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Development of Children's Executive Functioning Strategy Use and the Impact of Sleep on Executive Functioning Using Long...

Permanent Link: http://ufdc.ufl.edu/UFE0022649/00001

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Title: Development of Children's Executive Functioning Strategy Use and the Impact of Sleep on Executive Functioning Using Longitudinal and Microgenetic Methodologies
Physical Description: 1 online resource (96 p.)
Language: english
Creator: Mcnamara, Joseph
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: children, development, executive, function, london, longitudinal, microgenetic, sleep, strategy, tower
Psychology -- Dissertations, Academic -- UF
Genre: Counseling Psychology thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Research with young children can yield important information on both developmental processes and trajectories. This study was comprised of three primary components: a) examining the influence of sleep on executive function and strategy usage, b) utilizing a microgenetic approach to study executive function and strategy use, and c) evaluating the development of executive function and strategy use. This study longitudinally assessed the ability of 67 children that were tested in kindergarten and then again in the 1st grade to utilize high level problem solving strategies on the Tower of London (TOL), an effective neuropsychological task, and what impact their sleep has on their performance. Novel methods were employed to objectively quantify the planning and strategy use following a microgenetic approach. Results revealed that nap duration, the number of nighttime awakenings, and sleep quality rating had significant impacts on children's TOL performance. Additionally, children showed significant improvements in both executive functioning performance and strategy usage. Specifically, children benefited from increased task exposure and showed improvements with age. The findings from this study indicate that sleep, task experience, and development have an impact on executive functioning.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Joseph Mcnamara.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: McCrae, Christina S.
Local: Co-adviser: Berg, William K.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022649:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022649/00001

Material Information

Title: Development of Children's Executive Functioning Strategy Use and the Impact of Sleep on Executive Functioning Using Longitudinal and Microgenetic Methodologies
Physical Description: 1 online resource (96 p.)
Language: english
Creator: Mcnamara, Joseph
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: children, development, executive, function, london, longitudinal, microgenetic, sleep, strategy, tower
Psychology -- Dissertations, Academic -- UF
Genre: Counseling Psychology thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Research with young children can yield important information on both developmental processes and trajectories. This study was comprised of three primary components: a) examining the influence of sleep on executive function and strategy usage, b) utilizing a microgenetic approach to study executive function and strategy use, and c) evaluating the development of executive function and strategy use. This study longitudinally assessed the ability of 67 children that were tested in kindergarten and then again in the 1st grade to utilize high level problem solving strategies on the Tower of London (TOL), an effective neuropsychological task, and what impact their sleep has on their performance. Novel methods were employed to objectively quantify the planning and strategy use following a microgenetic approach. Results revealed that nap duration, the number of nighttime awakenings, and sleep quality rating had significant impacts on children's TOL performance. Additionally, children showed significant improvements in both executive functioning performance and strategy usage. Specifically, children benefited from increased task exposure and showed improvements with age. The findings from this study indicate that sleep, task experience, and development have an impact on executive functioning.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Joseph Mcnamara.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: McCrae, Christina S.
Local: Co-adviser: Berg, William K.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022649:00001


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1 THE DEVELOPMENT OF CHILDRENS EXECUTIVE FUNCTIONING: STRATEGY USE AND THE IMPACT OF SL EEP ON EXECUTIVE FUNCTIONING USING LONGITUDINAL AND MICROGE NETIC METHODOLOGIES By JOSEPH PATRICK HILL MCNAMARA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008

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2 2008 Joseph Patrick Hill McNamara

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3 ACKNOWLEDGMENTS I would like to thank Dr. Chri stin a S. McCrae and Dr. W. Keith Berg for their help and guidance. I never could have comp leted this study without them. I would also like to thank Teri DeLucca, Kim Anderson, Natalie Dautovich, Joe Dzierzewski, and all of the undergraduate students who worked on the project. I would also like to thank, God, my parents, family, and friends for their support. I also would like to thank Dr. Gary Geffken, Dr. Scott Miller, and Dr. Ken Rice for taking the time to be on my dissertat ion committee. I would also like to thank the Ester Katz Rosen Fund at the American Psycholog ical Foundation for thei r grant that helped make this research possible. I would also like to thank the parents of the participants, the children in the study, the school directors and princi pals, and the teachers for their cooperation in this study.

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4 TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 3LIST OF TABLES ...........................................................................................................................6LIST OF FIGURES .........................................................................................................................8ABSTRACT ...................................................................................................................... ...............9 CHAP TER 1 INTRODUCTION .................................................................................................................. 10Sleep and Executive Function ................................................................................................10Microgenetic Method ..............................................................................................................14Strategy ...................................................................................................................... .............15Tower of London ....................................................................................................................17Hypotheses .................................................................................................................... ..........192 METHODS ....................................................................................................................... ......22Participants .................................................................................................................. ...........22Procedure ..................................................................................................................... ...........23Measures ...................................................................................................................... ...........24Sleep Diary ......................................................................................................................24Traditional Tower of London Variables .......................................................................... 25Tower of London Strategy Variables ..............................................................................26Analyses ...................................................................................................................... ............283 RESULTS ....................................................................................................................... ........45Aim 1: The Impact of Sleep on Executive Function and Strategy Use ..................................45Multilevel Modeling Results ........................................................................................... 45Models .............................................................................................................................45Aim 2: Evaluating Executive Functioning and Strategy Use Changes with Experience ....... 50Proportion Solved ............................................................................................................51Goal Path .........................................................................................................................51First Move Time .............................................................................................................. 52Optimal Move Score ........................................................................................................52Holding Peg Strategy Usage ............................................................................................ 53Aim 3: Examining the Development of Executive Function and Strategy Use ..................... 53Proportion Solved ............................................................................................................54First Move Time .............................................................................................................. 54Holding Peg Strategy Usage ............................................................................................ 54Searching Strategy Usage ................................................................................................ 54

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5 4 DISCUSSION .................................................................................................................... .....77The Impact of Sleep on Executive Function and Strategy Use .............................................. 77Evaluating Executive Functioning and Stra tegy Use Changes with Experience ................... 80Examining the Development of Executive Function and Strategy Use ................................. 82Overall Implications of the Study ........................................................................................... 85APPENDIX A SCRIPTS OF THE TOWE R OF LONDON RULES ............................................................. 87B FEEDBACK SCRIPT .............................................................................................................88C TOWER OF LONDON STRATE GY SCORING SUMMARY ............................................89LIST OF REFERENCES ...............................................................................................................91BIOGRAPHICAL SKETCH .........................................................................................................96

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6 LIST OF TABLES Table page 2-1 Move classification system for the Tower of London ....................................................... 322-2 Conceptual definitions of strategies and major rules ......................................................... 332-3 Model construction procedure for proportion solved ........................................................ 342-4 Model construction procedure for goal path ...................................................................... 352-5 Model construction procedure for first move time ............................................................ 362-6 Model construction procedure for solution time ................................................................ 372-7 Model construction procedure for optimal move score ..................................................... 382-8 Model construction procedure for holding peg strategy usage .......................................... 392-9 Model construction procedure for complex matching strategy usage ...............................402-10 Model construction procedure fo r simple matching strategy usage ..................................412-11 Model construction procedure for searching strategy usage .............................................. 422-12 Model construction procedure for random/none strategy usage ........................................ 433-1 Means and standard deviations of sleep variables .............................................................563-2 Correlations between the sleep measures for the 60 participants ...................................... 573-3 The between-person and within-person in traclass correlation coefficients for each variable ...................................................................................................................... .........583-4 Null and final models for each Tower of London variable ................................................ 593-5 Sleep variables, years, and sets predicting proportion solved ...........................................603-6 Sleep variables, years, a nd sets predicting goal path .........................................................613-7 Sleep variables, years, and sets predicting first move time ............................................... 623-8 Sleep variables, years, and sets predicting solution time ................................................... 633-9 Sleep variables, years, and sets predicting optimal move score ........................................ 643-10 Sleep variables, years, and sets predicting holding peg strategy usage ............................. 65

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7 3-11 Sleep variables, years, and sets pr edicting com plex matching strategy usage .................. 663-12 Sleep variables, years, and sets pr edicting simple matching strategy usage ..................... 673-13 Sleep variables, years, and sets predicting searchi ng strategy usage ................................. 683-14 Sleep variables, years, and sets predicting random/none strategy usage ...........................693-15 Summary table showing pred ictive significance of sleep variables, years, and sets on Tower of London traditional and strategy variables .......................................................... 70

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8 LIST OF FIGURES Figure page 1-1 The Tower of London as pres ented to the participant. ......................................................21 2-1 The order of events pres ented to the participant ................................................................ 44 3-1 Proportion solved for sets and years .................................................................................. 71 3-2 Goal path length for sets and years ....................................................................................72 3-3 First move time for sets and years. .................................................................................... 73 3-4 Optimal move score for sets and years. ............................................................................. 74 3-5 Holding peg strategy usage for sets and years. ..................................................................75 3-6 Searching strategy usage for sets and years. ...................................................................... 76

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9 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THE DEVELOPMENT OF CHILDRENS EXECUTIVE FUNCTIONING: STRATEGY USE AND THE IMPACT OF SL EEP ON EXECUTIVE FUNCTIONING USING LONGITUDINAL AND MICROGENETIC METHODOLOGIES By Joseph Patrick Hill McNamara August 2008 Chair: Christina McCrae Cochair: W. Keith Berg Major: Counseling Psychology Research with young children can yield im portant information on both developmental processes and trajectories. This study was comp rised of three primary components: a) examining the influence of sleep on executive function and strategy usage, b) utilizing a microgenetic approach to study executive func tion and strategy use, and c) evaluating the development of executive function and strategy use. This study longitudinally assessed th e ability of 67 children that were tested in kindergar ten and then again in the 1st grade to utilize high level problem solving strategies on the Tower of London (TOL), an effective neuropsychological task, and what impact their sleep has on their performan ce. Novel methods were employed to objectively quantify the planning and strategy use following a microgenetic appro ach. Results revealed that nap duration, the number of nighttime awakenin gs, and sleep quality rating had significant impacts on childrens TOL performance. Additionally, children showed significant improvements in both executive functioning perf ormance and strategy usage. Specifically, children benefited from increased task exposur e and showed improvements with age. The findings from this study indicate that sleep, task experience, and development have an impact on executive functioning.

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10 CHAPTER 1 INTRODUCTION Executive functions are higher-order cognitive processes that can affect all aspects of life, such as planning and initiating ta sks; shifting of thought, strategy or attention; organization of actions; inhibiting inappropriate thoughts and be havior; and carrying out efficiently sustained and sequenced behavior (Nigg, Bl askey, & Huang-Pollock, 2002). The current study consists of three m ain components that are all related to exec utive function: a) investigating the impact of sleep on executive function and strategy use, b) evaluating strategy use change, using a microgenetic methodology, and c) examining the de velopment of executive function and strategy use. The rationale for examining sleep in this rese arch was provided by a va riety of studies that found sleep quality rating influences executive functioning, both in adults (Drummond, Brown, Salamat, & Gillin, 2004; Harrison & Horne, 1999) and children (Sadeh, Gruber, & Raviv, 2002). The study of strategy in problem solving has a lo ng history, and the presen t study will extend this with a microgenetic evaluation of strategy use (Siegler, 1995). Finally, examining these issues developmentally will shed additional light on the developmental processes of cognitive development. Each of these point s will now be discussed in turn. Sleep and Executive Function Many factors can affect child rens problem solv ing and strategy usage. One of the most understudied of these factors is how well a child sleeps. Given this it is surprising that the most common referral to mental health professionals for young children is related to complaints of dysregulation of sleep (Devera, 1997). Studi es examining the influence of young childrens sleeping behavior on executive f unctioning are especially sparse. Normative developmental data on children's sleep and executive functioning is still lacking (Sadeh, Raviv, & Gruber, 2000).

