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1 RETHINKING ACHIEVEMENT GAPS IN K 12 SCHOOLS: A LATENT GROWTH ANAL YSIS OF BIOLOGICAL, SOCIAL, AND CONTEXTUAL DETER MINANTS ON STUDENT PERFORMANCE By ERIC STEPHEN THOMPSON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 201 3
2 201 3 Eric S tephen Thompson
3 To my students, peers, and teacher s
4 ACKNOWLEDGMENTS I thank Dr. Harry Daniels for his mentorship Dr. Daniels taught me how to link research to important social issues of the day. Dr. Daniels has also been patient and has held me to a high academic standard. I also would like to thank other members of my committee. Dr. Jeffrey Roth has provided year s of outstanding mentorship on the link between education and biological determinants of well being. Dr. Roth has also provided significant mentorship through the dissertation process. I also want to thank Dr. Grant Thrall for his mentorship in Business Geography, Geospatial Analysis, as well as his emphasis on interdisciplinary work. I also thank Dr. Mary Ann Clark for her mentorship in developing me as a school counselor and a counselor educator. Her feedback about classroom presentation he lped m e in many ways professionally. I tha nk Dr. Ana Puig for her feedback and help with the dissertation. I also thank Dr. Walter Leite for his methodological advice I also thank Dr. Cheryl Pence Wolf for being my dissertation buddy. suggestio ns on timelines and formatting were priceless. It was great to have a friend to walk with across the finish line. I also thank Candy Spires and Patti Bruner for their office support and continued help through the doctoral program. I thank my wife and fami ly all of my family for the emotional support throughout this meaningful and challenging process.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ ........ 10 DEFINITION OF TERMS ................................ ................................ .............................. 11 ABSTRACT ................................ ................................ ................................ ................... 14 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 15 Background ................................ ................................ ................................ ............. 15 An Alternative Viewpoint ................................ ................................ ......................... 17 Statement of the Problem ................................ ................................ ....................... 20 Purpose of the Study ................................ ................................ .............................. 21 Research Questions ................................ ................................ ............................... 21 Theoretical Basis for the Study ................................ ................................ ............... 22 Significance of the Study ................................ ................................ ........................ 26 2 LITERATURE REVIEW ................................ ................................ .......................... 30 Addressi ng Achievement Gaps ................................ ................................ ............... 31 The National Center for Transforming School Counseling (NCTSC) ................ 31 American School Counseling Association ................................ ........................ 33 Reasoned Critique of Achievement Gap Research ................................ .......... 34 Inequity ................................ ................................ ................................ ............. 35 Education and Equity ................................ ................................ ....................... 36 Closing Achievement Gaps ................................ ................................ .............. 37 Florida Comprehensive Achievement Gap (FCAT) and Academic Performance ................................ ................................ ................................ .. 38 Alternative Framework ................................ ................................ ...................... 39 Self Action, Interaction and Transaction ................................ ........................... 39 Ecological Models ................................ ................................ ................................ ... 41 ................................ ................................ .. 42 Ecological Models and the Bio Psycho Social Ecological Model ..................... 44 Bio Psycho Social Ecological Model ................................ ................................ ...... 46 Personal Change ................................ ................................ .............................. 46 Context Model ................................ ................................ ................................ .. 51 Regulation ................................ ................................ ................................ ........ 54 Regulation and stress ................................ ................................ ................ 56 Socio economic status and regulation ................................ ....................... 57 Representation ................................ ................................ ................................ 59 Life Course Health Development Model ................................ ........................... 62
6 Adverse childhood experiences ................................ ................................ 64 Cumulative risk and allostatic load ................................ ............................. 65 Cumulative risk and stress ................................ ................................ ......... 68 Cu mulative risk and academic performance ................................ .............. 68 Socio Economic Status ................................ ................................ ........................... 70 Free Reduced Lunch as a Measure of SES ................................ ..................... 70 Alternative Measures of SES ................................ ................................ ............ 72 Geographic Information Systems and Academic Achievement ........................ 73 GIS and academic administration ................................ .............................. 75 GIS and school setting ................................ ................................ ............... 76 GIS and achievement gap research ................................ ........................... 77 Lifestyle Segmentation Profiling ................................ ................................ .............. 81 Methods in Lifestyle Segmentation Profiling ................................ ..................... 84 Methodological Issues ................................ ................................ ...................... 86 Linear Mixed Modeling ................................ ................................ ............................ 88 Method s of Growth Modeling ................................ ................................ ............ 88 Growth Modeling ................................ ................................ .............................. 91 Multilevel Models and Growth ................................ ................................ .......... 92 Latent Growth Models ................................ ................................ ...................... 98 Choosing a Model ................................ ................................ .......................... 103 Individual Family School Community (IFSC) Model ................................ .............. 104 Summary ................................ ................................ ................................ .............. 107 3 METHODOLOGY ................................ ................................ ................................ 108 Setting ................................ ................................ ................................ ................... 108 Individual ................................ ................................ ................................ ........ 109 Family ................................ ................................ ................................ ............. 109 School ................................ ................................ ................................ ............ 109 Community ................................ ................................ ................................ ..... 110 Subjects ................................ ................................ ................................ ................ 110 Data Linkage and Missing Data ................................ ................................ ............ 110 Research Variables ................................ ................................ .............................. 111 Dependen t Variable ................................ ................................ ........................ 111 Independent Variables ................................ ................................ ................... 112 Individual and biological determinants ................................ ..................... 112 Family and social determinants ................................ ................................ 113 School composition ................................ ................................ .................. 116 Research Questions ................................ ................................ ............................. 1 16 Preliminary Data Analysis ................................ ................................ ..................... 117 Model Building Procedure ................................ ................................ .............. 118 Mu lticollinearity ................................ ................................ ............................... 119 4 DATA ANALYSIS AND RESULTS ................................ ................................ ........ 120 Chapter Overview ................................ ................................ ................................ 120 Descriptive Statistics ................................ ................................ ............................. 120 Indi vidual Factors by PLSP ................................ ................................ ............ 122
7 Family Level Factors by PLSP ................................ ................................ ....... 123 School Level Factors by PLSP ................................ ................................ ....... 123 Statistical Analyses ................................ ................................ ............................... 124 Growth Trends ................................ ................................ ................................ ...... 126 Question 1: What is the Initial Status and Rate of Reading Development From Grade Levels 3 10 in the District Under An alysis? ............................. 127 Question 2: What is the Initial Status and Rate of Reading Development From Grade Levels 3 10 by PLSP Group? ................................ ................. 130 Question 3 To What Extent do Parent Education, Parent age, Birth Weight, Apgar Score, Gestational Age, Ethnicity, and Gender Demonstrate Different Rates of Reading Developme nt Across Grade Levels 3 10? ........ 132 Question 4 To What Extent Do Parent Education, Parent Age, Birth Weight, Apgar Score, Gestation al Age, Ethnicity, and Gender Demonstrate Different Rates of Reading Development Across Grade Levels 3 7 by PLSP Group? ................................ ................................ ........ 135 Summar y ................................ ................................ ................................ .............. 138 5 DISCUSSION ................................ ................................ ................................ ....... 172 Overview ................................ ................................ ................................ ............... 172 Methodology ................................ ................................ ................................ ......... 173 Study Procedures ................................ ................................ ................................ 174 Results ................................ ................................ ................................ .................. 176 Research Question 1 ................................ ................................ ...................... 176 Research Question 2 ................................ ................................ ...................... 176 Research Question 3 ................................ ................................ ...................... 178 Research Question 4 ................................ ................................ ...................... 180 Individual ................................ ................................ ................................ .. 180 Family ................................ ................................ ................................ ...... 181 School ................................ ................................ ................................ ...... 182 Implications of the Study ................................ ................................ ....................... 183 Implications for Practice ................................ ................................ ........................ 184 Implications for Research ................................ ................................ ..................... 187 Study Limita tions and Suggestions for Future Research ................................ ...... 190 Conclusions ................................ ................................ ................................ .......... 192 APPENDIX A UF IRB 01 APPROVAL FORM ................................ ................................ ............. 194 B DEPARTMENT OF HEALTH DATA USE AGREEMENT ................................ ...... 195 C IRB APPROVAL FROM ALACHUA COUNTY PUBLIC SCHOOLS ...................... 196 D DEPARTMENT OF HEALTH DATA IRB APPROVAL ................................ .......... 197 LIST OF REFERENCES ................................ ................................ ............................. 198 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 212
8 LIST OF TABLES Table page 4 1 Count and percent of participant gender ................................ .......................... 139 4 2 Count and percent of participant ethnicity ................................ ........................ 140 4 3 Descriptive statistics reading scores, school percent on free reduced lunch, and school minority percentage by grade level ................................ ................. 141 4 4 Percent of student ethnicity by PLSP ................................ ............................... 142 4 5 Individual level variables by PLSP group: birth weight in grams, Apgar score at 1 and 5 minutes, and gestational age in weeks ................................ ............ 143 4 6 status by performance based lifestyle segmentation profile (PLSP) ................. 144 4 7 School percent of students o n FRL in school, percent of students with minority status in schools, reading scale score ................................ ................. 145 4 8 Pearson correlations ( r ) of vari ables ................................ ................................ 146 4 9 Pearson correlations ( r ) of Reading Developmental Scale Scores and student free or reduced lunch status by grade level ................................ ...................... 147 4 10 Pearson correlations ( r ) of Reading Developmental Scale Scores and percent of students on free or reduced lunch sta tus (FRL) in schools .............. 148 4 11 Pearson correlations (r) of Reading Developmental Scale Scores and percent of minorities at student ................................ ... 149 4 12 Fit indices from the linear, quadratic, piecewise, and freed loading latent curve models ................................ ................................ ................................ .... 150 4 13 Fit indices by PLSP grouping from linear, quadratic, piecewise, and freed loading latent curve models ................................ ................................ .............. 151 4 14 Fit Indices by PLSP grouping with covariates from linear, quadratic, piecewise, and freed loading latent curve models ................................ ............ 152 4 15 Model 1: Parameter estimates and standard errors for reading achievement data ................................ ................................ ................................ .................. 153 4 16 Model 2: Multiple group latent growth model by PLSP, no covariates .............. 154 4 17 Model 3: Parameter estimates and standard errors for reading performance data by PLSP group with covariates ................................ ................................ 155 4 18 Model 3: Parameters and standard errors of covariates by PLSP group .......... 156
9 4 19 Model 3: R 2 par ameters and standard errors of covariate model ..................... 157 4 20 Model 4: Estimates and standard errors for reading performance data, grade levels 3 7 ................................ ................................ ................................ .......... 158 4 21 Model 4: Covariate estimates and standard deviation by PLSP group, grade levels 3 7 ................................ ................................ ................................ .......... 159 4 22 Model 4: School free and reduced lunch status on reading achievement scores by PLSP group ................................ ................................ ...................... 160 4 23 Model 4: R 2 Latent growth curve model with covariates, grade levels 3 7 ........ 161
10 LIST OF FIGURES Figure page 2 1 Latent growth model with covariates ................................ ................................ .. 99 2 2 I ndividual Family School Community (IFSC) Model ................................ .......... 105 3 1 Comparison of Reading Developmental Scale Scores by lifestyle segmentation profile (LSP) ................................ ................................ ............... 114 4 1 Plot of reading developmental scale score means by grade level .................... 127 4 2 Observed means for reading developmental scale score from grade levels 3 10 by PLSP group ................................ ................................ ............................ 129 4 3 Unconditional latent growth curve model, freed loadings ................................ 162 4 4 Latent growth curve for group PLSP 1 with Reading Developmental Scale Scores, grade levels 3 10 ................................ ................................ ................. 163 4 5 Latent growth curve for group PLSP 2 with Reading Developmental Scale Scores, grade levels 3 10 ................................ ................................ ................. 164 4 6 Latent growth curve for group PLSP 3 with Reading Developmental Scale Scores, grade levels 3 10 ................................ ................................ ................. 165 4 7 Significant covariates for PLSP1, ( p < 01), grade levels 3 10 ............................ 166 4 8 Significant covariates for PLSP2, ( p < 01), grade levels 3 10 ............................ 167 4 9 Significant covariates for PLSP3, ( p < 01), grade levels 3 10 ............................ 168 4 10 Performance Based Lifestyle Segmentation Profile 1: significant ( p<.01) time varying and time varying covariate latent growth model for grade levels 3 10 169 4 11 Performance Based Lifestyle Segmentation Profile 2: significant ( p<.01) time varying and time varying covariate latent growth model for grade levels 3 10 170 4 12 Performance Based Lifestyle Segmentation Profile 3: significant ( p<.01) time varying and time varying covariate latent gr owth model for grade levels 3 10 171
11 DEFINITION OF TERMS A CHIEVEMENT G AP hen one group of students outperforms another group and the difference in average scores for the two groups is statistically significant (that is, Para. 1). A LLOSTASIS (Hochberg et al., 2011) (p.447). A LLOSTATIC LOAD The biological and ho rmonal response rooted in the hypothalamic pituitary adrenal axis intended to return the body back to allostasis. B IOLOGICAL D ETERMINANT biological markers of risk include child gestational age a nd child birth weight (Halfon & Hochstein, 2002; Halfon et al., 2004; Larson et al., 2008) B IO P SYCHO S OCIAL M ODEL A developmental model that incorporates the individual child, the developmental context, how the child regulates his or her interaction with context, and finally how mental representations relate to the child and the context (Sameroff, 2010) B USINESS G EOGRAPHY "Business Geography integrates geographic analysis, reasoning, and technology for the improvement of the busi ness judgmental decision. Without the demonstrated ability to improve the business decision, there is no business geography. This differentiates business geography from the traditional descriptive or explanatory objective of economic and urban geography" ( Thrall, 2002, p. vii). C UMULATIVE R ISK MODELS A theoretical model that measures the accumulation of risk in an individual. E COLOGICAL M ODEL An examination of multi person systems of interactions across single or multiple settings across time (Bronfenbrenne r, 1977). E FFECTIVE S CHOOLS M OVEMENT A pervasive influence on education policy that claims that schools can act independently of family school contexts (Rea & Weiner, 1997) E QUALITY OF E DUCATIONAL O PPORTUNITY (EEO) STUDY The Equality of Educational Opportunity Study (EEO), alternatively titled the "Coleman Study," was funded in 1966 by the United States Depart ment of Health, Education, and Welfare in order to assess the availability of equal educational opportunities to children of different race, color, religion, and culture.
12 I NDIVIDUAL F AMILY S CHOOL C ONTEXT F RAMEWORK (IFSC) A framework influenced by the Bio Psycho Social Ecological model that considers the circumstances of the individual, family, and school in the study of achievement gaps. L IFE C OURSE H EALTH D EVELOPMENT (LCHD) A health framework that identifies how early life risk and support relate to poor health outcomes. L IFESTYLE S EGMENTATION P ROFILE (LSP) A measure of lifestyle that synthesizes measure of median age, disposable income, employment status, leisure activities and census data. It provides a proxy for Socio economic status. M EDIATED EFFECT OF PO VERTY overty associated with economic hardship may lead to family stress and have a negative impact on parental emotional well being and mental health, undermining p arenting behavior and increasing the likelihood of parents using harsh and (Engle & Black, 2008 p. 246) M ODERATED E FFECT OF P OVERT Y ne in which the effects of poverty vary across are poorly educated with poor decision making skills may have more difficulty protecting their children from the effects of poverty than families who are better educated with rational decision making (Engle & Black, 2008 p. 347) N O C HILD L EFT B EHIND (NCLB) A CT OF 2001 A bipartisan act of legislation by President George W. Bush that was intended to increase accountability, school choice, and flexibility in Federal education programs through increased accountability for states, school districts and schools, typically measured by stan dardized examinations ( NCLB, 2010) P OSITIVE S TRESS S hort increases in heart rate, blood pressure, and stress hormone levels (Shonkoff et al., 2009). P ROTECTIVE FACTOR Can be considered any stimulus, internal or external, that is being. R ISK F ACTOR Any stimulus that poses a risk to immediate, delayed, or long term well being (Mis try, Benner, Biesanz, Clark, & Howes, 2010) S ELF R EGULATION of attention and emotional arousal for the purposes of reflective, goal lf regulation directs attention and emotional processes to meet our interests and needs. Self regulation is related to executive functioning that includes memory, inhibitory control, and shifting attention (Blair & Raver, 2012).
13 S LEEPER E FFECT The cumulat ive exposure to risk factors and/or adverse life experiences that lead to adverse outcomes in adolescence and extend into adulthood (Maurer, Mondloch, & Lewis, 2007) S OCIAL D ETERMINANTS R efer s to family income and social class, but the definition is now being expanded to include education, quality of housing, school SES and racial composition, neighborhood composition, and type of housing (Carson, Cook, & Alegria, 2010; Denny & Brownell, 2010; Halfon, Larson, & Russ, 2010) Social determinants not only social context in which a child develops. S OCIO E CONOMIC S TATUS A complex multi dimensional construct that represents access to social resources, assets, rank in a socio economic hierarchy or material goods. It can be evaluated from gestation through adulthood (Matthews & Gallo, 2011) T OLERABLE S TRESS A physiological st ate that has the potential, through stress hormones, to disrupt brain architecture (Ganzel & Morris, 2011) Tolerable stress is buffered by supportive relationships. Experiences that can give rise to tolerable stress include the death of a loved one, a natural disaster, or homelessness. Tolerable stress occurs in a limited time period and protective relationships bring t he stress response system back to baseline, giving the brain time to recover. T OXIC S TRESS Refers to prolonged activation of the stress response system and the lack of buffering protection of adult support (Shonkoff et al., 2009). Toxic stress also refers to acute and traumatic stress. T RANSACTIONAL E FFECT OF P OVERTY reverberate through the relations between families and children, example, caregivers of temp eramentally difficult children are less likely to exhibit sensitive responsive caregiving and more likely to report depressive symptoms than caregivers of temperamentally (Engle & Black, 2008, p 246)
14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy RETHINKING ACHIEVEMENT GAPS IN K 12 SCHOOLS: A LATENT GROWTH ANALYSIS OF BIOLOGICAL, SOCIAL, AND CONTEXTUAL DETER MINANTS ON STUDENT PERFORMANCE By Eric Stephen Thompson August 2013 Chair: Marion Harry Daniels Major: School Counseling and Guidance The c ontents of this dissertation study examine the relationship between reading development and biological, social, and contextual factors. A research framework called the individual, family, school, and community contexts model (IFSC) was created to study multiple interacting systems. A new measure of socioeconomic status, based off of geo demographic analysis, was developed and tested as well. Reading development scale scores were studied over seven years studied using multiple group latent growth modeling over grade levels 3 10. Variables related to student background, health, school setting, and community were modeled as predictors of student reading development with significant findings. Implications for policy and practice will be discussed.
15 CH APTER 1 INTRODUCTION In this dissertation measured by reading performance on the Florida Comprehensive Assessment Test (FCAT) is affected by the interactions among individual, family, school, and community context s Bro nfenb r Bio Psycho Social Ecological model (BPSE, 1977), heory of D evel opment (2010), and Life C ourse H ealth Development theories (LCHD) (Halfon & Hochstein, 2002) provide the th eoretical frameworks used to interpret the emergence of reading achievement gaps. The significance of early life risk factors, stress, and self achievement will also be explored I introduce the I ndividual Family School Community Context model (IFSC) a model that is based on the BPSE and LCHD models. The letter IFSC model represents both comm reading scores develop I also argue for interdiscipli nary research and the use of innovative measures of socio economic status and family lifestyle derived from the field of Business Geography (Thrall, 2002) to s tudy student reading trajectories from grade levels 3 10 Background The National Center for Education Statistics (NCES) defines an achievement gap difference in average scores for the two groups is statistically significant, that is, larger NCES, 2011, Para. 1). Every state in the nation at every education level has statistically significant gaps in achievement on the National Assessment of Educational Progress (NAEP) test. While there are many types of
16 achievement gaps, the two most prominent are between minority and White students and between poor and wealthy students (Education Trust, 2006). Achievement in education is typically measured through administering state or national standardized tests. Most high stakes assessments tend to have school f unding attached to their outcomes. performance; yet, the use of such tests has proven controversial. The use of test scores in Kindergart en through twelfth grade (K 12) settings a s a sole measure of academic performance piques interest on both sides of the political continuum and leads to questions about the source or the reasons for the existence of achievement gaps. The Equality of Educat ional Opportunity (EEO) study, which is also known as the Coleman report (1968), suggested that the family context is the most influential factor affecting academic achievement in K 12 schools. In the 1960s, the Coleman report (1968) offered evidence that and that parenting had more to do with student success than schools. Col eman (1968) also asserted that the demographic and SES composition of schools is a key factor in academic achiev ement. In the 1970s Christopher Jencks at Harvard, reanalyzed the Jencks (1972) children were affected more by the home and community. These conclusions led to a reduction in funding for schools based on the premise that incr eased fin ancial resources in schools do not affect student performance (Jencks, 1972).
17 achievement, spurred a counter argument led by Ron Edmonds (1972) who created the effective sc hools movement. Edmonds lives and that the failures of are the failures of educators. A recent and compelling argument for the effective schools movement comes from another recent reanalysis of data. Borman and Dowling (2010) reanalyzed the Coleman report data using multilevel analysis of school level composition, resources, teacher characteri stics and peer characteristics after statistically taking into a (poverty or minority status). An Alternative Viewpoint While achievement gaps in SES and ethnicity have received an enormous amount of attention in research and in federal legislation such as the No Child Left Behind Act (NCLB 2001 ), these gaps persist. Educational researchers and school counselors have tended to focus on either the school or the family as the problem when achievement gaps are identified. This type of dichotomous thinking fails to capture the complexity o f human development and the structures and dynamics of the IFSC context. Human beings develop in multiple settings, and this development occurs over time and at different rates. Traditionally, research has focused on one main effect in relationship to acad emic achievement. Instead of fo cusing on one main effect, either school or family, our understanding of achievement gaps would be advanced by considering 1) multiple settings in conceptualization and analysis, and 2) how early life risk impacts child devel opment and student performance (Sameroff & Fiese, 2000) The interaction and tra nsactions that occur among the Individual, Family, S chool and C ommunity (IFSC ) contain varying degree s of risk and support. Further, a varying
18 s Experience risk and support. Risk is difficult to define empirically, yet a useful consensus among researchers has emerged. A risk factor refers to any stimulus that poses a threat to immediate, delayed, or long term well being (Mistry et al., 2010) Burchinal (2000) identified three ways to measure risk throug h (1) individual risk variables, (2) factor scores derived risk variables, and (3) risk index that is computed by totaling the number of risk conditions present. As Mistry et al, (2010 ) for defining risk within a cumulative risk framework are typically informed by empirical (p.434). According to Burchinal (2000), measures of risk are to be derived from empirical evidence. For example, low b irth weight is a risk factor for reading development and other health outcomes. Birth weight is empirically defined as less than 2500 grams (Dube, Felitti, Dong, Giles, & Anda, 2003; Power, Jefferis, Manor, & Hertzman, 2006) I argue that understanding the risk accumulation process in children will lead to a more robust understanding of how achievement gaps emerge and how educational professionals and school counselors can intervene effec tively. Researchers in different disciplines, including education and medicine, are actively pursuing ways of closing opportunity and achievement gaps using methods and theories unique, but not exclusive to their fields The medical community recognizes ed ucation as a significant determinant of individual well being ( Healthy People, 2020, 2011, Borman & Dowling, 2010) Not only do achievement gaps emerge as a product of
19 many interacting sys tems and settings, but early life stress, and exposure to cumulative risk factors result in increased levels of stress which hinder child development, school readiness, and executive functioning. Maurer, Mondloch, and Lewis (2007) refer to the delayed poor health outcomes of early childhood as the sleeper effect. According to the sleeper effect theory (Maurer et al., 2007) stress brought about by exposure to ris k in the IFSC context s impact child development T hese stressors are related to achievement gaps. Because of these multiple interacting systems and the influence of risk/protective factors, individuals change at different rates. An analogous example would be the difference between an Olympic athlete and a high school athlete. An Olympic athlete may have certain individual factors that help him/her perform well, but the Olympic training context is protective and intensive. It is a lifestyle that is focused on an exceptionally high degree of performance. Likewise a high school athlete may have the same individual factors that help him or her perform well, but the lifestyle of a high school athlete is not as conducive to athletic performance as the Olympic tra ining environment. Thus, it is much more likely that a high school athlete will not perform as well on a given sport when compared to someone of the same age with intensive style constant through time, the Olympic athlete will most likely be sent on a separate performance trajectory than the athlete with a lifestyle that is less conducive to exceptional athletic performance. Likewise, students born with low birth weights and in poverty are prone to develop on a separate academic performance trajectory than their counterparts from a more supportive environment (Osler et al., 2003; Power et al.,
20 2006; Taylor, Klein, & Hack, 2000; Zeka, Melly, & Schwartz, 2008) Interdisciplinary efforts to close achievement gaps that address these individual, fami ly, school and community contextual factors are needed. Statement of the Problem Before new interventions and policies are created, educational researchers, administrators and educators, and school counselors would benefit by reconsidering how the latest a dvances in developmental research and technology provide a more comprehensive understanding of the dynamics of achievement gaps. The discussion in this paper will focus on three critiques of educational practices. First, there is a lack of interdisciplinar y integration and case conceptualization of child development in the interventions currently used in K 12 schools. This lack of integration fails to adequately consider the biological (e.g. the person), social (e.g. family and school) and the contextual (e.g. neighborhood, lifestyle and community) elements of the IFSC framework that impact academic performanc e Secondly, the most commonly used measure of socioeconomic status, free and reduced lunch status (FRL) does not adequately consider how a child is affected by the interactions between IFSC contexts of the student. Third, effective interventions need to be informed by how risk factors Further, the contents of this dissertation will explore how selected biological and social determinants of student achievement interact to produce achievement gaps. A biological determi nant refers to factor s growth Some early biological markers of risk include child gestational age and child birth weight (Halfon & Hochstein, 2002; Halfon et al., 2004; Larson, Russ, Crall, & Halfon, 2008) Social determinants traditionally refer to family income and social class, but the definition is now being
21 expanded t o include education, quality of housing, school SES and racial composition, neighborhood composition, and type of housing (Carson et al., 2010; Denny & Brownell, 2010; Halfon et al., 2010) Therefore, social determinants not only refer to the individual t also refers to the social context in which a child develops. I will use social determinants to encompass social and contextual aspects of child development within the IFSC framework. Purpose of the Study The purpose of this dissertation is to examine bi ological and social determinants of student achievement in K 12 schools. I am particularly interested in assessing which social and biological determinants within the IFSC framework are related to academic trajectories in K 12 schools. I will investigate t he biological and social determinants of health within the IFSC framework and their relationship to academic performance. Unique to this study is an emphasis on lifestyle segmentation as a measure of socio economic status. lifestyle segmentation profiling (LSP) is a useful tool for estimating SES and its relationship to academic performance, and context (ESRI, 2009) According to the Environ mental Systems Research Institute (ESRI) Lifestyle segmentation study focused on growth models to investigate the relationship between social and biological determinants and performance in reading. Research Questions 1. What is the initial status and rate of reading development from grade levels 3 10? 2. What is the initial status and rate of rea ding development from grade levels 3 10 by PLSP group?
22 a) Do intercepts and slopes vary as a function of PLSP group assignment? 3. To what extent do parent education, parent age, birth weight, Apgar score, gestational age, ethnicity, and gender demonstrate diffe rent rates of reading development across grade levels 3 10? 4. To what extent do parent education, parent age, birth weight, Apgar score, gestational age, ethnicity, and gender demonstrate different rates of reading development across grade levels 3 7 and by PLSP group a) W hat is the yearly concurrent prediction between school percent FRL and school percent minority status on the initial status and rate of growth? In this paper I examine d selected features of the IFSC model, and their relationship s to student pe rformance and academic trajectories. A significant portion of the study focus ed on how academic performance varies as a function of the structures and dynamics of the IFSC model. I drew from the Bio Psycho Social Ecological model (BPSE; Bronfenbrenner, 1977) and life course health theories (LCHD ) (Halfon & Hochstein, 2002) to create the IFSC model and use this model to interpret the emergence of ac hievement gaps. Theoretical Basis for the Study The theoretical rationale for the study builds upon the Bio Psycho Social Ecological (BPSE) theory proposed by Bronfenbrenner (1977) a nd extended by Sameroff (2010), Sameroff and Fiese (2000), and Slominski, Sameroff, Rosenblum, and Kasser (2011) and Life Course Health Development (LCHD) theory proposed by Garner and Shonkoff (2012); Shonkoff (2009); Shonkoff, B oyce, and McEwen (2009); Shonkoff, Garner, and Seigel (2011); and Shonkoff, Richter, Van der Gaag, and Bhutta (2012) Bronfenbrenner (1974) set out to understand how person and cont ext affect development. In his time, developmental researchers used artificial or unfamiliar conditions that produced findings that are difficult to generalize to other settings.
