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Early Risk Factors for Later Mathematics Difficulties Paul L. Morgan, Ph. D. , Population Research Institute, The Pennsylvania State University George Farkas, Ph. D. , University of California, Irvine Steve Maczuga, M. S. , Population Research Institute, The Pennsylvania State University 1 This work is supported by grant #R 324 A 07270, National Center for Special Education, Institute of Education Sciences No official endorsement should be inferred

Sam and Cole 2

Sam and the joys of a productive disposition 3

And the constant close calls of informal learning 4

Theoretical and empirical framework Theoretical framework Children’s learning of mathematics is likely impacted by a wide range of socio-demographic, gestational and birth, and learner background characteristics Examples include the child’s birth weight, the mother’s level of education, the child’s language ability, and the child’s frequency of learning-related behavior Empirical framework Relatively few studies that are longitudinal, have investigated factors contributing to repeated learning difficulties, and estimate the predicted effects for a wide range of risk factors Relatively few studies have investigated very early precursors (e. g. , at 24 months of age) for later learning difficulties 5

Study’s purpose and suppositions Study’s purpose Is there a “common core” of factors that increase a child’s risk of experiencing repeated learning difficulties in mathematics? Study’s suppositions Identifying risk factors “early” is better than identifying these factors “late” Doing so helps guide earlier screening, monitoring, and intervention efforts Children who repeatedly fail to attain mathematical proficiency should be of elevated concern These children are consistently non-responsive to the instructional practices and routines being provided 6

Brief overview We used two population-based, longitudinal datasets (i. e. , the ECLS-K, the ECLS-B) to identify early risk factors for later, repeated mathematics difficulties (RMD) We estimated the predicted effects for a wide range of risk factors We were particularly interested in potentially malleable and “educationally relevant” factors We statistically controlled for the “autoregressor” and strong confounds in the analyses to more conservatively estimate predicted effects 7

Study’s two datasets Two NCES-maintained datasets Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K) Kindergarten-8 th grade longitudinal, nationally representative sample Early Childhood Longitudinal Study-Birth Cohort (ECLS-K) Birth-Kindergarten longitudinal, nationally representative sample Both datasets include individually-administered, adaptive measures of: academic achievement direct observation ratings of learning-related behaviors multi-source surveys of the children’s socio-demographic, gestational, and birth characteristics 8

Analytical samples, time periods, measures, operationalizations ECLS-K ECLS-B Analytical samples N=5, 838 N=5, 650* Time periods Spring of Kindergarten, 3 rd, 5 th, 24, 48, & 60 months & 8 th grade Measures Socio-demographics, birth characteristics, reading and mathematics achievement, & behavior Socio-demographics, gestational & birth characteristics, cognitive functioning, vocabulary, reading and mathematics achievement, & behavior Repeated Mathematics Difficulties (RMD) Score below 25% cut off at spring of 3 rd, 5 th, & 8 th grade administrations of ECLS-K Mathematics Test Score below 25% at both Preschool & Kindergarten administrations of modified ECLS-K Mathematics Test RMD % of analytical samples 16. 44% (n=960) 15. 68% (n=900*) 9 *Sub-sample rounded to nearest 50

Analytical methods ECLS-K Descriptive statistics Child- and family-level socio-demographics, child-level learner characteristics Logistic regression (Odds Ratios Step 1: Dichotomized as “ 0” & as the effect size metric) “ 1, ” with “ 1” as being in the group of children with scores in the lowest 25% of the score distribution of the spring of 3 rd, 5 th, & 8 th grade administrations of the Mathematics Test, and “ 0” as not being in this group Step 2: Predicted the child’s group membership, using a range of socio-demographic, birth, & learner characteristics, and controlling for the autoregressor, at spring of kindergarten 10 ECLS-B Step 1: Dichotomized as “ 0” & “ 1, ” with “ 1” as being in the group of children with scores in the lowest 25% of the score distribution of the 48 & 60 month administrations of the Mathematics Test, and “ 0” as not being in this group Step 2: Predicted the child’s group membership, using a range of socio-demographic, gestational & birth, & learner characteristic, and controlling for a strong confound (i. e. , cognitive delay), at 24 months

Study’s longitudinal designs Predictors measured by Criterions measured by ECLS-K Spring of Kindergarten Spring of 3 rd, 5 th, and 8 th grade ECLS-B 24 months Preschool (48 months) and Kindergarten (60 months) Datasets 11

