of the primeconcern of education is the development of cognitive potentials in the individual. Thusresearch is recommended to explore how teachers could best function as a catalyst fordeveloping cognitive potentials in students through the application of the understandingof the significant role of nonabsolute! relativistic (N/R) thinking in the development ofhigher order thinking.Cognitive development could be conceptualized as potentially multidirectionaland non-teleological (Chapman, 1988). The notion of multidirectional developmentimplies that there could be more than one developmental pathway. The notion of nonteleological development implies that it is not exactly necessary to establish a fixedendpoint of development. 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Paper presented at the Esther KatzRosen Symposium on the Psychological Development of Gifted Children:Developmental Approaches to Identifying Exceptional Ability, meeting February 28-29, 1992, at University of Kansas.178Appendix ATest Items of Test ofFormal Form of Nonabsohite/ relativistic(N/R) ThinkingA small toy wind—upturtle is placedon a shaded stripof paper. The paperstrip is linedupalong the edgeof a boardas shown in the picture.The turtle canbe moved along thepaperstrip. The paperstrip can also bemoved along the board.Both the toyand the paper stripcanbe moved forwardor backward. Thetoy, the end of thepaper strip, andthe starting pointonthe board are all linedup as shown.1. If the turtle movesforward at thesame speed that thepaper stripmoves backward, howfarwill the turtlebe from the startingpoint aftera short time (as longas theturtle is still onthe strip of paper)?A. It would be at thestarting point.B. One—fourth thedistance of thepaper strip from thestarting point.C. Double the distanceof the paperstrip from the startingpoint.D. It would be behindthe startingpoint.2. If the turtle moves forwardat 1/3 the speed thatthe paperstrip moves backward,wherewould the turtlebe after a short periodof time (aslong as the turtleis still onthe strip of paper)?A. Three timcs as farforward as thepaper strip is backwardfrom the startingpoint.B. One—third thedistance in front ofthe starting pointas the paper stripis behind thestarting point.C. it would be behindthe starting point.D. As farin front of thestarting point asthe end of thepaper stripis in back of it.179Two people are sitting on this trainas it passes througha long tunnel in thesideof a mountain. Mr.Red (R) is sittingat the front of the trainand Mr. Blue(B) is sitting atthe back of thetrain. For the followingtwo situations,decide whether Mr.R and Mr. B willstay in the tunnelfor the same amountof time..3. SITUATION1: After the trainenters the tunnel Mr.R gets up fromhis scat in thefront,and walks backto sit with Mr. B.How much timealtogether willMr. R spend in thetunnel?A. Less time in thetunnel than Mr.B.B. Twice the timein the tunnel as Mr.B.C. The same amountof time in thetunnel as Mr. B.D. More timein the tunnel thanMi. B.4. SiTUATION 2:After the train hasentered the tunnel1Mr. B gets up fromhis seat in theback. He walks forwardto sit with Mr.R. Halfway onhis trip forward,he decidesto go back to hisseat for hispaper. He getshis paper andthen goes forwardagainand joins Mr.R, while the train isstill in the tunncl.How much timedid Mr. Bspend in the tunnel?A. Less time inthe tunnel than Mr.R.B. More time Inthe tunnel than Mr.R.C. One—and—one—halfas much time inthe tunnel as Mr.R.D. Tue sameamount of time inthe tunnel asMr. R.180Appendix BThe Test of Minimal Formal Reasoning (FR)Test DescriptionThe purpose of this test is to assess the presence of the minimal ability rather thanthe maximal ability for formal reasoning. This test adopts 3 subtests of the Arlin’s Testof Formal Reasoning (ATFR) (Arlin, 1984b). The ATFR was originally designed toassess the ability to use all of the eight Piagetian concepts! schemata of formaloperations.The 3 subtests adopted for the present test are: 1) Multiplicative compensations,2) Probability, and 3) Correlations. The rationale for selecting these 3 subtests is thatthey make up the most elementary or the first tier of ATFR. Thus they should reflect thepresence of the minimal ability for formal reasoning.The 3 concepts of formal operations as assessed by the 3 subtests are brieflyintroduced as follows.“Multiplicative compensations” refers to “the concept which supports theunderstanding that when there are two or more dimensions to be considered in a problem,gains or losses in one dimensions are made up for by gains or losses in the otherdimensions (Arlin, 1984b, p.10)”.“Probability” refers to “a concept that supports the ability to develop arelationship between the confirming and the possible cases (Arlin, 1984b, p.10)”.“Correlations” refers to a concept that implies the ability “to conclude that there isor is not a causal relationship, whether negative or positive, and to explain the minoritycases by inference of chance variables (Arlin, 1984b, p.10)”.This test (FR) is a pencil-and-paper test made up of 12 multiple-choice itemsorganized into 3 subtests. The subtest of multiplicative compensations contains items 1to 4; the subtest of probability contains items 5 to 8; and the subtest of correlationscontains items 9 to 12.Test ItemsInsert test items about here(see next 4 pages)Scoring CriteriaThe correct answers for the test items are follows.Subtest I: 1. C 2. B 3. A 4. BSubtest II: 5. D 6. B 7. D 8. CSubtestlil: 9.D 10.A 11.C 12.AScore 1 point for each correct answer to an item. A subtest score is the sum of itsitem scores. An individual test score is the average of the scores of the 3 subtests, that is,(subtest 1+subtest 2+subtest 3)73.181Three cups.(Cup D, CupE, and CupF) are partially filledwith water.Beside the threecupsare threeballs of clay.These three ballsare exactly thesame sizeas each other. Thefirstball is placedin Cup Das shown. The waterlevel in CupD rises. Beforeplacing thesecondball intoCup E. itis flattened intoa pancake shapeas shown. Thethird ball ofclay isbroken intofive piecesas shownand then placedinto CupF.1. What doyou think willhappen to the waterlevel in CupE when this pancakeshaped pieceofclay is placedinto it?A. The waterlevel will riseup higher than thelevel in cupD.B. The waterlevel will riseto half the levelof cup D.C. The waterlevel will goup to the sameheight as thatin cup D.D. The waterlevel will riseto one—fifth theheight of thatin cup D.2. What isthe reason foryour answerto the questionjust above?A. The pancakeshape takes upmore space.B. The ballswere the samesize at the start.C. The pancakeshape is flat andtherefore It takesup less space.D. The ball andpancake weighthe same.3. What do you thinkWill happen to thewater levelin Cup F whenthe five small ballsof clayare placed inIt?A. The waterlevel will go upto the same heightas that in CupI).B. The water levelwill NOT riseup as high as thatin Cup D.C. The waterlevel will riseup higher thanthe level in CupD.I). The waterlevel will riseone— fifth theheight as thatin Cup D.4. Whatis the reasonfor your answerto the question justabove?A. The five bailsof clay takeup more space.B. The balls werethe same sizebcfore the oneball was brokeninto pieces..C. The five smallbails takeup less room.D. The five smallballs weigh thesame as the onelarge