23 Bronfenbrenner (1974) concluded that an overemphasis on this type of scientif ic rigor for the briefest possi Alternatively, Bronfenbrenner discussed the need for researchers to focus on social relevance. This BPSE approach brings meaning to research, but can lack scientific rigor. Bronfenbrenner suggested a middle ground that he called Naturalistic Observation (Bronfenbrenner, 1977). Naturalistic observation works around the implied split between scientific rigor a nd social relevance. This approach suggests that research should not be guided by hypotheses or experimental designs before data collection. Bronfenbrenner (1974) arg ued that human development needed to go beyond direct observation of behavior researched i n a single location. Ecological models require examination of multi person systems of interactions across single or multiple settings over time. An ecological model that incorporates context, like helps delineate the various sources of e xperience that can support or constrain child development. Since a child is involved in multiple social settings and institutions, the contextual model emphasizes that all of these experiences have an impact on his or her development (Bronfenbrenner, 1977) Sameroff, (2010) extends and expands psychological social model incorporate the individual child, the develo pmental context, how the child regulates his or her interaction with context, and finally how mental representations relate to child and context. Consistent with health research (Burchinal, Roberts, H ooper, & Zeisel, 2000 ; Felitti et al., 1998) ecological models consider these varying
24 perspectives and demonstrate that the total number of risk factors, not the type of risk factors, is generally the best determinant of child behavioral outcomes (Gutman, Sameroff, & Cole, 2003; Parmelee & Haber, 1973; Sameroff, 2010; Sameroff & Fiese, 2000 ; Furstenberg, Cook, Eccles, & Elder, 1999) Children growing up in poverty are exposed more frequently to a variety of risk factors and fewer protective factors than a more affluent counterpart (Engle & Black, 2008). A risk factor ref ers to any stimulus, internal or external, that poses a threat to immediate, delayed, or long term well being (Mistry et al., 2010) Alternatively a immediate, delayed or long term well being. Exposure to increased risk in early childhood is associated with both poor academic and health outcomes (Jutte, Brownell, Roos, Schippers, Boyce, & Syme, 2010; Sameroff, 2000, Halfon, Larson, & Russ, 2010). del (1994) to include insights from researchers from the emerging field of Epigenetics discovered that while genes are coded and unchanging, the expression of these genes can vary as a function of environment The relevant point to educators is that environment literally changes genetic expression. A toxic or high risk environment, such as a highly abusive home, impact s stress responses systems, which affects cognitive and soci o emotional development. Cognitive and socio emotional development are associated with education outcomes (Raver, 2004) A compelling aspect of the Bio psycho social ecological (BPSE) model is its compatibility with developmental theories from various
25 disciplines, including the proposed IFSC framework. The compatibility between disciplines that the BPSE, LCHD, and IFSC models provide is novel because they can encourage much needed inter disciplinary collaboration. The BPSE and LCHD models both emphasize that early stress and multiple risk factors impact cognitive development. Additionally, the models emphasize that a person interacts with a variety of settings that impact developmen t. T h ere is the person, the family and school context, regulate the relationship s among the three settings A person is impacted by his or her context and a person impacts the context. A more stressful context is likely to increase attentional arousal, or hyper vigilance ( Blair, Raver, Granger, Mills Koonce, & Hibel, 2011) Over arousal over a period of time leads to stress, creates wear and tear on the body, and negatively impacts attention (Chyu & Upchurch, 2011; Danese & McEwen, 2012; Ellis, Giudice, & Shirtcliff, 2012) On the other hand, a studen t who faces neglect may experience under arousal which is also less than optimal for learning and leads to other poor health and educational outcomes (Ellis et al., 2012) The arousal response is triggered by environmental or internal stimuli, and an optimal response is one where attention is carefully balanced between over stimulation or excitation and under stimulation or l axity (Broadhurst, 1957; Wallace & Shap iro, 2006; Winton, 1987) How a child regulates the interplay between individual and multiple contexts was explored in this dissertation. Student performance in various grade levels is examined as an emergent property of the interplay of student and mul experiences.
26 Significance of the Study It is anticipated that this dissertation will have particular relevance to school counselors and educators because it will provide an alternative interpretation of achievement gaps and how they emerge. The alternative interpretation is rooted in ecological theory, and enriched by an understanding of how risk and protective factors interact from birth to influence academic outcomes (Brewin, Andrews, & Valentine, 2000; Lucio, Hunt, & Bornovalova, 2012; Whipple, Evans, Barry, & Maxwell, 20 10; Risk impacts development through activating the stress response system (Ellis et al., 2012) An important premise of this ecologically grounded view of achievement gaps is how stress influences the manner in which a Children exposed to multiple risk factors in early life are likely to experience increased stress levels. If stress becomes intolerable, it impacts brain development and self regulation. Self regulation is defined as primarily volitional control of attention and emotional arousal for the purposes of reflective goal stress leads to poor academic and health outcomes in later life (Halfon & Hochstein, 2002; Larson et al., 2008; Sameroff, 2010) The measurement of early life risk can include poverty and other social determinants. In the 1990s, Felitti, Anda, and Nordenburg (1998) conceptualized early childhood risk as adverse childhood experiences (ACES). The ACES relate to child abuse and neglect, and growing up in a dysfunctional household. The authors found that children with high levels ACES were more likely to engage in risky behavior and are more likely to experience poor
27 educational and health outcomes. Additionally, the study clearly indicates that increased risk during childhood impacts academic outcomes and trajectories. According to Engle and Black (2008) poverty and the risks associated with it affect child development and educational outcomes starting early in life. This effect occurs directly and indirectly through mediated, moderated and transa ctional processes (Engle & Black, 2008) economic hardship may lead to family stress and have a negative impact on parental emotional well being and m ental health, undermining parenting behavior and increasing (Engle & Black, 2008 p. 246) According to Engle and Black (2008), a moderated effect of poverty refers to one in which the effects of poverty vary across characte ristics of families or children. For example, families who are poorly educated with poor decision making skills may have m ore difficulty protecting their children from the effects of poverty than families who are better educated with rational decision making skill Further, Engle and Black (2008) detail the transactional effect of poverty, which includes both moderated and m ediated effects on families and children: The effects of poverty reverberate through the relations between families example, caregivers of temperamentally difficult children are less li kely to exhibit sensitive responsive caregiving and more likely to report depressive symptoms than caregivers of temperamentally easy children (p. 246) The effects of pover ty are measureable. Children begin learning at birth; therefore an understanding of how early life stress, including maternal stress, is related to academic performance is useful for counselors and educators seeking to conceptualize student challenges thro ugh a broader, more ecological and systemic lens.
28 The incorporation of BPSE and LCHD perspectives into the IFSC model moves one that considers the structures and dynamics of the individual, family school and community contexts. This IFSC model includes multiple systems and their interactions with child development. Instead of looking at income, ethnicity, and gender as main factor s related to achievement gaps, this alternative perspective provides an opportunity to focus the conversation on the structures and dynamics that are relevant to education and health. The structures and dynamics that are of interest in this study include the net bio psychological result of cumulative s social interactions, and risk or protective factors. The extent to which these systems are impacted relate to how children perform in school and how they relate to teachers and peers. This dissertation presents th e results of an investigation of the school, neighborhood, and individual level s that emphasize how unique demographic features of school interact with the backgrounds of students to produce different results. Additionally, from the field of economics, lif estyle segmentation profile s (LSP) and Geographic Information Systems (GIS) have been used to map social demographics. with fewer risk factors and more protective factors perfo rm better academically than students with higher risk backgrounds? Likewise, do students from different SES backgrounds do as well as their peers who go to a more affluent school? Also, how do social and biological determinants relate to lifestyle segmenta tion profiles? If there is a
29 a student resides in a lifestyle segmentation profile that is associated with lower performance, will that student be set on a separate aca demic trajectory than those in higher performing lifestyle segmentation? If so, does attending a low poverty school have an effect on student performance for lower income students? How does mobility impact these relationships? In addition, I seek to unders tand more closely the relationship between early life stress (as measured by birth outcomes and other contextual variables) and academic performance in grades 3 10. This study may be valuable for education researchers, policy makers, educational administra tors, counselor educators, and school counselors in practice. This study tests themes from the Ecological and LCHD models that stress accumulates and if a child is not supported the bio psychological result becomes maladaptive and counters academic achieve ment. This study will seek to answer which early life stressors relate most closely to academic performance and if the impacts of these early life stressors vary by SES group. School counselors will have access to a new way of understanding and engaging st udents from high stress or neglected backgrounds. In Chapter 2, a detailed exploration of the theoretical frameworks that inform this study is provided. In addition, the methodology used to model the variables of interest in this study is described.
30 CHAPTER 2 LITERATURE REVIEW The following chapter surveys traditional research and methods to reduce academic achievement gaps and suggests alternative frameworks to consider and investigate these gaps. Much of the research on academic achievement gaps has focused on whether schools or families contribute to ach ievement gaps. The focus on schools or families can be enhanced with more current research models and methodologies found in developmental and life course health research. Drawing from these research models and methodologies, I developed the Individual Fam ily School Community ( IFSC ) model for considering child development and academic achievement gaps. The IFSC model is an integration of models based in ecological and transactional theory. The ecological theory was originally presented by Bronfenbrenner (19 74) and further developed by Sameroff (2010). Secondly, I draw from the Life Course Health Development theory (Garner & Shonkoff, 2012; Halfon & Hochstein, 2002; Halfon, Larson, & Russ, 2010; Larson, Russ, Crall, & Halfon, 2008; Shonkoff et al., 2011) wh ich is both an ecological and transactional theory that describes how various social and biological determinants relate to health over time. According to LCHD theories, a quality education is predictive of well being. The overarching theme of this chapter is to further explore how achievement gaps can emerge as a combined result of proximal and distal factors rooted in a variety of contexts and moments throughout childhood I also discuss statistical models that complement ecological and LCHD theories and t he IF SC model. These models include m ultilevel m odeling (MLM), latent growth modeling (LGM), and g rowth mixture m odeling (GMM).
31 Addressing Achievement Gaps Attempts to address academic achievement gaps have resulted in federal policies, including the No C hild Left behind Act of 2001 (NCLB, 2001) which was intended to promote academic achievement nationally by increasing accountability across states, districts and schools. A parallel purpose of the NCLB is to close gaps in achievement in education. Specifica lly, the NCLB states that by 2014 all students will satisfy proficiency standards in mathematics and reading as established by each state (NCLB 2001). In response to NCLB, the services that school counselors implement are changing from counseling, consulta tion, and collaboration, to include increased accountability, social justice, and increased efforts to close achievement gaps (Akos & Galassi, 2004; Dahir & Stone, 2009; Portman, 2009) Dahir and Stone (2009) assert that school counselors who fail to demonstrat e that they can effectively help students increase academic performance and close achievement gaps in the schools in which they work will be considered non central to the goals of education. Thus, it is imperative that school counselors are equipped to dev elop, implement and demonstrate the impact of their services and promote equity by working toward closing achievement gaps related to ethnicity, gender, and SES, among others. The National Center for Transforming School Counseling (NCTSC) responsibility. This role is discussed in counselor preparation standards as well as in practice standards. According to the Council for Accreditation of Counseling and Related Educational Programs (CACREP) standards of Diversity and Advocacy, a school counselor; 1) understands the ways in which student development, well being, and learning are enhanced by family school community collaboration; 2) identifies
32 community, environmental, and in stitutional opportunities that enhance or impede the academic, career, and personal/social development of students; 3) understands the ways in which educational policies, programs, and practices can be developed, adapted and modified to be culturally congr uent with the needs of students and their families (CACREP, 2009). The school counseling role of Model (Dixon, Tucker, & Clark, 2010) The Education Trust is an organization with a mission is to promote high academic achievement for all students at all levels and to close academic achievement gaps of all kinds. As a part of its goal to improve school counseling practice, the Education Trust and the Dewitt Wallace an agenda to change school counseling by initiating t he Transforming School stream of the mission of schools preparing all students for access and success in a wide array of postsecondary proactive programs to help students prepare for rigorous aca demic engagement (Education Trust, 2011). This initiative encourages school counselors to place more emphasis on building district wide interventions designed to close achievement gaps in schools by raising the performance levels of lower performing groups The Education Trust envisions school counselors in leadership and advocacy roles where counselors use data in collaboration with communities to promote high academic performance.
33 These standards include using data for program evaluation and accountabilit y. The TSCI model also asserts that school administrators need to promote significant school counselor engagement. American School Counseling Association In addition to the Education Trust, the American School Counseling Association (ASCA), the national p rofessional organization for school counselors, places student on academic, personal/social and career development so they achieve success in school and are prepared t ASCA provides professional development, publications and other resources, research and advocacy to more than 29,000 professional school counselors around the globe (ASCA, 2011, p.49). The Educati on Trust and the American School Counselor Association (ASCA) ASCA National Model presents guidelin es for school counselors to implement standards based school counseling programs and provides suggestions on how to close academic achievement gaps. It is considered the best practice standard for the school counseling profession. Counselors are encouraged by the ASCA National model to disaggregate and analyze data to expose evidence of access and equity issues. Using disaggregation and data analysis helps school counselors implement focused advocacy and intervention (ASCA, p.49). Once gaps and inequities a re found between groups, ASCA states that School counselors are to work as advocates. The advocacy work for school counselors includes partnerships with the community in order to remove
34 barriers that hinder academic success. The ASCA model further asserts that school counselors are expected to challenge school policies that do not promote student achievement or equal access to a rigorous curriculum. Finally, ASCA recognizes that achievement gaps occur on many levels including: race, gender, class, disabilit y status, geographic location and sexual orientation. School counselors are expected to address these gaps through research and services (ASCA, 2004; Singh, Urbano, Haston, & McMahan, 2010). The ASCA model, like Education Trust, envisions School Counselors as leaders and advocates that counselors must be proficient in using school data. Because school counselor roles range from leadership, to advocacy, to utilizing available data, school counselors are in a unique position to promote equity for every studen t. Additionally, school counselor educators are in a unique position to generate new research and counselor training that focuses on reducing achievement gaps by looking at broader and more systemic issues. Reasoned Critique of Achievement Gap Research Th ere are many types of inequities in schools and one of them is the academic achievement gap. The understanding and promotion of equity is crucial for school counselors. Inequity in schools contributes to SES achievement gaps. Equality and equity are two di fferent terms and frequently misunderstood (Brown & Bigler, 2005; Mickelson & Nkomo, 2012) Equality in schools refers to students receiving resources equally. Equity in schools denotes the acknowledgment of differences amongst groups and promotes the use of resources to create equa l access to a rigorous academic curriculum. These terms, equity and equality, can be synthesized as equal educational opportunity (EEO). The ideas of EEO consider similarities in students and attempts to provide a quality education to every student (Smith & Lusthaus, 1995)
35 Inequity Coleman (1968) defin ed inequity as consequences of the school created for those with equal backgrounds and capacities. In this definition, equal opportunity is equated with equal results, given that individuals have the same background or input. Those in poverty and minority groups are not equally represented, however, in the development of the curriculum and how school success is judged. Without equal representation, dominant groups will dictate the curriculum and hold others to that standard (Jencks, Jencks, Christopher, & Phillips, 1998) Instead of focusing solely on outcomes and opportunities, Coleman (1968) discussed how equal opportunity equates with equal results, even among students fro m various social backgrounds. According to this idea, schools are expected to move towards equal results with students who come from varying backgrounds. The No Child Left Behind Act focuses only on academic outcomes through assessment and attempts to prom ote equal results; a one size fits all model of curriculum. Providing a one size fits all curriculum to produce equal educational outcomes seems unfeasible because educational outcomes are affected by multiple forces ranging from culture to the individual child (Braveman, Egerter, Woolf, & Marks, 2011; Canadienne & Publique, 2 010; Shonkoff, Boyce, & McEwen, 2009; Whipple, Evans, Barry, & Maxwell, 2010) Efforts by NCLB and efforts by ASCA should begin to use a value added approach rather than determining school success or failures (Jordan, 2010) Jordan suggests that future efforts to close achievement gaps will consider a more individual or personal growth developmental model as discussed by Sameroff (2010). Value added assessments emphasizes student growth in achievement and takes into account two very important issues. First value added assessment takes into account the condition of
36 a student when he or she begins schools. Second, value added assessm ent o bserves how much students grow through time. The value added approach still expects equal results, however it accounts for initial starting points and growth trajectories. According to value added approaches, inequities start in the context in which t he student comes from. Students in poverty or from diverse cultural backgrounds tend to be exposed to more risk factors and have less cultural capital than more affluent and dominant cultures. Students come from a wide range of backgrounds, motivations, va lues, intelligence levels, and interests. It seems impossible to expect the education system to produce the same outcome for every student by giving the same curriculum. Models like ividual growth would benefit the ASCA National Model and academic research in general. Education and Equity According to Jordan (2010) the definition of equity in education has changed through time to incorporate a more ecologically consistent view that c onsiders student context. Historic social forces in the US have caused inequities in society and inequity in education is a result of these broader cultural/social inequities (Jordan, 2010) The Brown v. The Board of Education ruling decided that racially segregated schools were unequal (Roscigno, 2000) Jordan (2010) continues to state that this decision set t he foundation for the development of equitable programs in education. While schools are no longer racially segregated, issues of equal opportunity and access persist (Clark & Maas, 2012) Children in poverty have unequal access to quality e ducation and this inequity gives rise to academic achievement gaps. Jordan proposes that there are two views about inequity. The first view is that inequality is inevitable and policies and practices like affirmative action should be used to reduce the ine quities. On the other
37 hand, others propose that there are no inherent inequities, so everyone should receive equal treatment. According to the view that equity does not exist, background and context should not be considered. The No Child Left Behind is an example of the latter. The No Child Left Behind Act of 2001 is a national attempt to remove educational inequities by 2014 by educating all children to proficiency level or above on standardized tests. Under this law, schools are held accountable if stude nts perform below proficiency. The attempt to move equity forward by reducing variance in test scores is problematic because learning is complex, connected to human development, and nested within a cultural socio economic context (Del Giudice & Belsky, 2010; Jordan, 2010; Shanks & Robinson, 2011) Equity in education under the NCLB has focused on providing the same type of education to all students regardless of social status, gender, or ethnicity. Since learning is embedded within culture, Jordan (2010) suggests that equity be redefined to include the provision of knowledge, skills and worldviews which enable social mobility. This definition of equity is contextual and has different meanings in different cultures. Closing Ac hievement Gaps To examine achievement gaps, Chatterji (2006) estimated reading achievement gaps in ethnic, gender and socioeconomic groups of first graders in the US. In this study, 2,296 students from the Early Childhood Longitudinal Study (ECLS, 2002) from grades kinde rgarten to first grade were analyzed. Gaps existed between Caucasians and African American children, boys and girls, and children from neighborhoods with high levels of poverty. Poverty was measured with a composite score of parent education, occupation, a nd income and further broken down by quintile. Students at or
38 measure of poverty which is a stronger indicator of poverty than free reduced lunch status. While this study confirms the achievement gaps by gender, ethnicity, and SES, an emphasis on neighborhood level characteristics would have further enriched the study by observing the environment and neighborhood characteristics of the student. Florida Comprehensive Achie vement Gap (FCAT) and Academic Performance In another study of achievement gaps, five years of reading comprehension data The researchers wanted to see overall change in student performance with students on grade level and the reduction of percentage of students at high risk. Secondly, they looked at whether or not Reading First helped close the reading achievement gaps for disaggregated groups. Finally, they looked at student mobility e.g. do students who have been in Reading First have higher achievement than those with fewer years of reading First? The sample was 120,000 students from years 2003 2008. Gender, ethnicity, a nd SES, measured as FRL were taken into consideration. Foorman, Petscher, Lefsky, and Toste, (2010) aggregated students performing at levels 3, 4, and 5 into a group identified as at or above grade level performance Students at level 1 were designated as at high risk. There was no mention of level 2 data. Foorman et al. (2010) found that students at or above grade level (%GL) and the percentage of students at high risk (%HR) indicated improvement. Students involved in the free and/or reduced lunch (FRL) programs were more likely to be at high risk than the students not on the FRL program. These and other studies indicate that there are other factors that contribute to achievement gaps than families or schools. Theref ore, an alternative framework that considers student
39 growth and the multiple influences would add to the discussion about academic achievement gaps. Alternative Framework Below I review two ecological and transactional theoretical models consistent with a Bio Psycho Social Ecological model (BPSE) and the Life Course Health Development Model (LCHD). After I review these models; I propose a model that incorporates elements of the BPSE and LCHD models This new model is called the Individual Family School Community Context (IFSC) model, as this title includes the interrelated domains that impact Chapter 3 will use the IFSC model to model analyze and describe the re ading trajectories with a district wide school dataset. T he issue of achievement gaps in schools has roots in a historical debate regarding who is responsible for closing them, the school or the home. One argument asserts that all children are born equally and the schools should be the equalizing factor in a chi (Edmonds, 1986) ; the other argument states that students come to school from differing contexts and backgrounds (Coleman, 1968; Evans, 2005) These views, however, are founded on an overly simplified interpretation of the understanding of hum an development and a failure to understand group and multilevel differences. Below I describe ecological and transactional theories as proposed by Bronfenbrenner (1977), Sameroff (2010), and Shonkoff (2009) Self Action, Interaction and Transaction The concepts of interaction and transaction are useful because the person interacts and transacts with various contexts through life. From a transactional s development is a product of the dynamic interactions of the child
40 and the experience provided by his or her social settings (Sameroff, 2010). If a child and his educational setting are not matched, it is unlikely that a transaction will occur and therefo matched. Sameroff ( 2010) represents the transaction between child and exp erience provided by the context through time. Recent models of transaction use 3 different classifications for individual child development. For example the smallest level of analysis is the genotype. Genes have codes that impact how a child will develop a nd thought that genetics were simply a blueprint for human development but recent developments in the field of epigenetics shows that the context in which a child grows i mpacts how those genes are expressed (Hochberg et al., 2011; Neigh, Gillespie, & Nemeroff, 2009) The next level of analysis is the phenotype which constitutes the person. The way that genes are expressed impacts the development of the person. Personality traits an d temperament are examples of the phenotype. Finally, the environtype is made up of the entire micro, meso, exo, and macrosystems presented by Bronfenbrenner (1977) Depending on whic h context a problem lies, there will be different set of concerns experienced by a child. These problem contexts can vary by school, home, social setting, etc. With the transactional perspective problems are never located in the child or context but they a re always located in their relationships. As the number of settings are increased the opportunities for transactions increase as well (Sameroff, 2010) Once a child changes through one set of experiences, that set of experiences may be stopped and another set of
41 experiences will be activated in response to the changed child. Like genetics, environtypes are hypothesized to be composed of a serie s of represented codes within each setting. Codes represent potential responses that a person can have to a setting. Codes are not necessarily behaviors but are complex characteristics that organize development. Families have codes and so do schools. These codes are nested, serve to regulate development and are related to development. If codes are not congruent with the codes within a context, a mismatch occurs and leads to potential problems. curriculum. Problems occur when the codes do not match well or if a child fails to switch codes. An example from in my clinical experience shows that children will play videogames online and communicate to each other with antagonistic and exp licit language. This form of communication is accepted and encouraged by other players online. The problem occurs when these students who play these games for 5 to 10 hours per day come to school and fail to switch their codes to match the school setting. They get referred to the school counseling office on the basis of violent or bullying behavior when they are simply still running a code they learned while playing videogames online with their peers. As children develop and begin to engage in multiple sett ings, they are exposed to more codes that serve to organize and regulate his or her development. If a child develops more codes to fit the increasingly complex series of settings, healthy development occurs. Ecological Models Alternative and integrative frameworks to consider academic achievement, and how one draws conclusions about student performance may be a useful addition to the
42 discussion about closing achievement gaps. One option is to develop new lenses through interdis ciplinary collaboration (Duncan, 2012; Sameroff, 2010) Through this type of collaboration, one can begin to look at academic performance through integrating insights from many fields including: Child Development, Business Geography, and Pediatrics/Child Pathology. One model that has potential for integration is the Bio Psycho Social Ecological model (BPSE) (Sameroff, 2010). For example, the early debate between Coleman and Edmonds explored the impact of seemed to ask whether schools o r family context is connected to academic performance. Instead of asking if either families or schools are to blame, an ecological model considers how academic performance results from child, the school, the family context, policies, and their interaction between over time. It also acknowledges that the child impacts the school, family, and context. Bronfenbrenner (1977) set out to understand how human development is courses that each had tangible scientific results. On one side, there were many experiments related to development that involved artificial or unfamiliar c onditions that were difficult to generalize to other settings. Bronfenbrenner concluded that an children in strange situations with strange adults for the briefest possibl e periods of Alternatively, Bronfenbrenner discussed the need for researchers to focus on social relevance. This approach brings meaning to research, but can frequently lack scientific rigor. Bronfenbrenner suggested a middle ground that he called Naturalistic Observation. Naturalistic Observation rejects the implied split between
43 scientific rigor and social relevance. This approach stipulates that research should not be guided by hypotheses or experimental designs before data collection. Br onfenbrenner argued that human development needs to go beyond direct observation of behavior researched in the same location. Ecological models require examination of multi person systems of interactions and transactions across various settings. These vari ous systems were originally divided into 4 distinct systems: the Microsystem, Mesosystem, Exosystem, and Macrosystem. Microsystem The first structure proposed by Bronfenbrenner is the Microsystem. Microsystems comprise the relationships between developing person and the setting around the person (e.g. neighborhood, school). The place, time, activity, and other factors constitute the settings in a microsystem. The factors that make up a Microsystem interact with a child and a child interacts with those fact ors. Mesosystem A Mesosytem is the interrelations among settings at a point in a The interactions of a graduate student would encompass interactions among peers, professors, family, and even vocational activities. a mostly be interactional, as it is essentially systems interacting with other systems. Exosystem An exosystem is an extension of mesosystems that do not contain the develo ping person, but do impact the settings in which a child develops. Exosystems encompass neighborhoods, work, government, and social networks. For Macrosystem Finally, a macrosystem is not a context like the previous example, but refers to general overarching institutional patterns of the culture or
44 subculture. Examples of the macrosystem include economic, social, and educational, system. Macrosystems are examined in structural terms but also carry information and ideologies that bring meaning and motivation to agencies, networks, roles, and other interrelations. As Bronfenbrenner states, the priority that children and their caretakers have is important in determining how a child and his or her caretakers are treated and interact in different settings. The above systems interact and as a result of this interaction the child has to regulate his or her experience to manage the impact of stress brought about by these interactions. When an individual child begins to change as a result of these interactions and regulating emotions and physiology, a process of transaction begins to occur. Ecological Models and the Bio Psycho Social Ecological Model The underlying premises of the ecological mo del of development involve (1) mutual accommodation through the lifespan between human and the changing environment in which the organism lives as well as the larger social contexts; (2) that ecological environments are nested within each other; (3) and ec ological validity, which refers to the degree to which the environment under study has properties that it is assumed to have by the investigator (Bronfenbrenner, 1977; Halfon & Hochstein, 2002; Sameroff, 2010) Ecological validity is compelling because it focuses on how objects i n the environment are understood from an objective point of view, but also how they are perceived by the research subjects. For example, a researcher can examine poverty indicators in a neighborhood objectively, but it may not be ecologically valid if stud y participants do not perceive their neighborhood as poor. Essentially, cognitive representations of the environment are also a significant part of ecological models.
