Early Risk Factors for Later Mathematics Difficulties

1. 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 This work is supported by grant #R324A07270, National Center for Special Education, Institute of Education Sciences No official endorsement should be inferred

2. Sam and Cole

3. Sam and the joys of a productive disposition

4. And the constant close calls of informal learning

5. 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

6. 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

7. 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

8. Study’s two datasets • Two NCES-maintained datasets • Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K) • Kindergarten-8th 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

11. Study’s longitudinal designs

12. ECLS-K analytical sample’s socio- demographics

13. ECLS-K measures • ECLS-K Mathematics Test • Individually-administered, untimed IRT measure measure of a range of age- and 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 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

14. 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, learning-related 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)

15. Descriptive statistics for RMD and non-RMD groups, ECLS-K continuous data

16. Logistic regression of 3rd-8th grade RMD (ORs) using kindergarten predictors

17. ECLS-K results • Potentially malleable and educationally relevant risk factors by the end of kindergarten for 3rd-8th 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

18. ECLS-B analytical sample’s socio-demographics

19. 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 McArthur 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

20. 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)

21. Descriptive statistics for RMD and non-RMD groups, ECLS-B continuous data

22. Logistic regression of 48-60 month RMD using 24 month predictors

23. Logistic regression of 48-60 month RMD using 24 month predictors (cont.)

24. 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

25. 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

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