ECLS-K analytical sample’s sociodemographics Sample Characteristic Male Child age (months), ECLS-K Spring K Percentage 50. 95% 74. 82 Ethnic origin White, Non-Hispanic Black Hispanic Other Mother’s education, Kindergarten assessment Less Than High School Graduate 12 Some College after High School and Above Maternal age = 35 or older 63. 73% 15. 48% 13. 97% 6. 76% 9. 41% 27. 49% 63. 10% 11. 04%

ECLS-K measures ECLS-K Mathematics Test Individually-administered, untimed IRT measure of a range of ageand grade-appropriate mathematics skills (e. g. , identify numbers and shapes, sequence, multiply, use fractions) Reliabilities of the IRT scaled scores ranged from. 89 to. 94 “Low” score as having a score in the lowest 25% of the score distribution of the spring of kindergarten Mathematics Test distribution ECLS-K Reading Test Individually-administered, untimed IRT measure children’s basic skills (e. g. , print familiarity, letter recognition, decoding), vocabulary (receptive vocabulary), and comprehension (e. g. , making interpretations) Reliabilities of the IRT scaled scores ranged from. 91 to. 96 “Low” score as having a score in the lowest 25% of the score distribution of the spring of kindergarten Reading Test administration 13

ECLS-K measures (cont. ) Modified version of the Social Skills Rating Scale Kindergarten teacher rated the frequency of that the child engaged in the particular behavior Strong split half reliabilities in kindergarten (e. g. , . 89, learningrelated behaviors) Three sub-scales, using “worst” 25% cut-off criterion Learning-related behavior problems (e. g. , displays attentiveness, persists at tasks) Externalizing problem behaviors (e. g. , argues, disturbs the class) Internalizing problem behaviors (e. g. , seems anxious, lonely) Survey data of children’s socio-demographics, birth characteristics (e. g. , low birthweight, mother’s education level) 14

Descriptive statistics for RMD and non. RMD groups, ECLS-K continuous data RMD Non-RMD Mean (SD) SD Unit Differences Mathematics Test Score 25. 63 (5. 69) 40. 22 (11. 53) -1. 3 Reading Test Score 36. 87 (7. 21) 49. 47 (14. 19) -. 89 Approaches to Learning 2. 66 (0. 67) 3. 24 (0. 59) -. 98 Externalizing Problem Behavior 1. 85 (0. 68) 1. 63 (0. 56) . 39 Internalizing Problem Behavior 1. 65 (0. 51) 1. 53 (0. 46) . 26 Kindergarten Predictors 15

Logistic regression of 3 rd-8 th grade RMD (ORs) using kindergarten predictors Kindergarten Predictors Low Kindergarten Math Model 1 19. 79 *** Model 2 Model 3 Model 4 16. 90 *** 16. 94 *** 9. 76 *** Child is Male 0. 52 *** 0. 38 *** Child Age at Assessment 1. 06 ** Mother’s Education, Less than High School Grad. Mother’s Education, High School Grad. 5. 00 *** 4. 89 *** 1. 94 *** 1. 93 *** 1. 94 *** Mother’s Age at Birth > 35 years 0. 82 0. 84 Black 2. 85 *** 2. 86 *** 2. 75 *** Hispanic 0. 76 0. 82 Other 0. 92 0. 93 0. 90 Birth Weight <= 1500 grams 1. 23 0. 99 Moderately Low Birth Weight 0. 89 1. 03 Low Kindergarten Reading Low Approaches to Learning 2. 03 ** High Externalizing Behavior 1. 61 High Internalizing Behavior 16 2. 00 *** 1. 28

ECLS-K results Potentially malleable and educationally relevant risk factors by the end of kindergarten for 3 rd-8 th grade RMD include earlier history of MD, earlier history of RD, and earlier history of learning-related behavior problems These risk factors are not mediated by the child’s or family’s socio-demographics, or the child’s birth characteristics, despite their sometimes strong predicted effects The onset of MD by kindergarten is an especially strong risk factors for MD through the elementary and middle school years 17

ECLS-B analytical sample’s sociodemographics Sample Characteristic Male Child age (months) at Kindergarten Percentage 50. 54% 64. 80 Ethnic origin White, Non-Hispanic Black Hispanic Other 63. 00% 15. 05% 17. 74% 3. 94% Mother’s education, Birth assessment Less Than High School Graduate Some College after High School and Above Maternal age = 35 or older 18 Mother Not Married at Child’s Birth 19. 76% 32. 32% 48. 02% 13. 69% 31. 80%