45 Bio Psycho Social Ecolog ical model (2010) are useful frameworks to conceptualize the diverse factors associated with academic achievement gaps and the challenge of closing these gaps. The ecosystemic model includes childhood contexts such as home and neighborhood environment, fam ily lifestyle, schools and other macro systemic factors delineate the various sources of experience that can support or constrain child development. Since a child is invol ved in multiple social settings and institutions, the development (Bronfenbrenner, 1977). Moreover, this impact works both ways. The ecological model asserts that just as the social context cannot be separated from child development, child development cannot be separated from the social context. According to Bronfenbrenner, the individual, family, school and community are development (Bronfenbrenner, 1977). Although there have been many people who thought that families, schools, and lifestyles influence development, Bronfenbrenner created a comprehensive framework with hypotheses about how the various settings affect a chil d and vice versa. According to Evans (2003) many analytical methods for capturing these interactions are inadequa te to describe the ecology of human development and have yet to catch up to the current understanding of the various risk factors that impact human development. Rutter (1983) su ggested the alternative approach of modeling the effects of proximal and distal risk factors cumulatively. Proximal risk factors are those factors that are more closely related to the child, such as family context. Distal risk
46 factors are less closely rela ted, such as school context or the geopolitical sphere. The entanglement of variables makes it hard to separate the effects of poverty and stress because they are so closely tied. Bio Psycho S ocial Ecological Model To further the discussion on ecological developmental models, Arnold Sameroff (2010) proposed a unified theory of childhood development that asserts that contemporary developmental science requires four models to understand human growth and development: personal change, context, regulation, and representation. The exploration of achievement gap phenomena uniquely and sequentially through each of these models, provides a more comprehensive understanding of factors impacting academic performance. Personal Change The personal change model refers to understanding the complexity of the individual as he or she moves from infancy to adulthood. Generally speaking, change can be conceptualized as trait, growth, and developmental. Trait and growth approaches are precursors to the developmental change approa ch. A trait approach assumes that an individual is comprised of a set of unchanging traits. For example, if a education. If children were only composed of traits, ther e would be no need for developmental research (Sameroff, 2010). It is important; therefore, to consider what neighborhood, etc.) as well as what changes. The trait approa ch focuses on what is continuous, while the growth approach looks at what is discontinuous and new. From the growth perspective, every child has
47 the potential to do well. The challenge is that interactions with the environment can cause stress that can neg atively impact performance. For example, the Family Stress Model (Conger & Conger, 2002) suggests that economic pressures impact children effects of poverty are experien ced in children through disrupted family functioning. On the other hand, if parents experiencing economic hardship are able to regulate their emotion, avoid high levels of conflict and remain nurturing, their children experience much less trauma. The pe rsonal developmental stage approach emphasizes what is new and continuous, and looks at previous achievements as building blocks. This approach proposes that children experience periods of stable functioning. When they encounter a new stimulus, however, th ey must adapt and grow to meet the demands of the event. If the stimulus is not powerful enough, the child does not have to adapt. If the stressor is too powerful or becomes chronic, then a maladaptive response occurs and the child may experience levels of unhealthy stress. Under this stage approach, individuals move from beginner to experts to masters. In this progression a child not only gets better at a task but also does the task differently as ability increases (Ericsson & Charness, 1994) Piaget's (2002) model of cognitive development is a classic example of a personal stage approach. The development from novice to master is not linear, however. The process is marked by a dynamic dialectical interplay between opposites of progress and integration (Sameroff, 2010). For example, Sameroff (20 10) states as a child grows
48 there is a recycling of knowledge that does not balance the opposites but gives rise to the next stage of development. Sameroff states, in the social emotional domain where relationship experiences and representations derived f rom early parent child relationships are reworked as children enter into peer relationships and reworked again in the romantic relationships beginning resolved but through a b alancing of opposites provide the impetus for each succeeding Thus, it is important to focus not only on growth, but the nonlinear trajectories of growth that can account for diversity within and among individuals. Rather than assumin g that children will develop solely in a linear fashion, acknowledgement and exploration of nonlinear growth trajectories accounts for the dynamic and recursive nature of development. The second part of nonlinear development is the concept of differentiat ion and hierarchic integration. Sameroff (2010) states that children grow and move from a state of simplicity to increased differentiation, and hierarchical integration. Thus, as a child learns more vocabulary words he or she begins to use them. The child begins to integrate the new words into daily life. The child then moves to a new stage of differentiation by learning more vocabulary words and repeating the integration process. In addition to the developmental factors described above, there is a strong link between individual developmental stages and stress. A developmental stage approach gives rise to a discussion on how cumulative risk and supportive factors affect child development, and impact academic performance. Cumulative risk and the resulting
49 st ress impact child development and affect education and health outcomes in two ways (Shonkoff, Boyce, & McEwen, 2009) The first is through accumulating damage over time. Children exposed to cumulative stressors and risk factors (e.g., maltreatment, environmental stressors, or discrimination) are impacted through adulthood. Second, the biological embedding of risk factors during sensitive periods in development can lead to illness in adulthood (Halfon & Hochstein, 2002) For example inadequate nutrition and recurrent infections in early childhood are associated with increased rates of cardiovascular and psychiatric disease in adulthood (Shonkoff et al 2009). Additionally, a child living in poverty is more like ly to show heightened activity of stress response systems and limited exposure to new vocabulary. Both accumulated damage and biological embedding can alter the maturation of the prefrontal cortex having an impact on student performance. Alternatively, pos itive experiences or supportive factors like healthy parenting styles can decrease the stress related to risk factors. According to Shonkoff, Boyce, and McEwen (2009) the National Scientific Council on the Developing Child proposed three categories of str ess that affect young children: positive, tolerable, and toxic. Positive stress is essential to healthy development and helps to restore the stress response system to baseline. Positive stress refers to short increases in heart rate, blood pressure, and st ress hormone levels (Shonkoff et al., 2009) Developmentally appropr iate and supportive quality instruction is an example of a positive stressor that can promote academic achievement. Likewise, healthy and supportive relationships buffer the effects of stressors (Garner & Shonkoff, 2012)
50 Tolerable stress is a physiological state that has the potential, through stress hormones, to disrupt brain arch itecture (Ganzel & Morris, 2011) Tolerable stress is buffered by supportive relationships. Experiences that can give rise to tolerable stress include experiences such as the death of a loved one, a natural disaster, or homelessness. Tolerable stress occurs in a limited time period and p rotective relationships bring the stress response system back to baseline, giving the brain time to recover. In the academic setting, taking a high stakes test or a standardized achievement test is an example of a situation that gives rise to tolerable str ess. A support refers to anything that enables a healthy stress response, healthy adaptation and recovery from stressful events. Supports can range from supportive families, to having more income, to more advanced technology or medicine. If a child has ade quate support, the stress of taking a high stakes test can be buffered. However, without supportive relationships and a reduced ability to self regulate, a child may slip into toxic stress. Toxic stress refers to prolonged activation of the stress respons e system and the lack of buffering protection of adult support (Shonkoff, et al., 2009). Toxic stress also refers to acute and traumatic stress. Such risk factors for toxic stress include extreme poverty, recurrent abuse, neglect, maternal depression, and violence. Toxic stress disrupts the brain architecture (Ganzel & Morris, 2011) and can affect other organ systems. T oxic stress affects the development of stress management systems which, in turn, leads to lower thresholds for responsiveness. Children exposed to cumulative risk factors have more toxic stress and prolonged activation of the stress response systems. The s tress responses include: increased heart rate, anxiety and depression. The
51 cumulative effects of having prolonged increased stress responses create more wear hormone levels ar state (Lupien, King, Meaney, & McEwen, 2000) stress response and maternal depression/SES is stronger in the higher poverty group. Sadly, as children in the hig h poverty group age, the rate of salivary cortisol increases more rapidly than that of any other group. Toxic stress affects the development of stress management systems which, in turn, leads to lower thresholds for responsiveness. Children exposed to cumu lative risk factors have more toxic stress and prolonged activation of the stress response systems (Whipple et al., 2010) The effects of toxic stress increase the risk of stress related diseases and impair cognitive development. A child from poverty may arrive at elementary school at the same chronological age as another, more affluent student; however, due to stressors and fewer enrichment opportunities, the child experiencing poverty may function at different levels of maturity and physiological development (Halfon & Hochs tein, 2002) Context Model The contextual model builds on the developmental stage model. As mentioned in the personal developmental stage model, children grow at different rates and come to school with different levels of functioning. According to the contextual model, children develop in nested contexts starting with their more proximal family, peers, and school. The influence becomes more distal and reaches out to the geopolitical sphere. As a child develops he or she engages at increasingly complex l evels with these various contexts.
52 The contextual model refers to delineating the multiple sources of experience understanding of child experiences has shifted focus from the re lationship between the child and primary caregiver, to include the impacts on the child of multiple sources of socialization like schools, neighborhoods, and peers (Sameroff, 2010). This model essentially acknowledges that the family, school, and the commu nity SES in which a child develops are interconnected. The experience that a child has growing up with a teenage mother in poverty and with little education is quite different from a child raised by a well educated and more affluent mother in her 30s. For example, Evans (2005) states that kindergartners from low SES backgrounds start school a year behind others in reading and vocabulary. The contextual ecological model provides a powerful framework to investigate various risks from different domains. For ex ample Jutte et al explored the relationship between biological and social risk factors on childhood health and school performance by tracking a population sample of 4,667 infants from Manitoba, Canada ( 2010) Childhood hospitalization by age 19 was used to measure childhood health, while passage of a 12 th grade standardized examinati on was used to measure academic performance. The independent variables included biological risks (birth weight, marital status, and socio economic status measured by pa rticipation in the free or reduced lunch program. Logistic regression was used to examine the relationship among variables. The researchers found that low birth weight was associated with not passing the educational assessment. There was a 14% decrease in the odds of failure
53 by a child for each additional kg of birth weight. There was an 18 fold increase in odds of children not passing the test in families on income assistance Plus each level of SES had an increased risk of not passing over the highest SES category. This study is useful because it observes the relationship between two domains of influence on children: biological and environmental/social. Research that considers childhood context using the ecological model can be a useful way for school coun selors to impact inequity in schools and help close achievement gaps. The t heory of E xperiential C analization (Gottlieb, 1997) asserts that experience impacts behavior and physiology and interact with the environment to maximize functioning in a specific type of environment. According to this theory, the interaction between genetics and environment affect behavioral and psychological development. Genes and environment are the sources of information in developmental systems (Blair & Raver, 2012a, 2012b) For example, children developing i n poverty or in toxic stress environments and less to access to supportive environments will affect psychological and cognitive development. A key aspect of experiential canalization relevant to academic performance is that behavior is malleable. Behavior is not predetermined by genes. Behavior that seems to be instinctual is driven by both genes and experience. Experiential canalization focuses on both the inputs related to successful development and also the absence of inputs that shape development. The utility of this theory is that experiential canalization focuses on ways that multiple levels of, from genes to geopolitical, interact to affect developmental trajectories.
54 Blair and Raver (2012) related the theory of experiential canalization to various degrees of SES. Their analyses show how characteristics in the environment impact According to Experiential Canalization quality caregiving is a mediator between children component to experiential canalization is how stress physiology develops. Stress hormones impact how socioemotional and cognitive development are shaped by experience. The key poin t is that stress hormones impact the neural systems related to self regulation. Self emotion, and executive functions for the purposes of goal (Blair & Raver, 2012 p.3). The quality of the environment t hat a child grows up in leads to types of caregiving behaviors that impact physiological responses which lead to patterns of development that are adaptive and appropriate for that environment. Experiential canalization can also help to explain varying degr ees of stress reactivity in children as they grow. Regulation While child development is an adaptation process in which the environment and context stimulate individual adaptation, development is also affected by how a child relates to these experiences th rough self and other regulation. According to Zimmerman (1994) self motivationally, and behaviorally active participants in their own learning process (p.309). Acco rding to Engle & Black (2008) a component of school readiness is the ability to self regulate emotions and behavior. The regulation component of the universal dev elopmental model refers to a dynamic systems perspective that considers the
55 relationship between a person and his or her context. In early life, children are more other regulated than self regulated. For example, in infancy caregivers do their best to regu late when the child sleeps, provide warmth when cold, and feed a child when hungry. As a child grows and changes in a healthy manner, he or she becomes more self regulated. Adolescents strive for more time with their peers and for more independence from th e family. Interestingly, the ability to self regulate arises from the actions of the caregivers. That is the type of regulation that a mother gives her child affects how the child will self regulate. According to Gelman (2009) is derived from interpretations given from others rather than from direct experiences of the environment. Consistent with ecological theory, self and other regulations are within the c hild and family, but also are nested within the culture and economic status (Raver, 2004) Regulation occurs through a transactional process and considers child development as the res ult of continuous and dynamic interactions between a child and his or her experiences. A meaningful interpretation of the transactional model is that the context impacts a child by creating an opportunity for an adaptive response. A child also impacts the context causing an opportunity for change (Connor et al., 2009) For example, researchers have shown how transactions occur in teacher student relationships. They discuss how teachers and students contribute reciprocally to learning opportunities. Connor, Morrison, and Katch (2004) observed the transactional style. In addition, Connor et al. (2009) found that effective instruction and classroom environments depend on the language, literacy, and self regulation skills that children have when they enter school.
56 A classroom, for example, that has children working on multiple projects wi th peers is more likely to be stimulating and effective for children who come to the classroom with stronger language and self regulation skills. The same stimulating environment, however, would not be as effective for students with weaker language and sel f regulation skills. Regulation and s tress As a child develops and engages with the world, he or she becomes less other regulated and increasingly more self regulated (Sameroff, 2010). For instance, in a supportive family environment, a child is dictated a bedtime in his or her early years, but then is eventually encouraged to establish his or her own bedtime. Likewise, if an infant is distressed a loving parent may offer the infant a bottle or pacifier. As a child grows, he or she may be encouraged to in creasingly regulate his or her response to stress through activities like exercise, reading, or meditation. Self regulation is referred to as a emotional arousal for the purposes of reflective, goal (Blair & Raver, 2012 p.647). Self regulation directs attention and emotional processes to meet our interests and needs. Self re gulation is related to executive functioning which includes memory, inhibitory control, and shifting attention (Blair & Raver, 2012). A bidirectional theory of self regulation is asserted by the Yerkes Dodson law (Ganzel & Morris, 2011) The Yerkes Dodson law emphasizes how arousal and performance can be visualized as an inverted U shape curve. If a person is over or und er aroused, he or she will not perform well. Moderate arousal increases performance. Toxic stress would be on the extremes of the inverted U shaped curve of performance and arousal, while positive
57 stress would be at the apex of inverted U indicating optima l arousal and optimal performance. Stress response systems (SRS) are not homeostatic systems (e.g. body temperature) that have little variation; instead they are allostatic systems that have a wide range of responses. According to (Lupien et al., 2000) under conditions of in tense and frequent adversity, the SRS adapts and calibrates itself to a relatively higher or lower resting level. This adaptation limits the flexible regulation of the stress physiology. Under adverse conditions, stress hormone levels reach levels that ena ble more reactive emotional and attentional responses to the stimulation. Increasing such vigilance increases chances of survival, but takes a toll on an individual over time. On the other hand, when a child is put in a supportive environment, SRS readjust s to levels that are conducive to executive functioning and reflective self regulation. This understanding of the relationship between neurobiology and context sheds light on how children entering school from low quality environments will enter school with moderate to severe psychosocial disadvantages. Policies by local and national government that create a supportive home and learning environment for students would help change how the SRS is activated -from reactivity to reflection. Schools can not only e ducate children, but can also provide a supportive environment to that fosters reflective self regulation which supports increased executive functioning and emotional equilibrium. Socio e conomic s tatus and r egulation Communities have various levels of inc ome, values, lifestyles, and cultural influences and these various influence need to be considered too. In terms of
58 personal development and the person and not the broader con text, are missing a huge opportunity to create positive change. The context that a child comes from is important to consider. For example, Ratts, DeKruyf, and Chen Hayes (2007) use an example that environmental factors such as generational poverty leads to increased depression and fewer educ ational/career opportunities. In an earlier study, Parker, Greer, and Zuckerman (1988) where they are exposed to the risks in their homes and com munities, e.g. illness, family stress, or lack of stimulation. Secondly, children in poverty experience more serious consequences from these risks than children that come from higher SES families. A critique by Engle and Black (2008) about the study of pov erty asserts that even though there has been so much attention to the deleterious effects of poverty, poverty rates are still high. In fact, the number of people living in the US in poverty is at its highest level since 1993, with 16.1 million children liv ing in poverty (US Census Bure au, 2012) Engle and Black (2008) state that there has only been limited attention to the process in which poverty affects child education and development. One reason for the slowed progress is that researchers have relied on basic methods that emphasize the direct effects of poverty on performance. Researchers have not paid enough attention to how distal and proximal contextual factors, (e.g. neighborhoods a nd family), are linked (Bronfenbrenner, 1977; Bronfenbren ner & Ceci, 1994; Sameroff, 2010) can provide insight into how the environment impacts a child. The use of an ecological lens presents the opportunity for new ways to address how problematic childhood behaviors arise through: 1) personal development; 2)
59 multiple and interacting systems; 3) Self regulation; 4) how representations are managed. Counselors using the ecological model can emphasize the complexity of development and the number of environmental influences on children (Sameroff & Fiese, 2000) Furthermore, the merger of the ecological model with more precise measures of geographic location and more contextually sensitive me asures of SES can be a powerful method for addressing issues of inequity and academic performance. Risk factors like poverty are linked to regulation. Those from differing social classes have characteristics that act as boosters or barriers to psychologic al development. These characteristics can include how a mother interacts with her child, maternal mental health, family financial resources, and violence in the community (Sameroff & Fiese, 2000) As mentioned above, many children enter school at the same chronological age but arrive with different levels of ability. Instead of arguing that it is lt, one could consider that the differences in ability rate of development, the context from which a child comes, and his or her ability to self regulate or how he or sh e engages with experience. Self regulation is connected to academic performance (Pintrich & De Groot, 1990) Without the buffering support of supportive factors, a child who enters school with limited self regulation abilities because of poverty, exposure to chronic stress and other risk factors will perform differently than a more affluent peer with stronger self regulation abilities. Representation The representational model discussed by Sameroff (2010) refers to cognitive structures where lived experience s are encoded at abstract levels. These abstractions provide a structure for interpretation of new experiences that include sense of self and
60 other. In other words representational models assert that the encoding of experience yields an internal summary of the external world. As a child engages with the external world, the world is internalized and represented within his or her mind. These representations become working models that include SES, culture, self esteem and social relationships. Representations are adaptive because they help bring order to a world that is constantly in a state of flux. When one makes a representation of a social relationship, features of that relationship are included in the representation while other features are excluded. The q uality of representations of the child in relation to him or herself and in relation to others during infancy and childhood has long term effects for adult development (Strouf, 2005) Likewise, those who interact with a child also form representations of the child and behave accordingl y. The concept of representation A few exampl es of how representations impact school readiness are through social inequities, discrimination, and family stress. Children from minority groups experience early life stresses such as discrimination that impact their development (Sanders Phillips, Settles Reaves, Walker, & Brownlow, 2009) Representation plays an interesting role in academic performance. Teacher expectations of a student are shaped (Ogbu, 1987) Exposure to discrimination creates high stress levels that are related to poor health outcomes and can have an impact on student performance. Since children come to school with varying degrees of readiness, schools need to stop assuming that the whole class should learn
61 the same material the same way and that students should reach the same levels of achievement at the same time (Evans, 2005) According to Evans (2005), a more realistic approach than homogenous learning is to emphasize options like multiple texts, group projects, assignments offered at different levels of complexity, and assessments that measur e academic performance that consider a range of abilities. Since some students come from homes with high stress as a result of poverty and discrimination, these students are exposed to increased stress that may impact development and therefore academic per formance. Additionally, because schools are usually funded by property taxes, schools in low income areas are more likely to be underfunded and understaffed which is fundamentally inequitable. Evans (2005) asserts that all learning is personal and that tea chers with high expectations and strong support are more useful than the one size fits all curriculum. Additionally, school counselors can help intervene with students who have representations that are not functional by offering individual or group counsel ing. Low self esteem may be an example of a dysfunctional representation. If one adopts a unified theory of development that includes the personal development, regulation, context, and representation perspectives, comprehensive new strategies for examinin g differences in test score performance are possible. Specifically, new strategies need to consider the key points mentioned from the above developmental theories to address the complex interactions of factors associated with academic performance. With eme rging technologies like Geographic Information Systems and lifestyle segmentation profile s, counselor educators and education researchers are increasingly more able to look into the relationships among academic
62 performance, childhood context, and stress me asured through cumulative risk and supportive factors. A model such as the Life Course Health Development Model sheds light into the relationship between multiple contexts and cumulative risk on health and education outcomes. Life Course Health Developmen t Model While educators and counselors have focused on the relationship between context and academic outcomes, an inadequate conceptualization about the relationship among context, individual, and school systems persists. In addition to the theories discus sed above, the medical field has insights that are helpful in describing why context relates to performance. The Life Course Health Development (LCHD) model (Halfon & Hochstein, 2002) informs how context and individual relate to the academic environment through stress response systems. It also discusses how cumulative stress responses are intergenerational and can be handed down from mother to child. The LCHD model contains relevant assumptions about development and academic performance. The LCHD model acknowledges that health is a result of multiple determinants nested in genetic, biological, social, behavioral, and economic contexts that change as on e undergoes development (Halfon & Hochstein, 2002) Secondly, health is an adaptive process that is composed of many transactions cumulative risk and protective factors are programmed into regulation systems during critical and sensitive developmental stages and result in different health trajectories. Finally, the timing of these biological and social risk factors influence development.
63 Life C in multiple contexts. Halfon and Hochstein (2002) discuss how a child in poverty can be exposed to more environmental risk. Such risk may include interpersonal violence and inadequate access to healthy food and medical care. As a child in poverty begins to go to school, the same child may be less likely to attend a quality school which reduces the l ikelihood of developing relationships with more advantaged peers. Life pathways explain that as one experiences more risk and less support, the effects compound through time, like a snowball rolling down a hill, the negative effects of multiple risks accum ulate through time. Lower initial starting points on standardized test scores in third grade can lead to fewer opportunities as a disadvantaged child grows into adulthood. A discussion about how risk accumulates across context, individual, and how a child regulates the stress between self and context is important for counselors and example, the stress that results from poverty, discrimination, and inadequate resources embed itself into the biological system of children. If left without support, the earlier in time, frequency, intensity, and duration of stressors brought about by reduced opportuni ty and poverty impacts cognitive growth (Bryck & Fisher, 2012; Peskin, Raine, Gao, Venables, & Mednick, 2011; Plessow, Kiesel, & Kirschbaum, 2012) stress response systems (Del Giudice, Ellis, & Shirtcliff, 2011; Heim et al., 2002; Korte, Koolhaas, Wingfield, & McEwen, 2005) emotion regulation (Beauchaine, Neuhaus,
64 Zalewski, Crowell, & Potapova, 2011; Eisenberg & Spinrad, 2004; Gumora & Arsenio, 20 02) and peer interactions (Dishion, Ha, & Vronneau 2012) and reading and mathematics achievement gaps (Flores, 2007; Michael J. Kieffer, 2011; Robinson & Lubienski, 2011) One way to begin the discussion about cumulative risk and life pathways is to refer to the literatur e on adverse childhood experiences. Adverse c hildhood e xperiences In the 1990 s Felitti, Anda, and Nordenburg (1998) studied adverse childhood experiences (ACES ). They asked the sample of approximately 13,000 participants whether or not they had experienced any of 10 experiences that were determined to be traumatic risk factors in early life. The participants were given an ACES score by tallying up the 10 experie nces participants had experienced. Those with an ACE of 4 or more were 7 times more likely have alcohol abuse compared to those with a 0 ACE score. Additionally, participants with a score of 4 or more were 6 times more likely to have had sex before their 1 5 th birthday. Those with an ACE score of 6 or more were 30 times as likely to attempt suicide as those with an ACE score of 0. The ACES study shows that the more adverse experiences a child has in early childhood, the more likely he or she will have health complications. The 10 ACES items relating to abuse and drug use were selected by the authors to examine stress in early childhood. The ACES list of 10 risk factors is one scale. With a cumulative risk approach, for each person or environmental construct, a binary classification of risk is determined by a statistical cutoff (e.g. two standard deviations above the mean) on the basis of a categorization (e.g. above or below a poverty line). The cumulative risk is calculated by summarizing multiple risk catego ries.
65 The advantage of this approach is that it enables one to simultaneously model many factors without running into as many issues of statistical interpretation related to multiple interactions. The cumulative approach also helps avoid overlapping multic ollinearity issues frequently related to poverty and family stress. Multicollinearity happens when two or more phenomena are highly correlated. Until recently, statistical methods have not been able to adequately track the complex interactions of a child w ith the environment. And yet multiple interactions occur in factors related to child development outcomes. Cumulative r isk and a llostatic l oad Cumulative risk models converge with meaningful theoretical perspectives in both the life course health development models and ecological models. These theories explore issues in neurobiology that include allostasis and stress response systems (SRS). Allos tasis, unlike homeostasis, involves a set of multiple physiological systems continually adjusting its normal operating range to respond to various social and physical demands (Evans, 2003; Evans & English, 2012; Shonkoff et al., 2011; Shonkoff et al., 2009; Shonkoff, Richter, Van Der Gaag, & Bhutta, 2012) Halfon and (p.447). When one undergoes a stressor, the brain responds by secreting s tress hormones, increasing heart rate and blood pressure, and redistributing how blood flows through the brain in order to optimize vigilance and fear. This biological response that regulates the impact of stress is called the allostatic load. This respons e is usually protective, but when this response is activated consistently through time without any buffer, the stress responses become pathogenic and wear down the body. An increased
66 allostatic load is related to many undesirable outcomes in adults like ob esity, alcoholism, depression, cancer, drug abuse, mental health problems, and many other issues (Shonkoff et al 2009). Increased allostatic load and the subsequent reduced executive functioning in school age children affect learning and school performan ce (Reddy et al., 2001; Whipple et al., 2010) Cumulative risk is associated with allostatic load (Evans, 2003) It has been shown frequently that the cumulative risk approach is more powerful in explaining socio emotional de velopment than studying the unique effects of risk factors (Evans, 2003) Evans demonstrated this result with a conv enience sample of 339 children from low income families with a mean age of 9 years. Data were gathered from public schools, Head Start Programs, and other state/federal programs targeting low income families in upstate New York. Separate interviews were co nducted with children and their families. The researchers assessed whether or not participants experienced the following risk factors: poverty, single parent status, maternal high school dropout status, residential crowding, noise, housing problems, family turmoil, and child separation from the family, and exposure to violence. The Life Events and Circumstances Checklist (LEC) (Work, Cowen, Parker, & Wyman, 1990; Wyman, Cowen, Work, & Parker, 1991) was used to measure other psychosocial risk facto rs. Mothers were asked to indicate whether maternal ratings of psychological symptoms in the child as measured by the Rutter Child Behavior Questionnaire (Boyle, 1985 ). Measures of allostatic load included resting blood pressure, overnight urinary neuroendocrine measures lik e cortisol, epinephrine and norepinephrine, fat deposition measure by Body Mass Index, and six physiological
67 indicators. Researchers found cumulative risk exposure was significantly related to all measures except for diastolic blood pressure. This study al so demonstrated that psychological distress and perceived competency are affected by cumulative risk. In another study of cumulative risk, Sameroff (2010), observed 500 families with children between ages 11 14. Sameroff included 20 environmental risk fac tors to approximate an ecological model with six contextual subsystems: 1) family process (e.g. parent involvement/climate), 2) parent characteristics (e.g. self efficacy, involvement), 3) family structure (e.g. marital status, SES), 4) family management ( e.g. social resources/capital), 4) peers (e.g. pro anti social involvement), 5) community (e.g. census tract info, average income in neighborhood), and 6) youth developmental outcomes (e.g. academic performance). The environmental risk effects of each vari able were dichotomized with 1/4th of the families in the high risk group. The number of high risk conditions was summed. When increased risk was linked statistically with positive developmental outcomes, a negative relationship emerged. In other words, inc reased risk in early in life is negatively related to child psychological adjustment, self competence, positive conduct, extracurricular involvement, and academic performance. Although this study did not describe how contextual experiences impacted each st udent, the study did document that various factors are related to childhood outcomes. An ecological approach can help to conceptualize how a broad range of factors influence child development and thereby can contribute to academic performance gaps between groups of students.
68 Cumulative r isk and s tres s Cumulative risk and the resulting stress impact child development and affect education and health outcomes in two ways ( Shonkoff, 2009; Shonkoff et al., 2012) The first is through the accumulation of damage over time. Children exposed to cumulative stressors and risk factors (e.g., maltreatment, environmental stressors, or discrimination) are impacted through adulthood (Shonkoff, 2009). Second, the biological embedding of risk factors during sensitive periods in development can lead to illness in adulthood. For example inadequate nutrition and recurrent infections in early childhood are associated with increased rates of cardiovascular and psychiatric disease i n adulthood (Shonkoff, 2009). Cumulative r isk and a cademic p erformance The cumulative risk approach is more powerful in explaining socio emotional development than using the unique effects of risk factors (Evans, 2003). Lucio, Hunt, and Bornovalova (2012) experience of have to adapt, which creates more opportunity to activate the stress response system. Like health outcomes, academic success or failure depends on the number of predictors present not necessarily the type. Unfortunately, there is typically a strong positive relationship between risk factors and interventions. If a high number of risk factors is present, an effective intervention will likely have to be more intensive, comprehensive and resource demanding (Lucio et al., 2012) Therefore, Lucio et al (2012) argue for testing for the optimal number of predictors of acade mic failure.
69 Lucio et al. (2012) studied approximately 15,000 students from the Educational Longitu dinal Study of 2002 (ELS: 2002) Using academic achievement as the dependent variable, grade point average was dichotomized into above 2.0 and below 2.0. The authors controlled for SES, race, and gender. Many predictors of academic failure included academic expectations, self efficacy, attendance, school misbehavior, and teacher relationships, to name a few. Notably, socioeconomic status was father and mother occupation). The authors utilized the cumulat ive risk index (CRI) Gutman, Sameroff, & Cole, (2003) whe re each factor was correlated with GPA. Factors with a significant relationship to GPA were divided into 2 groups (lowest 25% and the remaining 75%). Categorical independent variables were dummy coded. If an independent variable was negatively correlated w ith GPA, then the students in the top quartile were coded as 1 and the remaining 75% were classified as 0. Hierarchal linear regression was used to identify variables that made a unique contribution to the model. The factors that were not eliminated during this process were used to create the CRI by Student Grade Point Average decreased by each number of risk factor. A receiver operating characteristic (ROC) curve analysis was used to det ermine the optimal number of risk factors that balance sensitivity and specificity. The ROC curve enables researchers to determine the capacity of an instrument to discriminate between groups and helps choose the best cutoff point (Cook, 2007) The ROC curve analysis in this study revealed a cutoff point of two risk factors for predicting academic failure (<2.0 GPA). Essentially, using two risk factors as a cutoff accurately identifies students at risk for
70 failure 81% of the time and incorrectly identifies non risk students 34% of the time. Of the many risk factors that are studied, socio economic status appears to be one of the most researched measures. Socio E conomic S tatus Socioeconomic stat us can be divided into subjective experience (phenomenon) or status classified systematically by researchers (Lucas & Beresford, 2010) Both the on a child. In regards to the sub jective approach, Jackman (1979) studied how Americans classify SES and found that the socioeconomic cues include income, job authority, and personal factors like lifestyle. These expressions of SES are less hierarchical than the research driven classifica tions of SES. Free Reduced Lunch a s a M easure of SES The relationship between socioeconomic status and student achievement exists in most industrialized countries. Socioeconomic status (SES) is the most commonly used contextual measure in education, but i economic resources (Harwell & Lebeau, 2010). Further, the common metric used to assess SES is free and reduced lunch status (FRL). This measure has numerous flaws. Many researchers use FRL status in research, but fail to provide a rationale for using this indicator to assess SES (Lubienski, 2006). More importantly, the way FRL status is obtained is flawed. Students are eligible for reduced lunches if household income is less than 185% of the federal poverty guideli ne and can receive free lunches if household income is less than 130% of poverty guidelines. According to data available for the 2007 2008 school year, 92% of all K 12 students in the US had access to FRL (Harwell & LeBeau, 2010) Another issue is that FRL eligibility relies on federal poverty
71 guidelines. As Hauser (1994) argued, many federal poverty guidelines are outdated. If FRL eligibility is based on a flawed guideline, then the results derived from FRL research are subject to the same flaw. Kurki, Boyle, and Aladjem (2005) argue that FRL does not capture the effects of concentrated poverty in a neighborhood. Essentially, FRL lacks context. Also, FRL participation reduces by grade level. Finally, there can be up to a 20% misc lassification rate when FRL is used as a research variable because of the errors associated with assigning someone FRL status. How has socioeconomic status (SES) historically been measured? One of the most commonly used proxies for SES in educational rese arch is free and reduced lunch (FRL). Sirin (2005) completed a meta analysis that looked into measures of SES. In 2005, Sirin reviewed 58 articles in a meta analysis of achievem ent gap literature between 1990 2000 to observe the connection between SES and academic achievement. He found that SES is linked to academic achievement directly, but also indirectly through multiple interacting systems like ethnicity, grade level, and sch ool neighborhood location. Sirin (2005) found that the impact of SES on families varies for individual students depending on where they live and the cohort the students go to school with. He also noted that SES is a stronger predictor of academic achieveme nt for white students than for minority students. Additional findings suggest that the location of the school determines the resources available for education which affect achievement gaps in schools. Another critique by Sirin (2005) about FRL as an SES m easure is that FRL is too commonly used and fails to take into account the nuances of family and neighborhood context. Neighborhood and context have been studied together by education
72 researchers ( Borman & Benson, 2010) Context generally refers to the geographic location, socioeconomic factors of a neighborhood and the racial/ethnic composition of the neighborhood/school. Researchers f requently consider context as groups of people bound by geography, e.g. neighborhood boundaries, or by the location of the organization, e.g. school (2010). Within these geographic contexts, processes of socialization and access to resources influence the lives of individuals and families in constructive and destructive ways (Brooks Gunn, Duncan, & Aber, 1997; Brooks Gunn, Duncan, Klebanov, & Sealand, 1993) While schooling has an impact on student achievement, it is not the only factor that contributes to student success. For example, around 90% of the variance in student math scores can be predicted by the following factors: the number of parents in the es, and the having any knowledge of the school. The origins of the achievement gaps are not only in the school nor are they only in the students (Evans, 2005). Alternat ive Measures of SES Given the flaws associated with using FRL to assess SES, researchers have suggested guidelines for other measures of SES. Harwell and Lebeau (2010) suggest 4 criteria for selecting a measure of SES. First, SES measures should be valid a nd reliably captured as conceptualized by the researcher. Second, SES measures should measures should show minimal nonresponse. Finally, SES measures should be accessible a nd priced reasonably.
