“ABOUT AVERAGE” A PRAGMATIC INQUIRY INTO SCHOOL PRINCIPALS’ MEANINGS FOR A STATISTICAL CONCEPT IN INSTRUCTIONAL LEADERSHIP A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy in Education University of Regina by Darryl Milburn Hunter Regina, Saskatchewan April 2014 Copyright 2014: Darryl M. Hunter UNIVERSITY OF REGINA FACULTY OF GRADUATE STUDIES AND RESEARCH SUPERVISORY AND EXAMINING COMMITTEE Darryl Milburn Hunter, candidate for the degree of Doctor of Philosophy in Education, has presented a thesis titled, “About Average” A Pragmatic Inquiry into School Principals’ Meanings for a Statistical Concept in Instructional Leadership, in an oral examination held on April 1, 2014. The following committee members have found the thesis acceptable in form and content, and that the candidate demonstrated satisfactory knowledge of the subject material. External Examiner: *Dr. Jerald Paquette, Professor Emeritus, University of Western Ontario Supervisor: Dr. William R. Dolmage, Educational Administration Committee Member: Dr. Ronald Martin, Educational Psychology Committee Member: **Dr. Larry Steeves, Educational Administration Committee Member: Dr. Katherine Arbuthnott, Department of Psychology Chair of Defense: Dr. Ronald Camp, Kenneth Levene Graduate School *via SKYPE **via Teleconference Abstract This mixed methods, sequential, exploratory study addresses the problem, “How significant are statistical representations of ‘average student achievement’ for school administrators as instructional leaders?” Both phases of the study were designed within Charles Sanders Peirce’s pragmatic theory of interpretation. In the first, phenomenological phase, 10 Saskatchewan school principals were each interviewed three times and invited to read aloud three different student achievement reports. Principals generally held a “centre-of-balance” conception for the average, which related to perspectives deriving from their organizational position. Abductive reasoning, a proclivity to act upon “below average” student achievement, leadership through asking leading questions, an inquiry cast of mind, and other pragmatic principles were clearly apparent. No evidence was found that school administrators were constrained by normative statistics into a uniform outlook, nor into purely instrumental behaviour. In a succeeding, overlapping phase based in the psychophysics of perception, Saskatchewan school leaders (principals and vice-principals) (n=210) were randomly assigned to one of four groups and asked to read an achievement report depicting student performance as a distribution of scores on a criterion scale. School leaders’ dispositions to be rational-analytical or intuitive-experiential were measured pre-and post-reading. A MANCOVA revealed small but significant changes in school leaders’ dispositions depending on the way the report was framed. Small but significant interactions between valence and audience on a reader’s rationality were observed. Negatively-framed test scores effected greater changes than positively-framed test scores in diminishing school leaders’ beliefs in their rationality. Principals’ and vice-principals’ dispositions did not differ. i I conclude that reading reports which depict student achievements within a normative distribution has little statistical significance in changing leadership practice. However, school principals’ interpretations demonstrate the substantial practical significance of statistics when leading change. School administrators consider average student achievement not with the inferential patterns assumed within contemporary notions of heuristic irrationality, but rather as a reasoned form of inquisitive thinking and behaviour that has been formalized and comprehensively described in North American philosophy for over 100 years. ii Enter your skiff of Musement, push off into the lake of thought, and leave the breath of heaven to swell your sail. With your eyes open, awake to what is about or within you, and open conversation with yourself; for such is all meditation. It is, however, not a conversation in words alone, but is illustrated, like a lecture, with diagrams and with experiments. Charles Sanders Peirce Acknowledgements Primary thanks are extended to Dr. Rod Dolmage, who contests the law of averages, and who has unceasingly removed blockages on the road of inquiry. Dr. Larry Steeves generously opened many doors, especially to the expansive literature on instructional leadership. Dr. Ron Martin steered me through the burgeoning research on (ir)rational decision-making, enthusiastically helping with design questions. Dr. Katherine Arbuthnott has enhanced this project’s prospects, both practically and theoretically. The University of Regina’s Graduate Student Scholarships and Dean’s Scholarship Program represent only a portion of the support this campus has given me on so many occasions. A Jack and John Spencer Middleton Scholarship defrayed some travel expenses, while a Saskatchewan Innovation and Opportunity Graduate Scholarship enabled a link through the Social Sciences Research Laboratory at the University of Saskatchewan. A League of Educational Administrators, Directors and Superintendents award gave me confidence that the project was important. I acknowledge the Government of Saskatchewan’s tuition support, and am particularly appreciative for a Social Science and Humanities Research Council Doctoral Scholarship and a Killam Trust Pre-Doctoral Fellowship which underwrote my initial forays in this realm: this document illustrates Peirce’s dictum that probabilities play out in the long run. iii Post Defence Acknowledgement I am grateful to Dr. Jerry Paquette at the University of Western Ontario for underlining the necessity of critiquing our notions of causation, for highlighting distinctions between morality and ethics, and for emphasizing the virtues of remaining hesitant when interpreting statistics. iv Dedication The time and insights of the ten school principals I interviewed in depth and the efforts of another 210 Saskatchewan school principals and vice-principals, who completed an inventory of their beliefs while in the midst of other pressing issues, are most appreciated. Several senior administrators, on campus and off, have smoothed my path in several ways. This project was conceived in stages through advice I received on several Canadian campuses. Dr. Scott Goble at the University of British Columbia “conducted” me into Peirce’s writings. As foil and friend, Dr. James Rude at the University of Alberta pointed out that economists’ notions of utility were the wrong starting point. At the University of Toronto, Prof. Diane Gerin-Lajoie persuaded me that qualitative methods could illuminate quantitative matters, even though their grammars differ. Dr. Trevor Gambell, now emeritus at the University of Saskatchewan, has always exemplified that the “Will to Learn” works in symbiosis with the “Will to Believe.” A thoughtful question about pragmatism and decision-making, posed years ago by Dr. Doug Stewart at the University of Regina, has sparked much reading. Across this same campus, Dr. Don Sharpe kindly helped with many statistical questions. Of course, Judy has once again been my quiet hero, patiently tolerating yet another academic excursion. However, she insists my February 14 insight about averages will remain a gift to myself, not to her. She, like my parents and my children, has always waved encouragingly from shore while I tack across the lake of thought. But I dedicate this document to my grandparents who, though now departed, continue to whisper. v Table of Contents Abstract ........................................................................................................................ i Acknowledgements .......................................................................................................... iii Post Defence Acknowledgement ..................................................................................... iv Dedication …. .....................................................................................................................v Table of Contents ............................................................................................................ vi List of Tables ................................................................................................................... ix List of Figures ....................................................................................................................x List of Abbreviations, Symbols, Nomenclature ............................................................ xi Chapter 1: Introduction and Inception of the Study .....................................................1 1.1 Background of the Inquirer ........................................................................................1 1.2 Beliefs of the Inquirer ................................................................................................6 1.3 Beginnings of the Inquiry .........................................................................................11 Chapter 2: The Interpretation of Average Student Achievement ..............................16 2.1 Management and Meaning .......................................................................................16 2.2 Research Purpose and Questions ..............................................................................21 2.3 Contexts for Considering the Average