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11 Existing sleep studies have focused on infancy and adolescence (Sadeh & Gruber, 1998). Furthermore, most research on children's sleep patterns have focused on sleep disturbances or populations with diagnosed diso rders, such as ADHD. Results from adult studies suggest a link betw een executive functioni ng and sleep. Bastein and colleagues (2003) found that in older adults, those with insomnia pe rform worse on attention and concentration tasks compared to those w ho were good sleepers. Furthermore, studies conducted with college age adults by Horne ( 1988; 1993) show that de ductive reasoning tasks are greatly affected by sleep depr ivation. These deficits are reve rsed after recovery sleep. The findings of these two Horne studies strongly s uggest that the prefrontal cortex obtains a particular benefit from sleep, as sleep deprivation leads to degraded cognitive functions that are regulated by the prefrontal cortex (Horne, 1993). Harrison and Horne (1999) conducted an experimental study with two counterbalanced groups (sleep vs. no sleep) and found that the effects of sleep deprivation on graduate stude nts led to more rigid thinking, increased perseverative errors, and marked difficult y in adapting to novel information. Drummond and colleagues (1999, 2001, 2004) conducted fMRI studies on brain functioning during executive function ing tasks in sleep deprived pa rticipants. They found that when participants are sleep deprived and perfor ming an executive functioni ng task, their parietal lobes show increased activation to maintain task performance. Based on their findings, Drummond and colleagues hypothesize an adap tive cerebral respons e during cognitive performance following sleep deprivation during wh ich the pattern of adaptation depends on the specific cognitive demands of the task. They expl ained that neuroimaging data revealed a linear increase in cerebral response with a linear increase in task demands in several brain regions after normal sleep. They found even more pronounced or steeper linear respon ses after total sleep

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12 deprivation in several brain regions including bilateral inferior parietal lobes, bilateral temporal cortex, and left inferior a nd dorsolateral prefrontal cortex (Drummond, Brown, Salamat, & Gillin, 2004), which is critically involved in pl anning efficiency (Unterrainer, et al, 2004). Despite these compensatory mechanisms, executive functioning performance was still significantly worse. Muzur, Pace-Schott & Hobson (2002) found that sleep depriv ation influences frontal executive functions (planning, logical reasoning, temporal memory, inhibition and decision making) in particular, which further emphasizes the sensitivity of the prefr ontal cortex to sleep. Furthermore, Pilcher and Huffcutt (1996) found that sleep deprivation results in poorer reaction times, less vigilance, an increase in perceptual an d cognitive distortions, a nd changes in affect in adults. In their meta-analysis, they report that partia l sleep deprivation meaning less than 5 hours of sleep per day resulted in performance two standard deviations below non-sleep deprived participants. Long-term sleep deprivation (mor e than 45 hours awake without sleep) and shortterm sleep deprivation (less than 45 hours awak e without sleep) resulted in performance one standard deviation below non-sleep deprived par ticipants. Their finding s suggest that partial sleep deprivation leads to greater impairments of performance than total sleep deprivation. This is important because partial sleep deprivation is likely the type of deprivation that both adults and children would experience in real life While the previously reviewed studies were conducted with adults, one would logically expect that poor sleep in child ren would have very large impacts on their executive functioning. Upon reviewing the literature, the impact of poor sleep on executive function with normally developing early elementary school children has not been thoroughly examined. However, many studies have found a link between ADHD symptoms (such as poor inhibitory control and set

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13 shifting) and sleep disruption. For example, Gruber, Sadeh, and Raviv (2000) found that instability of the sleep-wake system of children significan tly predicted ADHD symptoms, such as poor inhibitory control, in attention, difficulty in regulating behavior and hyperactivity. Additionally, Steenari and colleagues (2003) found that lower sl eep quality ratings, lower sleep efficiency or the proportion of tim e spent sleeping in comparison to the time attempting to sleep, and longer sleep latency have a negative impact on working memory performance in school age children. Very little data exists on the normal developm ent of sleep-wake patterns in the school-age period (Wolfson, 1996). The exception to this is the work of Sadeh and colleagues (1998, 2000, & 2002) who have conducted studies examining the sl eep of children ranging in age from four to 12. In one of their studies examining 2nd, 4th, and 6th graders; they found si gnificant correlations between sleep quality measures and executi ve functioning measures, especially among 2nd graders. Children with fragmented sleep pe rformed more poorly on executive functioning measures, especially the more complex tasks such as a continuous performance task (a test of sustained attention) and a symbol-digit substitu tion test (a test of working memory). These results suggest an association be tween sleep quality ra tings and executive functioning in children (Sadeh, Gruber, & Raviv, 2002). Additionally, thei r results raise important questions about the nature of these relationships and their de velopmental and clinical importance. Taken together these data suggest that sleep quality and quantity are important factors in executive functioning in adults, and the limited evidence available suggests the same may be true for children. However, additional research is needed to specifically examine the relationship between sleep and childrens executive functioni ng and strategy use on complex tasks, such as

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14 the Tower of London. The proposed studys goal is to begin this process. As discussed next, an effective procedure for examining this relatio nship in young children is the microgenetic method. Microgenetic Method Determ ining the course of change of performance is possibly the most fundamental issue in the study of cognitive development (Miller & Coyle, 1999; Siegler, 1995). Typical crosssectional studies allow researchers to determin e age differences, and longitudinal studies allow researchers to determine what changes have o ccurred over a more extended time period but do not yield shorter term informati on on the progression of change occu rring as a child develops the ability to solve particular types of problems (Siegler & Stern, 1998). However, the microgenetic method can yield such information (Siegler & Chen, 1998). Therefore, the microgenetic method is an effective technique for examining executi ve functioning and strate gy usage. Furthermore this data can be used to examine the relations hip between sleep and executive functioning and strategy usage. According to Siegler (1995,) strategies could be unc overed by analyzing the path, breadth, rate, variability, and sources of ch ange of the attempted solutions by using the detailed analysis of responses during the peri od of problem solving. This study will use the microgenetic method to examine childrens exec utive functioning performance and strategy usage on the Tower of London (TOL) task (description below). The microgenetic method has been suggested as a way to directly observe changes in behavior (Kuhn & Phelps, 1982). It has been defined as a technique that covers the entire period of change, contains frequent te sting sessions relative to the peri od of change, and involves in depth, trial-by-trial analyses (Siegler & Crow ley, 1991). Kuhn and Phelps (1982) advocated increasing the rate of change by giving the pa rticipants many opportunities to engage in the behavior being studied over a brief period of time. Concentrated exposure to a task may improve the likelihood of observing the process of change if it occurs (Kuhn, 1995).

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15 The microgenetic method is valuable for unde rstanding variability and consistency in patterns (Siegler & Crowley, 1992). For example, McNamara (2000) tested preschool childrens problem solving ability microgenetically using the TOL task. The 20 children who completed the study significantly improved over the course of 6 sessions, solving 44% of the problems in the first session and 80% in the la st session. Individual participants patterns of change fell into 3 categories: 1) gradual improvement; 2) abru pt, marked, and sustained improvement; and 3) little improvement. The comparison of the three groups seemed to indicate that some children were utilizing more complex st rategies more quickly and more consistently, as indicated by solving more complex problems in earlier sessions, than were other childre n. Alibali (1999) also found varying patterns of acquisition using the To wer of Hanoi. Strategy response patterns will be carefully examined in the proposed study. Strategy Many different researchers have studied executive functioning using problem solving and proposed theories to explain the strategies us ed in problem solving (e.g., Coyle & Bjorkland, 1997; Paiget 1976; Siegler, 1995). Defining a strategy is difficult because strategies can be task specific or more general. However, strategy use involves a combinati on of an individuals knowledge, conscious mental operations, and auto matic processes (Bjork lund & Harnishferger, 1990). An additional difficulty is developing a procedure for studying strategy. The microgenetic method provides an effec tive way to study strategy and has given interesting insights into young ch ildrens strategy use. Res earch has consistently found variability in a childs strate gy selection (Siegler, 2007). Sieg ler (1994) argued that conflicts between new strategies and older strategies explain the large amount of variability previous studies have found because children have acce ss to and employ several strategies. With increasing experience on a problem, some strategies are used more, and other strategies are used

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16 less and eventually not at all (Siegler, 1994, 2007). This results in increased variability as the strategies shift over time. An example of this is Shrager and Siegler s (1998) study that found pr eschool children are competent at choosing among compe ting strategies and discovering new strategies. They report that most 4and 5-year-olds use at least six strategies to add number s and that children use available strategies that are the most effectiv e depending on the problem. The discovery of one strategy can play a transitional role in the disc overy of a more advanced strategy. Additionally, strategy discovery can occur follo wing correct answers, incorrect answers, easy problems, or difficult problems (Shrager & Siegler, 1998). Once this new strategy is discovered, it does not typically replace all previous st rategies immediately, but rather the new strategys usage gradually increases. Presenting children w ith challenge problems can increase the new strategys usage (Shrager & Siegler, 1998). Strategy variability tends to be high in young children because children utilize different paths, rates, and generalizations to solve problems (Chen & Sieg ler, 2000; Siegler, 2006; Siegler & Svetina, 2006). Coyle and Bjorkland (1997) found that when children used an unsuccessful strategy on a multi-trial sort recall task, they we re more likely to switch strategies. When a strategy is no longer successful, many children revert to previously used strategies, even other unsuccessful ones. However, if this alternative strategy is still unsuccessful, children may discover a new strategy that is necessary to solve the task (Siegler & Crowley, 1991). Thus, strategy variability, and the explor ation of strategies involved, is an important way in which new successful strategies can be uncovered. Strategy variability has also been found on complex executive functioning tasks like the Tower of London (McNamara, Berg, & DeLucca, in preparation).

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17 The Tower of London, a task widely used in ne uropsychological testi ng, is a well known executive functioning task that is useful for studying strategy (McNamara, 2003; Shallice, 1982). The current study will incorporat e a new procedure for objectively assessing strategy use in the Tower of London task. Tower of London The TOL (Figure 1-1), a problem solving task similar to the Tower of Hanoi, is a spatial problem solving task in which a se t of three balls are arranged on three pegs of differing height. The balls must be rearranged to match anothe r configuration presented to the participant (Shallice, 1982). The Tower of London is an effective neuropsychological task because participants with lesions in the frontal lobes have been shown to not perform as well on the task which indicates that the frontal lobes are heavily utilized (e.g. Shallice, 1982). In addition, children whose frontal lobes are not fully developed can resemble lesioned adults in the TOL performance. The TOL provides a test with more graded levels of difficulty than does the Tower of Hanoi (Shallice, 1982). This task has been used to investigate aspects of problem solving, such as planning ability (Owen, Downes, Sahakian, Po lkey, & Robbins, 1990). Furthermore, the TOL requires a variety of approaches to plan diffe rent problems which allow for strategy usage and development to be examined more thoroughly. (S hallice, 1982). The TOL assesses planning and flexibility of thought which are important elemen ts of executive functions (Shallice, 1982). The TOL significantly correlates with a variety of other executive function tasks including the Wisconsin Card Sort task (Farro, 2001), the Continuous Performance Task (Farro, 2001), the Nback (Farro, 2001), the Stroop task (Welsh, Satte rlee-Cartmell, & Stine, 1999), the Tower of Hanoi (Welsh, et al., 1999), the Trail Making test (Anderson, Anderson, & Lajoie, 1996), and the Rey-Osterreith Complex Figure (Anderson, et al ., 1996). Furthermore, Culbertson and Zillmer

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18 (1998) found that the TOL variables had significan t factor loadings on the executive planning and inhibition factor ranging from 0.63 to 0.93. They also found that this factor was significantly correlated with executive concept fo rmation and flexibility factor. These findings suggest that the TOL contains aspects that require problem solving, inhibition, and working memory. Although the TOL was originally developed for testing adults (Shallice, 1982,) children have also been tested with the task. Few TOL studies have been conducted with young children, the focus of the present study. Luciana and Nels on (1998) found that 5to 8-year old children did not perform significantly differently on the nu mber of moves required to solve problems. Furthermore, these age groups were reported to not perform as well as young adults. However, performance on difficult problems and the number of perfect solutions improved with age. In contrast, McNamara (2000; 2003) who utilized multiple testing sessions found that children when given intense exposure to the TOL can pe rform at levels similar to adults on most measures but tend to have difficulty maintaining optimal performance. However, these studies did not address developmental changes that oc cur with age. The TOLs flexibility of measurement and the multitude of tasks that significantly correlate with TOL measurements suggest significant benefits and understanding from employing it to examine performance and strategy development. Given these interests and aims, children were te sted in two sessions separated by a year, in kindergarten and then again in 1st grade. Each session consisted of repeated sets of Tower of London problems. The computerized task asse ssed move-by-move information allowing for careful assessment of strategy use as well as providing basic performance information. Evaluation of the childrens sleep was provided by parent-provided sleep l ogs and interviews.

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19 Hypotheses The proposed study has three prim ary aims: 1) to explore the relati onship between sleep and executive function in early elementary schoo l children, 2) to explore how executive function and strategy usage will improve w ith increased task exposure, and 3) to explore the impact of developmental changes on executive functioning performance. H ypotheses related to each of these aims follow: Hypotheses based on aim 1. Based on the work of Horne and colleagues (1988, 1993, 1999), Drummond and colleagues (1999, 2001, 2004), and Sadeh and colleagues (1998, 2000, 2000, 2002), it is hypothesized that longer total sleep times, shorter total wake times, and increased sleep efficiency will significantly be asso ciated with better task efficiency and strategy usage. Specifically, better sleep is expected to be associated with increased Proportion of Problems Solved, longer Goal Path s, increased Optimal Move Score, faster First move-times, and faster Solution times. Furtherm ore, better sleep is expected to be associated with increased Holding Peg strategy and Complex Matching strategy usage. Bette r sleep is expected to be associated with less Simple Matching st rategy, Searching strategy, and the Random/None strategy usage. The examination of other sleep variables such as the number of awakenings, bed and wake times, and the number of naps is exploratory, beca use these topics have not been explored in previous research. However, it is tentatively hypothesized that more frequent awakenings, more naps, and later bed times will be associated w ith less efficient performance and poorer strategy use. Hypotheses based on aims 2 and 3. Based on th e work of Byrd, van der Veen, McNamara and Berg (2004) and McNamara (2 000), it is hypothesized that childrens optimal strategy use and planning performance will significantly impr ove with increased task exposure. Finally,

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20 based on the work of Hughes (1998), it is hypothesi zed that childrens optimal strategy use and planning performance will show significant improvement on the task during the second testing session, occurring 1 year after the initial testing session. The examination of potential changes in specific strategy use with age will also be of considerable interest, but lack of previous data here prohibits specific hypothe ses at this point.

