Strategy Use and Basic Arithmetic Cognition in Adults

STRATEGY USE AND BASIC ARITHMETIC COGNITION IN ADULTS A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Department of Psychology University of Saskatchewan Saskatoon By Arron W. S. Metcalfe ©Copyright Arron W. Metcalfe, October 2010. All Rights Reserved. PERMISSION TO USE In presenting this dissertation in partial fulfillment of the requirements for a Postgraduate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this dissertation in any manner, in whole or in part, for scholarly purposes may be granted by the professor or professors who supervised my dissertation work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this dissertation or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis/dissertation. Requests for permission to copy or to make other uses of materials in this dissertation in whole or part should be addressed to: Head of the Department of Psychology University of Saskatchewan Saskatoon, Saskatchewan S7N 5A5 Canada i ABSTRACT Arithmetic cognition research was at one time concerned mostly with the representation and retrieval of arithmetic facts in memory. More recently it was found that memory retrieval does not account for all single digit arithmetic performance. For example, Canadian university students solve up to 40% of basic addition problems using procedural strategies (e.g. 5 + 3 = 5 + 1 + 1 + 1). Given that procedures are less efficient than direct memory retrieval it is important to understand why procedure use is high, even for relatively skilled adults. My dissertation, therefore, sought to expand understanding of strategy choice for adults’ basic arithmetic. Background on this topic and supporting knowledge germane to the topic are provided in Chapter 1. Chapter 2 focused on a well-known, but unexplained, finding: A written word problem (six + seven) results in much greater reported use of procedures (e.g., counting) than the same problem in digits (6 + 7). I hypothesized that this could be the result of a metacognitive effect whereby the low surface familiarity for word problems discourages retrieval. This was tested by familiarizing participants with a subset of the written word stimuli (e.g. three + four = ?, six + nine= ?) and then testing them on unpractised problems comprised of practiced components (four + six = ?). The result was increased retrieval reported for unpractised problems with practiced components. This indicates that surface familiarity contributes to strategy choice. Chapter 3 focused on another classic phenomenon in the arithmetic cognition literature, the problem size effect: Response time, error, and procedure rates increase as a function of problem size. A previous study reported a reduced problem size effect for auditory multiplication problems compared to digit problems. I hypothesized that if this reduction was due to problem encoding processes rather than an effect on calculation per se, then a similar pattern would be observed for addition. Instead, I found that the size effect for addition was larger. I concluded that the auditory format promotes procedures for addition, but promotes retrieval for multiplication. Chapters 4 and 5 were concerned with a well-known methodological issue in the strategy literature, subjectivity of self-reports: Some claim self-reports are more like opinions than objective measures. Thevenot, Fanget, and Fayol (2007) ostensibly solved this problem by ii probing problem memory subsequent to participants providing an answer. They reasoned that after a more complex procedure, the memory for the original problem would become degraded. The result would be better memory for problems answered by retrieval instead of by procedure. I hypothesized that their interpretation of their findings was conflated with the effect of switching tasks from arithmetic to number memory. I demonstrated that their new method for measuring strategy choice was contaminated by task switching costs, which compromises its application as a measure of strategy choice (Chapter 4). In a subsequent project (Chapter 5), I tested the sensitivity of this new method to detect the effects of factors known in the literature to affect strategy choice. The results indicated that Thevenot et al.’s new method was insensitive to at least one of these factors. Thus, attempts to control for the confounding effects of task switching described in Chapter 4, in order to implement this new measure, are not warranted. The current dissertation expanded understanding of strategy choice in four directions by 1) demonstrating that metacognitive factors cause increases in procedure strategies, 2) by demonstrating that the process of strategy selection is affected differentially by digit and auditory-verbal input, 3) by investigating the validity of an alternative measure of strategy use in experimental paradigms, and 4) by discovering a critical failure in the sensitivity of this new measure to measure the effects of factors known to influence strategy use. General conclusions are discussed in Chapter 6. iii DEDICATION I would like to dedicate this dissertation to my wife Carrie, our acquaintance began about the same time as my graduate program of study and she has been there every step of the way. I don’t know if I would have finished without her constant and unwavering support. In turn, I also thank this document for my love and marriage to this woman, for without the circumstances related to the inception of my dissertation I would never have met her. iv ACKNOWLEDGMENTS I could not have completed this dissertation without the supportive presence of my adviser Jamie Campbell, who taught me everything I didn’t know about academia, writing, and arithmetic cognition. I would be fortunate to become even half the researcher this man is. The time and effort of my dissertation committee was much appreciated. Valerie Thompson, Ron Borowsky, and Shaun Murphy each contributed in their own unique way. Without their contribution many useful insights would have been missed. The research in this dissertation and my tenure as student may not have been possible without the continuing support of the Natural Sciences and Engineering Research Council of Canada and their various student funding initiatives that I count to be among the best on Earth. I owe a large part of the knowledge and techniques underlying my expertise in cognitive psychology to the many professors that contributed to my course work over the years. Though I could not possibly name all of these mentors, Jamie Campbell, R. Borowsky, and V. Thompson are most assuredly included. As well, I would add Professors Oleson, Edguer, and Corenblum whom were among my most difficult undergrad teachers and always challenged me to do more. I would also like to thank Dr. Barbara Gfellner who originally inspired me to be a researcher by giving me those all-important first lab opportunities in third year undergrad. I would like to recognize the support I have gotten from the Cognitive Science Lab at the University of Saskatchewan over the years, especially fellow grad students including Jamie Prowse Turner, David Lane, Erin Beatty, and Greg Krätzig. The value of their help and advice cannot be overstated. The commiserating and late Friday afternoons were instrumental to my function as well. This list also includes many other grad students throughout the department too numerous to name. The Lab Administrators always had a helping hand, including J. Shynkaruk, N. Robert, M. Bayly, L. Aspenleider, D. Canales, G. Pennycook, and S. Sacher; I am also appreciative of the contributions of numerous RAs that have worked with the lab over the years. Finally, I would like to thank my family, also too numerous to name, but without which I would have not had the formative experiences that make part of who I am. Although as we all grow older I find we grow further apart, I always keep my early reminiscences close at hand. v TABLE OF CONTENTS PERMISSION TO USE ................................................................................................................... i ABSTRACT .................................................................................................................................... ii DEDICATION ............................................................................................................................... iv ACKNOWLEDGMENTS .............................................................................................................. v LIST OF TABLES ....................................................................................................................... viii LIST OF FIGURES ....................................................................................................................... ix LIST OF ABBREVIATIONS ......................................................................................................... x CHAPTER 1 ..................................................................................................................................

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