73 School Level Socioeconomic status is typically measured at the school level and student levels. Generally speaking, school mean SES (usually measured as percent on Free reduced Lunch) is predictive of academic climate and quality instruction offered at the school (Mickelson & Nkomo, 2012) Kieffer (2011) used school level poverty as measured as a concentration of students on Free or Reduced Lunch status in the school. School SES was measured as the percent of students eligible for free or reduced l unch. Below I will briefly explore the use of Geographic Information Systems (GIS) and academic achievement. I argue that Geographic Information Systems have been used to study academic achievement and that they can also potentially be used as an alternati ve measure of SES. Geographic Information Systems and Academic Achievement A Geographic Information System is a computer based system that allows a researcher to represent data spatially and link it to demographic, census, and any other data that contains geographic coordinates (e.g. student address). GIS is a powerful tool that could be used to enhance School Counselor accountability and academic research. A Geographic Information System (GIS) is defined as a group of hardware and software that integrates computer graphics with relational databases to manage data about geographic location (Biggs & Garson, 1992) Geographic Information Systems take tabular data that have a spatial referent (e.g. zip code, address, and latitude/longitude) and represent it spatially as a map for visual analysis. For example, in schools, much of the data (e.g. attendance, GPA, achie vement scores, etc.) is in tabular form such as excel spreadsheets. With tabular data alone, it is difficult to analyze spatial patterns. For example, agencies and counselors may want to help set up a tutoring center for at risk students at a church or oth er community center but do not know which students to
74 select, how close they live to the center, etc. A query to locate students who have failing scores on an achievement test provides no information about how close the student lives to a community center if the data is tabular. Geographic Information Systems (GIS) help solve spatial problems like this by quantifying spatial distances and relationships between variables. GIS is used to solve spatial problems in many fields like geography, public health, and psychology. It is also a tool for rigorous academic research. A key component in education is that GIS can be used to map and reveal areas in the community where resources are most needed. Demographic information regarding geographic location and other d emographic information can be enhanced through the use of GIS. For example, the Georgia Department of Health used GIS to create demographic profiles based on age distribution, education as a percentage of the population, occupation, family structure, numbe r of dependents, and other factors. Four socioeconomic clusters were defined and from those four, 18 demographic clusters were developed. A description of one American group has a high representa tion of elderly people and single parent families with children. Not well educated and with lower than average incomes, this group lives in areas with high vacant housing and low housing values. Although poor, this cluster also demonstrates social stabilit y with almost 60% showing home ownership and 30% being married family (Thomas & Humenik Sappington, 2009 p.145). Another useful feature of GIS is that it organizes data into layers. For example, if one wanted to know if there is a relationship between income and absenteeism, GIS can display median income on the census tract or polygon level and map absenteeism
75 at the individual or point level. Geographic Information Systems also enables one to analyze multiple layers at different levels of information -visually and spatially. Another useful feature is that one can use queries based on spatial questions, e.g., how many students with low academic performance, live within 1 mile of a community center for literacy? In addition to the data that represents students visually on maps, neighborhoods can be estimated using lifestyle segmentation profile or psychographics. GIS and a cademic a dministration School counselors, principals, and district level student support can use GIS to present to stakeholders where the problems might lie. A map of where students are performing poorly on standardized test scores can be displayed and community members might be able to provide input on where to place a community center for tutoring. School counselors can use Community Information Systems (CINS ) to create maps online for the community members to create their own maps. Community Information Systems can empower members to create their own maps without having to purchase GIS software, encouraging a culture of inquiry for all community members. Comm unity project maps can be displayed online for the community to see progress. Additionally counselors can use GIS to help empower the community by presenting indicators online (e.g. public representatives, nonprofit and neighborhood based groups, statistic s on crime, schools, and housing).GIS can also be used to help with participatory planning. Maps create interest in people and help them see how changes in their neighborhood and school might affect them. Community asset maps can be viewed (Griffin & Galassi, 2010) a s a way to help counselors identify strengths in the community. Community asset mapping is defined as
76 the representation of valuable places and resources in communities on a map. The various levels of assets include gifts/capacities of individuals within t he community, citizen associations, and businesses and other institutions willing to help. Community mapping engages members of the school and surrounding neighborhoods to identify and utilize resources that are already present. Griffin and Galassi (2010) recommend using Google Maps as a resource to create the maps. Google Maps is free, but it does not have the capacity to integrate school data with contextual data and community assets like other GIS programs (e.g. ESRI) can provide. GIS and s chool s etting Meaney (2006) outlined applications of GIS in the school setting. The applications outlined include, GIS as an application that facilitates st udent controlled learning T he use of GIS to develop knowledge and skills in spatial learning among students T he ability of GIS to meet the needs of different styles of learning GIS as an application that promotes social learning as students are encouraged to collaborate; local projects to provide authentic learning experiences which are relevant and are likely to engage students T he potential for GIS projects to connect learning across disciplines; T he development of a technology skill set among students th at is challenging and unique A lignment of this application with our school goals so that GIS projects with a social justice focus could be identified, promoted, and developed (p 285). Of Meaney's list, the most relevant application of GIS for school counse lors is the use of GIS to promote equity and academic performance. A challenge in implementing GIS in school counseling practice is that the amount of time and cost associated with
77 purchasing an upgraded computer, the costly software, and the training invo lved to use the software can be difficult. On the other hand, GIS is a powerful tool and the benefits can outweigh the costs. GIS can help counselors map human behavior; identify relationships between students and specific measures of environment and neigh borhood. To implement GIS, collaborative partnerships with principals and student support services is essential. Mapping refers to taking data and placing it on a map. Students can be mapped according to their addresses. The idea of locating spatial relat ionships and mapping is not new to the counseling field. We frequently use genograms to visualize relationships. GIS adds to this approach by adding geographic and other components related to location. GIS allows school counselors to observe individuals an d groups in the context of their environment. Mapping students can help us understand cultural and contextual phenomenon in a larger context. Mapping student data over census data can reveal inequities within the community, but also how these inequities co ntribute to inequities in schools. GIS and a chievement g ap r esearch As mentioned, both the Education Trust and the ASCA National Model state that geographic location is a type of academic performance gap. The ASCA national model also asserts that effectiv e school counseling programs need to consider local demographic needs of the students. Unfortunately, the research in counselor education has not considered local demographic needs to the extent that is possible. It also appears that school counselor resea rch has done little to emphasize demographics and geographical location in their research. By failing to utilize the most advanced and
78 detailed methodologies available, school counseling research and our understandings of equity will be limited to flawed m easures that are more prone to the ecological fallacy than they have to be. Geographic location in counselor education research is generally divided into three parts (Rural, Urban, and Suburban). A search on the literature in the Professional School Counse ling, the school counseling flagship journal, reveals 11 studies that use geographic location as a variable. Every one of them used the three categories of rural, urban and suburban. Likewise of the 19 articles in the Journal of Counseling and Development that include geographic location only 1 article expanded geographic location categories from 3 to 5: rural, small town, small city, moderate size city, and large city (Huffman, Myers, Tingle & Bond, 2005). The US census classifies urban areas as a metropo litan statistical area having one urbanized area of 50,000 or more inhabitants. Suburban is classified as a metropolitan area having at least between 10,000 and 50,000 population. Rural is classified as an area with no urban areas with at least 10,000 inha bitants (Census, 2000). Using such imprecise measures leads researchers to believe that all people in one geographic location, e.g. rural have the same characteristics. Defining geographical region in 3 parts (urban, rural, and suburban) is too granular an d not sensitive enough to locate subtle differences within these groups. While students in a rural population may be more likely to have reduced income, it is likely that in the same zip code there are students who live in poverty and also live as milliona ires. While geographic location is a highly useful measure of student context, the current measures of geographic location are unfortunately too coarsely defined and are rarely discussed beyond simple descriptive statistics in school counseling literature.
79 The use of Geographic Information Systems is at an early stage in education research; however, GIS shows promise in its ability to use spatial data as predictors in educational outcomes. Geographic Information Systems (GIS) has been used to identify spat ial patterns of student achievement scores not likely to be seen in the general tabular format (Kerski, Linn, & Gindele, 2005) By mapping student scores and other variables, analysis of spatial patterns reveal information that would not be normally noticeable. GIS was used to boost school accountability at the district level in California (Wing & Berkeley, 2004) The authors mapped demographics, income, and other census data in addition to the school data. The data was analyzed at the state, school district, school level, and with individual students. The questions that arose from this analysis include: why are 10 th grade math scores in one county higher than other subjects at the school? What demographic variables might be associated with this discr epancy? The second analysis showed that where mobility is high (students moving from one school to another) the test performance was lower. Census data was mapped to show a higher percentage of residence renting versus owning homes. Finally the single scho ol level was examined. There was no difference in achievement scores notable as an obvious pattern. This study demonstrates how maps can show patterns and connections to promo te curiosity and discussion about the observed trends. Wing & Berkeley (2004) used GIS and geospatial reasoning to identify the relationship between median household income by zip code and the mean grade point average for 9 th graders. The authors state that there is a significant positive relationship between GPA and household income. The use of GIS was useful in identifying these
80 relationships; however no statistical tests were reported. In addition, the schools in affluent n eighborhoods might have a different curriculum, grading standards, differences in teacher ability and even parent support. Thus to state those in poor areas have lower achievement mi ght be a standardized achievement test such as the Iowa Test of Basic Skills or some other state test like the Florida Comprehensive Achievement Test (FCAT) in Florida. Geographic Information systems was used to display school district wide data by mappin g a performance indicator called the college opportunity ration (COR) across several political zones (Oakes, Mendoza, & Silver, 2006) The COR is an indicator of th graders to become college ready graduates. The COR is calculated by using data by the California Department of Education and by combining a 3 number ratio. T he 3 number ratio is first, ninth grade enrollment, second, number of graduates 4 years later, and finally the number of graduates that completed the college preparatory curriculum in California. For example, a high school with 300 freshmen in 1998 with 20 0 students graduating in 2002, and 100 graduates that completed the college preparatory program in California, the COR would be 100:67:33. Thus, for every 100 freshmen, the school had 67 graduates and 33 of the graduates completed the college preparatory p rogram. The COR can be calculated from the individual to state levels. The authors disaggregated the CORS by racial and ethnic groups across California by high schools and mapped the CORs across the 21 st senate district. Median household income was divide 35k, 36k 53k, 54k 76k, 77k 111k,
81 and 112k 200k) and mapped with increased shading corresponding to increased income. For example, those school zones with low income have a light shade of green and the school zones with higher income s have darker shades of green. The income levels by district and the CORs mapped revealed a discrepancy between income and college preparedness. Those with lower income levels had fewer students graduating as college ready. Additionally, considerable varia tion was found among CORs and ethnic groups, indicating a failure to provide equitable access to college amongst non white groups. Two schools with similar median incomes had differences in CORs indicating that neighborhood context and the related family i ncome level plays a role in college preparedness. The above study is a useful first start in presenting indicators of school equity (COR) to stakeholders. It also presents a new method of representing various types of data (census and school data) and analyzing them spatially. The authors sent this inform ation to legislators and school personnel as well as held legislative briefings thus demonstrating accountability. This study can be improved upon, however. The COR is one of the most useful measures available to analyze college preparation and graduation rates (Oakes et al., 2006) However, a problem with the COR is that it is not a longitudinal indicator. That is, Oakes et al (2006) measure the number of students as freshmen and the number of students who graduate 4 years lat er. Unfortunately, the COR failed to incorporate student mobility. Lifestyle Segmentation Profiling Lifestyle s egmentation p rofiling is p otentially a useful tool for estimating SES and its relationship to academic performance, context, and lifestyle. According to the Environmental Systems Research Institute (ESRI) Lifestyle segmentation profiling,
82 into 65 unique market segments based on methodology is used in business to understand lifestyle and life stages of consumers in type of geodemographic market segment that classifies U.S. neighborhoods into 65 market segments. The neighborhoods with similar characteristics are grouped or clustered together while neighborhoods with diverging characteristics are distinguished from eac h other. The 65 profiles can be reduced to 12 life mode categories for easier interpretation. Customers or students from any dataset with an address can be coded into these 65 segments or 12 tapestries. These segmentations are proprietary information and h ave to be purchased. C ounselors can code students into these tapestries by linking student data from schools According to ESRI, the segmentation system provides accurate descriptive marketing efforts that fit the profile of the business, while avoiding customers with lower buying potential. This technology is used to locate consumers with lifestyles that are more inclined to purchase the product. The terms found in the literature incl ude psychographic profiles, lifestyle segmentation, and tapestries (Fller & Matzler, 2008; ESRI, 2011) All have the purpose of systematically analyzing, classifying and producing results from what can often be an overwhelmingly large a mount of data about customers. In essence, market segmentation assumes that customers can be grouped by common characteristics. The shared traits of the customers help define similarities for one market and how they are dissimilar to other markets ( ESRI, 2011 ).
83 The lifestyle segmentation profiling methodology can be applied to education research that emphasizes an ecological framework A difference between busi nesses and schools is that schools have to receive all comers. I propose that LSP can be used to not help students buy products, but to help them buy into school. LSP is a composite of many factors rooted in a variety of contexts. Plummer (1974) asserted t hat lifestyle segmentation is the bringing together of two concepts into one unified system: lifestyle patterns and segments. Pattern is defined by Lazer (1963; as cited in Plummer, 1974 ) sense. It embodies the practice, lifestyle patterns are generally described as activities, interests, and opinions. Lifestyle measures how people spend their time, their int erests, values, and opinions of themselves and the world. It also refers to life stage, income, education, and location (Plummer, 1974). The essential premise of using lifestyle segmentation is to gain knowledge about customers to more effectively communic ate and market to them (Plummer, 1974). School counselors and education researchers can use LSP to understand the impact of SES and contextual differences on academic performance in a more refined way than using the flawed free or reduced lunch status as a measure of SES. Lifestyle segmentation is a process that begins by classifying individuals into different segments characterized by a unique way of living. The idea is to target groups of individ ual lifestyle s to market the product as a gateway to the lifestyle the customer identifies with most. The compelling factor is that one can use lifestyle segments of a population and neighborhoods. The information contained in the segments is used to
84 tailor messages to the target markets to buy their product. Us ing this methodology, students would be segmented into lifestyle groups and then identify which students value or perform well in school and which student segments are underperforming. Such a method has many applications. The curriculum could even be chang ed to target According to Thrall ( 2002) p sychograp hic profiles are an aggregation of individual attributes that relate to personality, values, attitudes, interests, and lifestyles. Psychographic profiles are used in businesses to explain market forces and predict and judge business or real estate activiti es. The information that can be gathered from a K institutions can be used to create segmentations or psychographic profiles of the students enrolled in the school district. This type of analysis can then be used to predict the needs of students and evaluate school board objectives and the curriculum. Methods in Lifestyle Segmentation Profiling Lifestyle segmentation profiles are created through a number of empirically based methods including cluster analysis, K Means analysis, ANOVAS and ad hoc analyses (e.g. Least Squared Difference tests). A commonly accepted first step to creating lifestyle segmentations is to begin with an exploratory factor analysis. Factor analysis can be used to reduce the size of variables and has been used as a preliminary analysis to cluster analysis (Naylor & Kleiser, 2002) Lifestyle segmentation profiles are also used to measure neighborhood determinants of student education perfo rmance (Sirin, 2005). According to Goss (1995) the LSP index is based on three assumptions:
85 1. Social identity can be reduced to meas urable characteristics and the population can be classified into a small number of coherent and stable segmentation categories. 2. LSP index once assigned to an individual or population can be predictive of behavior (Mitchell, 1984) 3. Residential location is either highl y correlated or a determinant of social identity and behavior. contains the most affluent and well educated groups in the nation and generates nearly one quarter of the US income. The median income is $100,983 and most of the households are married couple families. It is one of the least ethnically diverse groups. Lifestyle segmentation has been used in education research and shows promise. Webber and Butler (2007) used a national database of all stu dents in England to look for connections between SES, as measured by LSP, and student achievement. The authors suggested that the neighborhood in which someone resides is a better predictor of academic performance than parent occupation. Furthermore, Webbe r and Butler (2007) asserted that in relation to academic performance, neighborhood is as important a measure as social class. They looked at 61 mosaic types, similar to lifestyle segmentation profiles. They categorized the mosaic types into 2 groups more or less deprived. Those from the affluent families scored higher in academic achievement than those with less affluent families. They found that student neighborhood is the most useful predictor of performance. This study sheds light on the nature of SES a nd academic achievement; however, the study had some deficiencies. First, it was unclear if the researchers used individual or group level data to conduct the analysis, thus making them vulnerable to the ecological fallacy. Second, the mosaics were divided into two groups reducing the sensitivity of the data. A stronger study would explain and
86 discuss multiple mosaics and the differences amongst groups. The use of LSP categories with its 65 or 12 categories would make this type of study richer by increasing the precision of the SES measures. Sirin (2005), recommended that to study context, researchers should emphasize geographic location while looking at the link between SES and a cademic performance. Lifestyle s egmentation not only takes lifestyle, context, and income into consideration, it also uses a powerful tool called Geographic Information Systems (GIS) to represent data spatially. Geographical information systems and lifestyle segmentation profiles are frequently used together in Business Geography to study lifestyle differences and then displayed on a map to represent individuals, groups, and neighborhoods. The growing use of GIS gives rise to spatial statistics and geospatial reasoning (Thrall, 2002). The use of Geographic Information Systems is at it s beginning in education research. While the technology is a powerful way to study geographic location, it has not yet been introduced to the counseling literature. The purpose of the next section is to demonstrate the relevance of GIS to the school counse on achievement gaps. Methodological Issues Methodological issues to consider when researching the connection between SES and student achievement have been noted (Sirin, 2005). First, the unit of analysis is a major challenge. At what level can a researcher effectively predict student achievement? C hoosing aggregated data is more cost effective than individual level data, but it may not be sensitive enough to pick up subtle within group differences. Missing within group differences can lead to a common error called the ecological fallacy. The ecologi level
87 chance of committing this fallacy increases as one aggregates the data. There is a need to use data that will permit researchers to take student, neighborhood and school into account to reduce the risk of the ecological fallacy Sirin recommends analysis at the group and individual leve l. He also recommends a multi level analysis such as multi level modeling. Multi level models also called linear mixed models are also a useful fit for ecosystemic models. In addition to data level, researchers must als o consider the type of data (e. g. ca tegorical, dichotomous, etc.). Sirin (2005) found that when aggregated data was used to examine the SES achievement relationship at the student level in the meta analysis, the findings revealed ecological fallacy (Sirin, 2005). Thus, it is a problem to mak e assumptions at the individual student level from aggregated data. Sirin (2005) suggests a more precise measure of SES in place of FRL that takes student context into consideration. The popular three part model of SES proposed by Duncan, Featherman and D uncan, (1972) uses parental income, parent education and parent occupation. Sirin (2005) encouraged home resources to be considered as well as measures of SES. Home resources include household possessions like computers available, summer school and after s chool program availability (Sirin, 2005). Sirin recommended that SES be studied in relation to context, including: neighborhood, family income, diversity/heterogeneity of neighborhoods. Other recommendations by Sirin for contextual variables include: compe nsatory education, geographic location, and even lifestyle. lifestyle segmentation profiling meets these recommendations by providing more detailed and linked datasets.
88 Linear Mixed Modeling There are numerous analytic methods to understand growth and I w ill briefly review some of the most common methods of growth modeling. This overview sheds light on the varying approaches to the logic and analysis of nested data structures over time. In this section I will discuss multilevel modeling, latent growth curv e modeling, and general mixed m odeling (MLM, LGC, and GMM respectively). Each of these approaches assumes that the dependent variables measured are normally distributed. When a parameter coefficient is skewed or when few levels are represented, the coeffic ients can become be unreliable. Another issue is that the measurements should typically be measured at equal intervals or ratio levels. Although it would be optimal, m ultilevel m odeling does not require equal time intervals, but latent growth curve modelin g does (Burchinal et al., 2006; Muthen, 20 01, 2004) Another powerful aspect of growth modeling is that education and health researchers may want to know what aspects of an individual, family, school and community context pred ict variability in development. Methods of Growth Modeling There are three known issues in modeling individual academic development. These problems include inadequacies in the conceptualization, measurement, and design of research (Bryk & Raudenbush, 1987) The critique in the mid 1980s was that Ordinary Least Squares regression failed to focus on the variability of the relationships that o ccur among groups. Multiple regression techniques were useful to education researchers but it is difficult to overcome design effects for example correlations among repeated measures. Secondly, the academic measurements did not adequately distinguish the rate of change among individuals. Finally, the research designs typically
89 contained only two time points that were generally related to pre test and posttest designs (Aikens & Barbarin, 2008; Bryk & Raudenbush, 1987) A solution to the above concerns was proposed to education researchers called Multilevel m odeling (MLM) (Aitkin & Longford, 1986) The MLM method enabled investigators to examine the initial status (i.e. intercept) and change (i.e. slope) through time; to examine correlates of change; and enabled researchers t o test hypotheses about the effects of other variables on individual growth. As the ecological models discuss (Bronfenbrenner, 1977; Sameroff, 2010) individuals are nested in other contexts such as schools and neighborhoods. The MLM growth models enable researchers to study nested data structures, individual difference s among groups, and differences in groups through time. An appropriate betwe en subjects model has to include both main effects and interactions (Burchinal et al., 2006) The typical issues of sample size and the number of repeated measures limit the capability of growth models to investigate change patterns. Longitudinal methods also need to take into consideration the correlations among repeated measures (Burchinal & Appelbaum, 1991; Muthen, 2004) Nearly all bility. Previous skills, for example a standardized reading test, at time 1 are correlated to skills at time 2 or later. Groups of individuals also become more homogenous over time. If one fails to account for these correlations then the test statistics be come invalid because the variance can be underestimated. The MLM equation includes random effects, which makes it stand apart from a typical OLS regression that relies on fixed effects. The random effects enable variation
90 across intercepts and slopes Instead of focusing on the best level of analysis (e.g. school or family), Aitkin and Longford (1986) argued for analyses that maintain the data structure as well as possible. Using MLM or similar methods to develop growth models maintains complex data str uctures by incorporating nested levels into the analysis. Because of the complex nature of multiple interacting systems in child development, education research should model various levels and account for interactions across levels and variables (Bryk & Raudenbush, 1987) Multilevel m odeling and latent growth curves addres s these concerns. Nested longitudinal structures are prominent in education research. Students are nested in schools through time and student academic performance within in a school, for example, has shared variance. The MLM method looks into the variance within and between schools by using random effects. Random effects vary across individuals or groups; fixed effects are thought to be constant across individuals and groups. Alternatively, Ordinary Least Squares regression (OLS) uses fixed parameters and does not consider shared variance within nested structures. Thus a 2 level MLM has the capacity to consider student level characteristics (e.g. birth weight, gender, IQ, etc.) as well as level two variables (e.g. % of the school on free or reduced lunch st atus.). The varying percentages of students on FRL in each school, for example, can have an on to a two
91 Growth Modeling There are a wide range of statistical methods to factors related to development. A statistical ana lysis should integrate three fundamental elements in a longitudinal study, (1) a theoretical model of change, (2) longitudinal design, and (3) statistical models that are compatible with the structure of the nested data ( Burchinal, Nelson, & Poe, 2006 ; Burchinal & Appelbaum 1991) While there are a variety of analytic methods ava select a method that matches their theory of development and the data available ( Burchinal et al., 2006) Growth curve analysis is used to describe how patterns change over time. Growth patterns can be influenced by other covariates or independent variables and growth modeling helps to identify the impact of proximal and distal factors on development. With growth modeling, one can identify the developmental trajectories of its students and examine patterns that boost or hinder development over time. In statistical analyses, there are numerous ways to define change. Linear change trajectory may extend out in a straight line from the starting point or intercept; a line that either ascends, descends or is parallel to the x axis. Nonlinear change can be examined when a child develops over time at different rates. Sometimes the development occurs in spurts and other times growth plateaus. These non linear growth rates can be quantified as exponential or logistic functions of change (Muthen, 2004) Among the powerful features of modeling child growth is that one can identify the initial status of a group of individuals and then compare that starting point to others students. Next one can observe how these individuals or group develop over time.
92 Repeated measurement of a dependent variable, such as a reading test score, is one way to measure growth but too few measurements limits research models. It is imp ortant to consider the number of repeated measurements allow for the estimation of the hypothesized individual growth curves (Burchinal et al., 2006) As Burchinal et al (2006) state, with two repeated measures, one can determine an intercept or slope for individuals, but both are not possible. With three repeated measures, in dividual linear growth curves can be identified with the related intercepts and slopes. The intercepts and slopes describe rate of change in relation to time or age for individuals. With 4 time points nonlinear growth trajectories (e.g. quadratic polynomia l function or the exponential growth curve) can be estimated. With 5 or more repeated measurements, higher order polynomial functions like cubic growth curves become possible. A cubic growth curve enables one to describe S shaped change such as growth and decline across time. Multilevel Models and Growth Multilevel m odels (MLM) assess growth. The MLM growth model uses a similar concept as above and uses measurements of time (e.g. years) as its nested level 1 variable. For example years as a repeated measu (level 2), and school composition, percentage of students on free or reduced lunch status (level 3) can be modeled. The brief review of a study below uses a representative case of MLM to illustrate a 3 level MLM grow th model. Because the models become long and complicated, I will illustrate only the unconditional growth model formula in the study and then discuss how the authors further developed their conditional growth models
93 Aikens & Barbarin, (2008) examined the developmental trajectories of a cohort of kindergarteners through 3 rd grade using the Early Childhood Longitudinal S tudy data. A Multilev el m odel was used to examine the degree to which child, family, school, and reading. Child reading scores were observed monthly. The child variables included gender, race, age at first assessment, and SES. The family variables included parent interviews related to child characteristics, family practices and resources, parent well being, and home learning environment, number of books in the home, day care attendance, and parent rol e strain, among others. The family interview was derived into three variables home literacy environment, the frequency in which the child read outside of school, and the frequency in which household members visited the library with a child. School level va riables included self reports from classroom teachers about the classroom peers, classroom literary instruction, and teacher background and beliefs. School administrators also completed questionnaires related to the percentage of students in the school on free or reduced lunch. Other school level variables included school poverty status, teacher experience, child participation in literacy related activities and teacher preparation. Growth curve models were estimated to determine reading trajectories from k indergarten through third grade. Their model had three time periods at the first level. The level 1 model was nested within child, family, and neighborhood characteristics at level 2. School level characteristics were modeled at level 3. The authors began by creating an unconditional model of reading development which established the initial scores and the structure of reading growth in the entire sample. In this model, reading
94 tus trajectories were not linear. In fact, the reading growth rate differed across three time periods. This cohort of children demonstrated a spike in reading scores b etween kindergarten and the spring of first grade, reading growth was slower and after kindergarten and spring of first grade. There was also significant variation around the intercept and the linear slope terms that suggested reading trajectories varied a cross children. Therefore a three level unconditional piecewise growth model with the three slopes from three time periods is described as follows: Level 1: Y tij 0ij + 1ij 2ij (Slope 1) + 3ij pij (a pij ) + tij A piecewise grow th model describes segmented change of growth through time. In this case slope K represents the time period between the fall of kindergarten to the spring of kindergarten. Slope 1 refers to the time period between the spring of kindergarten to the spring o f first grade. Slope 3 included the time period between the spring of first grade to spring of third grade. In this model Y tij represented a child i in 0ij refers to the intercept or reading scores of child i in s 1ij refers to the linear slope (e.g. monthly learning rate) in reading of child i in school j between the spring of kindergarten and the 2ij refers to the monthly learning rate in child i in schoo l j between 3ij is 2ij but for the spring pij is the strength and direction of the relationship between added independent variables a pij a nd child i at time t. Finally tij represents the error of child i in j school at time t.
95 The Level 2 Model: 0ij 00j + 0pj (X 0pj ) + rij, 1pj (X 1pj ) + rij 2ij = 20j + 2pj (X 2pj ) + rij 3pj (X 3pj ) + rij 00j is the mean intercept (e.g. Reading performance) within school j at the initial 10j is the mean linear slope (e.g. reading development) within school j between fall 20j and 30j ) represe nt the linear reading growth rate for their respective time frames. The symbol 0pj refers to the strength and direction of the association between added independent variables X 0pj and 0i j The symbol Xpj is the strength and the direction of association between X pj 1ij, 2ij, 3ij ). Finally ing test sc ore as predicted by the model. The Level 3 Model (Between schools) 00j = 000 + 0p0 (X 0p0 ) + 00j, 10j = 100 + 1p0 (X 1p0 ) + 10j 20j = 100 + 2p0 (X 2p0 ) + 20j 30j = 100 + 3p0 (X 3p0 ) + 30j, reading performance at the first 100, 200, 300 each refer to the development rate in reading scores across schools between their respective time frames mentioned above. 0p0 is the strength and direction of the relationship between the predictor
96 variables X 0p0 00j The term X xp0 is the mean linear reading development rate within school j during the three 1 0j, 20j, 0j. Finally, u ij is the overall deviation across schools from the reading scores predicted by the model. The unconditional model simply observed the growth rates within the three level structure without the effect of other covariates. These co variates might include child or school SES or other variables. A conditional growth model observes the development rate but also examines variables that might affect the growth trajectory. In order to investigate the effect of student and school level cov ariates on student reading growth, the authors constructed a conditional growth model. The conditional growth model estimated the individual level demographic and school level growth across the three time periods. The lengthier and more complex conditional models can be found in (Aikens & Barbarin, 2008) This piecewise conditional growth mod el showed that older female children from higher SES households had increased reading scores at the first assessment. The high SES female students gained reading skills faster than their peers between fall and spring of kindergarten. Once this model was fi tted, the family covariates were added to the model to assess how much SES gaps in initial and monthly reading growth rates during each time period could be accounted for beyond the demographic variables. The family variables accounted for SES differences in initial reading scores, but the family characteristics did not account for the variability in the rate at which children developed. In other words, family characteristics predicted higher initial starting points in kindergarten reading but they did not relate to faster growth.