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21 Figure 1-1. The Tower of London as presented to the participant. CURSOR PARKING AREA Move Cursor Here nowDo not click! Can Be Solved in This Many Moves Game Board Goal Board 3G G R R B B

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22 CHAPTER 2 METHODS Participants Participan ts were tested in accordance with the Ethical Principles of Psychologists and Code of Conduct (American Psychological Association, 2002). In the first year of the study, 137 children in kindergarten were te sted and then 72 were tested ag ain in first grade. Analyses did not reveal any significant year 1 performance differen ces between the children who completed the first year and those that completed both the first and second years. In an attempt to maintain a high retention rate for the longi tudinal sessions, contact information from the parent or legal guardian was acqui red when he or she first agreed to allow his or her child to participate as well as a release of information for contact information to be acquired from the school board. Furthermore, contact information from additional family and friends was also obtained. Of this sample of 72, sleep information was obt ained on 67 participants. Furthermore, four participants data was excluded because their one day of sleep diary information was reported to be inconsistent with their typi cal sleeping patterns. Three pa rticipants data was excluded because parents were not able to provide informati on on all of the sleep vari ables. Therefore, the final sample consisted of 60 participants. Every effort was made for the sample to be representative. The final sample was 45% female and 55% male. The racial/ethnic backgr ound of the participants was 3% Asian or Asian American, 32% Black or African Americ an, 11% Latino/Latina American, and 54% White/Caucasian American.

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23 Procedure The goal for approxim ate time between the two testing sessions was 12 months ( months). However, the actual time between sess ions averaged one year and 66.79 days with a standard deviation of one year and 152.27 days. The range was 219 to 855 days with a median of 28. Participants were tested using a laptop which ran the customized TOL software, and the child sat next to the experimenter. The experime nter was the author of this paper, a trained graduate student, or trained undergraduate students. The testing protocol was manualized, and the author of this paper trained all of the experi menters. The testing se quence for each session is outlined in Figure 2-2. The children were given a warm-up task (drawing a smiley face). Before beginning the TOL task, participants were given a computerized version of the Peabody Picture Vocabulary Test (PPVTIII), which co rrelates strongly with IQ (Williams & Wang, 1997). Then the experimenter explained the TOL task and rules to the participant after which participants were given 1-move practice TOL pr oblems to make sure they understood the rules and goal of the task. Participants were instructed to move the balls using a computer mouse with the click and drag method. Primary testing invol ved three sets of 10 TOL problems separated by short breaks when children were allowed to watc h a brief cartoon on the laptop. The exact script is in Appendix A. Sixty seconds were allowed to solve each TOL problem After completion of each problem or expiration of the time limit, ch ildren were given graded feedback, which has been found to help facilitate strategy improve ments (Chen & Siegler, 2000). This graded feedback consisted of 1 of 4 anim ated characters that informed children about the efficiency of their performance. The Give-me 5 guy indicated that the child solved th e problem in the most efficient way with no extra moves, the Dancing guy indicated that the child solved the problem efficiently but took 1 or 2 extra moves, Good Job! indicated that the child solved the problem, but took more than 2 extra moves, and The clock indicated that the child ran out of time before

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24 solving the problem. See Appendix B for the script. Each of the animated feedback characters was illustrated and explained prior to testing. Each of the 10 problem sets included two problems at each of five difficulty levels: 3-mo ve (problems requiring a minimum of 3 moves to solve), 4-move, 5-move, 6-move, and 7-move. Each set of 10 problems was a color transformation of other sets but otherwise identical (cf. Berg & Byrd, 2002). Color transformations make the problem look different but leave the difficulty level and optimal solution path unchanged. Measures Sleep Diary The sleep d iary is a self-repor t daily log of sleep habits, wh ich is completed for 14 days upon awakening and required approximately 3 minut es/day to complete (Lichstein, Riedel, & Means, 1999). In the study, the childs primary caregiver filled out the sleep diary (C orkum, et al., 2001). Sadeh and colleagues (2000) review of the lite rature stated that sleep assessment based on subjective reports is by far the most frequently utilized approach. However, despite the informative value of this data, it is limited by the restricted parental awareness of night awakenings and awake time after sleep onset (Sadeh, 1994). Despite this limitation, this was the most feasible method for the present study. The primary caregiver was asked to provide subjective estimates of seven sleep-wake parameters, including (1) sleep onset latency, defined as the time from initial lights-out until sleep onset; (2) number of awakenings during the night, defined as the number of total awakenings during the night; (3) wake time after sleep onset defined as the time spent awake after initial sleep onset until the last awakening; (4) total sleep time, computed by subtracting total wake time from time in bed; (5) number of awakenings; (6) sleep qu ality rating, scaled from

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25 1 (very poor) to 5 (excellent); and (7) total nap time, defined as the total amount of time spent sleeping prior to bedtime. An additional variable of sleep efficiency percentage was calculated, defined as the ratio of total sleep time to total time spent in bed 100. A mean was computed for each of these variables for the 2-week record ing period. When compared to the data yielded by polysomnography or sleep EEG, considered to be the gold standard in the objective measurement of sleep, the sleep diary provides a reliable and relatively accurate index of sleep behavior (Espie, 2000). Additionally, in year 2 ch ildren were asked the questions from the sleep diary on the day they were tested. However, this data was not analyzed because children were not able to provide appropriate answers to questions regarding time. Parents were given the option to answer these questions on a website, a hard copy of the form, or over the phone. Unfortunately parents did not generally complete two weeks of sleep diaries, so sleep diary variables were averaged for the analyses meaning that only between person differences could be examined. Traditional Tower of London Variables To examine childrens planning and execu tive functioning performance, the following dependent variables were examined: proportion of problems solved Optimal Move Score, Goal Path (for solved problems only), First move-time, and Solution time (Berg & Byrd, 2002; McNamara, 2003). Proportion of problems solved is the number of problems the child solved correctly divided by the total number of problems. The Optimal Move Score is a measure that evaluates participants moves to determine overall strategy effectiveness. This formula takes into account both optimal moves, moves that get the partic ipant closer to solv ing the problem, and nonoptimal moves, moves that do not get the particip ant closer to solving the problem. The measure

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26 is obtained by subtracting the number of non-optim al moves from the number of optimal moves, and then dividing the difference by the total number of moves. This scor e can potentially range from -1 (all non-optimal) to + 1 (all optimal). Computer-created random move solutions produces OMS scores of appr oximately -0.15 to -0.20. First-move time is the time from when the problem is presented to when the participants complete their first move. Solution time is the total time spent on a problem minus the first move time. The last traditional variable is Goal Path the number of moves made by the participants in which they are getting consistently closer to the goal and eventually solve the problem. The goal path is the number of consecutive moves in which the participant is only making optimal moves prior to reaching the goal. An optimal solution would have a goal path length equal to the minimum number of moves required to reach a solution. Thus, on problems with more require d moves, longer goal pa ths are suggestive of more effective strategy use because the participan t is required to use the most effective strategy for a greater duration of moves. Tower of London Strategy Variables To determine strategy usage, performance patterns were assessed by examining each move to determine the type of move made using a new classification system. Every possible TOL move can be classified into one of several mutual ly exclusive types of moves (Table 2-1). This system was influenced by Phillips and colleague s (1999) move classification system of direct and indirect or counterintuitive moves on the 5-disc TOL task. The classification system (Table 2-1) in the current study is more complex because it adds additional characteristics to the direct and indirect or counterintuitive moves. The m ove classification system is basically a 2 by 2 factorial combination of two orthogonal dichotom ies: 1) Optimal/Non-Optimal is the position after the move closer to (Optimal) or not clos er to (Non-Optimal) the goal in terms of the minimum number of moves now need ed to reach the goal, and 2) Goal or Non-Goal was the

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27 ball placed in a position which matches that of th e goal position for that co lor ball (Goal) or in some other position (Non-Goal). In addition to th is basic classification, one of the four move types, the Non-Optimal, Non-Goal move, is subdi vided into two types based on the moves that were possible other than the one that was made. In one case, th e alternative move could have placed a ball into a final goal position and would constitute an optimal move (but the current move did not do that), and for the other case, no possibility of moving th e ball optimally into a goal position occurred. These two subsets of Non-Optimal, Non-Goal moves are labeled, respectively: a) Missed Goal Chance, and b) No Missed Goal Chance. Every possible legal move can be exclusively classified into one of these move types. Sequences of the five types of moves can be associated with a propos ed strategy use, and these strategies can also be arra nged hierarchically in terms of their level of sophistication and complexity (Table 2). The most complex woul d be use of the holding peg strategy, and at the least complex level, no evident strategy use an apparent random move pattern. Between these extremes are two levels of matching strategies and a searching strate gy. Matching refers to putting a ball in a location that matches the goa l. A matching strategy will work for simple problems, not more complex ones th at require some use of holding peg moves. Searching is a strategy where the participant appears to be at tending to the goal oppor tunities but is still exploring the problem space. All possible move sequences that end in a solution can be exclusively classified into one of these strategi es. The sequence of move s could involve one or more of these strategies. No single move, in isolation, can provide clear evidence of strate gy use. Rather, the sequence and combination of moves and the co nsistency over a predetermined period provides strong evidence of a strategys us e. To provide a more conc rete example, consider the

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28 distinction between two types of strategies, the highest level of strategy, Holding Peg strategy, and a lower level strategy, the Matching strategy. A solution to any problem with a goal path length of four or more moves requires using a co mbination of both types of optimal moves the non-goal optimal move (holding peg) and the optimal goal moves (Table 2-2). In contrast to this, consistent Non-Optimal goa l moves indicate a matching strate gy, where the participants are matching their ball to the goal without regard to wh ether this is optimal. Further, a distinction is made between simple matching strategy (matching that is not optimal) and complex matching (optimal matching). Other strategies lower on the hierarchy are presented in Table 2-2. It is important to note that as participants search for a solution to a problem, they might engage in a variety of different strategies within that single solution. Thus, they may start with simple searching, switch to a matching strategy, a nd finally to achieve a solution use the holding peg strategy. They may also switch back and forth between strategies wi thin a single solution. The dependent variables for the strategy analyses are the frequency of use for each of the five different possible task strate gies, the holding peg strategy, th e complex matching strategy, the simple matching strategy, the searching st rategy, and the random/none strategy. Analyses The current study used data from the sleep measures to predict the TOL variables by utilizing conditional growth models using a multi-level modeling (MLM) approach. MLM, also referred to as hierarchical linear modeling (H LM, Bryk & Raudenbush 1992), is an extension of the general linear model, and does not require observations to be independent. Thus, MLM is very flexible and especially suited for repeated data because of its autoregressive nature and hierarchical structure with repe ated observations nested within each participant (Singer et al. 1998; Singer et al. 1998; Willett et al. 1998; Zautra et al. 2005).

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29 Because of the hierarchical nature of the data (set and years nested within participants) and in order to increase the precision of predicting fluctuations in TOL variables with changes in sleep patterns, we modeled the data with an MLM approach. This provided the opportunity to examine how well sleep predicted TOL perfor mance for both within-persons and betweenpersons. Sleep measures were used to predict the TOL variables using the MIXED procedure in SPSS 15.0. All models were estimated using the Maximum Likelihood (ML) method. The ability of a model to predict TOL performance better than a baseline (null) model was used as an index of Goodness of Fit. Improvements in predictability were determined by the proportional reduction of withinand between-p erson residual variances comp ared to this baseline model (Bryk & Raudenbush 1992). Decreases in residual variances repr esent a proportional reduction of the prediction error, which is analogous to R2, and used as an estimate of effect size. One issue that has received substantial attention in work on longitudinal MLM is the issue of optimal modeling of repeated measures error structures (e.g., Singer & Willet 2003). The effect of different error structure specifications on model f it was tested and had little effect on the fixed and random parameter estimates or their patte rn of significance (Singer & Willet 2003). Several features of the modeling are briefly described here. First, between-person effects were estimated using predictors which varied between persons (the sl eep variables), and for which there was only one value per person. Second, with in-person effects were estimated using predictors which varied within persons, and fo r which there was a new value at each occasion of measurement (both sets and years). Models were built in a series of steps. Sl eep diary data from year 1 was used for all analyses unless data was not collected during that year. If this occurred, data from year 2 was

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30 utilized which occurred for three participants. In this statistical approach both sets and years are repeated variables. The sleep variables were used as the covariates along with the difference of days from the 365 days between year 1 and year 2 (a between-person variable). The 5 traditional TOL variables and the 5 TOL strategy variables we re the dependent variables. Because of the lack of previous literature in this area, all 11 sl eep variables were used in initial models until the best fitting model for all depende nt variables was established, and this model was run for all dependent variables. The criteria for selection in the final overall model was that a predictor needed to significantly predict two or more TOL variables at a significance level of p<.05. The only exceptions to these criterion were the aprior i decisions to include the Difference of Days (the deviation in days from the intended 365 day interval between year 1 and year 2 test dates), years (1, 2) and sets (1, 2, 3). For example, someone tested 5 days before 1 year would receive a score of -5 and someone tested 75 days after1 year would receive a score of 75. This allows for a more accurate examination of the impact of de velopment (comparison between year 1 and year 2). Years and Sets were included because of th e specific hypotheses regarding development and task experience. See Tables 2-3 through 2-12 fo r the steps of the model construction for each variable. The final model consisted of several co mponents: 1) the Difference of Days, 2) years 1 and 2, 3) sets, 4) nap duration, 5) number of night awakenings, and 6) sleep quality rating. To further examine the second and third aims of the proposed study, the impact of task exposure and the developmen t of executive functioning a nd strategy usage, follow up ANCOVAs were utilized to pursue evidence of significant relationshi ps in within-person results. Specifically, a repeated measures 2 (years: 1, 2) X 3 (sets: 1, 2, 3) ANCOVA for each of the significant models and any need ed follow-up analyses was conducted. Follow-up tests to these

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31 ANCOVAs used the Bonferonni correction. Both linear and quadratic tre nds were examined on sets. The proportion of problems solved, goal path, and optimal move scor e were expected to increase in a linear fashion for both task e xposure and development. For the development hypotheses, linear changes are the sa me as looking at differences because there are only two data points. Based on McNamara (2000), first-move time and solution time were expected to change in a quadratic fashion for task exposure (sets: 1, 2, 3). For all variable s, performance during the second year was expected to be significantly be tter than performance in the first year: higher proportion solved, longer goal paths, higher opti mal move score, and faster move times. Additionally, the analyses for the TOL strate gies will parallel the analyses for the traditional variables discussed in the previous paragraph if the within-person results of the MLM analyses suggest a significant relationship. Linear and quadratic trends were examined on sets. Based on McNamara (2003), the holding peg strategy is expected to improve in a linear fashion across sets. The searching strategy is expected to decrease in a linear fashion across sets. The other three strategies are not e xpected to significantly change across sets because of limited usage. For all strategies, perf ormance during the second year is expected to be significantly better than performance in the first year meani ng more usage of the holding peg strategy and complex matching strategy usage and less usage of simple matc hing, searching, and the random strategy.