ECLS-B measures Modified Bayley Individually-administered measure of children’s age-appropriate cognitive functioning as manifested in memory, habituation, preverbal communication, problem-solving and concept attainment. The interviewers ask children to complete specific tasks (e. g. , “turn pages in a book, ” “look for contents of a box, ” “put three cubes in a cup”). IRT reliability coefficient for the BSF-R mental scale at 24 months was. 88 (NCES, 2007) “Low” as having a score in the lowest 25% of the score distribution Modified Mc. Arthur Communication Development Inventory (CDI) Child’s parents asked if the child is saying each of 50 vocabulary words (e. g. , “meow, ” “shoe, ” “mommy, ” “chase”) CDI recently reported to classify children into language status groups with 97% accuracy (Skarakis-Doyle et al. , 2009) “Low” as having a total score in the lowest 25% of the score distribution 19

ECLS-B measures (cont. ) Learning-related behavior problems Modified version of the Bayley’s Behavior Rating System Field staff administering the Bayley also rated the children’s behavior on a frequency scale (e. g. , 1=“constantly off task, ” 5=“constantly attends”) Cronbach alpha of. 92 for the behavioral items (Raikes et al. , 2007) “High” as having a score in the highest 25% of the distribution of total scores for “inattentive, ” “not persistent, ” “no interest” Birth certificate data and parental survey on a range of socio- demographic, gestational, and birth characteristics (e. g. , preterm, low birthweight, congenital anomalies) 20

Descriptive statistics for RMD and non. RMD groups, ECLS-B continuous data RMD Non-RMD Mean (SD) SD Unit Differences Modified Bayley Score 121. 39 (9. 01) 128. 79 (10. 35) -. 71 Modified CDI Word Score 23. 67 (10. 85) 30. 35 (11. 62) -. 57 24 months 21

Logistic regression of 48 -60 month RMD using 24 month predictors 24 Month Predictors Low Bayley at 24 Months Child’s Age at 60 month Assessment Male Model 1 Model 3 Model 4 3. 02 *** 2. 95 *** 2. 23 *** 0. 79 *** 0. 71 *** 1. 18 1. 22 1. 12 African-American 1. 35 * 1. 32 * 1. 34 * Hispanic 1. 18 1. 21 1. 24 Other 1. 19 1. 16 1. 13 Mother’s Education, no diploma Mother’s Education, High School Graduate Mother’s Age over 35 at Child’s Birth Mother Not Married at Child’s Birth 22 3. 64 *** Model 2 4. 66 *** 4. 47 *** 4. 40 *** 2. 28 *** 2. 22 *** 2. 24 *** 0. 89 0. 86 0. 84 1. 22

Logistic regression of 48 -60 month RMD using 24 month predictors (cont. ) 24 Month Predictors Model 4 (cont. ) Very Pre-Term 1. 15 1. 09 Moderately Pre-Term 1. 34 1. 27 Very Low Birth Weight Moderately Low Birth Weight Labor Complications 1. 77 1. 65 1. 54 * 1. 58 ** 0. 75 * 0. 74 * Medical Risk Factors 1. 03 1. 01 Behavioral Risk Factors Obstetric Procedures 1. 14 1. 17 0. 93 0. 94 Congenital Anomalies 23 Model 3 (cont. ) 0. 80 0. 79 Low Word Score at 24 Months High L-R Behaviors at 24 Months 1. 58 ** 1. 41 **

ECLS-B results Potentially malleable and educationally relevant risk factors by 24 months for 48 -60 month RMD include earlier history of cognitive delay, language delay, and learning-related behavior problems These risk factors are not mediated by the child’s or family’s socio-demographics, or the child’s gestational or birth characteristics, despite their sometimes strong predicted effects 24

What do these analyses tell us? A “common core” of factors that increase a child’s risk of RMD may exist, that includes: MD or an early onset of cognitive delay Reading or language difficulties Learning-related behavior problems Being raised by a mother with a low level of education Prior history of learning difficulties and learning-related behavior problems may be particularly educationally relevant, and potentially malleable The effects of these risk factors are robust, and can be detected early, by children’s kindergarten or even toddler years Early screening, monitoring, and intervention efforts may need to be “multi-faceted” so as to account for the multiple developmental pathways that may result in children experiencing RMD 25

Thank you! For additional questions, please contact: Paul L. Morgan Department of Educational Psychology, School Psychology, and Special Education The Pennsylvania State University Park, PA 16802 (814) 863 -2285 [email protected] edu 26