bail.DEFDEF182In a new gameof chance, six plaintokens, six stripedtokens and sixdotted tokens are placedin a boxas pictured above.The box is heldahove your headso that you cannotsee the tokens.You are askedto draw one tokenout of the box.5. What do youthink your chancesare of drawinga striped tokenon your very first draw?A. One chanceout—of—two.B. One chanceout—of—eighteen.C. One chanceout—of—twelve.D. One chanceout—of-three.6. Why didyou choose youranswer for thequestion justabove?A. My chancesare the sameas those for flippinga coin and gettingheads.B. Mychances are basedon the fact thatthe numberof striped tokens hasto be comparedtothe total numberof tokens.C. My chancesare good to draw itin the first two orthree draws becauseI am lucky.D. My chancesarc based on thefact that thereare twelve tokensthat arc not striped andIneed to eliminatethese first.183There is a gameon a well—known TVquiz show that contestantsplay to win a newcar. Seventokens are placedIn a cloth bag. Threetokens contain anX. if these three tokensare drawnfrom the bag beforethe four numbersin the price ofthe car, the contestantloses. If,however, the contestantdraws the fournumbered tokens beforedrawing the thirdtoken markedwith an X, thecontestant wins anew car. Each timea token is drawn it remainsout of the bag.The following questionsare based onthis game.7. If a contestantdraws 3 numberedtokens and 1 tokenmarked X, whatare the chancesofwinning the car onthe next draw?A. Three— out—of—sevenB. Three— out—of— fourC. Two—out—of—threeD. One-out—of— three8. What is the reasonfor your answer tothis question?A. There are threetokens withoutnumbers that havCto be taken into account.B. Threeof the numbered tokenshave alreadybeen drawn andthere are four numberedtokensin all.C. Two of theremaining tokenscontain X’s out ofthe three possibletokens from whichyoucan draw.D. Thereis only one numberedtoken that remainsout of the totaL1849. Can you find a relationship betweenbody color and leg sizefor this type of dog, onthebasis of these 16cards?A. No, because there Is an evennumber of black and ofwhite dogs with shortlegs.B. No, because 8 dogs haveshort legs and 8 dogs havelong legs and thereforethere is norelationship.C. Yes, because allof the black dogs have shortlegs.D. Yes, because most ofthe black dogs have long legsand most of the whitedogs have shortlegs.10. What arc the chancesof a black dog havinglong legs based on the16 cards above?A. Six— out— of—eightB. Four—out—of—eightC. One—out—of—fourD. Nine— out— of—sixteen11. What are the chances ofa white dog having longlegs based onthese 16 cards?A. One-out—of—sixB. One-out—of—eightC. Two— out—of—eightD. One-out—of sixteen12. What arc the chancesof a black dog having shortlegs based on these16 cards?A. Two-out—of—eightB. Three— out— of—eightC. Three-out—of—sixteenD. No chanceat allYou are given a set of 16cards. Each cardhas a picture of a hounddog which is either blackor white in color, and who haseither long or short legs.Card 1 representsa black dog withlong legs. The followingquestions are tobe answered on the basisof these 16 cards.185InterpretationA score of 0 to 1 is interpreted as the absence of the minimal ability for formalreasoning due to insufficient evidence. A score of greater than 1 to 2 is interpreted as atransitional development of the minimal ability for formal reasoning. A score of greaterthan 2 to 3 is interpreted as a partial mastery of the minimal ability for formal reasoning.Finally, a score of greater than 3 to 4 is interpreted as a full mastery of the minimalability for formal reasoning. However, it must be emphasized that full mastery here doesnot refer to the full mastery of the maximal ability for formal reasoning which could berepresented as the mastery of all of the eight concepts of formal operations.Technical information about ATFRIn a multi-trait, multi-method validity study of the ATFR, the test-retestreliabilities yielded were of the order of .76 to .89 (Arlin, 1982). For the total test, theHoyt estimates of reliability ranged from .71 to .89. The Cronbach Alphas for the totaltest composites ranged from .60 to .73 (Arlin, 1984b).186Appendix CThe Test of Problem Finding (PF)Test DescriptionIn this study, this test is used to tap the minimal presence of postformal reasoningspecific to the model of Problem Finding. This test, originally known as the “ArlinProblem Finding Task” (Arlin, 1975, 1975-76), was designed to assess the ability ofproblem finding in the cognitive domain. According to Arlin (1975), problem findingwas operationally defmed in terms of three conditions: 1) a problematic situation; 2) anopportunity for subjects to raise questions; and 3) a way of categorizing the questionsraised.Thus the problem finding task consisted of a problematic situation: an array oftwelve objects. This array was accompanied by a set of directions which provided thesubjects with the opportunity, in a five-minute time period, to raise as few or as manyquestions as they could. Finally the data were analyzed according to the “intellectualproducts” categories of Guilford’s structure of the intellect model (1956).The test is in pencil-and-paper format.Test ItemsInsert test items about here(see next 2 pages)Scoring CriteriaThe data are analyzed according to the “intellectual products” categories ofGuilford’s structure of the intellect model (1956). The questions raised by the subjectsare categorized according to the following: 1) units, 2) classes, 3) relations, 4) systems,5) transformations, and 6) implications.187PROBLEM FINDING TASKPlease read the following instructions carefully before proceeding with this instrument:Please time yourself for: 5 minutes.In five minutes, please make up as few or as many auestions as you can about any objector objects that are listed and illustrated on the attacked task sheet. Your questions cantake any form that you wish them to take. They can be brainteasers, puzzles to solve,novel questions. An example is: “Can you form four triangles out of these six matchsticks?”. Your questions can be any type that you wish them to be. The only thing thatyou have to remember is that for each of your questions you must refer to one or more ofthe objects that are listed and illustrated on the attached response sheet.Thank you.188SOMEOBJECTSAILIN PROBLEM FINDINGTASi(Arlin,1975, 1975—76,19?C-clampblack woodenblock(2cm. x 2 cm.)plain woodenblock (1cm. x1 cm.)small indexcard (3” x5”) with a dime-sized holein the center.25 cent piecesmall boxtopsmall boxbottomsmall coloredcandleswoodenmatchesthumbtacks2-meter longcordspair ofscissors.1.2.3.4.5.6.7.8.1111111361021189Definitions and examples of the above six intellectual products categories arepresented in the following.The Intellectual Products CategoriesCategory Definition Example1. Units2. ClassesBasic units ofinformat ionClass can be embodiedusing different sets ofparticulars“How many objectsare there here?”“Can I arrangethese according tosize or color orshape?”3. Relations4. Systems5. Transformations6. ImplicationsConnections betweenobjects or units suchas opposition, part-whole, agent-action, etc.To talk about rules,principles, orders,orientations, andstructures is tospeak of thepsychological productof system.A transformation isany kind of changesuch as expanding,reversal, interchange,and so on.A connection betweentwo units ofinformation. Relationsare definable kinds ofconnections ... comesnearest to thetraditional notion ofassociation.