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32 Table 2-1. Move classification system for the Tower of London Optimal* Non-optimal* Goal** Optimal/goal move The ball is correctly placed in a goal position and never needs to be moved again. Non-optimal/goal move The ball is incorrectly placed in a goal position. The ball must be moved to solve the problem. Nongoal** Optimal/non-goal move The ball is correctly placed in a non-goal position, it later needs to be moved to a goal position. Non-optimal/non-goal/ move The ball is incorrectly placed in a non-goal position. There was not an opportunity to put it into a final goal position. Missed goal chance The ball is incorrectly placed in a non-goal position and could have been placed in a final goal position. Optimal refers to a move that is one move closer to the final goal board configuration. Nonoptimal refers to a move that moves no closer or even farther away from the final goal configuration. ** Goal refers to a move that places a ball in the same place as the corresponding ball for the goal board configuration. Non-goal re fers to a ball placed anywhere else.

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33 Table 2-2. Conceptual definitions of strategies and major rules Strategy Basic concept Major rule for strategy Holding peg Removing obstacle balls so that others can be placed in final goal positions. Moves one consistently closer to goal One or more optimal/non-goal moves followed by one or more optimal/goal moves Complex matching Places a ball in a final goal position but not immediately preceded by at least one removal of an obstacle ball. Moves one closer to goal One or more optimal/goal moves not preceded by an optimal/non-goal move Simple matching Places ball in a goal position. Does not move one closer to goal Non-optimal/goal move Searching Exploring of the problem space without clear use of strategies above Non-optimal/non-goal/no missed goal chance Random/none Failing to place a ball into a final goal position when it is the optimal move. Evidence of not attending to the goal board. Non-optimal/non-goal/ missed goal chance Notes: Appendix C describe s the specific rules.

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34 Table 2-3. Model construction procedure for proportion solved Models -2LL -2LLr2 b r2 w Null 9873.38 ---Difference of days added 5709.494163.890.49 -0.07 Year added 5561.40148.09-0.21 0.33 Set added 5488.7972.62-0.04 0.17 Nap duration added 2560.782928.010.03 0.03 Bedtime added 2567.13-6.350.02 0.00 Wakeup time added 2574.50-7.37-0.04 0.00 Sleep onset latency added 2571.522.99-0.04 0.00 Number of nighttime awakenings added 2556.5914.920.15 0.00 Waketime after sleep onset added 2550.925.67-0.03 0.00 Terminal wakefulness added 2546.744.18-0.05 0.00 Time in bed added 2546.740.000.00 0.00 Total sleep time added 2546.740.000.00 0.00 Sleep efficiency added 2526.1620.58-0.03 0.00 Sleep quality rating added 2509.3216.840.27 0.00 Set*year added 2501.238.090.00 -0.01 Reduced forma 2530.237343.150.58 0.43 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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35 Table 2-4. Model constructi on procedure for goal path Models -2LL -2LLr2 b R2 w Null 1484.85 ----Difference of days added 855.02629.840.01 0.04 Year added 858.71-3.690.00 0.00 Set added 828.6930.02-0.04 0.09 Nap duration added 378.75449.95-0.20 0.18 Bedtime added 397.91-19.16-0.04 0.00 Wakeup time added 414.87-16.960.04 0.00 Sleep onset latency added 423.45-8.58-0.05 0.00 Number of nighttime awakenings added 416.217.240.29 0.00 Waketime after sleep onset added 422.30-6.09-0.04 0.00 Terminal wakefulness added 429.60-7.30-0.05 0.00 Time in bed added 429.600.000.00 0.00 Total sleep time added 429.600.000.00 0.00 Sleep efficiency added 419.819.780.00 0.00 Sleep quality rating added 417.342.470.18 0.00 Set*year added 420.32-2.980.00 -0.01 Reduced forma 371.091113.770.17 0.29 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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36 Table 2-5. Model construction procedure for first move time Models -2LL -2LLr2 b r2 w Null 3632.17 ----Difference of days added 2051.371580.800.45 0.09 Year added 1944.95106.42-0.17 0.26 Set added 1903.1841.77-0.04 0.12 Nap duration added 899.391003.79-0.06 0.04 Bedtime added 915.54-16.15-0.03 0.00 Wakeup time added 930.78-15.24-0.01 0.00 Sleep onset latency added 936.56-5.78-0.04 0.00 Number of nighttime awakenings added 934.881.68-0.03 0.00 Waketime after sleep onset added 932.921.960.19 0.00 Terminal wakefulness added 937.37-4.45-0.05 0.00 Time in bed added 937.370.000.00 0.00 Total sleep time added 937.370.000.00 0.00 Sleep efficiency added 924.5812.790.01 0.00 Sleep quality rating added 920.214.370.12 0.00 Set*year added 916.124.090.00 0.02 Reduced forma 895.612736.560.29 0.43 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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37 Table 2-6. Model construction procedure for solution time Models -2LL -2LLr2 b r2 w Null 4369.22 ----Difference of days added 2546.371822.86-0.06 0.03 Year added 2536.979.40-0.03 0.02 Set added 2531.765.21-0.01 0.01 Nap duration added 1193.551338.210.01 0.02 Bedtime added 1207.78-14.240.05 0.00 Wakeup time added 1221.57-13.790.04 0.00 Sleep onset latency added 1226.19-4.62-0.03 0.00 Number of nighttime awakenings added 1222.953.240.08 0.00 Waketime after sleep onset added 1225.43-2.48-0.07 0.00 Terminal wakefulness added 1229.20-3.77-0.10 0.00 Time in bed added 1229.200.000.00 0.00 Total sleep time added 1229.200.000.00 0.00 Sleep efficiency added 1215.1214.070.07 0.00 Sleep quality rating added 1208.746.380.39 0.00 Set*year added 1207.391.350.02 -0.01 Reduced forma 1185.683183.540.19 0.09 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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38 Table 2-7. Model construction pr ocedure for optimal move score Models -2LL -2LLr2 b r2 w Null 9813.77 ----Difference of days added 5635.214178.560.24 0.10 Year added 5623.8811.32-0.01 0.01 Set added 5594.8829.01-0.01 0.06 Nap duration added 2592.383002.490.01 0.13 Bedtime added 2599.65-7.27-0.02 0.00 Wakeup time added 2606.72-7.07-0.03 0.00 Sleep onset latency added 2603.603.12-0.03 0.00 Number of nighttime awakenings added 2588.0215.570.17 0.00 Waketime after sleep onset added 2581.696.330.00 0.00 Terminal wakefulness added 2577.534.16-0.05 0.00 Time in bed added 2577.530.000.00 0.00 Total sleep time added 2577.530.000.00 0.00 Sleep efficiency added 2557.2020.33-0.05 0.00 Sleep quality rating added 2542.1415.060.22 0.00 Set*year added 2532.489.66-0.01 0.00 Reduced forma 2560.967252.810.5 0.28 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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39 Table 2-8. Model construction proce dure for holding peg strategy usage Models -2LL -2LLr2 b r2 w Null 9668.45 ----Difference of days added 5619.734048.720.37 -0.11 Year added 5565.3754.36-0.07 0.12 Set added 5498.3067.07-0.05 0.16 Nap duration added 2556.622941.68-0.23 0.11 Bedtime added 2564.01-7.40-0.02 0.00 Wakeup time added 2571.19-7.17-0.03 0.00 Sleep onset latency added 2568.452.73-0.04 0.00 Number of nighttime awakenings added 2552.7615.700.18 0.00 Waketime after sleep onset added 2547.555.20-0.04 0.00 Terminal wakefulness added 2543.374.18-0.04 0.00 Time in bed added 2543.370.000.00 0.00 Total sleep time added 2543.370.000.00 0.00 Sleep efficiency added 2523.0320.34-0.04 0.00 Sleep quality rating added 2510.4512.580.10 0.00 Set*year added 2499.9110.54-0.01 0.01 Reduced forma 2529.287139.170.33 0.27 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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40 Table 2-9. Model construc tion procedure for complex matching strategy usage Models -2LL -2LLr2 b r2 w Null 8877.25 ----Difference of days added 5167.273709.970.31 -0.04 Year added 5151.1416.14-0.04 0.02 Set added 5138.3612.77-0.03 0.02 Nap duration added 2411.112727.250.37 -0.06 Bedtime added 2420.66-9.56-0.08 0.00 Wakeup time added 2427.82-7.160.10 0.00 Sleep onset latency added 2425.901.930.02 0.00 Number of nighttime awakenings added 2417.238.670.01 0.00 Waketime after sleep onset Added 2413.263.97-0.06 0.00 Terminal wakefulness added 2409.663.600.06 0.00 Time in bed added 2409.660.000.00 0.00 Total sleep time added 2409.660.000.00 0.00 Sleep efficiency added 2391.3818.28-0.15 0.00 Sleep quality rating added 2383.577.81-0.11 0.00 Set*year added 2375.438.14-0.01 0.00 Reduced forma 2395.516481.740.47 -0.06 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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41 Table 2-10. Model construc tion procedure for simple matching strategy usage Models -2LL -2LLr2 b r2 w Null 9050.64 ----Difference of days added 5248.803801.84-0.10 0.04 Year added 5240.738.070.00 0.00 Set added 5232.388.35-0.01 0.01 Nap duration added 2434.462797.920.33 0.05 Bedtime added 2443.87-9.42-0.08 0.00 Wakeup time added 2451.24-7.370.03 0.00 Sleep onset latency added 2450.151.09-0.09 0.00 Number of nighttime awakenings added 2441.618.54-0.04 0.00 Waketime after sleep onset Added 2436.784.820.00 0.00 Terminal wakefulness added 2434.132.65-0.09 0.00 Time in bed added 2434.130.000.00 0.00 Total sleep time added 2434.130.000.00 0.00 Sleep efficiency added 2415.4118.72-0.09 0.00 Sleep quality rating added 2405.3810.030.11 0.00 Set*year added 2397.727.660.01 -0.01 Reduced forma 2417.116633.530.26 0.09 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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42 Table 2-11. Model construction proc edure for searching strategy usage Models -2LL -2LLr2 b r2 w Null 9369.23 ----Difference of days added 5452.363916.870.17 -0.04 Year added 5437.2715.09-0.01 0.02 Set added 5431.285.990.00 0.00 Nap duration added 2539.592891.690.35 -0.03 Bedtime added 2548.23-8.64-0.06 0.00 Wakeup time added 2555.64-7.41-0.01 0.00 Sleep onset latency added 2552.623.020.02 0.00 Number of nighttime awakenings Added 2543.089.54-0.06 0.00 Waketime after sleep onset added 2538.075.01-0.03 0.00 Terminal wakefulness added 2534.793.28-0.07 0.00 Time in bed added 2534.790.000.00 0.00 Total sleep time added 2534.790.000.00 0.00 Sleep efficiency added 2514.4620.320.00 0.00 Sleep quality rating added 2502.8311.630.18 0.00 Set*Year added 2494.658.190.01 -0.01 Reduced forma 2518.406850.840.52 -0.05 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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43 Table 2-12. Model construction proc edure for random/none strategy usage Models -2LL -2LLr2 b r2 w Null 9280.18 ----Difference of days added 5382.163898.030.14 0.00 Year added 5369.9912.160.00 0.01 Set added 5364.195.800.00 0.00 Nap duration added 2483.972880.220.50 0.07 Bedtime added 2488.27-4.300.30 0.00 Wakeup time added 2493.10-4.830.21 0.00 Sleep onset latency added 2491.641.46-0.11 0.00 Number of nighttime awakenings Added 2479.9011.740.08 0.01 Waketime after sleep onset added 2470.339.570.48 0.00 Terminal wakefulness added 2467.333.00-0.12 0.00 Time in bed added 2467.330.000.00 0.00 Total sleep time added 2467.330.000.00 0.00 Sleep efficiency added 2448.4218.91-0.10 0.00 Sleep quality rating added 2435.6912.730.53 0.00 Set*year added 2426.489.21-0.13 0.00 Reduced forma 2462.236817.950.62 0.09 Notes: a reduced model retained Difference of days, Years, Sets, Nap duration, Number of nighttime awakenings, and Sleep quality rating. -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an estimate of the amount of between subjects variance (estimated from null model) explained by fixed predictors; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance (estimated from null model) explained by fixed predictors. Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Bedtime what time did the participant go to bed; Wakeup time what time did the child wakeup in the morning; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Terminal wakefulness the time between waking up in the morning and getting out of bed; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor ) to 5 (excellent).