97 The next conditional growth model added neighborhood covariates to investigate the extent to which SES gaps and reading development and initial status could be explained beyond the child demographic and family characteristics. By adding the neighborhood variables, the SES intercept was lowered by 2% and the slope between spring of kindergarten and the spring of first grade was lowered by 1%, the slope between spring of first grade and spring of third grade was also reduced by 2%. T his model showed that in addition to demographic and family characteristics, neighborhood conditions did not account for a large amount of the expected differences in initial reading achievement in the fall of kindergarten but neighborhood characteristics did account for differences in monthly reading growth. The school characteristics of reading development were modeled as well. The SES intercept coefficient was reduced slightly with the addition of school level characteristics. While characteristics relat ed to the reading skills, the school characteristics accounted for larger differences in the monthly reading development during the three time periods studied. The largest effect was observed between the spring of kindergarten and spring of first grade. This means that reading status, the school effects were better at accounting for di fferences in reading development. Essentially, schools impact reading development but do not account for the initial status well. As shown above, MLM can be used to analyze reading growth with nested data structures that incorporate individual, family, sch ool, and neighborhood characteristics by looking at the random effects. Another type of growth modeling has become
98 available called latent growth modeling. Latent growth models treat the random effects as described in MLM as latent or unobserved variables. Latent Growth Models A random effects multilevel model can be examined as a latent variable model by 0i, 1i, 2i ) as latent variables. The MLM and Latent Variable Models (LVM) are close in form to MLM models, except (Jung & Wickrama, 2008) In the case of LVM and structural equation modeling ( SEM ) 1i 1i x t, where the symbol x t describes variation as a function of the ti me score x t at time point t (Muthen, 2004) Latent growth models assume that the individuals come from a single population and that one single growth trajectory can be developed to estimate a population (Jung & Wickrama, 2008) In latent models, the level 2 equations describe variation across individuals on the intercepts and the slopes and they relate this variation to a added in a l evel 1 equation (Muthen, 2004) The difference between MLM and latent 1i). Instead, a latent variable model holds time constant across indiv iduals. The subscript i generally is removed from the intercept and slope parameters at level 2 which indicates that the individuals come fr om a single population. Latent g rowth models are typically represented visually in diagrams. For example, below is a typical unconditional intercept and a three time point latent growth model:
99 Figure 2 1. Latent g rowth m odel with covariates. and time 3 representing Grade 5. As opposed to MLM where the intercept and the slope are considered random effects, the intercept and the slope in an LGM are considered latent variables. Figure 2 1 has observed continuous outcomes or latent variable indicators labele variables labeled x. In the above model the x variables might include child SES ethnicity or other variables of interest. The intercept and slope are the latent variables derived 0i 1i y y y
100 from continuou s y variables over three time periods. For example one can measure the impact of child SES on child reading development during times 1 3. To examine latent growth curves in reading development from kindergarten through 8 th grade, Kieffer, (2011 ) used a piecewise latent growth model to investigate nonlinear growth trajectories during multiple developmental periods. Unlike the usual latent growth model that calculates an intercept and a single linear slope; a piecewise latent growth model identifi es an intercept and multiple linear slopes, one slope for each time period estimated. In this case, three time periods under investigation are (1) kindergarten through first grade, (2) first grade through third grade, and (3) third grade through eighth gra de. This study used the Early Childhood Longitudinal Study Kindergarten cohort (ECLS K) to study the relationships among reading development, child socioeconomic status and the concentration of students on free or reduced lunch in schools. A cohort of 9,18 9 students was assessed for their reading ability. The reading tests were converted to vertical scale scores. The reading scale scores derived from the ECLS K dataset achievement was assessed on seven occasions fall of kindergarten, spring of kindergarten, fall of grade 1, spring of grade 1, spring of grade 3, spring of grade 5, and spring of grade 8. The author incorporated longitudinal sampling weights and oversampled minority groups In addition to reading scores, child socioeconomic status was measured on five occasions using a continuous composite of parent education, occupation, and household income developed by NCES during parent interviews. These composite scores are commonly cons idered in SES research (Sirin, 2005) School concentration of poverty was also measured five times. Both, child SES and school concentration of
101 students on free or reduced lunch were measured in the spring of kinde rgarten, first, third, fifth, and eighth grade. Small unstandardized estimates were avoided by rescaling the school concentration on FRL with a linear transformation. One unit equaled 10%. The latent growth analysis began with observed correlations. A pat h analysis was conducted to examine the simultaneous prediction of reading achievement by child SES and School concentration on FRL. The path analysis included five regression paths, each path related to each of the time points that child SES and school SE S were measured. Both variables predicted reading achievement at each time point. Interestingly, the relationship between child and school SES and reading was lower in magnitude between kindergarten and first grade but the strength of the concurrent predic tion of child and school SES and reading performance increased at third, fifth and eighth grade. A confirmatory factor analysis was used to determine whether or not the school and child SES variables could be observed as time invariant composites. The anal ysis revealed that child SES and school SES provided independent information Before establishing the growth trajectories, an empirical growth plot for a random sample of 100 students showed that a piecewise latent growth m odel fit well. Kieffer (2011) observed the means that and saw that the means were statistically significantly different from each other. For example, the mean annual growth rate in grades K 1 was over three times as large as the Grade 1 3 mean test scores. Grade 1 growth rate was three times larger than the mean Grade 3 8 annual rate of growth. Therefore instead of relying on a single growth rate, a four factor piecewise latent growth model was fitted. The four factors in the growth model include d the intercept,
102 and rates of growth in three distinguishable periods of development. To clarify, these growth periods are Kindergarten 1 st grade; Grade 1 3; and grade 3 8. According to the appropriate goodness of fit indices, the four factor model had a better fit than other models that included polynomial, cubic, and other growth terms. Both SES factors (i.e. child and school) significantly predicted initial reading status. Students with higher SES and who attended schools with lower SES had higher rea grew at lower rates than students reading scores from lower SES ba ckgrounds in two time periods, G rades k 1 and G rades 1 3. In grades 3 8, child SES had a large effect on growth rates. That is, students from higher SES in G rades 3 8 grew at faster rates than students from lower SES. While accounting for child SES, school concentration did not have statistically significant effects on growth in Grades K 1 and Grades 1 3; but Grades 3 8 were negatively affected by school concentration of poverty. Students that attended schools with higher concentrations of poverty had slower rates of growth while compared to students who attended schools with lower concentrations of school pov erty. This study by (Kieffer, 2011) is a powerful illustration of the ability of a latent growth curve to distinguish between initial reading status and growth rates among individuals. It also shows that in some scenarios, child SES is more related to initial reading test scores, while school concentration of poverty can be mor e related to reading growth in G rades 3 8. One issue with latent growth and MLM models is that the models assume that groups come from the same population. Are students a part of the same population or are there different populations? If there ar e different populations, do
103 growth trajectories vary by population? Do students come from the same population, or do different groups have their own developmental trajectories and variances that differ from the overall population? Growth mixture models (GM M) help to answer this question. Choosing a Model The growth curve models discussed in using MLM are useful because they focus on individual differences across time. The MLM approach is useful because it allow for random effects and growth parameters can vary across individuals. The SEM approach to latent growth curves focuses on the relationship among observed and latent variables. Both SEM and MLM relate because in SEM random coefficients can be viewed as continuous latent variables. Modeling a latent va riable in SEM is useful because not only does it look at the random effects; it also observes the relationship between observed and unobserved latent variables. In the SEM framework, one can study the random effects of regressions among random effects, ana lyze growth in latent variables measured by multiple indicators, analyze sequential growth and analyze parallel growth at the same time. In MLM individual observed development is seen as a function of an individual growth trajectory as determined by a set of parameters at the individual level (e.g. child SES). At the group level, the individual parameters are assumed to vary as s function of measureable characteristics in the background and context (e.g. school composition) (Bryk & Raudenbush, 1987) The MLM approaches estimate an individual growth curve for each individua l and are estimated using empirical Bayesi an or maximum likelihood methods The advantage
104 of MLM analysis is that individual growth curves are allowed to vary in the init ial starting point and the growth rate. Another advantage of MLM is that it handles missing data well. It also includes time varying covariates and is flexible enough to incorporate varying assessment times across individuals. Latent growth curves are equ ivalent to MLM in their ability to estimate individual growth curves. Muthen, (2004) suggested a structural equation modeling (SEM) method where fixed paths in the measurement model estimate indivi dual growth curves. Estimated paths in the structural equation model can describe the direct and indirect relationship among the unobserved, latent variables. The SEM approach operates under the assumption that all individuals were measured at each time po int and then estimates a latent intercept and slope for each individual. It estimates the slope and intercept for each individual by fixing the loads of the observed variables onto the latent variables. The latest SEM software, MPlus, allows for missing da ta and also allows for assessment times to vary among individuals. The loading factors of all of the repeated measurements is constrained to the intercept to specify the latent intercept while the latent linear slope loadings become constrained to each tim e of assessment ( Burchinal et al., 2006) The major advantage of the SEM approach to latent growth curves is that it is able to account for errors in predictors and it can test mediation hypotheses. The SEM or latent growth m odeling approach also yields stronger fit indices and has an advantage over the MLM approach. Individua l Family School Community (IFSC) Model This chapter has reviewed elements of two models, ecological and LCHD, and relevant statistical models. Below I propose a framework for investigating how a ntexts. In the IFSC
105 model, the individual represents, phe notype and biology. As seen in F igure 2 2 the individual overlaps with his or her school and peers. Variables that may be considered in the individual portion of the model include gestational age, birth weight, ethnicity, and gender. The family variables include: lifestyle segmentation, SES, income status, number of household members and occupation. School variables relate to the factors in the educational setting Variables in school may include percent on free and reduced lunch, percent of race within school, and class size. Finally, community context refers to data at the census tract level Figure 2 2 Individual Family School Community ( IFSC ) Model
106 The I FSC model is an ecological and transactional model that acknowledges multiple contexts that range from the individual through the community. The IFSC model also includes the biological and social determinants spanning childhood Risk and protective factors are included in the model and can be considered proximal (most immediate) or distal (related to more indirect and community effects), as the arrows indicate. The risk and protective factors are both products of and contributors to the intersection of the individual family school and community. The current study was designed to investigate elements of the Individual Family School Community context model IFSC. In particular the study is designed to and biological determinants (i.e. birth weight, gestational age at birth gestational age at birth, Apgar) family and LSP) and school composition factors (i.e. school composition % of school SES, % of 10 th grade. The IFSC model also incorporates developmental trajectories. It is of interest to consider how SES and other factors predic trajectory. One can then ask, what covariates or independent variables account for the initial levels of growth and how does the growth rate change over time. This study investigates how elements of the IFSC model mi ght relate to variability in the initial status of student reading scores and can help explain the differing rates of change based on the covariates specified by the IFSC model.
107 Summary This paper chapter started with a discussion of the argument between who is responsible for achievement gaps in academic performance; families or schools. I argued that neither is solely responsible, academic performance needs to be considered within a broader developmental perspective (i.e. personal development, context, regulation, and representation). Of the four approaches discussed, individual developmental and contextual approaches appear to be the most useful for reevaluating achievement gaps and the role of school counselors in addressing achievement gaps. Cumulativ e risk approaches from the contextual perspective across multiple settings risk by locating students in the LSP segment identifying median age of the neighborhood, school level characteristics parent education level, and many other factors at the neighborhood level
108 CHAPTER 3 METHODOLOGY This dissertation was designed to examine the degree to which selected biological and social determinants of student impact achievement in K 12 schools. To conduct this investigation I developed the Individual Family School Community (IFSC) framework to de termine how these factors relate to academic trajectories of students in K 12 schools. In addition, the biological and social determinants of health within the IFSC framework and their relationship to academic performance were investigated. Unique to this study was the emphasis on lifestyle segmentation as a measure of socio economic status. In this chapter, the research design and methodology, including the research subjects and variables of interest, are described below. Setting This study was conducted with data from the Alachua County School District. Alachua County is located in north central Florida, approximately midway between the Atlantic Ocean and the Gulf of Mexico. Alachua County is a community of 247,338 individuals with 51.6% females and 48.4% males (wellflorida.org/data reports/Alachua county data/). The Florida Department of Health (FLDOH) website provides charts and aggregated data related to birth outcomes from years 1988 2002 ( http://www .floridacharts.com/charts/ ). In addition, the nonprofit organization WellFlorida provides reports about mother education and birth weight data ( http://wellflorida.org/data reports/ala chua county data/ ). Finally, the Florida Department of Education has a website that enables researchers to investigate state and district wide standardized test scores by demographics
109 ( https://app1. fldoe.org/FCATDemographics/ ). The data from the above websites were used to develop a description of Alachua County as categorized by the IFSC model. Individual From years 1988 2010, an approximate average of 200,000 children per year were born ( http://www.floridacharts.com/charts/ ). Of those approximate 200,000 children, a range of 2,300 2,500 children were born each year in Alachua County. Roughly 8 10 percent of these children were born with low birth weights Of the total births in Alachua County, roughly 13% of children born in 1990 2002 were born preterm or fewer than 37 weeks. Family 2011. In the state of Florida, 20.4% of mothers between years 20 02 2005 gave birth with less than high school education ( http://www.floridacharts.com/charts/ ). During the same years, in Alachua County 14.7% of mothers with less than high school education gave birth t o children Thus, Alachua County has a higher rate of maternal education than the stat e of Florida ( http://wellflorida.org/data reports/alachua county data/ ). No data was provided abo ut School 2011, but in 2004 2005, it schools. For grade levels 3 10, the schools in the county have app roximately 16,000 students per school year with 51% males and 49% females. Fifty nine percent of students in Alachua County perform at satisfactory or higher reading levels.
110 Community The per capita income 551. The median household income for Alachua County ($40,644) is roughly $7,000 less than the state as a whole ( $ overall unemployment rate is 10.5%. The percent of persons below the 100% pover ty ( http://wellflorida.org/data reports/alachua county data/ ). Subjects The study sample was drawn from two popu lation datasets. The first dataset contain the birth certificates of all children born between 1985 and 2003 (N ~1,000,000). The BVS dataset contains variables pertaini ng to prenatal and perinatal events Apgar scores. The second dataset contained district wide public school data on students in Alachua County, Florida over the school years ending in 2005 2011. The school dataset contained variables on student standardized test performance, demographic information, and school level information. Data Linkage and Missing Data The school dataset described above was linked to the BVS datas et at the Family name, last name, birth date, gender, and race. There was a 61 percent match rate between BVS and ACPS reco rds. This match rate corresponded to previous l inkages that have been conducted at the FDC between BVS and student records. The
111 unmatched records consist ed of children who die d before enrolling in school, move d out of state before beginning school, enroll ed in private school, or attended home school. T he two datasets were used to create a single longitudinal dataset for years 2005 2011. The dataset was organized by grade level which enabled the analysis of growth for each year at each grade (Bollen & Curran, 2005; Kline, 2010) The linked datasets had greater than 5% missing observations in all X and Y variables. Missing observations were estimated using F ull Information Maximum Likelihood (FIML). The FIML approach has been shown in Monte Carlo studies to function equally or better than other approaches for missing data (Enders & Bandalos, 2001) Research Variables Dependent Variable Reading p erformance was examined as the dependent variable in this study. The reading section on the Florida Comprehensive Assessment Test (FCAT) was observed on five occasions, one for each ye ar. The reading FCAT is a criterion referenced test with six to eight reading passages. Students respond to multiple choice questions for each passage and are assessed by: words and phrases in context, main idea, comparison and cause and effect, and refere nce and research. FCAT reading reliability contain three results: a developmental scale score ranging from 86 3,008, a scale score ranging from 100 500, and an achievement level ranging from 1 5. The developmental scale score was used. The developmental scale score ranging from 86 3,008 indicates the academic development of student s across time. The scale score ranging from 100 500 adjusts for
112 grade level. For example the devel opmental scale score ranges from 86 3,008 and tracks student development through time, the scale score ranges from 100 500 and is meant to focus on students at each grade level. Finally the most commonly expressed result is the achievement level score whic h ranges from 1 5. Students with reading level of 1 2 indicate below grade level proficiency, level 3 indicates grade level proficiency, and scores of 4 and 5 represent above grade level proficiency. The Reading Developmental Scale Score was used. The Read ing Scale Score was assessed every year from 3 rd through 10 th grade. To reduce high variance levels in the estimates and to increase the likelihood of model convergence, the variable was linearly transformed so that 1,000 points equals 10 points. In other words, a 1 unit increase is a 100 point increase on the original scale score. Independent Variables The independent variables utilized variables from the different elements of the IFSC model. For example, Individual determinants included gender, while school determinants included school percent enrolled in free or reduced lunch. These variables were cont rolled and regressed on the dependent variable, Reading Developmental Scale Scores. Individual and biological determinants Gender was coded as 1 for male and 0 for female. Minority status was coded as 1 for Latino, Black, Mixed, Native American while non minority status was coded as 0. Gestational age at birth (in weeks) was calculated as the duration from date of last menstrual period (LMP) and date of delivery. These estimates may vary from those estimated using gestational age based on obstetrical c onsultation. Gestational age is a continuous variable.
113 Birth w eight grams. High birth weight is approximately 3,500 grams while low birth weight is 2,500 grams and very low birth weight is <=1,500 grams The average birth weight for the district under analysis was 3,300 grams. To reduce high variance levels in the estimates and to increase the likelihood of model convergence, the variable was linearly transformed so that 2,500 points equals 25 grams One minute Apgar score was determined by documenting five factors A ctivity, P ulse, G rimace, A ppearance, and R espiration. The scores range d from 1 10. A low score indicated that the infant needed medical attention. A sc ore of three and below ind icated cr itically stressed, 4 6 indicated concern and a score of 7 10 indicated normal. Family and social determinants Family Socio economic Status was measured using student PLSP. Each Coder (Esri & Paper, 2009) using the methods described in the Daniels Thrall Education Index Assessment (Daniels & Thrall, 2007) ss was assigned to a Lifestyle s egmentation p rofile (LSP), the students classify U.S. residential neighborhoods into 65 unique market segments or 12 lifestyle tapestries based on socioeconomic and demographic characteristics. from 2005 2011. The 12 LSP categories were further collapsed into three categories based on natural breaks in student performance. These categories were called performance based lifestyle segmentation profile s or (PLSP). Category 1 was the highest perform ing
114 PLSP on reading FCAT DSS scores, category 2 was the average performing PLSP, and category 3 was the lowest performing PLSP. Figure 3 1 demonstrates the mean difference between LSP groups. Performance based lifestyle segmentation profiles (PLSP) were collapsed into three groups for the county under analysis. To locate lifestyle segmentation in this study, the student addresses from the entire ACPS dataset geocoded with ESRI Community Coder. This coding process is described in the Daniels Thrall Educati on Index Assessment (Thrall & Daniels, 2008) The Community Coder assigned one of 12 LSPs to each student. Based on the 2005 2011 datasets, the students were further categorized into 3 e mpirically based groups called p erformance based lifestyle segmentation profile s (PLSP). Figure 3 1. Comparison of Reading Developmental Scale Scores by lifestyle segmentation profile (LSP) Reading Developmental Scale Score Difference
115 Performance b ased lifestyle segmentation profile s (PLSP) were created by comparing the means of each LSP to the highest performing LSP group on the Reading Developmental Scale Scores. The highest performing LSP group wa s L1, L2, and L5. Figure 3 1 shows the ranking of each LSP group. As indicated in Figure 3 1, the groups labeled L1, L2, and L5 appeared to cluster and were approximately 100 points lower than the next LSP group, L7. The groups L7, L12, L6, L10, L4, and L1 1 also appeared to cluster with a natural break between the following three groups (l3, L9, and L8). Thus, if a student was coded in groups L1, L2, or L5, a PLSP code of 1 was assigned to that student. Likewise, if a student was coded in groups L7, L12, L6 L10, L4, or L11 he or she was assigned a code labeled PLSP 2. Finally if a st udent was coded with an LSP of L 3, L9, or L8 he or she was coded as PLSP 3. Of the data coded, a pproximately 32.3% of the students coded were in the highest performing PLSP gro up (group1). A little over half (51.9%) were coded in the mid performing group (group2) while 15.6% were coded in the lowest performing third group (group3). Approximately 21% of the students were not coded with a PLSP category. Table 4 4 shows the percent that the higher performing group (PLSP) has a higher percentage of students with a White and Asian ethnicity students than the lowest performing group (PLSP 3). This trend existed on every grade level. Like wise there was a reversed trend with African American students. No similar trend occurred for other ethnicities. Maternal continuous variable. Paternal age is the age of the father measured
116 were less than high school education, high school graduate, and post secondary education. School composition School percent FRL refers to the percentage of students in schools on free or reduced lunch status. Free or reduced lunch status in schools was used to measure school concentration of poverty. The percent age of students on FRL was added to the ( https://app1.fldoe.org/FCATDemographics/ ) To avoid small unstandardized estimates, these vari ables were rescaled with a linear transformation so that 1 unit equals 10 percent. School percent minority status was also studied as a measure of school poverty. Again this variable was rescaled with a linear transformation so 1 unit equals 10 percent. R esearch Questions 1. What is the initial status and rate of reading development f rom grade levels 3 10 in the district under analysis? 2. What is the initial status and rate of reading development from grade levels 3 10 by PLSP group? a) Do intercepts and slopes vary as a function of PLSP group assignment? 3. To what extent do parent education, parent age, birth weight, Apgar score, gestational age, ethnicity, and gender demonstrate different rates of reading development across grade levels 3 10? 4. To what extent do pa rent education, parent age, birth weight, Apgar score, gestational age, ethnicity, and gender demonstrate different rates of reading dev elopment across grade levels 3 7 and by PLSP group? a) F or grade levels 3 7 what is the yearly concurrent prediction betw een school percent FRL and school percent minority status on the initial status and rate of growth?
117 Preliminary Data Analysis Prior to conducting the laten t growth modeling analyses, correlations were observed to investigate the relationship between variables and grade level. Piecewise latent growth modeling was used at grades 3 10 to investigate elements of the IFSC academic re ading trajectories were analyzed from third grade to tenth grade while accounting for the variables of the IFSC model. To test for differences in slopes and without and with covar iates. Finally to include time varying covariates (i.e. percent FRL in schools and percent minority in schools) three latent growth models were conducted by grade level (3 10). Students with accommodations were not mentioned in the hypotheses and will be e xcluded from the research dataset. It is unclear what effect accommodations have on student outcomes, so this potential confound was not included in the study. This study used one dependent variable: Reading FCAT and multiple independent variables related to elements of the IFSC model. Research Question s 1 4 sought to establish a link among elements of the IFSC model, early life experiences, school SES and minority composition, PLSP, and developmental reading trajectories. A Latent growth curve a nalysis wa s used for each Research Question to analyze the relationship among variables organized by the IFSC Model and reading growth from 3 rd through 10 th grade. Given the high likelihood of missing data, a few measures were taken to adequately model growth trajec tories. The available data includes information from grades 3 10, seven reading observations were available. Empirical growth plots (i.e. lattice plots) of 100 students
11 8 per time period were observed for linear and non linear growth trends. The empirical g rowth plots indicated non linear growth through grades 3 10. Thus, four types of models were tested (Linear, quadratic, piecewise, freed loading). The model with the best fit indices was used and its estimates were reported. Model Building Procedure To an swer the research questions, 4 types of latent growth models were l atent growth model or means only model for the entire district. The unconditional model analyzed the variance across the multiple levels of the dataset without adjusting for covariate effects or by sorting the data into multiple groups. The second model was an unconditional multiple group latent growth model which generated 3 simultaneous latent growth curve models, one for each PLSP group. Running the multiple group analysis provided information about whether or not the intercepts or slopes at various grade levels varied by PLSP group. The third model was a multiple group by PLSP latent growth model with time variant covariates. The multipl e group analysis provided information about whether or not covariates impact individuals in each PLSP differently. The covariates were centered around the grand mean to help with interpretation of the intercepts and slopes. A series of multiple group (by PLSP ) growth models with time invariant and time varying covariates were conducted at each grade level individually. The multiple group analysis at each school level provided information about time varying covariates including student FRL status, school pe rcent on free reduced lunch and percent of student minority in each school The covariates were centered around the grand mean to help with interpretation of the intercepts and slopes.
119 Multicollinearity Another issue that was considered in the data analysi s is multicollinearity. Multicollinearity occurs when the intercorrelations among variables are high e.g. >.85 (Raudenbush & Byrk, 2001) Multicollinearity occurs when variables appear to be separate variables but they actually measur e the same phenomenon. For example X1 and education status was removed due to multicollinearlty. A correlation matrix for all variables in the study was created to inspect multicollinearity among all variables (Raudenbush & Byrk, 2001)
120 CHAPTER 4 DATA ANALYSIS AND RESULTS Chapter Overview The purpose of this dissertation was to examine the biological and social determinants o f student achievement in K 12 schools. A longitudinal by grade design (Bollen & Curran, 2005; Duncan, Duncan, & Strycker, 2006) was used for the study. An Individual Family School Community Contexts model (IFSC) was introduced as a framework to investigate the reading achievement in grade s 3 10. Specifically, this study investig ated the relationship between elements of the IFSC model and reading development. The elements of the IFSC model included selected individual level variables (i.e., birth weight, Gestational Age, Apgar scores, and minority status ), family variables (i.e., free and reduced and percentage of non white students in each school), and a community con text variable (i.e., performance based lifestyle segmentation profile (PLSP). In this chapter, I present the results of the study. Correlation analysis, factor analysis, and piecewise latent growth models were used to answer the Research Question s in this study. The type 1 error rate of .05 was established as statistically significant. Descriptive Statistics Data were obtained from a mid sized school district located in north central Florida. A total of 49,056 reading performance scores were analyzed for this study over 7 school years ending in 2005 2011. Student reading scores were analyzed by grade
121 level ranging from third to tenth grade. Because the Research Question s did not ask about students in exceptional student education (ESE), students marked wit h ESE accommodations were removed from the study. Approximately 2,200 2,400 students per grade level were deleted from the sample. With the remaining sample there were approximately 12,000 students in each grade level for grade levels 3 10. Table 4 1 show s the percent and count of gender in the district at each grade level. For the available sample, 49.8% were Female and 50.2% were Male. Table 4 2 shows the disaggregation of students by ethnicity. Approximately 4.3% of students were Asian, 34% were identif ied as black/African American, 6.5% were Latino/Hispanic, 4.5% were mixed, and 50.5% were White. Less than 1% of the population was Native American. In this district, approximately 54.75% of the students were not on free or reduced lunch status (FRL) while 45.25% were on FRL status. The average read ing scale scores are listed in T able 4 3 by grade level, birth weight in grams, one minute Apgar age, school percent on free and reduced lunch status, and schoo l percent by grade level. In addition to means and counts, standard deviation, skew and kurtosis is included for each variable by grade level. Reading developmental scale scores from grade 3 to grade 4 indicate a large initial jump in from 1,453 points to 1,633 points. There is a relatively consistent rate of development in grade levels 5 10. Birth weight in grams averaged 3,295 grams with a standard deviation of 565 grams Both Apgar one minute and five minute Apgar scores averaged 8 and 9 points respectiv ely. The average of gestation time was 39 weeks, with a standard deviation of 2.6 weeks.
122 As shown in Table 4 3, the average maternal age for students in the district was 25.8 years with a standard deviation of 6.4 years while the average father age was 29 years with 7.32 years standard deviation. The average father had 13.2 years of education with a standard deviation of 2.3 years; indicating some college. The average mother had 12.6 years of education, indicating some college with a standard deviation of 2.3 years. Percent of students on free or reduced lunch status varied across grade level. For example, grade levels three through five averaged 53.5 percent with a standard deviation of 23 percentage points. The average proportion of FRL students for grade levels 6 8 was 47% with a standard deviation of 9 percentage points. Grade levels 9 10 averaged 35 percentage points with a standard deviation of 11.5 points. The proportion of minority enrolled in schools followed a similar trend as school percent free o r reduced lunch status. Individual Factors by PLSP Table 4 4 shows the distribution of student ethnicity by PLSP grouping in each grade level. p erformance based lifestyle groups are used as a measure of family socio economic status at the neighborhood lev el. Student street addresses were assigned one of 12 lifestyle segmentation profiling codes (LSP) and further grouped into performance based lifestyle segmentation profiles (PLSP) based on reading performance scores. Group 1 had the highest reading scores while group 3 had the lowest reading scores at each grade level. In grade level three, Sixty nine percent of students in PLSP group 1 were white, 10.8% were Black, 7.9% were Asian, 6% wer e Latino, and .3% were Native American/Indian, and 6.2% were of mixed ethnicity. In PLSP 2, 48% of students were White, 33.9% were Black, 3.6% were Asian, 6.8 % were Latino, .2% were Native
123 American/Indian, and 7.5% of students were mixed In PLSP group 3, 11.5% were White, 79.3% were Black, .9% were Asian, 3% were Indian, and 5.3% were mixed The patterns of these proportions by PLSP and grade level varied little at each grade level. Table 4 5 shows individual level variables including Apgar score at 1 min ute and at 5 minutes, gestational age in weeks, and birth weight in grams by PLSP group. Gestational age and Apgar scores remain the same across grade levels and PLSP groups. Birth weight in grams varied across PLSP levels. For instance, PLSP level 3 frequ ently had birth weights that ranged from approximately 3,180 to 3,202 while PLSP level 1, the highest performing group, ranged from 3,387 to 3,442 grams. Family Level Factors by PLSP Table 4 6 exhibits the means and standard deviations of the mother and fa age and educational attainment as well as unemployment status at the zip+4 level. For 3 years higher than PLSP2. addition, m others in PLSP1 had three years more of education than mothers in PLSP3, indicating that mothers in PLSP1 had more years of college, while mothers in PLSP3, as mothers by PLSP group; however the standard deviations for fathers were slightly smaller than the standard deviations for mothers. In addition, unemployment for PLSP group 1 was 4.5% lower for than PLSP group 3. School Level Factors by PLSP Table 4 7 show s reading developmental scale scores, school percent FRL status, and school percentage minority reading developmental scale score. While it was expected that group 2 would have the highest n a clear pattern emerged in the reading
124 scores, percent free and reduced lunch status in schools, and percent school minority. Group 1 consistently has the highest average score, followed by group 2, then group 3. This pattern remains the same with school percent FRL and school percent m inority. Statistical Analyses Pr ior to conducting the latent growth analyses, preliminary analyses were conducted to determine whether the structure of the data met the assumptions of the statistical techniques Observed correlations for all variables were estimated to understand the ma gnitude and probability of statistically significant relationships. All analyses were conducted with the statistical software MPLUS Version 7. To explore the relationship between reading scale scores and other dependent variables, a Pearson correlation wa s conducted on the independent variables and dependent variables. T hese correlations are shown in T able 4 8. Reading development significantly correlated with ethnicity (Black, White, Asian) at p values of less than .001. Asian students (r=.10) and White s tudents positively related to reading (r=.33) black students negatively correlated with reading scores (r= .39). Birth weight in grams and gestational age in weeks significantly correlated with reading performance at p values less than .001. Apgar scores a t 1 minute and 5 minutes did not relate to reading scores. (r (r=.38 ) had moderate correlations with reading scores and were significant at the p <.001 level. Student lev el FRL status did not relate to any variable including reading scale scores. School percentage on free or reduced lunch status (SCHFRL) negatively correlated with reading development scale scores at a p<.001. Likewise, percent of minority students in schoo ls (SCHMIN) negatively correlated to reading development with p<.05 but the magnitude of that correlation was not very strong (r= .07).