“If this paper’shole was bigger, Icould put thisquarter through it.Maybe, can I put thequarter through thehole without rippingit?”“I bet this box,open up, how do youopen it, there is away, isn’t there?”“If you were giventhis steel thing,what could youchange it into?What could youmake?”“In what ways canyou arrange theobjects on the tableto represent how youfeel at thismoment?” “How couldThese matches beman’s enemy?”Note. From the chapter “New Psychological Conceptions ofMemory” in Intelligence, Creativity and their EducationalImplications, by J. P. Guilford, 1968.190For the purpose of this study, the original scoring criteria were adapted in order totap the minimal presence of postformal reasoning specific to the model of ProblemFinding. A subject’s response would be scored according to the following 3 groupings ofthe above 6 categories: score 1 for the presence of category 1, 2 or 3; score 2 for thepresence of category 4; and score 3 for the presence of category 5 or 6 both of whichrepresent the presence of postformal reasoning.When the values of the yielded item scores vary, the highest score value would betaken as the individual test score to indicate the highest level of performance attained bythe subject.Should there be more than one rater, the final score would be the average of theindividual test scores provided by the different raters.InterpretationA score of 1 to less than 2 would be interpreted as the absence of postformalreasoning specific to the model of Problem Finding. A score of 2 to less than 3 would beinterpreted as the transitional development of postformal reasoning specific to theaforementioned model. A score of 3 would be interpreted as the minimal presence ofpostformal reasoning specific to the aforementioned model.Technical information about Arlin Problem Finding TaskArlin (1975/76) reported that the inter-rater reliabilities for classificationaccording to the six intellectual products categories were of the order of .80.191Appendix DThe Test of Dialectical Reasoning (DR)Test DescriptionIn this study, this test is used to tap the minimal presence of postformal reasoningspecific to the model of Dialectical Reasoning.The original test designed by Basseches (1980) consists of a set of structuredquestions to be administered through an interview. The content of these questions isadapted for use in this study. The test is in pencil-and-paper format. The adapted itemsare presented in the following.Test ItemsPlease respond to the following questions about “saving the environment”.1. How would you go about deciding what does “saving the environment” mean?2. How do you think “saving the environment” is being done in your community (e.g.your family, school, town)?3. What do you see as the relation between your idea about “saving the environment”and your experience and activities as a member of your community?4. Some people believe in “saving the environment”. Others think that it could causemajor problems in the country such as the loss of jobs, etc. How do you feel aboutthis? What is your opinion?Scoring CriteriaThe original scoring criteria were designed to produce a Dialectical SchemataIndex. The presence of dialectical reasoning would be scored according to 24 dialecticalschemata (or “moves in thought”) which are organized into 4 categories of schemata. Forthe purpose of this study, a simplified version of Arlin’s adaptation of Basseches’ scoringsystem is used.In the adapted scoring criteria, a subject’s responses are scored for the presence ofthe following 4 categories of schemata.A. A Motion-oriented schemata1. Thesis-antithesis-synthesis movement in thought2. Affirmation of the primacy of motion3. Recognition and description of thesis-antithesis-synthesis movement4. Recognition of correlativity of a thing and its others5. Recognition of ongoing interaction as a source of movement6. Affirmation of the practical or active character of knowledge7. Avoidance or exposure of objectification, hypostatization, and reification8. Understanding events or situations as moments (of development) of a processB. Form-oriented schemata9. Location of an element or phenomenon with the whole(s) of which it is a part10. Description of a whole (system, form) in structural, functional, or equilibrationalterms11. Assumption of contextual relativismC. Relationship-oriented schemata12. Assertion of the existence of relations, the limits of separation and the value ofrelatedness13. Criticism of multiplicity, subjectivism, and pluralism19214. Description of a two-way reciprocal relationship15. Assertion of internal relationsD. Meta-formal schemata16. Location (or description of the process of emergence) of contradictionsor sources ofdisequilibrium within a system (form) or between a system (form) and externalforces or elements which are antithetical to the system’s (form’s) structure17. Understanding the resolution of disequilibrium or contradiction in termsof a notionof transformation in developmental direction18. Relating value to (a) movement in developmental direction and/or(b) stabilitythrough developmental movement19. Evaluative comparison of forms (systems)20. Attention to problems of coordinating systems (forms) in relation21. Description of open self-transforming systems22. Description of qualitative change as a result of quantitative change within a form23. Criticism of formalism based on the interdependence of form and content24. Multiplication of perspectives as a concreteness-preserving approach to inclusivenessScore 1 for any schema in the following 3 categories of schemata: the motion-oriented schemata, the form-oriented schemata and the relationship-oriented schemata.Score 2 for schema 16 in the meta-formal schemata (location of contradictions)which is taken in this study to represent the transitional development of postformalreasoning, because the subjects in the original study who had the ability to employ thisschema also included those classified under elementary dialectical reasoning.Score 3 for any schema in the meta-formal schemata (excepting schema 16)which are taken to represent the presence of postformal reasoning, because most of thesubjects in the original study who had the ability to employ these schemata wereclassified under intermediate or advanced dialectical reasoning.When the values of the yielded item scores vary, the highest score value would betaken as the individual test score to indicate the highest level of performance attained bythe subject.Should there be more than one rater, the final score would be the average of theindividual test scores provided by the different raters.InterpretationA score of 1 to less than 2 would be interpreted as the absence of postformalreasoning specific to the model of Dialectical Reasoning. A score of 2 to less than 3would be interpreted as the transitional development of postformal reasoning specific tothe aforementioned model. A score of 3 would be interpreted as the minimal presence ofpostformal reasoning specific to the aforementioned model.193Appendix EThe Test of Relativistic Operations (RO)Test DescriptionIn this study, this test is used to