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44 Figure 2-1. The order of events presented to the participant. War m -up tas k 3rd set of 10 TOL Problems Cartoon Brea k 2nd set of 10 TOL Problems 3-move, 4-move, 5-move, 6-move, 7-move p roblems 3-move, 4-move, 5-move, 6-move, 7-move problems TOL Instructions and Practice Cartoon Brea k 1st set of 10 TOL Problems3-move, 4-move, 5-move, 6-move, 7-move problems Peabody Picture Vocabulary Test

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45 CHAPTER 3 RESULTS Aim 1: The Impact of Sleep on Executive Function and Strategy Use Table 3-1 shows the m eans and standard devi ations for the sleep variables for the 60 participants with sleep data. Table 3-2 shows the correlations between the sleep measures. This data indicates that while some of the sleep va riables are significantly co rrelated, a large amount of variance still needs to be explained. Multilevel Modeling Results An initial step in Multilevel Modeling (MLM ) is determ ining how much variance can be accounted for by improving upon the null (baseline) model of predicting executive functioning performance with the sleep variables; which in cludes estimates of between and within person variability. Intraclass correlation coefficients (ICC) serve as an index of these variability estimates (Bryk & Raudenbush, 1992). For each variable, the between-person and within-person variability is presented in Table 3-3. This initial analyses revealed that there was a significant amount of variability at both the between and within person levels which could be explained by the models. Models An overview of the m odel result s can be found in Table 3-4. This table shows the model fit results for the final and null models for each TOL variable, the between-subjects pseudo R2 (an estimate of the amount of between subjects variance), and with in-subjects pseudo R2 (an estimate of the amount of within subjects variance). The final m odels resulted in a reduction in 2LL, a measure indicating fitness, for the m odel indicating better fit. The between subjects pseudo R2 ranged from 0.17 to 0.62 for the 10 models. The within subjects pseudo R2 ranged from -0.06 to 0.43 for the 10 models. Overall, the models explained a larger portion of the

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46 between-person variance. Interestingly, the mode ls explained a larger portion of the withinperson variance for the traditional TOL variable s (within: 0.09 to 0.43 ve rsus between: -0.06 to 0.27). In contrast, the models explained a larger portion of the between-p erson variance for the TOL strategy variables (within: 0.15 to 0.58 versus between: 0.23 to 0.62). More specific information on the models for each TOL variable are shown in Tables 3-5 through 3-14 and will now be discussed in turn. Table 3-5 shows the predictor variables and significance for the model pred icting proportion solved. Betw een person results suggested significant negative relationships for nap duration, number of ni ghttime awakenings, and sleep quality rating indicating that as ratings increased the proportion of problems solved decreased. The direction of the associations between nap duration and number of nighttime awakenings and proportion solved were in the expected direction. However, the direction of the association between sleep quality rating and proportion solved was in the oppos ite direction. Within person results suggested a significant positive relationshi p for both years and sets indicating that as years and sets increased the pr oportion of solved problems increas ed. The followup analyses to further examine this relationship will be discussed in the sections for Aims 2 and 3 of the results section. Table 3-6 shows the predictor variables a nd significance for the model predicting goal path. Between person results suggested a sign ificant negative relati onship for number of nighttime awakenings indicating that as the number of nighttime awakenings increased the length of the goal path decreased. The direc tion of the association between the number of nighttime awakenings and goal path was in th e expected direction. Within person results suggested a significant positive relationship for sets indicating that as sets increased the length of

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47 the goal path increased. The followup analyses to further examine this relationship will be discussed in the section for Ai m 2 of the results section. Table 3-7 shows the predictor variables and significance for the model predicting first move time. Between person results suggested a no significant relationships. Within person results suggested significant negative relationships for both years and sets indicating that as years and sets increased the first move time decreased. The followup analyses to further examine this relationship will be discussed in the sections for Aims 2 and 3 of the results section. Table 3-8 shows the predictor variables and significance for the m odel predicting solution time. Between person results suggested no signi ficant relationships. Within person results suggested no significant relationships. Table 3-9 shows the predictor variables and significance for the model predicting Optimal Move Score. Between person results suggest ed significant negative relationships for nap duration, number of nighttime awakenings, and sleep quality rating indicating that as nap duration, number of nighttime awakenings, and sleep quality rating increased Optimal Move Score decreased. The direction of the asso ciations between nap duration and number of nighttime awakenings and proportion solved were in the expected direction. The direction of the association between sleep quality rating and Optimal Move Score was in the opposite direction. However, when controlling for the number of an alyses only the relationship between the number of awakenings and Optimal Move Score remained significant. Within person results suggested a significant positive relationship for sets indicating that as sets increased Optimal Move Score increased. The followup analyses to further exam ine this relationship will be discussed in the section for Aim 2 of the results section.

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48 Table 3-10 shows the predictor variables and significance for the model predicting Holding Peg strategy usage. Between person results s uggested significant negative relationships for nap duration and number of nighttime awakenings indicating that as nap duration and number of nighttime awakenings increased the Holding Peg strategy usage decreased. The direction of the associations between nap durati on and number of nighttime awakenings and proportion solved were in the expected direction. However, when controlling for the number of analyses neither of these relationships remained significant. With in person results suggested a significant positive relationship for both years and sets indicating that as years and sets increased the holding peg strategy usage increased. The followup analyses to further examine this relationship will be discussed in the sections for Aims 2 and 3 of the results section. Table 3-11 shows the predictor variables and significance for the model predicting Complex Matching strategy usage. Between person results suggested no significant relationships. Within person results suggested a significant positive relationship for years and a negative relationship for sets indicating that as years increased Complex Matching strategy usage increased and as sets increased Complex Matc hing strategy usage decreased. However, when controlling for the number of analyses neither of these relationships remained significant. Table 3-12 shows the predictor variables and significance for the model predicting Simple Matching strategy usage. Between person results suggested no si gnificant relationships. Within person results suggested no significant relationships. Table 3-13 shows the predictor variables and significance for the model predicting Searching strategy Usage. Between person result s suggested no significant relationships. Within person results suggested a significant positive relationship for years indicating that as years increased Searching strategy usage increased. However, when controlling for the number of

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49 analyses this relationship did not remain significant but this relationship will be further discussed in the section for Aim 3 because p=.005. Table 3-14 shows the predictor variables and significance for the model predicting Random/None strategy usage. Between pers on results suggested a significant positive relationship for number of nighttime awakenings indicating that as the number of nighttime awakenings increased the Random/None strategy usage increased. The direction of this association was in the expected direction. Howeve r, when controlling for the number of analyses this relationship did not remain significant. Within person results suggested no significant relationships. In summary, these 10 analyses revealed num erous significant pred icative relationships with both the traditional and strategy TOL variables. Specifically, nap duration showed significant relationships with proportion solved, length of goal path, and optimal move score (Table 3-15). Nap duration also showed a signi ficant relationship with Holding Peg strategy usage (Table 3-15). All of these relationships indicate that as nap duration increases, TOL performance becomes worse meaning that fewer pr oblems are solved, goal paths become shorter, move efficiency decreases, and Ho lding Peg strategy usage decreases. The number of nighttime awakenings showed significant relationships with proportion solved, length of goal path, and optimal move score (Table 3-15). Number of nighttime awakenings also showed a significant rela tionship with Holding Peg strategy usage and Random/None strategy usage (Table 3-15). Like nap duration, all of the relationships between nighttime awakenings and TOL performance i ndicated that as the number of nighttime awakenings increased, TOL performance become s worse. Specifically fewer problems are

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50 solved, goal paths become shorter, move effi ciency decreases, Holding Peg strategy usage decreases, and Random/None strategy usage increases. The sleep quality rating showed significant relationships with proportion solved, length of goal path, and optimal move score (Table 3-15) No significant relationships between sleep quality rating and the TOL strate gy variables existed (Table 3-15). Unlike nap duration and number of nighttime awakenings, all of the re lationships between sleep quality rating and TOL performance indicated that as sleep quality ra ting increased, TOL performance becomes worse. Specifically fewer problems are solved, goal pa ths become shorter, and move efficiency decreased. The year and sets variables presented in this table will be discussed in each of the following sections. Aim 2: Evaluating Executive Functioning and Strategy Use Changes with Experience In this study, experience was m a nipulated by looking at the effects of repeated exposure to TOL problem, identified here as problem Sets. Being that the MLM analyses yielded information on the relationship between sets and the TOL performance variables, only significant findings will be further explored to determine th e nature of differences among the sets. Follow up repeated meas ures ANCOVAs for each of the significant findings for sets will now be discussed. For all analyses, independent variables were Years (1 and 2) and Sets (1, 2 and 3), and the covariate was the Difference of Days. In summary, the MLM analyses revealed sets had a significant relationship with the fo llowing dependent variables: proportion solved (positive relationship), goal path (positive relati onship), first move time (negative relationship), optimal move score (positive relationship), a nd holding peg usage (positive relationship). Because the present study required 10 differe nt MLMs, as well as a number of follow-up tests, the critical level for signi ficance has been reduced to .005. Interactions for all variables were all non-significant, F< 1, unless otherwise specified.

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51 Proportion Solved Participants performance clearly improved ac ross sets. Participants showed dramatic improvement across the sets improving from solv ing 66% of the problems in the first set to solving 77% of the problems in the second se t and 79% in the thir d set (figure 3-1). Both significant linear and quadratic trends occurred for proportion so lved across the three sets, F (1,65)=66.358, p<.001, p 2= .505 and F (1,65)=11.705, p=.001, p 2= .153, respectively. Followup tests using the Bonferonni correction revealed the first set was significantly lower than the second and third sets ( ps<.001). There was not a significant difference between the second and third sets ( p=.468). This leveling off of the proportion solved by the third set is what led to the significant quadratic sets effect. Goal Path As with proportion solved, pa rticipants goal path perfor mance clearly improved across sets. Participants showed improvement across the sets with goal paths that in comparison with the first set were 7% longer in the second set an d 9% longer in the third set, respectively (figure 3-2). Both significant linear and quadratic trends occurred for length of goal path across the three sets, F (1,63)=20.378, p<.001, p 2= .244 and F (1,63)=9.465, p=.003, p 2= .131, respectively. Followup tests us ing the Bonferonni corr ection revealed the goal path length in first set was significantly shorter than the second and third sets ( ps<.001). There was not a significant difference between the second and third sets ( p =.127). Again, th e evidence of a leveling off of the impact of sets was th e source of the quadratic trend over sets.

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52 First Move Time Participants clearly improved across sets. Pa rticipants showed faster first move times across the sets with the second set being 16% faster than th e first set and th ird set being 22% faster than the first set (figure 3-3). Both significant linear and quadratic trends occurred for first move time across the three sets, F (1,63)=44.914, p<.001, p 2= .416 and F (1,63)=4.055, p=.048, p 2= .060, respectively. Followup tests using the Bonfer onni correction revealed the fi rst set was significantly longer than the second and third sets ( ps <.001). The third set was also faster than the second faster ( p=.030). Although the changes in th is variable continued into th e third sets, unlike that for proportion solved and goal path, th e increase from set 2 to 3 was smaller than for that between sets 1 and 2. Hence, the quadratic as well as linear trends over sets. Optimal Move Score Participants clearly improved across sets. Participants showed dramatic improvement across the sets with the Optimal Move Scores th at in comparison with the first set were 26% higher in the second set and 22% higher in the third set, respec tively (figure 3-4). Both significant linear and quadratic trends occurred for Optimal Move Score across the three sets, F (1,65)=18.941, p<.001, p 2= .226 and F (1,65)=11.874, p=.001, p 2= .154, respectively. Followup tests using the Bonferonni correction revealed the first set was significantly lower than th e second and third sets ( ps<.001). There was not a significant difference between the s econd and third sets ( p=1.000). As before, this latter finding is the cause of the quadratic trend seen.