125 The following correlation analyses were conducted by grade level to observe the probability and magnitude of correlation s between the RDSS, student percent on FRL and school percent minority. Table 4 9 displays the correlations for reading scores and students on FRL status. While it is apparent that RDSS scores by grade level are highly correlated, the STFRL variables by gr ade level did not significantly correlate to reading scores. The STFRL variables by grade level are highly correlated with each other. Given that there were no substantial correlations between FRL and RDSS, student level FRL status was removed from the lat ent growth model. Table 4 10 shows reading scale scores by grade level and Pearson correlations with school percent on free and reduced lunch status (SCHFRL). Percentage of students on FRL status in schools was significantly correlated with reading scores at all time points. For example, RDSS at grade 3 was moderately associated with SCHFRL (r= .329, P<.01), at grade 4(r=. 31), and at grade 5 (r= .32). The negative association suggests that at each grade level, reading scores decrease as the percent of stu dents on FRL status increase. The trend continues at each grade level but the relationship weakens from 6th 8 th grade (r. = 11, 09, 12) but strengthens again in grade levels 9 (r= .17) and grade level 10 (r= 19). A similar relationship pattern was found in (Kieffer, 2011a) Table 4 11 displays correlations between percent of nonwhite students at a studen between SCHMIN and reading scores appeared to differ by grade level. For example, the relationship between reading scores and SCHMIN at grades levels 3 5 were negatively related with grade 3 (r= .246, p<.01), grade 4 (r= 219, p<.01) and grade 5
126 (r= .225, p<.01). The relationship seemed to shift at grade 6 8 to weakly positive correlation with grade 6 (r=.054, p<.01), grade 7 (r=.058, p<.01), and grade 8 (r .032, p<.01). The relati onship between reading scores and SCHMIN shifted back to a negative correlation at grade level 9 (r= .046, p<.01) and grade 10 was also weakly negatively related to reading scores (r= .061, p<.01). These estimates may be exaggerated because of the large sa mple size. Growth Trends Means plots and individual plots were generated to assess the overall growth trend from grade levels 3 10. The means plot, indicated in Figure 4 1, revealed that there is a non linear pattern of change from grade levels 3 10. The mean rate of reading change from grade 3 4 is 182 points while grade 4 5 changed by only 42 points. The rate of change from grades 6 10 range from 71 to 100 points but the change from 9 10 th grade is only 23 points. The growth plots indicated a large jump in performance between grade levels 3 and 4 but the growth levels off between grades 4 10. Between 6 th and 8 th grade the growth rate appeared to follow a linear or straight line pattern. In this case a nonlinear latent growth model from grades 3 10 would fit the model well. To test which growth would provide adequate model fit, a series of growth models were generated for each Research Question The series of growth models included ( 1) a linear trajectory with o nly the intercept and slope, (2) a growth model with the intercept, slope and a quadratic term, (3) a piecewise growth model, and (4) a freed loading latent curve model. The linear, quadratic, and piecewise models each have factor loadings on the dependent variable in increments of one. For example reading scale scores for grade level three is specified as 0, while grade level four is specified as 1, and so on. Alternatively a freed loading latent curve model fixes the first grade level
127 (level 3) to zero an d the final grade level was set to one. Grade levels 4 through 9 were freely loaded. Fixing grade level 3 to 0 and the grade level 10 to 1, and all of the loadings in between as freely loading, leads to a useful interpretation (Bollen & Curran, 2005) The freed loadings reflect the proportions of change between time points rela tive to the overall change incurred from the first and the last time points enabling us to estimate the percent of change by grade level. Figure 4 1. Plot of reading developmental scale score means by grade level. Question 1: What i s the I nitial S tatus and R ate of R eading D evelopment F rom G rade L evels 3 10 in the D istrict U nder A nalysis? Research Question 1 asked about the initial status and rate of reading development from grade levels 3 10 in the district under analysis. The dependent
128 variable was rea ding achievement across grade levels 3 10. As mentioned in Chapter 3, reading scale scores and the independent variables were linearly transformed by multiplying the value by .01. Thus a reading score of 1,500 points will frequently be shown in the below t ables as 15 points. Table 4 12 shows the comparison of fit indices for the four types of growth models. Of the four models, the freed loading model demonstrated the best model fit and had a significant chi square value [x 2 (df=25, N= 38,221) = 1,747.1, p < .001]. A significant chi square value indicates poor model fit, however the chi square value may be overly sensitive given the large sample size (Kline, 2010) Other model fit indices demonstrated adequate fit (CFI=.96 and TLI = .955, and RMSEA = .042). Table 4 15 shows the nonlinear freed loading growth model with grade level 3 fixed to 0 and grade level 10 fixed to 1. The parameter loadings reveal the proportion of growth between each grade level. For example between grades 3 4, 30% of reading developme nt occurred. Likewise there were significant variances in the intercept ( = 11.319), and slope ( = 2.362) These variances indicate that the starting point and the rate of reading development have individual differences. It can be concluded that for this sample, reading development changes in a nonlinear way over time and does not follow a strict linear, quadratic, or piecewise trajectory. The covariance between the intercept and the slope revealed a negative and statistically significant ( 2.172) re lationship showing that students who start with a higher reading score do not demonstrate reading growth as rapidly as a student with a lower initial reading score. relates to a reduced growt h rate of 217 points from 3 rd through 10 th grade. The average
129 reading start point was 1,382.9 points while the rate of reading development was 584 points. The unique residual variance of the repeated measures shows the variance of a repeated measure not ex plained by the growth process. For example the amount of variance not explained by the growth process at grade level 6 is 220 points. Grade level 8 had the least amount of variance not explained by the growth trajectory while grade level 10 had the most am ount of variance unexplained. Figure 4 2 exhibits the mean of reading developmental scale scores by PLSP grouping. The developmental scale scores were linearly transformed so that 15 points equates to 1,500 points. Figure 4 2. Observed means for read ing developmental scale score from grade levels 3 10 by PLSP g roup
130 Figure 4 3 shows the path diagram of the latent curve model with the intercept and slope variances, covariance, and loadings on the dependent variables. The intercept and slopes are regressed on the RDSS scores by grade level. The intercepts and slopes for each model were not fixed. Question 2: What is the Initial S tatus and R ate of R eading D evelopment F rom G rade L evels 3 10 by PLSP G roup? Research quest ion 2 asked about the initial status and rate of reading development in grade levels 3 10 by PLSP group. Table 4 13 shows the comparison of fit indices for the four types of growth models. Of the four models, the freed loading model demonstrated the best m odel fit and had a significant chi square value [x 2 (df=87, N= 38,221) = 1,949.5 p <.001]. A significant chi square value indicates poor model fit, however the chi square value may be overly sensitive given the large sample size (Kline, 2010) Other model fit indices demonstrated adequate fit (CFI=.952 and TLI = .954, and RMSEA = .046). It can be concluded that reading development changes by PLSP group in a nonlinear way over time and does not follow a strict linear, quadratic, or piecewise trajectory. Table 4 16 shows the nonlinear freed loading growth model with grad e level 3 fixed to 0 and grade level 10 fixed to 1 by PLSP group. The parameter loadings show the proportion of growth between each grade level. For example, 30% of reading development occurred between grades 3 4. There were significant variances in each PLSP group. For example there were significant intercept variances for each group; PLSP1 ( = 9.692), PLSP2 ( = 10.369), and PLSP3 ( = 8.258). The slope variances were also significant; PLSP1 ( = 2.247), PLSP2 ( = 2.327), and PLSP3 ( = 2.444) These variances indicate
131 that differences in the starting point and the rate of change over time have individual differences. There were fewer individual differences at the intercept in grade 3 for PLSP3, and more individual differences in the slop e in group PLSP3 than in the other groups. The covariance between the intercept and the slopes for each PLSP group revealed negative and statistically significant relationships (PLSP1= 2.94, PLSP2= 2.365, PLSP3= 1.995), showing that students who start with a higher reading score do not demonstrate reading growth as rapidly as a student with a lower initial reading score. The initial starting point in PLSP3 is not as strongly related to the reading developmental trajectory, than the initial starting point in PLSP1 is related to its reading PLSP3 relates to a growth rate of approximately 200 points from 3 rd through 10 th grade core in PLSP1 relates to a reduced growth rate of 294 reading points. The average initial reading score in third grade for PLSP1 was 15.67, PLSP2 was 13.629, and PLSP3 was 12.173 points. It is clear that PLSP1 had the highest mean score at grade level 3, w hile PLSP3 had the lowest mean score at grade level 3. The rate of reading development, or slope, for each group was 5.83 points for PLSP1, 6.04 for PLSP2, and 5.95 for PLSP3. The unique residual variance of the repeated measures shows the variance of a re peated measure not explained by the growth process. For example the amount of variance not explained by the growth process at grade lev el 6 for PLSP1 is 2.33 points. F igures, 4 4 through 4 7, display the variances and factor loadings for the intercept and slopes for each PLSP grouping.
132 Question 3 To W hat E xtent do P arent E ducation, P arent age, B irth W eight, Apgar S core, G estational A ge, E thnicity, and G ender D emonstrate D ifferent R ates of R eading D evelopment A cross G rade L evels 3 10? The analysis used to answer Research Question 3 incorporated time invariant covariates into the multiple group latent growth model. Table 4 14 shows the comparison of fit indices for the four types of growth models. Of the four models, the freed loading mo del demonstrated the best model fit. There was a significant chi square value [x 2 (df=25, N= 38,221) = 1,299, p <.001]. A significant chi square value indicates poor model fit, however the chi square value may be overly sensitive given the large sample size (Kline, 2010) Other model fit indices demonstrated adequate fit (CFI=.96 and TLI = .958, and RMSEA = .032). It can again be concluded that reading development changed in a nonlinear way over time and did not follow a strict linear, quadratic, or piecewise trajectory, even when covariates were considered. Table 4 17 shows the nonlinear freed loading growth model with grade level 3 fixed to 0 and grade level 10 fixed to 1. The parameter loadings reveal the proportion of growth between each grade level. For example between grades 3 4, 31% of reading development occurre d. There were significant variances in each PLSP group. For example there were significant intercept variances for each group; PLSP1 ( = 6.533), PLSP2 ( = 6.929), and PLSP3 ( = 6.198). The slope variances were also significant; PLSP1 ( = 1.893), PLSP2 ( = 2.259), and PLSP3 ( = 1.41) These variances indicate that individual differences in the starting point and the rate of change over time have individual differences. The covariance between the intercept and the slopes for each PLSP group revealed negative and statistically significant relationships (PLSP1= 2.075, PLSP2= 1.731, PLSP3= .908), showing that students who start with a higher reading score did not demonstrate reading growth as rapidly as a student with a
133 lower initial readi ng score. The initial starting point in PLSP3 was less significantly related to the reading developmental trajectory, than the initial starting point in PLSP1. growth rat e of 90 points from 3 rd through 10 th grade while a 100 point increase on a points. Untransformed, the average reading start point in third grade for PLSP1 was 1,575, PLSP2 was 1,363.9, and PLSP3 was 1,222.4 points. It is clear again that PLSP1 had the highest mean score at grade level 3, while PLSP3 has the lowest mean score at grade level 3. The rate of reading development for each group did not seem to have meaningful diff erences. Untransformed, for PLSP1 the mean growth rate score was 563 points for group 1, 582 for PLSP2, and 561 for PLSP3. The unique residual variance of the repeated measures shows the variance of a repeated measure not explained by the growth process. F or example the amount of variance not explained by the growth process at grade level 6 for PLSP1 is 2.106 points. Table 4 18 exhibits the parameters and standard errors of the covariates by each PLSP group. The inclusion of time invariant covariates helpe d improve model fit. The results demonstrate the effects of the covariates on the intercept and slope. Being male had a negative relationship across each PLSP group (PLSP1= 509, p <.001; PLSP2=. .603, PLSP3= .717, p <.001) as did minority status (PLSP1= 1.31 6, p <.001, PLSP2= 1.997, PLSP3=2.710). It is important to note that the relationship between minority status and gender appeared to be higher in PLSP 1 than in PLSP3. Third grade males in PLSP1 scored approximately 51 points lower than females; whereas mal es in PLSP3 started approximately 20 points lower (7.17) than males in PLSP1. Likewise, the
134 reading test scores for third grade individuals in PLSP1, who are of minority status, scored approximately 131 points lower than those not with minority status. Min ority students in PLSP3 tested in 3 rd grade approximately 140 points lower than minority students in PLSP1. PLSP group: (PLSP1=.57, PLSP2=.45, PLSP3=.32). Essentially, a one year increase in ger effect for to the intercept. The slope from grade levels 3 10 was not affected by the covariates as clearly as the intercept. For example there was a significant effe ct for birth weight for PLSP2 (.024) indicating that a gram birth weight increase related to a 2 point increase growth ( .125) but no other significant effects were found for PLSP2 or PLSP3. Finally, Apgar score was significantly related to reading scores for PLSP2, but not for the other PLSP groups. Table 4 19 exhibits the R 2 values of the factors and covariates of model 3. The R 2 values for the reading scores (i.e. RDSS3 RDSS10) are over .70, indicating that the variation in the observed outcome measures are well explained by the growth factors (e.g. intercept and slope). The covariates explained 27.7% of the intercept for PLSP1, 27.2% for PLSP2, and 17% for PLSP3. The ot her covariates did not significantly explain the slope in any PLSP group. Figures 4 7 through 4 9 exhibit the time invariant
135 covariates and their relationship to the intercept and slope factors by PLSP grouping. It is important to note that each intercept and slope have different significant covariates by PLSP group. Question 4 To W hat E xtent D o P arent E ducation, P arent A ge, B irth W eight, Apgar S core, G estational A ge, E thnicity, and G ender D emonstrate D ifferent R ates of R eading D evelopment A cross G rade L evels 3 7 by PLSP G roup? Research question 4 asked about the inclusion of the time invariant and time variant covariates into the development of reading performance from grade levels 3 7. These grade levels were chosen because of the limitations of the dat a. A latent growth birth weight Apgar score, gestational age, ethnicity, gender, school free reduced lunch status and school percent minority statu s. This final model incorporated independent variables that in clude elements from each part of the individual, family, school, and community contexts model. Table 4 20 shows the estimates and standard errors for the reading performance data for grade levels 3 7 by PLSP grouping. The parameter loadings show the propor tion of growth between each grade level. For example for grade levels 3 7, between the grades 3 4, 34.6% of reading development occurred. There were significant variances in each PLSP group. For example there were significant intercept variances for each g roup; PLSP1 ( = 4.085), PLSP2 ( = 4.934), and PLSP3 ( =3.365). The slope variances were also significant with p <.01; PLSP1 ( = 1.065), PLSP2 ( = 1.404), and PLSP3 ( = .792) These variances indicate d that differences in the starting point and t he rate of change over time varied individually The covariance between the intercept and the slopes for each PLSP group revealed negative and statistically significant relationships (PLSP1= .663, PLSP2= .676, P LSP3= .229), showing that students who started with a
136 higher reading score did not demonstrate reading growth as rapidly as a student with lower initial reading scores. The initial starting point in PLSP3 was less significantly related to the reading deve lopmental trajectory, than the initial starting point in PLSP1. Thus, a 100 point points from 3 rd through 7 th sc ore in PLSP 1 related to a reduced growth rate of 66 reading points. The average reading start point in third grade for PLSP1 was 16.52, PLSP2 was 15.32, and PLSP3 was 13 points. It is clear that PLSP1 has the highest mean score at grade level 3, while PLS P3 has the lowest mean score at grade level 3. The rate of reading development for each group appeared to have meaningful differences. For PLSP1 the mean slope was 3.62 points for group 1, 3.73 points for PLSP2, and 5.03 for PLSP3. The group PLSP3 had the lowest initial score but it had the fastest gains compared to PLSP1 or PLSP2. The unique residual variance of the repeated measures shows the variance of a repeated measure not explained by the growth process. For example the amount of variance not explain ed by the growth process at grade level 6 for PLSP1 was 185.7 points. Table 4 21 exhibits the parameters and standard errors of the covariates by each PLSP group. The results demonstrate the effects of the covariates on the intercept and slope. Gender had a negative effect for PLSP1 but not the other groups: (PLSP1= .456, p =.02; PLSP2=. 267 p =.088, PLSP3= .103, p <.174). Minority status had an effect on the intercept across all PLSP groups (PLSP1= 1.234, p <.001, PLSP2= 1.865, PLSP3=
137 2.133, p <.001). The rea ding test scores for individuals in PLSP1, who are of minority status; in third grade is approximately 90 points lower than those without minority status. PLSP: (PLSP1=.376, PLSP2=.323, PLSP3=.216). Essentially, a one year increase in test scores. In third grade a year increase in increase for students than for PLSP3. While significant for PLSP3 (. 06, p= to the intercept. The slope from grade levels 3 7 was not affected by the covariates as clearly as the intercept. For example there was a significant effect for birth weight for PLSP2 (.031) indicating that a gram birth weight increase related to a 1.6 point increase education on the slopes. Finally, Apgar score was significantly related to reading scores for PLSP2 ( .135, p= .006), but not fo r the other PLSP groups. Table 4 22 exhibits the reading scores regressed on the school level time varying covariates, school percent FRL and school percent minority status. School free reduced lunch status was significant for PLSP2 at grade level 3 ( .01 1, p=.029) but no other group was affected by school percent free/reduced lunch status. Overall, PLSP1 was affected by school percent free/reduced lunch status and school percent minority status at nearly each grade level. The group PLSP2 also was affected by school free or reduced lunch status at nearly each grade level. There seems to be a stronger relationship between school percent FRL status and school percent minority status on reading scores for PLSP1 than PLSP2. The group PLSP3 only had a significan t
138 relationship to reading scores in grade level 4. For every point increase in percent school free reduced lunch status, there is a decreased reading score of 2.6 points. A percent increase in percent school minority, relates to a 3.5 point increase a read ing test score. Table 4 23 exhibits the R 2 values of the factors and covariates of model 4. Most of the R 2 values for the reading scores (i.e. RDSS3 RDSS7) are over .65, indicating that the variation in the observed outcome measures were generally well ex pla ined by the growth factors (i.e. intercept and slope). However, the variations of the growth factors (i.e. intercept and slope) were not explained as well. The covariates explained 22.8% of the intercept for PLSP1, 26.8% for PLSP2, and 27.9% for PLSP3. The covariates significantly explained the slope only in PLSP2 ( 5.8%, p=.004). F igures (4 10 through 4 12) show the path diagrams for model 4 by PLSP groups. Summary In Chapter 4 I have provided a description of the sample, an examination of correlations and growth trends, and four latent growth models that relate to elements of the IFSC model. A freed latent growth model yielded the best model fit indices in each late nt growth model. Significant covariances, variances, and time varying and time invariant covariates were found and discussed. The relevance of these findings to the existing body of achievement gap research, along with implications for future research is d iscussed in Chapter 5.
139 Table 4 1. Count and p ercent of participant g ender Grade Total Male Female Level N n % n % 3 14023 6992 49.86% 7031 50.14% 4 13707 6849 49.97% 6858 50.03% 5 13184 6532 49.54% 6652 50.46% 6 13785 6834 49.58% 6951 50.42% 7 13726 6877 50.10% 6849 49.90% 8 14574 7313 50.18% 7261 49.82% 9 16902 8701 51.48% 8201 48.52% 10 16536 8326 50.35% 8210 49.65% Total 116437 58424 4.01% 58013
140 Table 4 2. Count and percent of p articipant ethnicity Grade Level Total Asian Black Latino Indian/ Native American Mixed White N n % n % n % n % n % n % 3 14023 660 5 4756 34 888 6 28 0.2% 937 7 6754 48 4 13707 703 5 4501 33 912 7 29 0.2% 810 6 6752 49 5 13184 653 5 4247 32 875 7 21 0.2% 751 6 6637 50 6 13785 640 5 4480 32 887 6 28 0.2% 656 5 7094 51 7 13726 570 4 4507 33 893 7 20 0.1% 638 5 7098 52 8 14574 577 4 5022 34 922 6 24 0.2% 566 4 7462 51 9 16902 608 4 6041 36 1086 6 33 0.2% 517 3 8615 51 10 16536 608 4 5948 36 1095 7 26 0.2% 461 3 8395 51 Total 116437 5019 39502 7558 209 5336 58807
141 Table 4 3. Descriptive s tatistics r eading s cores, s chool p ercent on f ree r educed l unch, and s chool m inority percentage by g rade l evel Variable n Range Mean Standard Deviation Skew ness Std. Error Kurt osis Std. Error RDSS3 12080 2428 1453.42 368.915 .070 .022 .920 .045 RDSS4 12240 2343 1633.36 319.691 .292 .022 1.312 .044 RDSS5 11758 2239 1689.97 341.239 .177 .023 .946 .045 RDSS6 11818 2219 1756.48 331.018 .172 .023 1.112 .045 RDSS7 11887 2096 1842.83 313.598 .152 .022 1.096 .045 RDSS8 12412 1904 1896.52 265.142 .444 .022 1.406 .044 RDSS9 13005 2238 1963.46 310.601 .372 .021 1.486 .043 RDSS10 12707 2164 2003.13 365.940 .303 .022 .520 .043 BWGRAM 26811 8601 3294.84 595.820 .559 .015 1.94 .030 APGAR 26711 10 8.06 1.460 2.57 .015 7.61 .030 APGAR5 26711 10 8.95 .675 4.42 .015 39.05 .030 GSTWK 26681 54 38.93 2.692 .506 .015 11.30 .030 MAGE 26803 44 25.81 6.390 .385 .015 .563 .030 FAGE 20508 69 29.73 7.323 .651 .017 .729 .034 FEDU 19566 17 13.15 2.276 .070 .018 .246 .035 MEDU 26768 17 12.62 2.294 .062 .015 .354 .030 SCHFRL3 13442 85 54.06 23.256 .080 .021 .924 .042 SCHFRL4 13256 85 53.39 23.000 .099 .021 .877 .043 SCHFRL5 12731 85 53.24 23.081 .111 .022 .892 .043 SCHFRL6 13324 77 47.37 9.517 .750 .021 1.339 .042 SCHFRL7 13016 48 47.25 8.992 .387 .021 .157 .043 SCHFRL8 13621 62 47.28 8.979 .325 .021 .343 .042 SCHFRL9 15132 59 35.43 11.591 .466 .020 .002 .040 SCHFRL10 14859 55 35.08 11.520 .453 .020 .106 .040 SCHMIN3 13442 93 51.54 21.971 .649 .021 .404 .042 SCHMIN4 13256 93 50.79 21.525 .689 .021 .276 .043 SCHMIN5 12731 93 50.79 21.656 .660 .022 .326 .043 SCHMIN6 13324 94 48.90 14.026 .047 .021 .158 .042 SCHMIN7 13016 94 48.76 14.114 .074 .021 .086 .043 SCHMIN8 13621 94 48.93 13.954 .045 .021 .161 .042 SCHMIN9 15132 88 46.35 15.245 .572 .020 .948 .040 SCHMIN10 14859 49 46.16 15.181 .595 .020 .922 .040 Note Percentages based on total number of participants in each class. The above variable column contains the following variables: RDSS3 RDSS10 = reading score at the appropriate grade level. SCHFRL3 SCHFRL10 = the percentage of students on Free or Reduced Lunch Status by school, SCHMIN3 SCHMIN10 = the percent age of students in school on free or reduced lunch status by grade, BWGRAM=birth weight in grams, APGAR=Apgar score at one minute after birth, GSTWK gestational age in M
142 Table 4 4 Percent of s tudent e thnicity by PLSP Grade PLSP n White Black Asian Latino Indian Mixed Level 3 Total 10685 47.7% 35.2% 4.4% 5.9% 0.2% 6.7% 1 3186 68.9% 10.8% 7.9% 6.0% 0.3% 6.2% 2 5640 48.0% 33.9% 3.6% 6.8% 0.2% 7.5% 3 1859 11.5% 79.3% 0.9% 3.0% 0.0% 5.2% 4 Total 10942 49.0% 33.9% 4.8% 6.1% 0.2% 6.0% 1 3406 68.1% 11.2% 8.2% 6.6% 0.2% 5.8% 2 5661 49.9% 32.5% 3.9% 6.9% 0.2% 6.6% 3 1875 12.0% 79.3% 1.3% 2.6% 0.2% 4.7% 5 Total 10497 50.2% 33.1% 4.8% 6.0% 0.2% 5.8% 1 3360 68.1% 11.2% 8.2% 6.8% 0.1% 5.6% 2 5449 51.0% 32.1% 3.8% 6.7% 0.2% 6.3% 3 1688 12.2% 79.7% 1.1% 2.2% 0.1% 4.7% 6 Total 10668 51.7% 32.7% 4.6% 6.0% 0.1% 4.9% 1 3541 68.8% 11.5% 7.6% 7.0% 0.2% 4.8% 2 5514 52.1% 32.6% 3.6% 6.5% 0.1% 5.0% 3 1613 12.8% 79.1% 1.2% 2.0% 0.0% 4.9% 7 Total 10637 52.1% 32.5% 4.3% 6.3% 0.1% 4.7% 1 3570 70.3% 11.1% 7.0% 6.7% 0.2% 4.6% 2 5508 51.7% 32.7% 3.5% 7.1% 0.1% 4.9% 3 1559 12.5% 79.5% 1.1% 2.3% 0.1% 4.6% 8 Total 10936 51.8% 33.8% 4.1% 6.1% 0.1% 4.0% 1 3652 70.7% 11.4% 7.1% 6.8% 0.2% 3.8% 2 5643 51.5% 34.5% 3.2% 6.7% 0.1% 4.0% 3 1641 12.3% 79.5% 1.0% 2.7% 0.0% 4.4% 9 Total 11136 52.9% 32.8% 4.3% 6.4% 0.2% 3.4% 1 3846 72.4% 10.7% 6.7% 6.8% 0.2% 3.2% 2 5646 51.8% 33.9% 3.5% 7.2% 0.2% 3.4% 3 1644 13.8% 78.3% 1.5% 2.8% 0.1% 3.6% 10 Total 9402 53.6% 32.0% 4.5% 6.7% 0.2% 3.1% 1 3409 73.0% 10.1% 6.8% 7.0% 0.1% 2.9% 2 4715 51.4% 33.9% 3.8% 7.5% 0.2% 3.1% 3 1278 13.4% 78.9% 1.4% 3.0% 0.1% 3.2% Note: PSLP refers to performance based lifestyle segmentation groups
143 Table 4 5. Individual level v ariables by PLSP group: b irth weight in g rams, A pgar score at 1 and 5 minutes, and g estational age in weeks Grade PLSP n APGAR APGAR5 GSTWK BWGRM Level Mean SD Mean SD Mean SD Mean SD 3 Total 10685 8.1 1.4 8.9 0.6 38.6 2.0 3303 587.7 1 3186 8.1 1.3 8.9 0.6 38.7 2.0 3390 581.3 2 5640 8.1 1.4 8.9 0.6 38.6 2.0 3300 592.6 3 1859 8.0 1.5 8.9 0.6 38.4 2.1 3185 561.9 4 Total 10942 8.1 1.4 8.9 0.6 38.6 2.1 3313 591.0 1 3406 8.1 1.3 8.9 0.6 38.8 2.0 3387 566.5 2 5661 8.1 1.4 8.9 0.6 38.6 2.1 3318 604.2 3 1875 7.9 1.6 8.9 0.7 38.5 2.1 3179 569.2 5 Total 10497 8.1 1.4 8.9 0.6 38.7 2.1 3326 583.3 1 3360 8.1 1.3 8.9 0.6 38.9 1.9 3403 547.1 2 5449 8.1 1.4 8.9 0.6 38.7 2.1 3327 601.1 3 1688 8.0 1.5 8.9 0.6 38.5 2.1 3188 565.7 6 Total 10668 8.1 1.4 8.9 0.6 38.7 2.2 3323 592.0 1 3541 8.1 1.3 9.0 0.6 38.9 2.0 3408 557.5 2 5514 8.0 1.5 8.9 0.6 38.7 2.2 3324 602.7 3 1613 8.0 1.5 8.9 0.7 38.4 2.2 3160 587.9 7 Total 10637 8.1 1.4 8.9 0.7 38.8 2.1 3336 601.1 1 3570 8.1 1.3 9.0 0.7 39.0 1.9 3427 562.9 2 5508 8.1 1.4 8.9 0.6 38.8 2.2 3326 610.5 3 1559 8.0 1.7 8.9 0.7 38.4 2.5 3186 611.9 8 Total 10936 8.0 1.5 8.9 0.7 38.8 2.2 3327 603.6 1 3652 8.1 1.3 9.0 0.7 39.1 1.9 3427 563.3 2 5643 8.0 1.5 8.9 0.7 38.8 2.3 3313 613.8 3 1641 7.9 1.7 8.9 0.7 38.5 2.5 3184 612.0 9 Total 11136 8.1 1.5 9.0 0.7 38.9 2.2 3342 599.5 1 3846 8.2 1.2 9.0 0.7 39.2 1.9 3442 552.4 2 5646 8.0 1.5 9.0 0.7 38.9 2.3 3334 610.6 3 1644 7.9 1.8 8.9 0.7 38.4 2.6 3182 612.6 10 Total 9402 8.1 1.5 9.0 0.7 39.0 2.4 3353 598.3 1 3409 8.2 1.2 9.1 0.6 39.3 1.9 3438 541.7 2 4715 8.1 1.5 9.0 0.7 39.0 2.5 3345 622.8 3 1278 7.9 1.9 8.9 0.8 38.5 2.6 3202 597.4 Note APGAR = Child Apgar score at 1 minute after birth, APGAR5=Apgar score at 5 minutes after birth, GESTAGE=Gestational age of child in weeks, BWGRAM = Birth weight in grams.