tap the minimal presence of postformal reasoningto the model Relativistic Operations.This test is adapted from one of the six problem sets, namely the “Bedroom”problem set, developed by Sinnott (1984). These 6 problem sets were originallydesigned to assess the presence of both formal and relativistic operations. However, onlyrelativistic operations are scored in this adapted version.The rationale for selecting the “Bedroom” problem set is that it is argued to beone of the more discriminative problem sets for detecting the presence of relativisticoperations, specifically self-referential ordering of multiple solutions. (For substantialsupport of this rationale, see technical information about RO presented at the end of thetest description.)This is a pencil-and-paper test containing one problem set.Test ItemA family consisting of a mother in her forties, a father in his forties, a 10-year-oldgirl, a 12-year-old girl, and a 15-year-old boy live in a small two-bedroom house. Oneof the bedrooms is large and has a single bed; the other bedroom also has a single bed.This summer the family learns that a grandfather who lives alone in a one-bedroomapartment two blocks away can no longer live alone. He might move in with the family.Question: What are all the possible ways that the six persons can use the two bedroomsin the house? Explain your answer.Scoring CriteriaResponses are scored for the presence of the relativistic operations listed below(Sirmott, 1984p.314):1. Metatheory shift: There is the production of abstract and practical (real-life)solutions as well as a shift between conflicting abstract and real a priories. This shift isstated by the subject. The solution always included problem definitions. For example,the subject might ask whether we want the hypothetical solution that is logical on paperor the solution that would really be viable. (The respondent may or may not thenproceed to give both solutions.)2. Problem definition: There is a statement of the meaning and demands of theproblem for the subject. There is also the decision to define problems in a certain,chosen way. The subject indicates a change in the types of parameters from solution tosolution. Defining the problem is the first concern, but the subject need not givealternative solutions since these solutions might be precluded by the problem definition.The problem definition may include a metatheory shift. For example, the subject mightwonder what the real problem is, whether it is the need to have peace in the family or touse all the space. The subject might then decide to treat it like an algebra problem.3. Process/product shift: There is a description of a process as one answer andan outcome as another answer. Or there may be a description of two processes thatachieve the9 same outcome. Often there is a statement by a subject that there is a solutionand that finding the solution is actually a never-ending process. There may be adiscussion of process differences in arriving at two different outcomes.1944. Parameter setting: The subject names key variables to be combined or madeproportional in the problem other than those given in the written demands of theproblem. Often the subject explicitly writes out key variables. Alternatively she or hemay change the variables that limit the problem from solution 1 to solution 2. Parametersetting differs from problem definition in that it is less inclusive.5. Pragmatism: One can choose a best solution among several, or, one canchoose the best variant of a solution that has two processes. For example, the subjectmight say that if you want the most practical solution, it’s number 2, but if you want thequickest, easiest solution, it’s number 1. This is the only operation that cannot be given apassing score unless the subject actually gives more than one solution.6. Multiple solutions: There is a direct statement that there are many correctsolutions intrinsic to a problem with several causes, or that no problem has only onesolution. Also, the subject may create several solutions. For example, the subject mightrespond that he or she sees four solutions that could be termed correct or there arelimitless arrangements that would be correct if your change the constraints.7. Multiple causality: There is a statement that multiple causes exist for anyevent or that some solutions are more probable than others. For example, some subjectsstate that the solution depends on all past relations of the persons in the problem. Assuch, when the three persons in the problem get together anything could happen,depending on personalities and on how each reacts.8. Paradox: The subject gives a direct statement or question about perceived,inherently conflicting demands that are integral to the problem, not simply two solutionswith different parameters. For example, the Bedroom Problem can be read in twoconflicting ways. The subject notices that two different things are being said at once,both of which could change the way the problem should be solved.Score 1 for the total absence of the above listed relativistic operations typicallyexemplified by the giving of a single solution.Score 2 for the presence of the sixth relativistic operation, i.e. Multiple Solutiois,but without a direct statement implying that there can be an indefinite number ofsolutions, because the subjects might hold the opinion that the number of solutions isfinite and they are merely naming a few solutions. There is also the possibility that someor all of the solutions given are irrelevant.Score 3 for the presence of at least one of the above relativistic operations. IfMultiple Solutions was given as the only relativistic operation, the subject would alsohave to give a direct statement implying that there can be an indefinite number ofsolutions in order to receive a score of 3.When the values of the yielded item scores vary, the highest score value would betaken as the individual test score to indicate the highest level of performance attained bythe subject.Should there be more than one rater, the final score would be the average of theindividual test scores provided by the different raters.InterpretationA score of 1 to less than 2 would be interpreted as the absenceof postformalreasoning specific to the model of Relativistic Operations. A score of 2to less than 3would be interpreted as the transitional development of postformal reasoning specific tothe aforementioned model. A score of 3 would be interpreted as the minimal presence ofpostformal reasoning specific to the aforementioned model.195Technical information about ROFindings of Sinnott’s studies (1984, 1989) revealed that the social problem setswere most often stimuli for self-referential thought and were sometimes the only problemthat occasioned such a pattern. The “Bedroom” problem set elicited this response patternin seven of the eight cases selected from a pool of 80 subjects for an individual-intensiveanalysis. Findings also revealed that of the five social problem sets, the “Bedroom”problem set differed most from the abstract “Alphabet” problem set in that the“Bedroom” problem set was associated with more cases of multiple solutions(F(1,73)=25.73, p<.OOl). The abstract “Alphabet” problem set was most unlikely toelicit relativistic operations. The above information