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53 Holding Peg Strategy Usage Participants clearly improved across sets. Participants showed dramatic improvement across the sets with th e Holding Peg strategy usage increasin g by 16% in the second set and 24% in the third set (figure 3-5). A significant linear trend occurred for Holdi ng Peg strategy usage acr oss the three sets, F (1,65)=32.084, p<.001, p 2= .330. Followup tests using the B onferonni correction revealed the first set was significantly lower th an the second and third sets ( ps<.001). The third set was also higher than the second faster ( p=.017). In summary, for all of the variables presen ted performance in the second and thirds sets were significantly improved over the first set. Sp ecifically, participants solved fewer problems, showed less depth of planning, initiated ball movement more slowly, solved problems less efficiently, and used the holding pe g strategy less in the first set than they did in either the second or third set. Lastly the second and thir d sets did not show any significant differences. However, the initiation of ball movement and holding peg strategy usage did approach significant improvements. Aim 3: Examining the Development of Executive Function and Strategy Use Being that the MLM an alyses yielded inform ation on the relationship between years and the TOL variables only significant fi ndings will be further explored to determine the nature of differences between the years. Follow up repeated measures ANCOVAs for each of the significant findings for years will now be discussed. All analyses will parallel the analyses on sets discussed in the previous section. In summary, the MLM analyses revealed years had a significant relationship with the following de pendent variables: proportion solved (positive relationship), first move time (negative relationship), holding peg usage (positive relationship), and searching strategy use (positive relationship).

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54 Proportion Solved Participants clearly improved across years. Participants showed dramatic improvement across the two years improving from solving 65% in the first year to so lving 84% in the second year (figure 3-1). A significant differen ce occurred for proportion solved across years, F (1,130)=113.870, p<.001, p 2= .637. First Move Time Participants clearly improved across years. Pa rticipants showed faster first move times across the two years with the sec ond year being 30% faster than the first year (figure 3-3). A significant difference occurred for fi rst move time across the years, F (1,126)=43.089, p<.001, p 2= .406. Holding Peg Strategy Usage Participants clearly improved across two y ears. Participants showed dramatic improvement across the years with the Holding Peg strategy usage increasing by 19% in the second year (figure 3-5). A si gnificant difference occurred for Holding Peg strategy usage across the years, F (1,130)=32.084, p<.001, p 2= .330. Searching Strategy Usage Participants had increased Sear ching strategy usage across two years. Participants showed a difference across the years with the Searching strategy usage increasing by 6% in the second year (figure 3-6). No significant difference o ccurred for Searching strategy usage across the two years, F (1,130)=3.865, p>.05, p 2= .056. In summary, for all of the variables presented except the searching strategy performance in the second year was significantly improved over performance in the first year. Specifically, with

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55 the additional year of development participants solved more problems, initiated ball movement more quickly, and used the holding peg strategy more often.

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56 Table 3-1. Means and standard deviations of sleep variables Measure Mean Std Nap duration (minutes) 9.43 25.43 Sleep onset latency (minutes) 16.05 14.15 Number of nighttime aw akenings (count) 0.18 0.40 Waketime after sleep onset (minutes) 1.39 4.37 Time in bed (minutes) 597.89 62.40 Total sleep time (minutes) 573.81 62.09 Sleep efficiency (ratio) 96 3 Sleep quality rating (scale) 4.51 0.57 Notes: Nap duration how long did the nap last ; Sleep onset latency the time from initial lights-out until sleep onset; Number of nighttime awakenings the number of total awakenings during the night; Wake time after sleep onset the time spent awake after initial sleep onset until the last awakening; Time in bed the total number of minutes spent in bed during the night; Total sleep time the total number of minutes sp ent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor) to 5 (excellent).

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57 Table 3-2. Correlations between the sleep measures for the 60 participants Measure 1 2 3 4 5 6 7 8 Nap duration -.25 -.17 -.12 -.09 -.17 -.30 .07 Sleep onset latency -.21 .23 .08 -.15 -.83 ** -.23 Number of nighttime awakenings -.67 **-.05 -.18 -.42 ** -.30 Waketime after sleep onset -.07 -.06 -.40 ** -.30 Time in bed -.96 **-.06 -.07 Total sleep time -.23 .04 Sleep efficiency -.35 ** Sleep quality rating -Values in bold and with refer to a significant value at p<.05, ** re fer to a significant value at p<.01. Notes: Nap duration how long did the nap last; Sleep onset latency the time from initial lights-out until sleep onset; Numb er of nighttime awakenings the number of total awakenings during the night; Wake time afte r sleep onset the time spent awake afte r initial sleep onset until the last awakening; Time in bed the total number of minutes spent in bed during the night; Total sl eep time the total number of minutes spent asleep during the night; Sleep efficiency the ratio of total sleep time to total time spent in bed 100; Sleep quality rating scaled from 1 (very poor) to 5 (excellent).

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58 Table 3-3. The between-person and within-person intraclass correlation coefficients for each variable TOL variable Between person vari abilityWithin person variability Proportion solved 0.44 0.56 Goal path 0.26 0.74 First move time 0.33 0.67 Solution time 0.09 0.91 Optimal move score 0.38 0.62 Holding peg 0.40 0.60 Complex matching 0.13 0.87 Simple matching 0.12 0.88 Searching 0.21 0.79 Random 0.25 0.75 Notes: Proportion of problems solved the number of problems solved correctly divided by the total number of problems; Goal pa th the number of moves made by the participants in which they are getting consiste ntly closer to the goal and eventually solve the problem; First-move time the time from when the problem is presented to when the participants complete their first move; Solution time the total time spent on a problem minus the first move time; Optimal move score a measure that evaluates participants moves to determine overall strategy effec tiveness; Holding peg strategy Removing obstacle balls so that others can be placed in final goal positions getting consistently closer to the goal; Complex matching strategy places a ball in a final goal position but not immediately preceded by at least one removal of an obstacle ball moving closer to the goal; Simple matching strategy places ball in a goal position but does not move closer to the goal; Searching strategy Exploring of the problem space while attending to goal opportunities; Random/none strategy not attending to the goal board.

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59 Table 3-4. Null and final models for each Tower of London variable Models -2LL -2LLr2 b r2 w Proportion solved Null 9873.38--Final 2530.237343.150.58 0.43 Goal path Null 1484.85 --Final 371.091113.770.17 0.29 First move time Null 3632.17 --Final 895.612736.560.29 0.43 Solution time Null 4369.22 --Final 1185.683183.540.19 0.09 Optimal move score Null 9813.77 --Final 2560.967252.810.50 0.28 Holding peg Null 9668.45 --Final 2529.287139.170.33 0.27 Complex matching Null 8877.25 --Final 2395.516481.740.47 -0.06 Simple matching Null 9050.64 --Final 2417.116633.530.26 0.09 Searching Null 9369.23 --Final 2518.406850.840.52 -0.05 Random Null 9280.18 --Final 2462.236817.950.62 0.09 Notes: -2LL = -2 log likelihood; -2LL = change in LL relative to preceding model; r2 b = between-subjects pseudo R-squared, an esti mate of the amount of between subjects variance; r2 w = within-subjects pseudo R-squared, an estimate of the amount of within subjects variance. Proportion of problems solved the number of problems solved correctly divided by the total number of probl ems; Optimal move score a measure that evaluates participants moves to determine overall strategy effectiveness; First-move time the time from when the problem is presente d to when the participants complete their first move; Solution time the total time spen t on a problem minus the first move time; Goal path the number of moves made by the participants in which they are getting consistently closer to the goa l and eventually solve the prob lem; Holding peg strategy Removing obstacle balls so that others can be placed in final goal positions getting consistently closer to the goal; Complex matc hing strategy places a ball in a final goal position but not immediately preceded by at leas t one removal of an obstacle ball moving closer to the goal; Simple matching strategy places ball in a goal position but does not move closer to the goal; Searching strate gy Exploring of the problem space while attending to goal opportu nities; Random/none strategy not attending to the goal board.

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60 Table 3-5. Sleep variables, years, and sets predicting proportion solved Proportion solved Predictor variable BSEdf t p Within-person Year 199.3018.47166.12 10.79 0.000 Set 61.2811.23164.46 5.46 0.000 Between-person Difference of days -0.030.1229.66 -0.28 0.782 Nap duration -3.031.0429.59 -2.93 0.007 Number of nighttime awakenings -165.1249.5632.38 -3.33 0.002 Sleep quality rating -98.9334.1529.91 -2.90 0.007 Notes: Proportion of problems solved the number of problems solved correctly divided by the total number of problems; Difference of days the number of days from the 365 days between the test dates in year 1 and y ear 2; Year TOL performance during years 1 and 2; Set TOL performance during each se t; Nap duration how long did the nap last; Number of nighttime awakenings the num ber of total awakeni ngs during the night; Sleep quality rating scaled from 1 (very poor) to 5 (excellent)

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61 Table 3-6. Sleep variables, year s, and sets predicting goal path Goal path Predictor variable BSEdf t p Within-person Year 0.040.07165.490.55 0.586 Set 0.180.04163.664.00 0.000 Between-person Difference of days 0.000.0029.411.20 0.239 Nap duration -0.010.0029.89-2.57 0.015 Number of nighttime awakenings -0.620.1732.84-3.61 0.001 Sleep quality rating -0.260.1229.72-2.22 0.034 Notes: Goal path the number of moves ma de by the participants in which they are getting consistently closer to the goal and eventually solve the problem; Difference of days the number of days from the 365 days be tween the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Numb er of nighttime awakenings the number of total awakenings during the night; Sleep qua lity rating scaled from 1 (very poor) to 5 (excellent)

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62 Table 3-7. Sleep variables, years, and sets predicting first move time First move time Predictor variable BSEDf t p Within-person Year -2.550.28165.60-9.23 0.000 Set -0.840.17164.15-4.98 0.000 Between-person Difference of days 0.000.0030.26-0.22 0.831 Nap duration 0.030.0230.601.86 0.073 Number of nighttime awakenings 0.740.7632.840.97 0.341 Sleep quality rating 0.740.5230.501.41 0.168 Notes: First-move time the time from when the problem is presented to when the participants complete their first move; Differe nce of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Number of nighttime awakenings the number of total awakenings during the night; Sleep quality rating scaled from 1 (very poor) to 5 (excellent)

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63 Table 3-8. Sleep variables, years, and sets predicting solution time Solution time Predictor variable BSEdf t p Within-person Year -1.150.64167.63-1.81 0.073 Set -0.580.39165.05-1.49 0.138 Between-person Difference of days 0.000.0029.500.86 0.395 Nap duration 0.030.0230.681.21 0.236 Number of nighttime awakenings -0.151.0436.18-0.14 0.889 Sleep quality rating 1.390.7030.072.00 0.055 Notes: Solution time the total time spen t on a problem minus the first move time; Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance dur ing years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Number of nighttime awakenings the number of total awakenings during the night; Sleep quality rating scaled from 1 (very poor) to 5 (excellent)

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64 Table 3-9. Sleep variables, years, and sets predicting optimal move score Optimal move score Predictor variable BSEdf t p Within-person Year 24.0420.31166.421.18 0.238 Set 41.4012.35164.523.35 0.001 Between-person Difference of days -0.060.1229.52-0.47 0.645 Nap duration -3.081.0229.46-3.01 0.005 Number of nighttime awakenings -178.1349.2832.83-3.61 0.001 Sleep quality rating -93.5333.8029.83-2.77 0.010 Notes: Optimal move score a measure that evaluates participants moves to determine overall strategy effectiveness; Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Number of nighttime awakenings the num ber of total awakeni ngs during the night; Sleep quality rating scaled from 1 (very poor) to 5 (excellent)

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65 Table 3-10. Sleep variables, years, and se ts predicting holding peg strategy usage Holding peg strategy usage Predictor variable BSEdf t p Within-person Year 113.3818.38166.25 6.17 0.000 Set 73.5911.18164.64 6.59 0.000 Between-person Difference of days 0.070.1329.86 0.57 0.571 Nap duration -2.751.0529.79 -2.63 0.014 Number of nighttime awakenings -150.1550.0632.52 -3.00 0.005 Sleep quality rating -70.1734.5130.11 -2.03 0.051 Notes: Holding peg strategy Removing obstacl e balls so that others can be placed in final goal positions getting consistently closer to the goal; Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Number of nighttime awakenings the number of total awakenings during the ni ght; Sleep quality rating scal ed from 1 (very poor) to 5 (excellent)

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66 Table 3-11. Sleep variables, years, and se ts predicting complex matching strategy usage Complex matching strategy usage Predictor variable BSEdf t p Within-person Year 29.8114.13168.322.11 0.036 Set -22.048.62165.39-2.56 0.012 Between-person Difference of days -0.010.0629.14-0.14 0.890 Nap duration 0.520.4629.181.15 0.261 Number of nighttime awakenings 13.3622.7936.110.59 0.561 Sleep quality rating 8.6315.1629.760.57 0.574 Notes: Complex matching strategy places a ball in a final goal position but not immediately preceded by at least one remova l of an obstacle ball moving closer to the goal; Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL perfor mance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Number of nighttime awakenings the number of total awakenings during the night; Sleep quality rating scaled from 1 (very poor) to 5 (excellent)

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67 Table 3-12. Sleep variables, years, and se ts predicting simple matching strategy usage Simple matching strategy usage Predictor variable BSEdf t p Within-person Year 18.2914.78166.201.28 0.218 Set 9.209.02163.261.02 0.309 Between-person Difference of days 0.040.0627.360.63 0.536 Nap duration 0.290.5227.370.57 0.573 Number of nighttime awakenings 3.1725.4933.270.13 0.902 Sleep quality rating 21.0817.0827.891.23 0.227 Notes: Simple matching strategy places ball in a goal position but does not move closer to the goal; Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Number of nighttime awakenings the number of total awakenings during the night; Sleep quality rating scaled from 1 (very poor) to 5 (excellent)