144 Table 4 6. Mean and s tandard d eviations of m f a ge and e ducation s tatus by p erformance b ased l ifestyle s egmentation p rofile (PLSP) Grade PLSP N MAGE FAGE MEDU FEDU UNEMP Level Group Mean SD Mean SD Mean SD Mean SD Mean SD 3 Total 10685 26 6.4 30 7.3 13 2.3 14 2.2 11.3% 8.1 1 3186 29 6.0 32 6.8 15 2.2 15 2.1 9.2% 6.0 2 5640 26 6.3 29 7.1 13 2.2 13 2.0 11.5% 8.8 3 1859 24 6.1 28 8.0 12 1.8 12 1.6 14.7% 8.3 4 Total 10942 27 6.5 30 7.3 13 2.3 14 2.2 11.1% 7.9 1 3406 29 6.0 32 7.0 14 2.2 15 2.1 8.9% 5.4 2 5661 26 6.4 30 7.1 13 2.2 13 2.0 11.4% 8.6 3 1875 24 6.3 28 8.0 12 1.8 12 1.7 15.0% 8.7 5 Total 10497 27 6.5 31 7.3 13 2.3 14 2.2 11.0% 7.7 1 3360 29 5.9 33 6.9 14 2.2 15 2.1 9.0% 5.8 2 5449 26 6.4 30 7.0 13 2.1 13 2.1 11.1% 7.9 3 1688 24 6.3 29 8.4 12 1.8 12 1.7 15.2% 9.2 6 Total 10668 27 6.6 31 7.4 13 2.3 14 2.3 11.3% 8.1 1 3541 30 6.0 33 6.9 14 2.2 15 2.2 9.5% 7.1 2 5514 26 6.5 30 7.3 13 2.2 13 2.1 11.5% 8.9 3 1613 24 6.4 28 8.2 12 1.8 12 1.6 14.5% 6.7 7 Total 10637 27 6.6 31 7.3 13 2.3 14 2.3 11.3% 8.5 1 3570 30 6.0 33 6.9 14 2.2 15 2.3 9.3% 6.7 2 5508 26 6.4 30 7.2 13 2.1 13 2.0 11.9% 9.4 3 1559 24 6.4 29 7.7 12 1.8 12 1.6 14.8% 7.9 8 Total 10936 27 6.6 31 7.3 13 2.3 14 2.3 11.4% 9.4 1 3652 30 6.1 33 6.9 14 2.2 15 2.2 9.4% 7.8 2 5643 26 6.3 30 7.1 13 2.1 13 2.0 11.8% 10.0 3 1641 24 6.4 29 7.8 12 1.9 12 1.7 14.9% 9.2 9 Total 11136 27 6.4 31 7.0 13 2.3 14 2.3 11.1% 8.3 1 3846 30 5.8 33 6.6 14 2.2 15 2.2 9.4% 7.3 2 5646 26 6.2 30 6.9 13 2.1 13 2.1 11.3% 8.4 3 1644 24 6.1 29 7.5 12 1.8 12 1.7 15.1% 8.8 10 Total 9402 27 6.4 31 7.0 13 2.3 14 2.3 11.3% 8.2 1 3409 30 5.6 33 6.3 14 2.2 15 2.2 9.4% 6.5 2 4715 26 6.2 30 6.9 13 2.1 13 2.1 11.6% 8.7 3 1278 24 6.2 29 7.8 12 1.9 12 1.9 15.4% 9.3 Note education status at time of childbirth, Unemp=Unemployment at Zip+4 level.
145 Table 4 7 School percent of students on FRL in school, percent of students with minority status in schools, reading scale score Grade PLSP n RDSS SCHFRL SCHMIN Level Mean SD Mean SD Mean SD 3 Total 10685 1453 368 55% 23.0 52% 22.2 1 3186 1627 349 40% 20.0 44% 15.1 2 5640 1419 349 57% 20.2 50% 21.1 3 1859 1257 326 73% 20.1 75% 21.2 4 Total 10942 1638 318 54% 22.9 51% 21.7 1 3406 1786 296 40% 20.1 44% 14.8 2 5661 1609 302 56% 20.0 49% 20.6 3 1875 1459 287 73% 20.1 74% 21.4 5 Total 10497 1695 341 53% 23.1 51% 21.8 1 3360 1851 314 40% 20.5 44% 14.9 2 5449 1658 326 55% 20.3 49% 21.0 3 1688 1501 305 73% 20.1 74% 21.0 6 Total 10668 1767 330 47% 9.2 49% 14.1 1 3541 1908 303 45% 8.4 51% 11.2 2 5514 1732 320 47% 9.8 46% 14.8 3 1613 1573 289 51% 7.4 59% 12.0 7 Total 10637 1857 310 47% 8.8 49% 14.2 1 3570 1987 282 45% 8.2 51% 11.2 2 5508 1823 301 47% 9.2 46% 14.8 3 1559 1678 280 51% 6.9 59% 12.0 8 Total 10936 1912 260 47% 8.7 49% 13.9 1 3652 2021 230 45% 8.0 50% 11.0 2 5643 1884 253 47% 9.2 46% 14.7 3 1641 1761 245 51% 6.7 59% 11.9 9 Total 11136 1994 295 35% 11.3 47% 15.4 1 3846 2124 261 31% 10.9 44% 13.5 2 5646 1959 288 36% 11.4 45% 15.3 3 1644 1816 266 40% 8.3 59% 14.5 10 Total 9402 2044 351 35% 11.2 47% 15.4 1 3409 2196 312 31% 10.8 45% 13.4 2 4715 1996 342 37% 11.1 45% 15.4 3 1278 1815 308 40% 8.2 59% 14.7 Note RDSS=Reading Developmental Scale Score, SCHFRL=School Percent on FRL status, SCHMIN=school percent on minority status. PLSP = Performance based lifestyle segmentation profile
146 Table 4 8. Pearson correlations ( r ) of variables Measure N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 RDSS 97907 2 MALE 97907 0.05 3 WHITE 97907 0.33 0.02 4 BLACK 97907 0.39 0.01 0.72 5 ASIAN 97907 0.10 0.01 0.21 0.15 6 LATINO 97907 0.01 0.00 0.27 0.19 0.06 7 INDIAN 97907 0.01 0.00 0.04 0.03 0.01 0.01 8 MIXED 97907 0.00 0.01 0.22 0.16 0.05 0.06 0.01 9 BWGRM 52703 0.13 0.12 0.21 0.23 0.01 0.02 0.01 0.01 10 APGAR 52545 0.04 0.00 0.04 0.07 0.01 0.03 0.00 0.01 0.10 11 APGAR5 52537 0.06 0.00 0.06 0.07 0.01 0.01 0.00 0.00 0.15 0.54 12 GSTWK 52604 0.11 0.00 0.11 0.11 0.01 0.01 0.01 0.01 0.55 0.12 0.20 13 MAGE 52689 0.29 0.00 0.30 0.32 0.09 0.03 0.02 0.05 0.11 0.02 0.03 0.03 14 FAGE 43042 0.22 0.00 0.17 0.19 0.08 0.01 0.01 0.05 0.08 0.01 0.02 0.02 0.75 15 FEDU 41268 0.37 0.01 0.22 0.28 0.15 0.01 0.00 0.01 0.12 0.03 0.03 0.05 0.45 0.39 16 MEDU 52657 0.38 0.01 0.31 0.34 0.11 0.01 0.00 0.02 0.15 0.03 0.05 0.06 0.55 0.39 0.66 17 STFRL 47450 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.00 0.00 0.01 0.00 0.00 0.01 0.00 0.00 0.01 18 SCHFRL 97907 0.27 0.05 0.12 0.15 0.02 0.04 0.00 0.02 0.05 0.01 0.03 0.07 0.09 0.07 0.10 0.08 0.01 19 SCHMIN 97907 0.07 0.07 0.21 0.21 0.06 0.04 0.00 0.02 0.07 0.01 0.02 0.06 0.04 0.01 0.05 0.01 0.01 0.79 Note RDSS=Reading Scale Scores, BWGRM= Birth weight in grams, APGAR= 1 minute Apgar, APGAR5=5 minute Apgar, GSTWK=Gestational age in weeks, ced Lunch in school, SCHFRL=School Percent on FRL sta tus, SCHMIN=Percent of school with minority status, r = |.062|, p < .05; r = |.081|, p < .01; r = |.104|, p < .001 (two tailed)
147 Table 4 9. Pearson correlations ( r ) of Reading Developmen tal Scale Scores and s tudent free or reduced lunch status by grade lev el Measure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 RDSS3 2 RDSS4 0.76 3 RDSS5 0.74 0.79 4 RDSS6 0.73 0.77 0.79 5 RDSS7 0.71 0.75 0.77 0.80 6 RDSS8 0.67 0.75 0.76 0.79 0.81 7 RDSS9 0.72 0.72 0.72 0.77 0.77 0.81 8 RDSS10 0.90 0.74 0.74 0.76 0.76 0.80 0.82 9 STFRL3 0.00 0.01 0.02 0.00 0.01 0.04 0.02 0.27 10 STFRL4 0.01 0.01 0.02 0.02 0.01 0.05 0.02 0.09 0.91 11 STFRL5 0.01 0.00 0.01 0.00 0.02 0.02 0.01 0.02 0.87 0.92 12 STFRL6 0.03 0.02 0.01 0.01 0.03 0.00 0.01 0.02 0.83 0.88 0.93 13 STFRL7 0.06 0.01 0.00 0.00 0.01 0.00 0.01 0.01 0.77 0.84 0.88 0.92 14 STFRL8 0.09 0.03 0.01 0.01 0.02 0.01 0.01 0.00 0.77 0.82 0.86 0.89 0.93 15 STFRL9 0.06 0.01 0.05 0.01 0.02 0.00 0.02 0.00 0.73 0.75 0.77 0.84 0.89 0.93 16 STFRL10 0.68 0.02 0.08 0.02 0.01 0.00 0.00 0.01 .c 0.77 0.76 0.78 0.83 0.89 0.93 Note c =cannot be computed because at least one of the variables is constant or there is a sample of 0. Variables are labeled by gra de level. RDSS3=Reading Developmental Scale Score at grade level 3. STFRL3=Students in 3 rd grade on FRL status. r = |.062|, p < .0 5; r = |.081|, p < .01; r = |.104|, p < .001 (two tailed).
148 Table 4 10. Pearson correlations ( r ) of Reading Developmental Scale Scores and percent of students on f ree or reduced lunch status (FRL) in schools Measure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 RDSS3 2 RDSS4 0.76 3 RDSS5 0.74 0.78 4 RDSS6 0.73 0.77 0.79 5 RDSS7 0.71 0.75 0.77 0.80 6 RDSS8 0.67 0.75 0.76 0.79 0.81 7 RDSS9 0.71 0.72 0.72 0.77 0.78 0.81 8 RDSS10 0.90 0.74 0.74 0.76 0.77 0.80 0.82 9 SCHFRL3 0.33 0.34 0.33 0.36 0.35 0.37 0.34 0.08 10 SCHFRL4 0.29 0.31 0.31 0.34 0.34 0.34 0.33 0.40 0.88 11 SCHFRL5 0.30 0.31 0.32 0.33 0.33 0.34 0.34 0.37 0.83 0.97 12 SCHFRL6 0.05 0.07 0.06 0.11 0.08 0.07 0.07 0.09 0.39 0.43 0.47 13 SCHFRL7 0.04 0.07 0.04 0.07 0.09 0.11 0.07 0.08 0.37 0.40 0.44 0.85 14 SCHFRL8 0.06 0.06 0.03 0.04 0.06 0.12 0.09 0.09 0.38 0.41 0.43 0.76 0.86 15 SCHFRL9 0.06 0.08 0.07 0.09 0.10 0.14 0.17 0.16 0.30 0.41 0.39 0.46 0.49 0.57 16 SCHFRL10 0.21 0.08 0.07 0.11 0.12 0.12 0.15 0.19 0.38 0.40 0.40 0.48 0.47 0.51 0.90 Note c =cannot be computed because at least one of the variables is constant or there is a sample of 0. Variables are labeled by gra de level. RDSS3=Reading Developmental Scale Score at grade level 3. SCHFRL3=Students in 3 rd grade on FRL status. r = |.062|, p < 05; r = |.081|, p < .01; r = |.104|, p < .001 (two tailed).
149 Table 4 11. Pearson correlations ( r Note Correlation is significant at the 0.05 level (2 tailed) c =cannot be computed because at least one of the variables is constant or there is a sample of 0. Variables are labeled by grade level. RDSS3=Reading Developmental Scale Score at grade level 3. SCHMIN3=Percent of minorities le vel 3. r = |.062|, p < .05; r = |.081|, p < .01; r = |.104|, p < .001 (two tailed). Measure 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 RDSS3 2 RDSS4 0.76 3 RDSS5 0.74 0.78 4 RDSS6 0.74 0.77 0.79 5 RDSS7 0.72 0.75 0.77 0.80 6 RDSS8 0.68 0.75 0.76 0.79 0.81 7 RDSS9 0.72 0.72 0.72 0.77 0.78 0.81 8 RDSS10 0.90 0.74 0.74 0.76 0.77 0.80 0.82 9 SCHMIN3 0.25 0.24 0.23 0.25 0.23 0.25 0.25 0.08 10 SCHMIN4 0.20 0.22 0.20 0.22 0.22 0.23 0.23 0.30 0.89 11 SCHMIN5 0.19 0.21 0.23 0.23 0.22 0.23 0.24 0.27 0.84 0.90 12 SCHMIN6 0.08 0.08 0.07 0.05 0.07 0.07 0.06 0.05 0.51 0.52 0.56 13 SCHMIN7 0.09 0.08 0.09 0.09 0.06 0.06 0.07 0.07 0.50 0.51 0.55 0.92 14 SCHMIN8 0.09 0.09 0.09 0.10 0.09 0.03 0.06 0.06 0.48 0.48 0.53 0.87 0.92 15 SCHMIN9 0.01 0.02 0.03 0.01 0.01 0.02 0.05 0.03 0.43 0.43 0.44 0.59 0.60 0.63 16 SCHMIN10 0.02 0.03 0.05 0.01 0.02 0.01 0.02 0.06 0.65 0.37 0.45 0.57 0.58 0.61 0.92
150 Table 4 12. Fit i ndices from the linear, q uadratic, p iecewise, and f reed l oading l atent c urve m odels Model 2 (df) CM 2 (df) CFI TLI RMSEA SRMR 1 Linear 3,437.2 (31) 0.000 0.921 0.929 0.054 0.203 2 Quadratic 4,196.5 (31) 1.000 0.000 0.903 0.913 0.059 0.217 3 Piecewise 4,196.5 (31) 1.000 0.000 0.900 0.913 0.059 0.217 4 Freed Loading 1,747.1 (25) 1.000 1,400.280 (6) 0.960 0.955 0.042 0.186 Note 2 = chi square test of model fit; df = degrees of freedom; Bentler chi square difference test ; CM = comparison model in the 2 ; CFI = comparative fit index; TLI = Tucker Lewis index; RMSEA = root mean square error of approximation; SRMR = stand ardized root mean square residual; EP = model retained given estimation problems (negative or non significant variances) in the previous one.
151 Table 4 13. Fit indices by PLSP g rouping from linear, q uadratic, p iecewise, and f reed l oading l atent c urve m odels Model 2 (df) CM 2 (df) CFI TLI RMSEA SRMR 1 Linear 3,573.9 (93) 0.910 0.919 0.061 0.205 2 Quadratic 2,856.0 (81) 1.000 704.780 (12) 0.929 0.926 0.058 0.190 3 Piecewise 4,176.7 (93) 1.000 0.000 0.899 0.905 0.066 0.234 4 Freed Loading 1949.5 (87) 1.000 1,550.550 (06) 0.960 0.955 0.042 0.187 Note 2 = chi square test of model fit; df = degrees of freedom; Bentler chi square difference test ; CM = comparison model in the 2 ; CFI = comparative fit index; TLI = Tucker Lewis index; RMSEA = root mean square error of approximation; SRMR = standardized root mean square residual; EP = model retained given estimation problems (negative or non significant variances) in the previous one
152 Table 4 14. Fit Indices by PLSP g rouping with covariates from linear, q uadratic, p iecewise, and f reed l oading l atent c urve m odels Model 2 (df) CM 2 (df) CFI TLI RMSEA SRMR 1 Linear 2,668.493 (219) 0.91 0.919 0.061 0.205 2 Quadratic 1,939.746 (186) 1 590.61(33) 0.929 0.926 0.058 0.19 0 3 Piecewise 2,291.970 (150) 1 492.81(69) 0.899 0.905 0.066 0.234 4 Freed Loading 1,299.519 (195) 1 832.79(24) 0.96 0 0.955 0.042 0.187 Note 2 = chi square test of model fit; df = degrees of freedom; Bentler chi square difference test ; CM = comparison model in the 2 ; CFI = comparative fit index; TLI = Tucker Lewis index; RMSEA = root mean square error of approximation; SRMR = standardized root mean square residual; EP = model retained given estimation problems (negative or non significant variances) in the previous one.
153 Table 4 15. Model 1: Parameter estimates and standard errors for reading achievement data Parameter Estimate Standard Loadings 0 .000 0.304 0.003 0.392 0.004 0.514 0.004 0.676 0.004 0.797 0.003 0.941 0.003 1 .000 Variances 11.319 0.173 2.362 0.194 Covariance 2.172 0.161 Means 13.829 0.027 5.847 0.032 Unique variances RDSS3 2.777 0.093 RDSS4 1.896 0.062 RDSS5 2.526 0.071 RDSS6 2.196 0.065 RDSS7 1.894 0.058 RDSS8 1.066 0.031 RDSS9 1.409 0.054 RDSS10 2.941 0.079 Note All p Values are <001.
154 Table 4 16. Model 2: Multiple g roup l atent g rowth m odel by PLSP, n o c ovariates PLSP1 PLSP2 PLSP3 Parameter Estimate Standard Estimate Standard Estimate Standard Loadings 0.000 0.000 0.000 0.000 0.000 0.000 0.304 0.003 0.304 0.003 0.304 0.003 0.389 0.004 0.389 0.004 0.389 0.004 0.510 0.004 0.510 0.004 0.510 0.004 0.673 0.004 0.673 0.004 0.673 0.004 0.795 0.004 0.795 0.004 0.795 0.004 0.939 0.004 0.939 0.004 0.939 0.004 1.000 0.000 1.000 0.000 1.000 0.000 Variances 9.692 0.300 10.369 0.229 8.258 0.394 2.247 0.295 2.327 0.242 2.444 0.671 Covariance 2.940 0.276 2.365 0.208 1.995 0.472 Means 15.670 0.047 13.629 0.037 12.173 0.060 5.839 0.054 6.043 0.042 5.957 0.079 Unique variances RDSS3 3.091 0.171 2.572 0.123 2.691 0.245 RDSS4 1.982 0.100 1.818 0.089 1.997 0.156 RDSS5 2.557 0.121 2.383 0.096 2.765 0.199 RDSS6 2.332 0.112 2.146 0.093 2.060 0.158 RDSS7 2.014 0.101 1.846 0.079 1.753 0.168 RDSS8 1.118 0.056 1.022 0.043 1.077 0.088 RDSS9 1.504 0.091 1.290 0.070 1.485 0.174 RDSS10 3.047 0.131 2.732 0.103 3.124 0.258 Model TML(df = 87) 1949.500 Note All p Values are <001.
155 Table 4 17. Model 3: Parameter e stimates and s tandard e rrors for r eading p erformance d ata by PLSP group w ith c ovariates PLSP1 PLSP2 PLSP3 Parameter Estimate Standard Estimate Standard Estimate Standard Loadings 0.000 0.000 0.000 0.000 0.000 0.000 0.311 0.004 0.311 0.004 0.311 0.004 0.402 0.005 0.402 0.005 0.402 0.005 0.526 0.005 0.526 0.005 0.526 0.005 0.69 0 0.005 0.69 0 0.005 0.69 0 0.005 0.807 0.005 0.807 0.005 0.807 0.005 0.948 0.005 0.948 0.005 0.948 0.005 1.000 0.000 1.000 0.000 1.000 0.000 Covariance 2.075 0.294 1.731 0.225 0.908 0.439 Intercepts 15.752 0.055 13.639 0.042 12.224 0.07 0 5.63 0 0.07 0 5.822 0.053 5.612 0.095 Unique variances RDSS3 3.156 0.207 2.518 0.138 2.961 0.274 RDSS4 1.771 0.104 1.773 0.118 1.746 0.152 RDSS5 2.445 0.15 0 2.221 0.108 2.58 0 0.228 RDSS6 2.106 0.145 2.107 0.129 1.978 0.203 RDSS7 1.992 0.131 1.858 0.11 0 1.762 0.222 RDSS8 1.097 0.087 1.02 0 0.06 0 1.438 0.166 RDSS9 1.451 0.135 1.382 0.102 1.494 0.231 RDSS10 2.802 0.17 0 2.357 0.134 2.818 0.315 Intercept 6.533 0.283 6.929 0.226 6.198 0.392 Slope 1.893 0.378 2.259 0.309 1.41 0 0.623 Note All p Values are < 001.
156 Table 4 18. Model 3: Parameters and s tandard e rrors of c ovariates by PLSP g roup PLSP1 PLSP2 PLSP3 Parameter Estimate Standard Estimate Standard Estimate Standard Covariates Intercept MALE 0.509 0.108 0.603 0.079 0.717 0.133 MIN 1.316 0.136 1.997 0.084 2.710 0.207 BWGRAM 0.008 0.012 0.016 0.009 0.006 0.015 GSTWK 0.016 0.035 0.011 0.026 0.061 0.039 MEDU 0.566 0.032 *0.454 0.023 *0.315 0.042 MAGE 0.022 0.011 0.002 0.007 0.021 0.012 APGAR 0.038 0.045 *0.080 0.028 0.054 0.041 Slope MALE 0.145 0.129 0.035 0.098 0.049 0.178 MIN 0.124 0.159 0.108 0.106 0.109 0.259 BWGRAM 0.013 0.014 0.024 0.011 0.023 0.021 GSTWK 0.020 0.043 0.055 0.032 0.049 0.053 MEDU 0.125 0.035 0.014 0.028 0.010 0.055 MAGE 0.021 0.013 0.005 0.009 0.016 0.016 APGAR 0.036 0.054 0.089 0.034 0.079 0.053 indicate s significant at the p <.001 level.
157 Table 4 19. Model 3: R 2 p arameters and s tandard e rrors of c ovariate m odel. Observed Variable Two Tailed Estimate S.E. P Value PLSP1 RDSS3 0.741 0.015 0.000 RDSS4 0.813 0.009 0.000 RDSS5 0.752 0.013 0.000 RDSS6 0.770 0.013 0.000 RDSS7 0.769 0.013 0.000 RDSS8 0.854 0.010 0.000 RDSS9 0.811 0.015 0.000 RDSS10 0.688 0.017 0.000 Intercept 0.277 0.017 0.000 Slope 0.038 0.019 0.053 PLSP2 RDSS3 0.791 0.010 0.000 RDSS4 0.829 0.010 0.000 RDSS5 0.792 0.009 0.000 RDSS6 0.797 0.010 0.000 RDSS7 0.814 0.009 0.000 RDSS8 0.888 0.006 0.000 RDSS9 0.855 0.009 0.000 RDSS10 0.777 0.012 0.000 Intercept 0.272 0.012 0.000 Slope 0.015 0.008 0.079 PLSP3 RDSS3 0.716 0.024 0.000 RDSS4 0.801 0.015 0.000 RDSS5 0.729 0.019 0.000 RDSS6 0.777 0.019 0.000 RDSS7 0.796 0.021 0.000 RDSS8 0.828 0.017 0.000 RDSS9 0.824 0.024 0.000 RDSS10 0.715 0.026 0.000 Intercept 0.170 0.018 0.000 Slope 0.025 0.025 0.315 Note All p Values are <001.
158 Table 4 20. Model 4: Estimates and s tandard e rrors for r eading p erformance d ata, g rade l evels 3 7 PLSP1 PLSP2 PLSP3 Parameter Estimate Standard p Estimate Standard p Estimate Standard p Loadings 0.000 0.000 0.000 0.000 0.000 0.000 0.346 0.045 0.000 0.346 0.045 0.000 0.346 0.045 0.000 0.499 0.048 0.000 0.499 0.048 0.000 0.499 0.048 0.000 0.723 0.057 0.000 0.723 0.057 0.000 0.723 0.057 0.000 1.000 0.000 1.000 0.000 1.000 0.000 Covariance 2.076 0.294 0.031 1.731 0.225 0.005 0.907 0.439 0.039 Intercepts 16.500 0.250 0.000 15.324 0.213 0.000 13.002 0.393 0.000 3.619 0.428 0.000 3.731 0.294 0.000 5.031 0.822 0.000 Unique variances RDSS3 2.889 2.889 0.000 2.615 0.239 0.000 2.776 0.592 0.000 RDSS4 1.330 1.330 0.000 1.627 0.156 0.000 1.522 0.221 0.000 RDSS5 2.349 2.349 0.000 1.983 0.156 0.000 3.017 0.495 0.000 RDSS6 1.857 1.857 0.000 1.895 0.156 0.000 1.615 0.258 0.000 RDSS7 1.599 1.599 0.000 1.312 0.192 0.000 0.864 0.203 0.000 Intercept 4.085 0.337 0.000 4.934 0.299 0.000 3.365 0.500 0.000 Slope 1.065 0.365 0.004 1.404 0.294 0.000 0.792 0.499 0.112 Note All p Values are <001.
159 Table 4 21. Model 4: Covariate e stimates and s tandard d eviation by PLSP g roup, g rade l evels 3 7 PLSP1 PLSP2 PLSP3 Estimate Standard p Estimate Standard p Estimate Standard p Covariates Intercept MALE 0.456 0.196 0.02 0 0.267 0.157 0.088 0.299 0.299 0.317 APGAR 0.044 0.091 0.631 0.086 0.061 0.161 0.103 0.076 0.174 MIN 1.234 0.24 0 0 .000 1.865 0.184 0 .000 2.133 0.465 0 .000 BWGRAM 0.018 0.023 0.438 0.006 0.017 0.71 0 0.015 0.035 0.676 GSTWK 0.033 0.062 0.591 0.063 0.048 0.188 0.031 0.086 0.716 MEDU 0.376 0.052 0 .000 0.323 0.042 0 .000 0.216 0.087 0.012 MAGE 0.025 0.018 0.17 0 0.01 0 0.014 0.48 0 0.06 0 0.024 0.012 Slope MALE 0.22 0 0.18 0 0.222 0.047 0.137 0.734 0.143 0.268 0.595 APGAR 0.141 0.076 0.063 0.135 0.048 0.005 0.081 0.083 0.329 MIN 0.133 0.21 0 0.526 0.386 0.154 0.012 0.113 0.448 0.802 BWGRAM 0.022 0.021 0.311 0.034 0.016 0.029 0.027 0.032 0.388 GSTWK 0.02 0 0.053 0.709 0.064 0.043 0.137 0.028 0.075 0.706 MEDU 0.037 0.049 0.446 0.01 0 0.035 0.782 0.028 0.067 0.676 MAGE 0.012 0.018 0.494 0.002 0.012 0.882 0.049 0.025 0.051 Note The above variable column contains the following variables: RDSS3 RDSS10 = reading score at the appropriate grade level. BWGRAM=birth weight in grams, APGAR=Apgar score at one minute after birth, GSTWK gestational age in
160 Table 4 22. Model 4: School f ree and r educed l unch s tatus on r eading a chievement s cores by PL SP g roup PLSP1 PLSP2 PLSP3 Parameter Estimate Standard p Estimate Standard p Estimate Standard p Covariates RDSS3 ON ON ON SCHFRL3 0.013 0.007 0.062 0.011 0.005 0.029 0.007 0.014 0.635 SCHMIN3 0.014 0.009 0.118 0.006 0.005 0.246 0.014 0.015 0.355 RDSS4 ON ON ON SCHFRL4 0.019 0.005 0 .000 0.017 0.004 0 .000 0.026 0.009 0.004 SCHMIN4 0.021 0.007 0.002 0.017 0.004 0 .000 0.035 0.009 0 .000 RDSS5 ON ON ON SCHFRL5 0.014 0.006 0.016 0.008 0.004 0.038 0.009 0.012 0.471 SCHMIN5 0.021 0.007 0.004 0.01 0 0.005 0.032 0.014 0.013 0.277 RDSS6 ON ON ON SCHFRL6 0.021 0.008 0.013 0.014 0.006 0.021 0.018 0.016 0.246 SCHMIN6 0.022 0.007 0.002 0.012 0.005 0.011 0.01 0.012 0.408 RDSS7 ON ON ON SCHFRL7 0.014 0.008 0.084 0.009 0.006 0.1 00 0.002 0.018 0.899 SCHMIN7 0.016 0.008 0.036 0.007 0.004 0.112 0.006 0.012 0.616 RDSS3 ON ON ON SCHFRL3 0.013 0.007 0.062 0.011 0.005 0.029 0.007 0.014 0.635 SCHMIN3 0.014 0.009 0.118 0.006 0.005 0.246 0.014 0.015 0.355 Note The above variable column contains the following variables: RDSS3 RDSS10 = reading score at the appropriate grade level. SCHFRL3 SCHFRL7 = the percentage of students on Free or Reduced Lunch Status by school, SCHMIN3 SCHMIN7 = the percentage of students in school on free or reduced lunch status by grade.