could be used as support to theselection of the “Bedroom” problem set for use in the present study.Regarding the use of the eight relativistic operations, Simiott (1984) reported thatno one individual subject articulated a complete profile of these relativistic operations.In addition, not every problem elicited statements confirming the presence of all eightoperations. Similar findings were also reported by Lee (1989).196Appendix FThe Test of Reflective Judgment (RJ)Test DescriptionIn this study, this test is used to tap the minimal presence of postformal reasoningspecific to the model of Reflective Judgment (King, Kitchener, Davison, Parker &Wood, 1983; Kitchener & King, 1981).This test is adapted by Arlin from the “Reflective Judgment Interview” (RJI)copyrighted by King and Kitchener in 1978. The original RJI was designed to assesshow people justify their beliefs or decisions when faced with ill-defined problems.The original version of RJI is comprised of four ill-defined problems and a set ofstandardized probe questions. The four problems represent four domains: history,science, current events and religion (see King et al., 1983; Kitchener & King, 1981 forexamples). Each problem contains two contradictory points of view. Subjects are askedto state and justify their point of view about the issues in each problem. The probequestions are designed to elicit information from subjects about how certain they areregarding their knowledge about each issue, how they have obtained that knowledge andhow they justify their beliefs about the issue.The present test adopts one of the four subtests from the RH, namely the “FoodAdditives” subtest which falls within the domain of science. The rationale for selectingthis subtest is that it is argued to be the most neutral among the four problems in terms ofvalue judgment.This test is in pencil-and-paper format.Test ItemsDilemma:There have been frequent reports about the relationship between chemicals that are addedto foods and the safety of these foods. Some studies indicate that such chemicals cancause cancer, making these foods unsafe to eat. Other studies, however, show thatchemical additives are not harmful, and actually make the foods containing them moresafe to eat.Questions:1. What do you think about these statements?2. How did you come to hold that point-of-view?3. Can you ever know for sure that your position is correct? How or Why not?4. When people differ about matters such as this, is it the case that one opinion is rightand one is wrong?(If yes) What do you mean by right?(If no) Can you say one opinion is better and one is worse? Why or Why not?(If yes) What do you mean by better?5. How is it possible that people can have such different points-of-view about thissubject? What does it mean when experts in the field disagree?Scoring CriteriaThe responses are scored according to the match between the type of reasoningobserved in the responses and the type of reasoning described in the7 stages ofdevelopment of reflective judgment (King & Kitchener, 1978). These developmentalstages are presented in the following:197Stage 1: Subjects use the simplest of black and white, concrete categories.Knowledge is seen as absolute, and authorities are seen as the source of knowledge.Problems are solved simply by following rules, tradition, or the norm. Judgment is seenas unnecessary since alternatives are not acknowledged.Stage 2: Subjects perceive alternative views but reject them withoutexamination. They believe that “right” answers exist and that authorities usually “have”them. Their arguments are often not coherent; they offer pieces of unrelated informationas “evidence”, and then decide on the basis of the norm or others’ views.Stage 3: Subjects acknowledge the existence and temporary legitimacy ofdifferent views. Authority and knowledge become further separated and they begin tosee authorities as “biased” or arbitrary. Without their formerly-held absolutes, decision-making is confusing. Everyone’s view is seen as equally correct andJor equally biased.Decisions are based predominantly on personal whim or bias.Stage 4: Subjects acknowledge the lack of absolutes in some areas, but notothers. They begin to evaluate evidence, but do not understand that evidence entails aconclusion. They use both unsupported belief and considered judgment in decision-making. Cynicism toward the expertise of authorities is evidenced.Stage 5: Subjects here begin to understand that knowledge is embedded in acontext and that a frame of reference is important for understanding a point of view.Authorities are seen as experts who have a reasoned point of view. They evaluateevidence on several sides of issues, from several perspectives. They try to present abalanced view of an issue, but do not integrate evidence into their own view.Stage 6: Subjects acknowledge different points of view, they analyze themseparately, and see the need for synthesis. Usually they rely on the synthesis of others(e.g. experts) rather than offering a synthesis of their own. They rely on experts onlyafter personally examining the evidence and alternatives. That is, experts’ views, too, areseen as subject to evaluation.Stage 7: These subjects present an examined point of view. It is based on anintegration of evidence, the opinions of experts, as well as their own personal experience.They understand that one’s point of view may need to be reformulated in light ofadditional formation gained in the future. Their point of view is presented as beingprobably correct.Score 1 for the presence of stage 1, 2 or 3.Stages 1-3 imply that there is no recognition that real uncertainty of knowledgeexists. Rather it would be assumed that ultimately uncertainty can be translated tocertainty, for example, by consulting an authority or by waiting until the truth is knownsometime in the future.Score 2 for the presence of stage 4.Stage 4 implies the recognition of the uncertainty of knowledge in some areas butnot in others and that knowledge is uncertain for situational reasons. Stage 4 isconsidered more advanced than Stage 3 in that there would be the recognition thatuncertainty is not a temporary condition of the knowing process but a legitimate part ofit.Score 3 for the presence of stage 5, 6 or 7.Stages 5-7 imply the recognition of the real uncertainty of knowledge but withsubtle differences in the understanding of the causes of uncertainty. What appears to198advance in the later stages is the understanding of how judgments can be made in theface of this uncertainty.When the values of the yielded item scores vary, the dominant score value (themost frequently occurred) would be taken as the individual test score to indicate thedominant stage of reflective judgment demonstrated by the subject.Should there be more than one rater, the final score would be the average of theindividual test scores provided by the different raters.InterpretationA score of 1 to less than 2 would be interpreted as the absence of postformalreasoning specific to the model of Reflective Judgment. A score of 2 to less than 3would be interpreted as the transitional development of postformal reasoning specific tothe aforementioned model. A score of 3 would be interpreted as the minimal presence ofpostformal reasoning specific to the aforementioned