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68 Table 3-13. Sleep variables, years, and sets predicting sear ching strategy usage Searching strategy usage Predictor variable BSEdf t p Within-person Year 54.5619.18167.292.85 0.005 Set -0.5111.70164.46-0.04 0.965 Between-person Difference of days 0.130.0828.501.63 0.114 Nap duration 1.150.6728.511.72 0.097 Number of nighttime awakenings 58.8833.2134.561.77 0.085 Sleep quality rating 41.0122.2529.041.84 0.076 Notes: Searching strategy Exploring of the problem space while attending to goal opportunities; Difference of days the numbe r of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance dur ing years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Number of nighttime awakenings the number of total awakenings during the night; Sleep quality rating scaled from 1 (very poor) to 5 (excellent)

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69 Table 3-14. Sleep variables, years, and sets predicting random/none strategy usage Random/none Strategy Usage Predictor variable BSEdf tp Within-person Year 27.7716.52166.14 1.680.095 Set 5.7410.07163.29 0.570.569 Between-person Difference of days 0.000.0727.50 0.060.956 Nap duration 0.300.6027.50 0.500.620 Number of nighttime awakenings 64.8129.4433.10 2.200.035 Sleep quality rating 34.3519.7828.01 1.740.093 Notes: Random/none strategy not attending to the goal board; Difference of days the number of days from the 365 days between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set; Nap duration how long did the nap last; Number of nighttime awakenings the number of total awakenings during the ni ght; Sleep quality rating scal ed from 1 (very poor) to 5 (excellent)

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70 Table 3-15. Summary table showi ng predictive significance of sleep variables, ye ars, and sets on Towe r of London traditional a nd strategy variables Traditional TOL Measures Strategy TOL Measures Variable Proportion solved Goal path First move time Solution time Optimal move score Holding peg Complex matching Simple matching Searching Random Within-person Year 10.79** 0.55 -9.23** -1.80 1.18 6.17** 2.11* 1.24 2.84* 1.68 Set 5.46** 4.00** -4.98** -1.49 3.35** 6.58** -2.56* 1.02 -0.04 0.57 Between-person Difference of days -0.28 1.20 -0.22 0.86 -0.47 0.57 -0.14 0.63 1.63 0.06 Nap duration -2.92* -2.57* 1.86* 1.21 -3.01* -2.62* 1.15 0.57 1.72 0.50 Number of nighttime awakenings -3.33** -3.61** 0.97 -0.14 -3.61** -3.00* 0.59 0.12 1.77 2.20* Sleep quality rating -2.90* -2.22* 1.41 2.00 -2.77* -2.03 0.57 1.23 1.84 1.74 Values in bold and with refer to a significant value at p<.05, ** re fer to a significant value at p<.005. Notes: Proportion of problems solved the number of problems so lved correctly divided by the total number of problems; Goal pa th the number of moves made by the participants in which they are getting consistently closer to the goal and eventually solve the problem; First-move time the time from when the problem is pres ented to when the participants complete their first move; Solu tion time the total time spent on a problem minus the first move time; Optimal move score a measure that evaluates participants moves to determine overall strategy effectiveness; Holding peg strategy Removi ng obstacle balls so that othe rs can be placed in fin al goal positions getting consistently closer to the goal; Complex matching st rategy places a ball in a final goal position but not i mmediately preceded by at least one removal of an obstacle ball moving closer to the goal; Simple matching strategy places ball in a goa l position but does not move closer to the goa l; Searching strategy Exploring of th e problem space while attending to goal opportunities; Random/none strategy not attending to the goal board; Difference of days the number of days from the 365 day s between the test dates in year 1 and year 2; Year TOL performance during years 1 and 2; Set TOL performance during each set ; Nap duration how long did the nap last; Numb er of nighttime awakenings the number of total awakenings during the night; Sle ep quality rating scaled from 1 (very poor) to 5 (excellent)

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71 Figure 3-1. Proportion solved for sets and years. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 123 SetsProportion Solved Year 1 Year 2

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72 Figure 3-2. Goal path length for sets and years. 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 5.10 123 SetsGoal Path Length Year 1 Year 2

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73 Figure 3-3. First move time for sets and years. 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 123 SetsFirst Move Time (s) Year 1 Year 2

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74 Figure 3-4. Optimal move score for sets and years. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 123 SetsOptimal Move Score Year 1 Year 2

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75 Figure 3-5. Holding peg strate gy usage for sets and years. 0.00 0.20 0.40 0.60 0.80 1.00 123 SetsHolding Peg strategy usage Year 1 Year 2

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76 Figure 3-6. Searching strategy usage for sets and years. 0.00 0.20 0.40 0.60 0.80 1.00 123 SetsSearching strategy usage Year 1 Year 2

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77 CHAPTER 4 DISCUSSION The Impact of Sleep on Executive Function and Strategy Use Several hypotheses proposed in the introduction were supported and several were not. The exam ination of sleep variables such as the numbe r of awakenings, nap dur ation, and sleep quality rating had significant associations with TOL pe rformance. Specifically, the hypotheses that more frequent awakenings and nap duration would have significant negati ve associations with proportion solved, goal path, optimal move scor e, and holding peg strategy usage were supported. Furthermore, number of night awakenings was positively associated with increased random/none strategy usage. The findings that the number of night awakenings would have a negative impact on executive function is cons istent with both Drummond and colleagues (1999, 2001, 2004) and Sadeh and colleagues (1998, 200 0, 2000, 2002) work. As Sadeh (1994) discussed, parents awareness of night awakenings is limited; therefore, it should be noted that the awakenings variable in the pr esent study indicates that this variable is pa rents awareness of the number of awakenings. The finding that nap duration also has a negative impact on executive functioning has not been explored for young school age children in previous literature. This finding suggests that young school age children must get sufficient sleep at night in order to perform well in school and that napping is not a substitute for lost nocturnal sleep. The hypothesis about sleep quality rating havi ng a positive association with better TOL performance was not supported. In fact, this vari able had significant negative associations with proportion solved, goal path, and optimal move score. Sleep quality rating was reported by parents. It seems likely that parents are reporting that their child slept well because their child fell asleep quickly and slept through the night wh ich is supported by the relationships shown in the correlation table (Table 3-2). Despite high sl eep quality ratings by pare nts, it is also possible

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78 that some of these children are also sleep depr ived and not getting enough sleep which leads to poorer executive functioning performance. Basica lly, children are not gett ing enough sleep; even though, they are sleeping well according to sleep m easures observed by their parents. The hypotheses that longer tota l sleep times, shorter total wake times, and increased sleep efficiency would be significantly associated with increased proportion of problems solved, longer goal paths, increased optim al move score, faster first move-times, and faster solution times were not supported. Furthermore, longer to tal sleep times, shorter total wake times, and increased sleep efficiency were not significantly associated with any st rategy usage variable. Bed and wake times were also not significantly a ssociated with any TOL variable. These sleep variables did not meet the criteria to be included in final overall models. Several possible explanations of the lack of signi ficant findings here exist. The first is that these sleep variables do not have a significant relati onship with executive functioning performance, specifically TOL performance. The second possibility is that th e TOL variables are not sensitive enough to detect the impact on executive functioning performance. A third possibility is that parents are not able to provide accurate enough info about these vari ables to make them potentially good predictors. The findings regarding the relationship between sleep and executive functioning have numerous implications. The results of the study indicate clinicians should be aware of the importance of the relationship between sleep and executive functioning. This increased awareness could hopefully reduce the misdiagnoses of childhood disorders such as Attention Deficit Disorder (Wiggs, Montgomery, & Stores 2005). An additional implication is that parents should be encouraged to ascertain their childrens sleep needs and work to accommodate this need so that children are better able to fully reach their executive functioning potential.

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79 Researchers examining executive functioning in child ren should also take sleep in account when trying to examine group or age differences. The sleep data in this sample was limited in several ways, 1) sleep data was not successfully collected over the two weeks so the impact of sl eep variability could not be examined, 2) sleep information was limited to parental report which while common for sleep data for this age group has limitations in terms of accuracy, and 3) there was not much variability in the sample. Despite this la ck of variability with the sleep measures in this non-clinical sample, significant results were found. Furthermore, the sleep data that was collected was from parents who were able to be cont acted and agreed to participate which opens the possibility of a selection bias despite the attempt to make the sample representative. Several new directions should be explored with this data. An important one would be to evaluate the utilization of actigraphy (Wiggs, Montgomery, & St ores, 2005). Actigraphy, which is a device similar to a wrist watch, allows for the objective measurement of sleep for up to a 60 day period. Actigraphy would allow for multiple days of data to be collected before the testing date which would allow for the impact of sleep on executive functioning to be examined more thoroughly. Additionally the concern about accuracy and objectivity would also be reduced. As such, it would be a tool to help address several of the limitations outlined above. Another direction is suggested by Berg, By rd, and McNamara (in preparation), who proposed that TOL variables can be combined in to three factors: an efficiency factor, a solution speed factor, and a planning speed fact or. These factors were derived from a factor analysis of a larger set of variables with a moderately large data set, and found to be valuable in evaluating what characteristics of a problem helped determine what made some problems particularly difficult. Therefore, exploring the impact of sleep on these factors rather than each

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80 variable individually would be useful. The impact of task experience and development on these factors could also be examined. However, th ese factors were based on adult performance and would need to be established for children. Evaluating Executive Functioning and St rateg y Use Changes with Experience Of the 7 proposed hypotheses about the impact of problem experience, five were supported. The proportion of problems solved, lengt h of the goal path, optimal move score and first move time all showed significant linear and quadratic changes with experience. Furthermore, holding peg strategy usage also sh owed a significant linear improvement across the sets. These results indicated that improvement occurred with the biggest improvement occurring between the first and second set a nd then leveled off in the third set, producing the quadratic as well as linear changes with sets. This leveling off is especially important because one of the criteria for a microgenetic examination of data is that the entire period of change be examined. The quadratic trends in the data and the lack of significant differences between sets 2 and 3 for most measures indicate that th is criterion was met. The hypotheses regarding the effects of experience on solution time and searching strategy use while not significant were in the expected direction. The microgenetic method has several inherent problems. One of these is that the microgenetic approach is inherently a time intensive process and typica lly means that sample sizes over 50 are quite rare. This concern was a voided in the present study since the sample in the present exceeded this sample size by r eaching 67. Another problem inherit in the microgenetic method as with any repeated measures design is a confound of the familiarity with the test situation generally with the specific increased knowledge of the problem solving task as a result of repeated exposure. However, the im pact of this was minimized by the utilization of a

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81 warm-up procedure, the presentation of the Peabody Picture Vocabulary Test, and TOL practice prior to assessing the TOL performance. The overall results of this study have a number of broad implications, some of which have already been addressed. One that has not is that the TOL and the microgenetic technique seem to complement one another well. The TOL has several different strategies that can be used and is a novel task for participants. By using the microgene tic technique, these differe nt strategies can be examined. Another implication is that as more is learned about how children solve problems, better methods can be developed to help children deve lop their problem solvi ng skills. In the present study, problems were initially difficu lt for children but after repeat ed exposure their performance improved because of the scaffolding provided within the task presentation. Using this method to teach children in specified topics for longer periods of time than is currently done in early elementary school to provide additional scaffo lding which could help children more fully develop their capabilities. This topic needs further exploration. For example, a study using this approach could be utilized for teaching mathematics. Several other future directions are warrante d. To further examine strategy usage, the length of each strategys usage could be explored. For exam ple, at least two levels of this strategy might be proposed: a simple holding peg strategy and an advanced or complex holding peg strategy. The simple holding peg strategy would consist of a single holding peg move followed by a goal optimal move. The advanced or complex holding peg strategy would consist of at least two holding peg moves followed by a goal optimal move. In the present study, both a 2-move holding peg sequence was scored the same as, a six move holding peg sequence. Each was scored as one instance of the use of the holding peg strategy.