161 Table 4 23. Model 4: R 2 Latent g rowth c urve m odel with c ovariates, g rade l evels 3 7 Variable Estimate S.E. p PLSP1 RDSS3 0.653 0.031 0.000 RDSS4 0.795 0.016 0.000 RDSS5 0.68 0 0.023 0.000 RDSS6 0.732 0.02 0 0.000 RDSS7 0.763 0.028 0.000 I ntercept 0.228 0.037 0.000 S lope 0.06 0 0.043 0.165 PLSP2 RDSS3 0.724 0.021 0.000 RDSS4 0.798 0.015 0.000 RDSS5 0.759 0.015 0.000 RDSS6 0.768 0.016 0.000 RDSS7 0.832 0.021 0.000 I ntercept 0.268 0.027 0.000 S lope 0.058 0.028 0.004 PLSP3 RDSS3 0.625 0.054 0.000 RDSS4 0.743 0.031 0.000 RDSS5 0.592 0.047 0.000 RDSS6 0.736 0.037 0.000 RDSS7 0.846 0.035 0.000 I ntercept 0.279 0.064 0.000 S lope 0.119 0.094 0.205
162 Figure 4 3. Unconditio nal latent growth curve model, f reed l oadings
163 Figure 4 4 Latent growth curve for group PLSP 1 with Reading Developmental Scale Scores, grade levels 3 10
164 Figure 4 5. Latent growth curve for group PLSP 2 with Reading Developmental Scale Scores, grade levels 3 10
165 Figure 4 6. Latent growth curve for group PLSP 3 with Reading Developmental Scale Scores, grade levels 3 10
166 Figure 4 7. Significant c ovariates for PLSP1, ( p <01), g rade l evels 3 10
167 Figure 4 8. Significant c ovariates for PLSP2, ( p <01), g rade le vels 3 10
168 Figure 4 9. Significant c ovariates for PLSP3, ( p <01), g rade levels 3 10
169 Figure 4 10. Performance Based Lifestyle Segmentation Profile 1: significant ( p<.01) t ime v arying and t ime v arying c ovariate l atent g rowth m odel for g rade l evels 3 10
170 Figure 4 11. Performance Based Lifestyle Segmentation Profile 2: significant ( p<.01) t ime v arying and t ime v arying c ovariate l atent g rowth m odel for g rade l evels 3 10
171 Figure 4 12. Performance Based Lifestyle Segmentation Profile 3: significant ( p<.01) t ime v arying and t ime v arying c ovariate l atent g rowth m odel for g rade l evels 3 10
172 CHAPTER 5 DISCUSSION Research investigations of academic achievement have resulted in a debate over family and school responsibility and a lack of emphasis on the systemic, interrelated factors that affect academic reading development. Academic performance is predictive of long term well being outcomes, including a greater likelihood for financial stability and becoming a productive member of society. Therefore, exa mining predictors of academic achievement has relevance beyond the educational scope. In the current study, an individual, family school, community (IFSC) model was created and used to examine individual, family, school, community, and contextual determin ants of student academic achievement. The current study investigated reading development by socio economic status and elements from the IFSC model. The purpose of this chapter is to discuss the findings of that investigation. This chapter begins with a bri ef overview of the literature review and the methods used in this dissertation. After this discussion of the literature and methods, implications for education, policy, and practice, and study limitations and recommendations for future research are offered This chapter concludes with a brief summary. Overview The overall focus of this study was to investigate an alternative explanation to understanding achievement gaps in K 12 schools. The theoretical foundation for this study was an integration of multip le theories and disciplines, namely, a Model of Ecological Development (Bronfenbrenner, 1977) Unified Human Development Theory (Sameroff, 2010) Life Cours e Health Development theory (Halfon & Hochstein, 2002) and Lifestyle Segmentation analysis (ESRI, 2009 ) This integration led to the creation of
173 the Individual Family School Community Contexts (IFSC) model to provide an alternative framework investigating achievement gaps. These theories, along with an exploration of cumulative risk ( Burchinal et al., 2000) (Ellis et al., 2012) provided the theoretical foundation for the IFSC model. For example, a child who grows up in poverty may be exposed to more environmental risk factors than a child who grows up in a wealthier environment (Halfon & Hochstein, 2002). The IFSC model focuses on (1) multiple settings in the conceptualization and analysis of early life challenges to reading development, (2) how early life stress and risk fac tors impact child development, executive functioning, and student performance, and (3) the interactions and transactions that occur among the individual, family, school, and community contexts. Each context contains various degrees of risk and support that can have an immediate or delayed impact on reading performance. Contexts were explored through the use of performance based lifestyle segmentation profiles (PLSP). Methodology The study was designed to examine the reading development of a mid sized schoo l district in north central Florida. The study also focused on effects of selected variables that relate to the IFSC model on reading development. Multiple group latent growth modeling was used to estimate the growth factors (i.e. intercept and slope) from third through 10 th age, birth weight, Apgar score, gestation time, gender, ethnicity, and PLSP) and time varying covariates (i.e. school percent FRL, school percent minority status). Vital Statistics (BVS) which contain the birth certificates of children born between 1985
174 2003. The second dataset contained data from a mid sized school district in north centra l Florida over the years 2005 2011. The school dataset contained variables on student standardized test performance and demographic information. The two datasets Flori birthdate. This linkage yielded a 61% match rate, or 38,221 subjects. Study Procedures The dependent variable was the reading developmental scale scores on the Florida Comprehens ive Assessment Test (FCAT). The FCAT was taken yearly by students over years 2005 2011. The reliability estimate for the FCAT was .90 and the scores range from 86 3,008. The dependent variable was linearly transformed so that 1,000 points equaled10 points. The independent variables related to each section of the IFSC model. For example, birth weight, gender, and minority status were selected as available individual Fa reduced lunch status and school percent minority status; community contexts element used PLSP. Students were coded into one of three PLSP groups based on methods used in the D aniels Thrall Education Instruction Assessment (DTEIA) (Thrall & Daniels, 2008) and student reading performance. The Research Question s asked were: 1. What is the initial status and rate of reading development from grade levels 3 10 in the district under analysis?
175 2. What is the initial status and rate of reading development from grade levels 3 10 by PLSP group? Do intercepts and slopes vary as a func tion of PLSP group assignment? a) Do intercepts and slopes vary as a function of PLSP group assignment? 3. To what extent do parent education, parent age, birth weight, Apgar score, gestational age, ethnicity, and gender demonstrate different rates of reading de velopment across grade levels 3 10? 4. To what extent do parent education, parent age, birth weight, Apgar score, gestational age, ethnicity, and gender demonstrate different rates of reading development across grade levels 3 7 and by PLSP group? a) In addition to model #4, for grade levels 3 7, what is the yearly concurrent prediction between school percent FRL and school percent minority status on the initial status and rate of growth and time varying covariates? Four separate latent growth models wer e created to answer each of the Research Question s. The examination of growth trends indicated that reading development occurred in a nonlinear way. For each of the Research Question s, four types of models were compared using multiple fit indices. These mo dels included a linear term, quadratic term, piecewise model, and a freed loading model. In each instance a freed loading model provided the best model fit. Thus, for each research question, a freed loading model was utilized. The first model was an uncond itional growth model, which analyzed the variance across the dataset and provided an overall growth model of the district. The second model introduced community contexts and family SES from the IFSC model as represented by PLSP groupings. This second mode l generated three latent growth curve models, one for each PLSP group and found that the intercepts and slopes differ by group. The third model used PLSP as the grouping variable with the inclusion of time invariant covariates. This third model utilized th e individual, family, and community aspects of the IFSC model. Finally, the fourth model studied grade levels 3
176 7 by PLSP group using time variant (school percent FRL and school percent minority) and the other time invariant covariates (i.e. birth weight, status at time of childbirth, gestational age, Apgar score, gender, minority status). This model incorporated all elements of the IFSC model. The results of the analysis for the four models are provided in the following section. Results Research Question 1 Research Question 1 development from grade levels 3 asked to determine the overall means and variances of the growth fac tors and the dependent variable. The key findings from Research Question 1 demonstrated that adequate model fit using a freed loading growth model can be achieved. Additionally, from 3 rd through 4 th grade, approximately a third of the reading development o ccurred. The significant variances provided an overall sense of how much reading performance differs individually in the initial test in third grade and the rate of growth. The transformed intercept ( = 11.319), and slope variances ( = 2.362) showed that students in grade three vary by over a thousand points. The individual rate of growth from grades 3 10 varied by approximately 240 points. Finally, the negative covariance between the intercept and slope ( 2.172) revealed that students who perform well in third grade proceed at a slower rate. Research Question 2 Research Question 2 development from grade levels 3 10 by PLSP group? Do intercepts and slopes vary as a function of PLSP
177 PLSP group differences at the intercept in 3 rd grade and the growth rate or reading slope. Before the model is discussed, a brief background that describes the three PLSP groups may be helpf ul. According to the results in chapter 4, PLSP1 performed the highest on reading development scale scores and PLSP3 performed the lowest at each grade level. The characteristics of these groups have similar trends in the sense that PLSP1 has more non mino rity students (68% White) and fewer minorities (10% Black) than in PLSP2 (48% White, 33% Black), or PLSP3 (11.5% White, 79% Black). The trend did not seem to continue for Apgar score s and gestation weeks. However, students in PLSP3 had approximately 100 20 0 grams lower birth weight than PLSP1. The groups showed that mothers and fathers were both consistently between 4 5 years apart, with PLSP1 mothers having children around age 29, while mothers in PLSP3 had y 31 years for PLSP1 and 28 years for PLSP3. Mothers and fathers had approximately 3 more years of education in PLSP1 compared to mothers in PLSP3. Finally, school proportion on FRL status and proportion of students in schools with minority status, showed that PLSP1 had fewer percent minority and fewer students on FRL status than PLSP3. These statistics showed that there are clear differences on many variables among PLSP group. Thus it was important to explore a latent growth model by PLSP grouping. The fr eed loading model yielded the best model fit. The proportion of growth between grade levels was approximately the same as the Question 1. There were differences in the intercept variances: PLSP1 ( = 9.692), PLSP2 ( = 10.369), and PLSP3 ( = 8.258), with PLSP3 having the least amount of variance. The slope variances differed by group: PLSP1 ( = 2.247), PLSP2 ( = 2.327), and PLSP3
178 ( = 2.444), showing that PLSP3 had the highest amount of variance around the slope while PLSP1 has the least amou nt of variance. These results indicate that in the lower performing PLSP group (PLSP3) students individually vary around the slope mean more than students in PLSP1. The covariances between PLSP group (PLSP1= 2.94, PLSP2= 2.365, PLSP3= 1.995) also showed a stronger relationship between the intercept and slope in PLSP1 than in PLSP3. Essentially, those in PLSP1 with higher intercepts, or grade 3 scores, demonstrated a slower rate of growth than a student in PLSP3 with a high intercept. The group PLSP1 had an intercept that was higher than PLSP3. Research Question 3 Research question 3 birth weight, Apgar score, gestational age, ethnicity, and gender demonstrate different rates of reading development acro ss grade levels 3 focused on how the time invariant covariates from the individual (gender, ethnicity, age at childbirth) and community (PLSP grouping) impact the intercept and slope from grade levels 3 10. The results are presented below by individual and family factors. School variables are included in model 4. The discussion is presented by PLSP group. Individual and Biological Factors. At t hird grade, or the intercept, males were expected to perform 50 points lower than females in PLSP1, 60 points lower in PLSP2 and approximately 72 points lower in PLSP3. Clearly, there is a gender effect and it is stronger in PLSP3 than in PLSP1 or PLSP2. The same relationship occurred with students in minority status. The group PLSP1 expected a 131 point decrease if black, Latino, mixed or Indian, PLSP2 expected a 200 point difference if minority, and PLSP3
179 expected approximately 271 point difference betwe en minority and non minority status. The finding that minorities and males in PLSP3 have a lower reading score in grade three suggests the link between increased risk factors and student performance. This finding appears consistent with the cumulative risk paradigm that acknowledges that it is the aggregate effect of multiple risk factors that can negatively impact child development (Seeman et al., 2008) Family Factors. ing the intercept group is stronger for PLSP1 (.56) and weaker for PLSP3 (.31). This indicates that for a student in PLSP1 with a mother who has an extra year of education sco red 56 reading points higher in grade level 3 than a student with a mother who has one year less of education. Likewise, for PLSP3, a student in grade level 3 whose mother has an extra year of education scored 31 points higher than a student whose mother h ad a year less low as he or she is already scoring highly on the standardized test scores. This appears to be a regression to the mean for children with highly educated mothers. It is interesting to note that education and would have reduced the sample size.
180 Finally, an R 2 analysis showed that 27% of the intercept was explained by the covariates in PLSP1, PLSP2, and 17% in PLSP3. The intercept and slope did however frequently explain over 75% of the variance in the observed reading scores. Research Question 4 Research ques tion 4 birth weight, Apgar score, gestational age, ethnicity, and gender demonstrate different rates of reading development across grade levels 3 The model used time invariant co variates from the Individual (gender, ethnicity, gestational age, and community (PLSP). This model also utilized time varying school level covariates (i.e. school prop ortion FRL status and school proportion minority status) to investigate the impact of the time invariant covariates on the intercept and slope from grade levels 3 7. This model also examined how school level covariates impact reading scale scores. This mo del investigated grade levels 3 7 in order to use the time varying covariates. It would not have been possible to model eight grade levels (3 10) with only 7 years of data due to covariance convergence issues. Covariance coverage in this study refers to th e proportion of students in grade 3 who also have a reading score in grade 10. With only 7 years of data, it is not possible to model time varying covariates with 8 grade levels. Therefore, five grade levels (3 7) were used with 7 years of data. The discus sion of the results will be presented in terms of the IFSC model below. Individual While accounting for other variables, the effect for males on reading scores was statistically significant for PLSP1 ( .099). No other PLSP group was significant. While
181 st atistically significant, the effect of being male was minor, with an approximately 10 point difference between males and females in grade level three. The effect for minority status on the intercept at grade three was significant across all groups. The mag nitude was strongest in PLSP2 ( .35). The group PLSP1 had the weakest magnitude ( .22) while PLSP3 was close to PLSP2 at ( .33). This finding indicates that students of minority status in PLSP1 are somehow protected and fare a bit better than minorities in other PLSP groups. Due to increase d income and social status, it is possible that minority students in PLSP1 are buffered from the effects of stress or have fewer stressors. Gestation weeks, Apgar score, and birth weight in grams did not predict the inter Family each PLSP grouping. The relationship was strongest in PLSP1 (.337) and weakest in PLSP3 (.077). This finding suggests that students with mothers who have 4 years extra education will perform approximately 120 points higher than a student in PLSP1 with a mother who has fewer years of education. In PLSP3, however a student of a mother with four years extra education will be expected to score 80 poin ts higher. Therefore, age is predictive of an 18 point increase in student test scores. The average mother age for PLSP 3 was 24 years, compared to 30 years in PLSP1 or 26 years in PLSP2.
182 in reading d evelopment scale scores School The school variables included percent of students with FRL status in schools and percent of minority students in schools. In many grade levels, school free reduced lunch status had a statistically significant but slight effect on each PLSP group development however some only had one or two significant effects. For example, in third grade, school FRL status predicted PLSP2 ( .011), but not in other PLSP groups. School percent FRL only predicted grade level 4 rea ding scores ( .026) in PLSP3. The effect for school percent FRL was consistently negative and small. For example in PLSP1, for grade level 6, school percent FRL was ( .02) which indicated that for every percentage point increase in school percent FRL, a st udent is expected to perform 2.1 points lower. This relationship at first may seem weak, however the percent FRL status in schools in PLSP3 in third grade was 73% and its standard deviation was 20 percentage points. A student in PLSP group 3 with 50% of st udent on FRL status is expected to perform approximately 40 reading points better in third grade than a student going to a school with 70% student FRL status. The magnitude between school percent FRL status decreases in 6 th grade. For example instead of PL SP3 having 73% school percent FRL, in grade six, 51% of students were on FRL status and the standard deviation decreased from 20 points in grade 3 to 7.4 percentage points in grade 6. School percent minority enrollment also had small but occasionally stati stically significant relationships. On each occasion, the estimate was positive indicating the
183 higher the percentage of minority students the greater the reading test score at each grade level. The R 2 values for model 4 indicated that the covariates predi cted between 22 and 28 percent of the intercepts. The addition of the time varying covariates led to R 2 values in the intercepts that reverses the pattern of R 2 values in model 3 without the time varying covariates. In model 3, the covariates predicted 27% of the intercept variance in PLSP1 and 17% for PLSP3; in model 4, the covariates predicted 27% of the variance of the intercept in PLSP3 while PLSP1 had only 22% of the intercept predicted by the covariates. Implications of the Study The results of this study support the value of the IFSC model in educational research and school counseling practice. Educational researchers frequently examine individual student factors in a piece meal way, without a comprehensive view of the individual factors that directl y impact educational outcomes. The use of the IFSC model provides a useful framework to examine multiple individual factors as well as family and community factors. The use of latent growth models provide a viable means to investigate context and increasin gly complex models. these results indicate that children experience different rates of growth related to the risk and protective factors in the IFSC model. Minority status and gender related more education level impacted the intercept more in PLSP1 than in P LSP3. Risk factors appear to be amplified in PLSP3 and protective factors appear to be stronger in PLSP2.
184 These study results also suggest that correlates of individual starting points should be examined and taken into consideration when designing educatio nal programs and interventions. Implications for Practice School counselors are tasked to help close academic achievement gaps, and unessential in the educational arena (Dahir & Stone, 2009). Therefore, school counselors would benefit from implementing the IFSC model, both in case conceptualization of student issues as well as in the organization and administration of the overall school counseling program. School counselors who use the IFSC model could create targeted interventions to address each aspect of the model. The findings in this study are consistent with a comprehensive school counseling program that focuses on prevention and intervention, rather than remediation. Adv ocacy is one of the key roles of school counselors (ASCA, 2005; CACREP, 2009). For the school counseling field to remain relevant, it must appropriately address academic achievement gaps. School counselors can be more effective advocates for all academic success by understanding and implementing the IFSC model. School counselors are in the unique position to address individual student needs, while also having a broader view of the needs of the entire school community. With this understanding, scho ol counselors can take a leadership role in the school community to help teachers, administrators, and staff examine their own underlying assumptions about students. Student s in lower SES are not as likely to have a home routine that is like the school rou tine and expectations and more conflicting family environments ( L evin & Belfield, 2002). Considering how the cumulative effects of life stress can impact
185 executive functioning can also be useful in helping students who are underperforming and are from lower SES backgrounds. School counselor roles can be informed by eco systemic models like the IFSC model into the practice of counseling. Counselors can cont inue to be extended beyond the counseling office into an increased focus on advocacy, collaboration, and engaging with community stakeholders. Incorporating a more systemic model provide more empirical support for current CACREP and ASCA National Model sta ndards. School counselors can influence success and achievement when they work with diverse groups. One discussion pertains to the question of whether or not students should be differentiated by magnet schools or do they blend school enrollment to integra te students from differing backgrounds. An increased focus on neighborhood schools and their demographic characteristics, curriculum, and funding may help to reduce achievement gaps. Education can be diversified by expanding the number of value platforms u sed in the academic curriculum. Rather than expecting all students in a class to be equally ready to learn, school counselors can help educate the school community about the consequences of differential exposure to stress and other risk factors that indiv idual students may experience. In other words, rather than assuming that all members of a class are ready to learn material and can successfully learn it in the same manner, schools can begin to recognize how individual students arrive at school with diffe rent levels of readiness to learn and different optimal learning styles (Evans, 2005). School counselors can help teachers tailor their lesson plans to the needs of the individual students in their classrooms. Moreover, rather than viewing the need for dif ferent approaches as a
186 failure of the student or the teacher, school counselors can help advocate for the benefits of individualized instructional approaches while educating the entire school community about the various IFSC factors that impact student per formance. As previous research has shown (Sirin, 2005) child and school level SES were associated with initial reading levels at the start of school in kindergarten. In this study, the effect of SES on growth was studied from grade levels 3 10. Kieffer (2011) showed that the effect of SES was stronger during grades 3 8, while earlier years had a weaker association. The current study found that children from different socio economic status groups (PLSP) begin at di fferent levels of performance, growth rates are different, and the rates of change all favor PLSP1, the most affluent of the PLSP groups. Student level free reduced lunch status was not used in this study because of the poor correlations to the reading dev elopmental scores at each grade level. Instead of free reduced lunch status as a measure of SES, PLSP was used. The PLSP grouping was an effective way to investigate SES by using lifestyle, census data, and student performance data. The process of reading development involves multiple environmental influences and the current study shows that as a child develops the environmental factors contribute less to the reading growth rate. This was evidenced by the non significant scores of birth weight and other in dividual factors at time of birth. In other words, early education and age, de monstrated a relationship to the intercepts among all PLSP groups.
187 The research findings have implications to address the existence of reading achievement gaps. These study findings highlight three developmental periods: 1) early school age, 2) middle sch ool age, 3) early high school age. By demonstrating that reading gaps exist as a function of SES, and that these gaps persist, even though there are shifts in this relationship during middle school, these findings indicate the power of the IFSC framework f or analyzing student performance and longitudinal academic trajectories. Further, the findings suggest the need for attention to early educational environment and pre kindergarten programs to help offset the effects of individual, family and community risk factors. Early intervention is essential to equalizing educational outcomes in lower SES neighborhoods. Implications for Research The current study proposed an interdisciplinary approach to examine the problem of acad emic achievement gaps. Further i nterd isciplinary research is needed to address the complex, persistent problem of academic achievement gaps. Educational and health researchers are examining how to close educational achievement gaps, with approaches that are unique to their respective fields ( Healthy People 2020, 2011). What is needed now is an integration of the best theories and methodologies that various fields have to create comprehensive research studies. Educational researchers cannot fail to include pivotal health data in their explorati ons of academic achievement. Failure to include health data amounts to an exclusion of variables that, according to the current study, account for a large percentage of the variance in student achievement, as measured by their scores on the reading FCAT. The current findings also support the use of lifestyle segmentation profile methods in future research projects as an accurate indicator of student SES status. The
188 current findings support previous findings regarding the stratification of the public school the transmission of low socio economic s (Rouse & Barrow, p.116, 2006). Willis (1977) upward mobility and rejected schooling through delinquent behav ior. The issue is that in this resistance, students recreated the same life trajectory as their families and thus created the same occupational conditions that their parents had after leaving school (Lucas & Beresford, 2010). Rouse and Barrow (2006) also a ssert that children from higher SES families will tend to go to better schools than those from poorer families. The better schools tend to attract better teachers and provide more resources and opportunities for social mobility. SES has tended to be defin ed as the economic resources, occupational location, and educational attainment of a person or family (Lucas & Beresford, 2010) Duncan, Featherman, and Duncan (1972) created a socioeconomic index (SEI) that used occupational educati on and income to measure SES and is connected to concepts of regularly. Also, parent occupation, income and education levels are difficult items of information to gath er for a larger district level analysis. PLSP does not have these limitations. The use of PLSP as an indicator of SES is a unique contribution of this study for the field of educational research.
189 Moreover, the IFSC model breaks the disciplinary boundaries that sometimes impede progress in addressing challenging, multi faceted issues such as academic achievement gaps. By examining academic achievement gaps from an interdisciplinary stance, use of this model may allow for more comprehensive research examinat ions in the ongoing search for solutions to this seemingly intractable educational problem. The as to the reasons for it Therefore, the results of this investigation p rovide preliminary evidence for the utility of the IFSC model in framing complex, interdisciplinary research questions and analyzing complex data sets. The current study findings support the use of the IFSC model to examine complex and multi faceted issues such as student academic achievement gaps. This model can be of benefit to many fields, including school counseling, educational research, educational psychology, and developmental psychology. The results also inform the debate between the Coleman (Coleman, 1968) report and the Effective Sch ools Movement (Edmonds, 1972) This debate shifts between how family is the most important factor in student performance, while the Effective Schools Movement argues that schools are the most important factor in student performance. The models in this study showed that individual factors and family context matters, but so does the school context. The PLSP grouping variables a re indicators of family SES and of family context. The results clearly showed that in each of these family contexts, student performance varied. Students in PLSP1 were generally more affluent and performed higher in 3 rd grade through 10 th grade while stude nts in PLSP3 were
190 generally the least affluent and performed approximately 150 points lower than PLSP 1 at each grade level. Approximately 100 point difference relates to a grade level difference so students in PLSP3 perform approximately 1.5 grade levels below PLSP1. level 3. onal attainment on a generational nature of educational achievement and outcomes should be addressed by public policy. Rather ad outcome that only impacts that individual, policy makers would be wise to consider the longer term impact on future generations. Family context is one of many contexts that directly ccess to education is needed, not only for individuals who would benefit, but also for their current or future children. The school percent FRL status information also supported the effective schools movement. Students in PLSP1 and PLSP2 were affected by t he percent of students on FRL status. Percent of school on FRL was intended to be an indicator of school resources. Students in PLSP2 and PLSP1 in high percent FRL schools might benefit from evaluating how the reading curriculum relates to the lifestyles a nd backgrounds of their students. Study Limitations and Suggestions for Future Research This study contained several limitations. Existing errors within the original data sets could be a potential limitation of this study. However, an advantage of data us ed in
191 the study was that it was not self report data. Attrition was a limitation of this study, as some potential participants moved away, left the public school system, or died. Therefore, their data could not be included in the analysis. The existing data sets used in this study were linked by a data center. While precautions were taken to carefully match each individual and then de identify the resulting combined data set, it is possible that errors could have occurred in the linking proc ess. Multicollinearity was also a concern in the creation of the PLSP Groups. This study was intended to describe the differences and degree of effects of the covariates by SES grouping. Further research can model the 12 lifestyle segmentation profile gro ups to further address the multicollinearity issue. Family dynamics may have influenced the results of this study, but were not captured in this dataset. For example, this study did not investigate characteristics of marriage and family. The inclusion of variables such as marriage status of mother or father, occupation, and income may have led to more insight into the impact of family context on student performance. This study was conducted with subjects from a single county in Florida, which may limit t he generalizability of the results. However, despite this limitation, the sample size was large for social science research, allowing for some confidence that the results would generalize to other school districts with similar socio demographics Future research studies could be conducted to examine these research questions in other areas of the United States, as well as internationally, to see if these results are replicated.
192 Conclusions educational attainment of his or her mother, and his or her neighborhood context have a strong impact on his or her academic trajectory. This impact can be seen not only in the early years of the educational journey, but well into middle and high school. These results suggest that more interventions to support the multiple systemic determinants of Further, these study results support the ongoing examination of systemic interventions to address persistent academic achievement gaps. The longstanding debate of family versus school in the academic achievement literature is supplanted by a more complex, comprehensive view that acknowledges the onal outcomes. This study indicates that numerous factors at the individual, family, school, community, and contextual levels, as represented by the IFSC model developed as part of this study, Am ong the unique contributions of this study was the exploration of contextual factors utilizing both traditional measures of context as well as lifestyle segmentation profiling (LSP), which has been successfully used in the business geography field (Thrall & Daniels, 2008 ; Miguis, Camanho, & Falco e Cunha, 2012) This approach allowed for the grouping of students into different neighborhoods to demonstrate the geographic distribution of students. Using LSP allowed for a more nuanced metric of SES than could have been obtained without using this approach. In addition, the linking of multiple data sets was a unique feature of this study. R ather than being limited to one data set in one academic discipline, the inclusion of
193 linked data sets allowed for a deeper level of exploration using census data, health gitudinal trajectory from 2005 2011 was examined, with multiple factors examined and analyzed. The results of this study suggest the invaluable nature of linking data sets of this nature, despite the challenge of obtaining data sharing agreements and IRB a pproval from multiple cooperating institutions and agencies. Interdisciplinary research is challenging and requires patience, but these results suggest that it is worth the effort. Moreover, an examination of how health and educational outcomes are interco nnected and interrelated could not have been obtained with the linkage of these types of data sets. Further, the development of the IFSC model, that guided the research design and data analyses of the current study, represents a contribution to future rese archers from multiple disciplines who seek to examine academic outcomes using health and educational data.
194 A PPENDIX A UF IRB 01 APPROVAL FORM
195 APPENDIX B DEPARTMENT OF HEALTH DATA USE AGREEMENT
196 APPENDIX C IRB APPROVAL FROM ALACHUA COUNTY PUBLIC SCHOOLS Dear Eric S. Thompson, I am pleased to inform you that your research request has been approved by the School Board of Alachua County and the De p artment of Research and Evaluation. We have reviewed your materials and have d achievement gaps in K 12 schools: A Multi level analysis of Early Biological, and school board policies. We look forward to work ing with you towards the completion of this project. Sincerely, Hidahis F Mesa Manager of Research and Evaluation firstname.lastname@example.org 352 955 7685
197 APPENDIX D DEPARTMENT OF HEALTH DATA IRB APPROVAL
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212 BIOGRAPHICAL SKETCH Eric S tephen Thompson graduated from New College of Florida in 2002 and attended the University his M aster of Education (M.Ed.) and Education Specialist (Ed.S.) degr ees in 2006 and worked as a guidance counselor in rural and experimental development s chools. In 2007 Eric began the d octoral p rogram in 2007, and earned his doctoral degree in 2013. During his doctoral training, Eric taught online wellness, career managem ent courses, and an in class Mindful Living course. He also continued to gain experience as a school counselor and began statistical consulting and working in various research positions at the Department of Family Data Center (FDC)