model.Technical information about RJIIn general, inter-rater reliability was reported to be moderate to high, dependingon the heterogeneity of the sample tested, and the inter-rater agreement for first-roundratings (the most conservative index) consistently ranged between 70 and 80 percent(Kitchener & King, 1990). Test-retest reliability on four small homogeneous samplesover a three-month period ranged from .71 to .83 (Sakalys, 1982). Cronbach’s alpha, ameasure of internal consistency, ranged from .62 (Welfel, 1982) to .92 (Kitchener &King, 1981) for a homogeneous and a heterogeneous sample respectively.Note. The responses obtained from the pencil-and-paper format of this test may not becomparable to those obtained from the original interview format of RH. Consequentlytheir respective scores may not be comparable.Appendix GA Sample of the Complete Set of Tests199200THE UNIVERSITY OF BRITISH COLUMBIADepartment of Educational Psychologyand Special Education________Faculty of Education_______2125 Main Mall_____Vancouver, B.C. Canada V6T I Z4Tel: (604) 822-8229Fax: (604) 822-3302INTRODUCTORY NOTESA study about the devçlopment of reasoning ability.(Project title:-“Nonabsolute/ relativistic Thinking: a Possible UnifyingCommonality underlying theModels of Postformal Reasoning”)Dear Participant:Thank you very much for volunteering to participatein this study. Brieflyspeaking, the purpose of this study is to try to understand how peoplereason. It is hopedthat the benefits of this study will help us to understand betterthe development ofreasoning ability and will contribute towards the improvementof education.You will be asked to do a pencil-and-papertask made up of a set of questions.You are free to refuse to participate or to withdraw atany time. Your refusal orwithdrawal will not affect your grades or class standingif you were contacted throughyou teacher or course instructor. The amount of time requiredto answer this set ofquestions is I session of about 1 1/2 hours or 2 sessions of about45 minutes each. Butyou are free to finish in a shorter or longer period of time.Your name will be kept confidential, as you willbe assigned a code number.Results will be analyzed by group, not by individuals using this code number.Thank you for your willingness to participate inthis study. If the pencil-and-paper task is completed it will be assumed that consenthas been given to participate inthis study.If you have any further questions, please contact us at the phone numbers below.Identification of investigators:Dr. Patricia Arlin, Ph.D. (Faculty Advisor)Professor and HeadDepartment of Educational Psychology & Special EducationUniversity of British Columbia(Phone: 822-6223)Bernice Yan (Doctoral Student)Ph.D. CandidateDepartment of Educational Psychology & Special EducationUniversity of British Columbia(Phone: 738-9923)Age:________Sex:________ EducationalLevel:201SECTION I. Please choosethe best answer foreach question.Three cups,(Cup D, CupE, and Cup F) are partiallyfilled with watci.Beside the threecupsare three ballsof clay. These threeballs are exactly thesame size as cachother. The firstball Is placed InCup D as shown.The water level inCup D rises. Beforeplacing thesecondball into CupE, It is flattenedinto a pancakeshape as shown.The third ballof clay isbroken into fivepieces as shownand theta placed intoCup F.1. What do youthink will happento the water level inCup E when thispancake shapedpiece ofclay is placedinto It?A. The water levelwill riseup higher than the levelin cup D.B. The water levelwill rise tohalf the level ofcup D.C. The water level willgo up to the sameheight as thatin cup D.D. The water levelwill rise to one—fifththe height ofthat in cupD.2. What Is thereason for youranswer to the questionjust above?A. The pancake shapetakes up more space.B. The balls werethe same sizeat the start.C. The pancake shapeIs flat and thereforeit takes up lessspace.D. The ball andpancake weighthe same.3. What do you thinkwill happento the water levelin Cup F whenthe five small ballsof clayare placed inIt?A. The water levelwill go up to thesame heightas that in CupD.B. The water levelwill NOT riseup as high as thatin Cup D.C. The water level willrise up higherthan the level inCup D.I). The waterlevel will rise one—filththe height as thatin Cup D.4. What Isthe reason for youranswer tothe question justabove?A. The fiveballs of clay takeup more space.B. The balls werethe same sizebefore the one ballwas brokeninto pieces.C. Tue five smallballs take upless room.D. The five smallballs weighthe same as the onelarge ball.DEFDF202In a new gameof chance, sixplain tokens,six striped tokensand six dottedtokens are placedin a boxas pictured above.The box is heldabove your headso that you cannotscó the tokens.You are askedto draw onetoken out of thcbox.5. What do youthink your chancesarc of drawinga striped token onyour very first draw?A. One chanceout—of—two.B. One chanceout— of—eighteen.C. One chanceout— of—twelve.D. One chanceout—of—three.6. Why did youchoose your answerfor the questionjust above?A. My chances arethe same as thosefor flipping a coinand gettingheads.B. My chancesare based on the factthat the numberof striped tokens hasto be compared tothe total numberof tokens.C. My chances aregood to drawit in the first twoor three draws becauseI am lucky.D. My chancesare based onthe fact that there arctwelve tokens thatarc not striped and Ineed to eliminatethese ftrst203There is a game ona well—knownTV quiz showthat contestantsplay to win, a newcar. Seventokens are placedin a cloth bag. Threetokens contain anX. if these three tokensare drawnfrom the bagbefore the four numbersin the priceof the car, thecontestant loses. If,however, thecontestant drawsthe four numberedtokens before drawingthe third token markedwith anX, the contestant winsa new car. Each timea token is drawnit remains out of thebag.The followingquestions are basedon this game.7. If a contestantdraws 3 numbered tokensand 1 token markedX, what are thechances ofwinning the caron the next draw?A. Three— out— of—sevenB. Three—out—of—fourC. Two—out—of—threeD. One—out—of—three8. What is the reason for youranswer to thisquestion?A. There arethree tokens withoutnumbers that havCto be takeninto account.B. Three ofthe numbered tokenshave already beendrawn and thereare four numberedtokensin all.C. Two of the remainingtokens containX’s out of the three possibletokens from whichyoucan draw.D. There is onlyone numbered tokenthat remains outof the total.2049. Can you find a relationshipbetween body color andleg size for this typeof dog, on thebasis of these 16cards?A. No, because there is an evennumber of blackand of white dogs withshort legs.B. No, because 8dogs hare short legsand 8 dogs have longlegs and therefore thereis norelationship.C. Yes, because all of the blackdogs have short legs.D. Yes, because most of the blackdogs have long legs and mostof the white dogs haveshortlegs.10. What arc the chances ofa black dog havinglong legs based on the16 cards above?A. Six—out— of—eightB. Four—out—of—eightC. One—out—of—fourD. Nine—out—of—sixteen11. What are the chancesof a white dog havinglong legs based onthese 16 cards?A. One—out—of—sixB. One— out—of—eightC. Two— out—of—eightD. One—out—of sixteen12. What arc the chancesof a black dog having shortlegs