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82 Another possible future direction would be to explore some individual differences in style of strategy employment. For example, one might compare children who did not give up (persisters) on problems when they ran into difficulty to children who did give up (nonpersisters) on problems when they ran into di fficulty (Diener & Dweck, 1978). This could be possibly measured by examining the time between each move. For example, if an abrupt lengthening in inter-move interval s occurred and the problem wa s not solved the participant would be considered a non-pers ister with the abrupt lengthening of the inter-move interval indicating the point where they gave up. After this determination has been made, the two groups performance could be compared. Examining the Development of Executive Function and Strategy Use Several hypotheses regarding developm ent proposed in th e introduction were supported and several were not. The proportion of probl ems solved, first move time, and holding peg strategy usage showed significant improvement w ith development. Furthermore, searching strategy use increased in the second year but did not reach significance. The increase of searching strategy use was not expected which po ssibly indicates children were more likely to use this exploratory strategy unt il a way to use the holding peg strategy became apparent. The other hypotheses were generall y in the expected direction but did not approach the .005 significance level. An important contribution of this study is solidifying the usefulness of the Tower of London task with young children. This is the fourth study conducte d by Keith Bergs research team and the first longitudinal study (i.e., Byr d, van der Veen, McNamara, & Berg, 2002) that has failed to replicate the fi ndings of Luciana and Nelson (1998) and Hughes (1998) which argued that young children were not ab le to solve more complex problems of this sort. However, the differences between our studies and theirs could have occurred because Luciana and Nelson

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83 (1998) used a pocket version of the TOL and Hughes (1998) used the physical model. Interestingly, the present study used more difficult problems th an either Luciana and Nelson (1998) or Hughes (1998). If anything, this should have made it more difficult for the young children in this study than in the previous st udies (Hughes, 1998; Lucian a & Nelson, 1998). This studys findings appear to make it clear that young children are capab le of solving quite complex, multi-step problems. An important implication of the present study is that young childrens performance as indicated by the goal path findings indicate th at young children are capab le of using optimal strategies effectively for almost 5 consecutive moves which is similar to the levels found in adults (Berg, Byrd, & McNamara, in preparation). This is important because children are almost as capable as adults at successfully executing optim al strategies when provided with scaffolding. However, even though young children might be almost as capable as adults on the task, they are not as effective in consistently implementing th eir capabilities, as indicated by proportion solved which is significantly lower than for adults. The findings of this study support Klahrs (1985) study using the Dog-Cat-Mouse problem to examine young children strategy usage on a task with ambiguous subgoal ordering. Klahr (1985) reported three important findings: 1) young children reluctantly go back or undo previous moves, 2) young children are awar e of their progress on the ta sk, and 3) young children are capable of planning 2to 3moves ahead. Kl ahrs first finding cannot be easily supported empirically by the present study, but based on inform al observation this certainly seems to be the case. His second finding is supported in this study by the relative low frequency of the None/Random strategy usage. Participants who were not aware of thei r progress on the task would be expected to use this strategy much mo re frequently than it was used in the present

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84 study. Klahrs third finding rega rding planning might be an undere stimate of child rens abilities according to the present study, but this discrepanc y between these studies may occur because of task differences, that goal path is only measured on solved problems, or that Klahrs sample was younger. Several future directions are warranted. The first would be to test an additional group of children that are first tested at the same age as the children tested in year 2. This cross-lag design would allow for a more thorough examination of de velopment. More sp ecifically this would allow an examination of development that w ould not be confounded with task experience. Another possibility would be to explore the impact of problem difficulty level. This examination could examine potential interactions of difficulty with variables of interest in all three aims of the present study: the impact of sleep on executive functioning, the impact of task experience, and the impact of development. According to Sadeh and colleagues (2000; 2002), McNamara (2003), and Hughes (1998) another alternative would be to examine the most difficult problems with sleep, task experience, and de velopment. Another future direction would be to include physiological measures such as Respiratory Sinus Arrhythmia (RSA) since this measure has th e potential to discriminate active processing of information from a passive, non-engaged manner. RSA refers to the synchronization of heart rate with respiration. When someone is in a relaxed state and breathes in and out, heart rate increases and decreases along with th e breathing. This situation seems to provide an index of the parasympathetic system being activated. When someone is active, even if the activity is cognitively engaging, heart rate and respiration do not stay in sync h, and the result is low RSA. This situation seems to result from a decrease in parasympathetic activity and perhaps an increase in sympathetic activity. Ideally participan ts will start a session in a relaxed state with

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85 RSA high, and then when the task begins th e RSA would decrease indicating active cognitive processing. A pattern such as this would likely result in optimal pe rformance for the participant. When deviations occur, it suggests either stress about the task prior to beginning or a failure to engage in the task when it begins. On executive functioning tasks, it is believed that people will have lower RSA than they do when they are at rest. This would indicate that the person is actively processing information. Participants RSA would be measured when they are at rest (Blair, 2003; Blair & Peters, 2003; Gianaros, Van Der Veen, & Jennings, 2004; Hansen, Johnsen, & Thayer, 2003). Then the participants would be given the TOL task. De Lucca, McNamara, and Berg (2006) found that as the difficulty of the Tower of London problems increased, RSA decreased in a linear fashion. However this has not been explored developm entally. RSA provides excellent insight into executive functioning because it is responsive to inhibition, both spatia l and verbal working memory, planning, and the impact of difficultly level. Overall Implications of the Study Broadly this study suggests that sleep, task experience, and developm ent have an impact on executive functioning. The implications for clinical assessment s uggest that young childrens sleep should be assessed to dete rmine if sleep problems are presen t that might be impacting their cognitive ability. The implications of this study fo r future research suggest that all three domains should be assessed when examining the executi ve functioning performance of young children. The implications for teaching indicate that child ren should be provided with challenge problems or scaffolding (Shrager & Siegler, 1998) to help them fulfill their potent ial. Furthermore, the study suggests that the same scaffolding can be used to help young child ren approximately one year apart in age. Another important aspect of this study is the utility of the TOL to evaluate

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86 executive functioning with a task with minimal verbal requirements whic h makes the assessment less dependent on language skills.

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87 APPENDIX A SCRIPTS OF THE TOWER OF LONDON RULES Experim enter instructions appear in parentheses. Rules for Tower of London instructions segment: We are going to be playing a game on the computer today and to play the game you will have to slide some balls across this screen using a mouse. Sometimes this can be hard so we are going to practice sliding the balls befo re we play the game for real. All you have to do is slide the ball in the botto m picture so that it is sitting on the same place as the ball in the top picture. Keep the a rrow on the ball until it is on the peg where you want it, otherwise it will fall. (Use 3-D apparatus to show that if you let go of a ball while moving it, it will fall.) See, if I let go of the ba ll before I put it on a peg, it will just fall. The same thing will happen with the computer ball s. Okay, we are going to practice now and you can ask me any questions that you have. Do you have any questions? Rules for Tower of London practice segment: We are going to play this game on the computer (show 3D TOL). It is called the Tower of London. The way that you play this game is to move the balls from one peg to another (move a ball on 3D). To win the game you move the balls to look just like a picture of the balls (show 3D picture of TOL). The rules are that you can only move one ball at a time. Also, you can only put one ball on the small peg (point to peg), two balls on the middle peg (point) and thre e balls on the tall peg (point). If you put too many balls on a peg they w ill fall off. (Make a ball fall off the middle peg on the 3D). See, the middle peg is only tall enoug h for two balls. This ball can't fit on the peg. The last rule is that you can't move a ball if it has another one on top of it (try to move the trapped ball on the 3D). See? It is stuck under the other ball. (Put away 3D game) You will play the game on the computer. Here is what the game will look like (point to the screen). You will move the balls in the bottom picture (point to the bottom picture) by sliding them across th e screen like we practiced before. You win the game when you make the bottom picture (point) l ook exactly like the top picture (poi nt to the top picture). This means that all of the ball colors in the bottom picture are on the same pegs and in the same place as the ball colors in the top picture.

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88 APPENDIX B FEEDBACK SCRIPT The Give Me Five Guy m eans you solved th e game in the fewest number of moves. The Dancing Guy means you solved the game ve ry quickly but in an extra move or two. Good Job means it took you a little longer to solve the game, but you tried really hard and figured it out. The Clock means you tried really hard but just ran out of time.

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89 APPENDIX C TOWER OF LONDON STRATEGY SCORING SUMMARY Strategy scoring is don e in two basic parts o Assign a strategy categ ory to each m ove strategies actually cover several moves but this is an initial step. Th e assignment is often contingent on what happens with category assignmen ts in subsequent moves. o Once all strategies categories have been a ssigned to moves, scan the strategies across moves from beginning to the end to look for changes in the type of strategy category. A strategy is defined as a sequence of moves all of which fall into the same category. Thus the following strategy st atistics are calculated for each type of strategy: The strategy can occur or not occu r in any problem (strategy use) The strategy can contain fewer or more moves (strategy run length), The strategy can occur multiple times as it appears, say, initially, then changes to some other category, then reoccurs (strategy frequency) The number of times there is a change from one strategy to a different one (Strategy Change) The number of different strategies used on a problem (Number of Different Strategies) Strategy categories o There are five strategy categories plus a category for occasional unscorable strategies usually occurring at the end of unsolved problems Holding peg strategy Complex matching strategy Simple matching strategy Searching strategy Random strategy Unscorable o The assignment of a strategy category to a move is determined by the TOL strategy scoring macro by examining the Move type previously assigned by previous macros. These Move types are: Optimal Goal (O/G) Optimal Non-Goal (O/nG) Non-Optimal, Goal(nO/G) Non-Optimal, non-Goal with chance for final goal move (nO/nG/MGC) Non-Optimal, non-Goal with no chance for final goal move (nO/nG/nMGC) o Note: Strategy categories use the same names as the strategies themselves. The only difference is the categories are assigne d to single moves, and strategies to sequences of moves with same category names. The word category is added to make it clear where there might be ambiguity e.g., Holding Peg Categor y, rather than just Holding Peg. Criteria for the strategy categories: o When the Move type is O/G

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90 Assign Holding Peg Category if the previous move was also Holding Peg category. Otherwise assign Complex Matching Category o When the Move type is O/nG Assign Holding peg if next move is an Optimal goal Assign Holding peg to all moves of an unbroken series of O/nG moves which are followed immediately by an Optimal goal Assign Simple Matching if this is th e first move of the problem and next move is nO/G Assign Searching if none of the above are true Assign Unscorable to all moves of an unbroken series of O/nG moves which are the last moves of an unsolved problem o When the Move type is nO/G Assign simple matching o When the Move type is nO/nG/nMGC If not first move assign Searching If first move and followed by nO/G assign Simple Matching If first move and followed by nO/nG/MGC then assign Random If first move and not followed by either of those, assign Searching o When the Move type is nO/nG/MGC Assign Random o Note each Move type is associated pr imarily with one single category, unless modified by moves that follow it. Most of the complications of the above rules arise from these contingency modifications. Searching is both a primary category for nO/nG/nMGC and is also usually the default category for sequences of O/nG when followed by anything other than O/G As noted above, once each move is assigne d a strategy category, then strategies themselves are simply sequences of identical strategy category assignments. Typically these will be runs longer than one move, but not always. Longer r uns of Searching and of Holding Peg are more common, with the s earching associated with not consistently moving toward the goal, and Holding peg in sequences moving toward the goal.

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91 LIST OF REFERENCES Alibali, M. W. (1999). How children change th eir m inds: Strategy change can be gradual or abrupt. Cognitive Psychology, 35 127-145. American Psychological Association. (2002). Ethi cal principles of psychologists and code of conduct. American Psychologist, 57 1060-1073. Anderson, P., Anderson, V., & Lajoie, G. (1996) The tower of london test: Validation and standardization for pediatric populations. Clinical Neuropsychologist, 10 54-65. Bastien, C.H., Fortier-Brochu E., Rioux I., Le Blanc, M., Daley, M., & Morin, C.M. (2003). Cognitive performance and sleep quality in the elderly suffering from chronic insomnia. Relationship between objective and subjective measures. Journal of Psychosomatic Research, 54 39-49. Berg, W. K., & Byrd, D. L. (2002). The Tower of London spatial pr oblem solving task: Enhancing clinical and research implementation. Journal of Clinical and Experimental Neuropsychology, 24 586-604. Berg, W. K., Byrd, D. L., & McNamara, J. P. H. (in preparation). A towering problem: How do we measure solution performance difficulty and what makes those problems difficult? Bjorklund, D. F., & Harnishferger, K. K. (1990) Childrens strategies : Their definition and origins. In D. F. Bjorklund (Ed.), Childrens strategies: Contemporary views of cognitive development (pp. 309-322). Hillsdale, NJ: Erlbaum. Blair, C. (2003). Behavioral inhibition and behavioral activa tion in young children: Relations with self-regulation and adaptation to preschool in ch ildren attending head start. Developmental Psychobiology, 42 301. Blair, C., & Peters, R. (2003). P hysiological and neurocognitive co rrelates of adaptive behavior in preschool among children in Head Start. Developmental Neuropsychology, 24 479. Byrd, D.L., van der Veen, T., McNamara, J.P.H. & Berg, W.K. (2002).Requirements of speech and motor movements differently impact pr eschoolers' problem solving performances. Journal of Cognition and Development 5, 427-449. Chen, Z., & Siegler, R. S. (2000) Intellectual development in childhood. In R. J. Sternberg, ed., Handbook of intelligence. Cambridge University Press, New York. Corkum, P., Tannock, R., Moldofsky, H., H ogg-Johnson, S., & Humphries, T. (2001). Actigraphy and parental ratings of sleep in children with attenti on deficit/hyperactivity disorder (ADHD). Sleep, 24, 303-312. Coyle, T. R., & Bjorklund, D. F. (1997). Age di fferences in, and consequences of, multipleand variable-strategy use on a multitrial sort-recall task. Developmental Psychology, 33 372380.

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96 BIOGRAPHICAL SKETCH Joseph P. H. McNam ara graduated from the Un iversity of Florida with highest honors in 2000. He graduated from the University of Flor ida with a masters degree in developmental psychology in 2003. He then enrolled in the coun seling psychology program at the University of Florida. He received his doctorate in 2008. His research focuses on the development of executive functioning, specializing in the impact of sleep on childrens executive functioning.