based on these16 cards?A. Two— out—of—eightB. Three-out—of—eightC. Three—out—of—sixteenD. No chanceat allYou are givena set of 16 cards. Each cardhas a picture ofa hound dog which is eitherblackor white in color,and who has eitherlong or short legs.Card I representa black dog withlong legs. The followingquestions arc tobe answered on the basisof these 16 cards.205A small toy wind—upturtle is placedon a shaded stripof paper. The paperstrip is linedupalong the edgeof a boardas shown in the picture.The turtle canbe moved along thepaperstrip. Thepaper strip canalso be moved alongthe board. Both thetoy and the paper stripcanbe moved forwardor backward. Thetoy, the end ofthe paper strip,and the startingpoint onthe board areall lined up asshown.13. If the turtlemoves forwardat the same speed thatthe paper strip movesbackward, how farwill the turtlebe from the startingpoint aftera short time (as long astheturtle isstill on the strip of paper)?A. it would be atthe starting point.B. One—fourth thedistance of the paperstrip from the startingpoint.C. Double thedistance of thepaper strip from thestarting point.D. It wouldbe behind the startingpoint.14. If the turtlemoves forwardat 1/3 the speedthat the paper stripmoves backward,wherewould the turtle beafter a short periodof time (as longas the turtle is still on(lie strip of paper)?A. Three timesas far forward as thepaper strip is backwardfrom the startingpoint.B. One—thirdthe distance in frontof the starting pointas the paper strip isbehind thestarting point.c. It would be behindthe starting point.D. As far in frontof the startingpoint as the cud ofthe paper stripis in back ofit.206Two peopleare sitting on this trainas it passes througha long tunnel in the sideof a mountain. Mr.Red (R) is sitting atthe front of the trainand Mr. Blue (B)is sitting atthe back ofthe train. For the followingtwo situations, decidewhether Mr. R and Mr. Bwillstay in the tunnel forthe same amountof time..15. SiTUATION 1: After thetrain enters the tunnelMr. R gets up fromhis seat in the front,and walks back tosit with Mr. B. Howmuch time altogether willMr. R spend in thetunnel?A. Less time in thetunnel than Mr.B.B. Twice the timein the tunnel as Mr.B.C. The same amount oftime in the tunnel asMr. B.I). More time inthe tunnel than Mr.B.16. SITUATION 2: After the trainhas entered the tunnel,Mr. B gets up from hisseat in theback. He walks forwardto sit with Mr.R. Halfway on his tripforward, he decidesto go back to his seatfor his paper. Hegets his paper andthen goes forward againand joins Mr.R, while the train is stillin the tunnel. Howmuch time did Mr. Bspend in the tunnel?A. Less time in the tunnel thanMr. R.B. More time in thetunnel than Mr.K.C. One-and-one-halfas much time in the tunnelas Mr. R.D. The same amountof time in the tunnel asMr. K.207SECTION II. Please answer the following questions.(PART A)1. “A” grows 1 cm per month. “B” grows 2 cm per month.Who is taller?ANSWER:Why? Explain your answer.2. City “A” is120C. City “B” is100C.Which city is warmer?ANSWER:Why? Explain your answer.3. “A” can run at 15 k.p.h. “B” can run at 12 k.p.h.Who would arrive earlier?ANSWER:Why? Explain your answer.4. “A” weighed 8 kg. “B” weighed 9 kg.Which one is heavier?ANSWER:Why? Explain your answer.208(PART B)1. How do you know about the world around you?a. through your senses (eyes, ears, nose, etc.)b. through your own interpretation (thinking).c. othersWhy? Explain your chosen answer.2. It is possible for you to understand something completely without doubt.a. agreeb. disagreec. othersWhy? Explain your chosen answer.3. When three persons have three different solutions to the same problem, at least one ofthem must be wrong.a. agreeb. disagreec. othersWhy? Explain your chosen answer.4. Some things will never change.a. agree (What are they?______________________________b. disagreec. othersWhy? Explain your chosen answer.209(PART C)PROBLEM FINDING TASKPlease read the following instructions carefiully before proceeding with this instrument:Please time yourself for: 5 minutes.In five minutes, please make up as few or as many questions as you can about any objector objects that are listed and illustrated on the attacked task sheet. Your questions cantake any form that you wish them to take. They can be brainteasers, puzzles to solve,novel questions. An example is: “Can you form four triangles out of these six matchsticks?”. Your questions can be any type that you wish them to be. The only thing thatyou have to remember is that for each of your questions you must refer to one or more ofthe objects that are listed and illustrated on the attached response sheet.Thank you.210ARLIN PROBLEMFINDINGTASK(Arlin, 1975,1975—76,197ISOMEO8JECTS1C-clamp1black woodenblock(2cm. X 2cm.)1plain woodenblock (1cm. X1 cm.)1small indexcard (3” x5”) with a dime-sized hole inthe Center.125 cent piece1small boxtop1small boxbottom3small coloredcandles6woodenmatches10thumb tacks22-meter longcords1pair ofscissors.1.13.4.5.6.7.8.211(PART D)Please respond to the following questions about “saving the environment”.1. How would you go about deciding what does “saving the environment” mean?2. How do you think “saving the environment” is being done in your community (e.g.your family, school, town)?3. What do you see as the relation between your idea about “saving the environment” andyour experience and activities as member of your community?4. Some people believe in “saving the environment”. Others think that it could causemajor problems in the country such as the loss ofjobs etc. How do you feel aboutthis? What is your opinion?212(PART E)A family consisting of a mother in her forties, a father in his forties,a 1 0-year-old girl, a12-year-old girl, and a 15-year-old boy live in a small two-bedroom house. One of thebedrooms is large and has a single bed; the other bedroom also has a single bed. Thissummer the family learns that a grandfather who lives alone in a one-bedroom apartmenttwo blocks away can no longer live alone. He might move in with the family.Question: What are all the possible ways that the six persons can use the two bedroomsin the house? Explain your answer.213(PART F)Dilemma:There have been frequent reports about the relationship between chemicals that are addedto foods and the safety of these foods. Some studies indicate that such chemicals cancause cancer, making these foods unsafe to eat. Other studies, however, show thatchemical additives are not harmful, and actually make the foods containing them moresafe to eat.Questions:1. What do you think about these statements?2. How did you come to hold that point-of-view?On what do you base that point of view?3. Can you ever know for sure that your position is correct?How or Why not?(to be continued)214(PART F)4. When people differ about matters such as this, is it the case that one opinion is rightand one is wrong?(If yes) What do you mean by right?(If no) Can you say one opinion is better and one is worse? Why or Why not?(If yes) What do you mean by better?5. Flow is it possible that people can have such different points-of-view about thissubject? What does it mean when experts in the field disagree?215Appendix HGlossary of Abbreviations and SymbolsFR Test of Minimal Formal ReasoningN/R Thinking Nonabsolute/ relativistic ThinkingN/R Tests:N/R-F Test of the Formal Form of N/R ThinkingN/R-PF Test of the Postformal Form of N/R ThinkingN/R-EV Test of the Epistemic View of N/R ThinkingPostformal Tests:PF Test of Problem FindingDR Test of Dialectical ReasoningRO Test of Relativistic OperationsRT Test of Reflective Judgmentis a necessary but not sufficient condition for216Appendix IExplanation of Fit Indices in Confirmatory Factor AnalysisCu-SQUAREChi-square statistics can be used to test whether there is any significant differencebetween the observed and the reproduced covariance/correlation matrices. Inconfirmatory factor analysis, contrary to conventional interpretation of Chi-squarestatistics, a small Chi-square value and high probability (p) level would indicate a goodfit. The degrees of freedom (df) would serve as a standard for judging the size of a Chisquare value. Some researchers proposed a Chi-square/df ratio(Q)of below 2 or 3 as acriterion of fit (Carmines & Mclver, 1981). Thus the size of CM-square is affected bythe number of parameters to be estimated.In this study, a significance level of p=O.05 is used. In other words, a CM-squarevalue associated with a probability level greater than 0.05 would be consideredsignificant.ROOT MEANS SQUARE RESIDUAL (RMR’)RMR can be interpreted as an average of the fitted residuals. Specifically, it isthe square root of the average of the squared fitted residuals. Theoretically, an RMR of0.00 indicates a perfect fit.STANDARDIZED ROOT MEANS SQUARE RESIDUAL (SRMR)SRMR represents the standardized RMR. Its interpretation is similar to that ofRMR. Theoretically, an SRMR of 0.00 indicates a perfect fit.GOODNESS OF FIT INDEX (GFI’GFI is based on the properties of the observed and the reproduced correlation(covariance) matrices. The index should be between 0 and 1 although it is theoreticallypossible for it to be negative. Theoretically, an GFI of 1.00 indicates a perfect fit.ADJUSTED GOODNESS OF FIT INDEX (AFGI)AGFI refers to an adjusted GFI for degrees of freedom in the model. The indexshould be between 0 and 1 although it is theoretically possible for it to be negative.Theoretically, an AGFI of 1.00 indicates a perfect fit.NORMED FIT INDEX (NFl’)NFl is based on the notion of improvement of fit provided by a given model ascompared with some baseline model. A general pattern of the baseline model has thenumber of factors set equal to the number of variables. The NFl may range from 0 to 1.Theoretically, an NFl of 1.0 indicates that the improvement of fit has reached amaximum limit. It is suggested that 0.9 could be used as a threshold (Bentler & Bonett,1980). Models with an NFl less than 0.9 can usually be improved substantially.NON-NORMED FIT INDEX (NNFI’)NNFI is similar to NFl except that it is adjusted for degrees of freedom. Unlikethe NFl, it is possible for the NNFI to have a negative value. Theoretically, an NNFI of1.0 also indicates that the improvement of fit has reached a maximum limit.
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Nonabsolute/relativistic (N/R) thinking: a possible unifying commonality underlying models of postformal.. Yan, Bernice Lai-ting 1995
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Title | Nonabsolute/relativistic (N/R) thinking: a possible unifying commonality underlying models of postformal reasoning |
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Yan, Bernice Lai-ting |
Date | 1995 |
Date Issued | 2009-06-04T20:47:16Z |
Description | This dissertation identified and addressed four of the unresolved issues pertaining to the proposition that nonabsolute/ relativistic (N/R) thinking is one of the possible unifying commonalities underlying the selected models of postformal reasoning, namely Problem Finding, Dialectical Reasoning, Relativistic Operations and Reflective Judgment. A total of 254 participants aged 10 to 48 and attending Grade 5 to doctoral studies were involved. Each participant was administered eight tests in pencil-and-paper format to measure eight different constructs of thinking. Different specific hypotheses were evaluated through different statistical approaches. The four identified issues were addressed as follows: Firstly, nonabsolute/ relativistic thinking was reconceptualized and operationally defined as a multidimensional and multilevel construct. Two dimensions were proposed: the basic form and the epistemic view. Within the basic form dimension, two levels were proposed: the formal and the postformal forms. Secondly, a battery of three tests was specifically designed by Arlin and the author to measure the different dimensions and levels of nonabsolute/ relativistic thinking. Thirdly, strong empirical evidence was obtained supporting the general hypothesis that nonabsolute/ relativistic thinking is a possible unifying commonality underlying the four selected postformal models. Within the construct of nonabsolute/ relativistic thinking, two dimensions, the basic form and the epistemic view, can be differentiated as hypothesized. Fourthly, empirical evidence was also obtained supporting the general hypothesis that nonabsolute/ relativistic thinking is an instance of both formal and postformal reasoning. Specifically within the basic form dimension, two qualitatively different forms, the formal and the postformal, can be differentiated as hypothesized. Findings also suggested that the development of a nonabsolute epistemic view might play a crucial role in the development of the postformal form. Therefore, the emergence of the postformal form can be explained by a paradigm shift from an absolute to a nonabsolute epistemic view. Performances in the tests of the postformal form and of the epistemic view in combination were found to be good predictors of performances in the selected postformal tests. Significant implications of the findings are that nonabsolute/ relativistic thinking represents a form of metamorphosis from closed-system to open-system thinking and it might serve as a potential springboard in the development of higher order thinking. |
Extent | 4582823 bytes |
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Reasoning (Psychology) Creative thinking. Relativity. |
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Thesis/Dissertation |
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File Format | application/pdf |
Language | eng |
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Retrospective Theses and Dissertations, 1919-2007 |
Series | UBC Retrospective Theses Digitization Project |
Date Available | 2009-06-04 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0088813 |
URI | http://hdl.handle.net/2429/8746 |
Degree |
Doctor of Philosophy - PhD |
Program |
Educational & Counselling Psychology & Special Education |
Affiliation |
Education, Faculty of Educational and Counselling Psychology, and Special Education (ECPS), Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 1995-05 |
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Japan | 1 | 0 |
City | Views | Downloads |
---|---|---|
Unknown | 34 | 17 |
Putian | 7 | 0 |
Lewes | 6 | 0 |
Columbia | 5 | 0 |
Ashburn | 5 | 0 |
Shenzhen | 4 | 69 |
Seattle | 4 | 5 |
Mountain View | 4 | 0 |
Redmond | 3 | 0 |
Findlay | 3 | 0 |
Tiran | 2 | 0 |
Columbus | 2 | 0 |
Vancouver | 2 | 0 |
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