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
Early Risk Factors for Later Mathematics Difficulties
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This work is supported by grant #R324A07270, National Center for Special Education, Institute of Education Sciences
No official endorsement should be inferred
Sam and Cole
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Sam and the joys of a productive disposition
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And the constant close calls of informal learning
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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 frameworkRelatively 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
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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
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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
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Study’s two datasets Two NCES-maintained datasets
Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K) Kindergarten-8th grade longitudinal, nationally representative
sampleEarly Childhood Longitudinal Study-Birth Cohort (ECLS-K)
Birth-Kindergarten longitudinal, nationally representative sample
Both datasets include individually-administered, adaptive measures of:academic achievementdirect observation ratings of learning-related behaviorsmulti-source surveys of the children’s socio-
demographic, gestational, and birth characteristics
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Analytical samples, time periods, measures, operationalizations
ECLS-K ECLS-B
Analytical samples N=5,838 N=5,650*
Time periods Spring of Kindergarten, 3rd, 5th, & 8th grade
24, 48, & 60 months
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 3rd, 5th, & 8th 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*)
*Sub-sample rounded to nearest 50
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Analytical methods ECLS-K ECLS-B
Descriptive statistics Child- and family-level socio-demographics, child-level learner characteristics
Logistic regression (Odds Ratios as the effect size metric)
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 spring of 3rd, 5th, & 8th grade administrations of the the Mathematics Test, and “0” as not not being in this groupStep 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
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 the Mathematics Test, and “0” as not not being in this groupStep 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
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Datasets
Predictors measured by
Criterions measured by
ECLS-K Spring of Kindergarten Spring of 3rd, 5th, and 8th grade
ECLS-B 24 months Preschool (48 months) and Kindergarten (60 months)
Study’s longitudinal designs
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ECLS-K analytical sample’s socio- demographics Sample Characteristic Percentage
Male 50.95%Child age (months), ECLS-K Spring K 74.82Ethnic origin
White, Non-Hispanic 63.73% Black 15.48% Hispanic 13.97% Other 6.76%Mother’s education, Kindergarten assessment Less Than High School 9.41% High School Graduate 27.49% Some College after High School and Above 63.10%Maternal age = 35 or older 11.04%12
ECLS-K measuresECLS-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 TestIndividually-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
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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)
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Descriptive statistics for RMD and non-RMD groups, ECLS-K continuous data
RMD Non-RMD
Mean (SD) Mean (SD) SD Unit Differences
Kindergarten PredictorsMathematics 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
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Logistic regression of 3rd-8th grade RMD (ORs) using kindergarten predictors
Kindergarten Predictors Model 1 Model 2 Model 3 Model 4
Low Kindergarten Math 19.79 *** 16.90 *** 16.94 *** 9.76 ***
Child is Male 0.52 *** 0.52 *** 0.38 ***
Child Age at Assessment 1.06 ** 1.06 ** 1.06 **
Mother’s Education, Less than High School Grad.
5.00 *** 5.00 *** 4.89 ***
Mother’s Education, High School Grad.
1.94 *** 1.93 *** 1.94 ***
Mother’s Age at Birth > 35 years 0.82 0.82 0.84
Black 2.85 *** 2.86 *** 2.75 ***
Hispanic 0.76 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 2.00 ***
Low Approaches to Learning 2.03 **
High Externalizing Behavior 1.61
High Internalizing Behavior 1.2816
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
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ECLS-B analytical sample’s socio-demographics
Sample Characteristic Percentage
Male 50.54%Child age (months) at Kindergarten 64.80Ethnic origin
White, Non-Hispanic 63.00% Black 15.05% Hispanic 17.74% Other 3.94%Mother’s education, Birth assessment Less Than High School 19.76% High School Graduate 32.32% Some College after High School and Above 48.02%Maternal age = 35 or older 13.69%Mother Not Married at Child’s Birth 31.80% 18
ECLS-B measuresModified 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
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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)
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Descriptive statistics for RMD and non-RMD groups, ECLS-B continuous data
RMD Non-RMD
24 monthsMean (SD) 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
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Logistic regression of 48-60 month RMD using 24 month predictors
24 Month Predictors
Model 1 Model 2 Model 3 Model 4
Low Bayley at 24 Months
3.64 *** 3.02 *** 2.95 *** 2.23 ***
Child’s Age at 60 month Assessment
0.79 *** 0.79 *** 0.71 ***
Male 1.18 1.22 1.12African-American
1.35 * 1.32 * 1.34 *
Hispanic 1.18 1.21 1.24Other 1.19 1.16 1.13Mother’s Education, no diploma
4.66 *** 4.47 *** 4.40 ***
Mother’s Education, High School Graduate
2.28 *** 2.22 *** 2.24 ***
Mother’s Age over 35 at Child’s Birth
0.89 0.86 0.84
Mother Not Married at Child’s Birth
1.24 1.22 1.2222
Logistic regression of 48-60 month RMD using 24 month predictors (cont.)24 Month Predictors
Model 3 (cont.)
Model 4 (cont.)
Very Pre-Term 1.15 1.09Moderately Pre-Term
1.34 1.27
Very Low Birth Weight
1.77 1.65
Moderately Low Birth Weight
1.54 * 1.58 **
Labor Complications
0.75 * 0.74 *
Medical Risk Factors
1.03 1.01
Behavioral Risk Factors
1.14 1.17
Obstetric Procedures
0.93 0.94
Congenital Anomalies
0.80 0.79
Low Word Score at 24 Months
1.58 **
High L-R Behaviors at 24 Months
1.41 ** 23
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
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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 difficultiesLearning-related behavior problemsBeing 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
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Thank you! For additional questions, please contact:
Paul L. MorganDepartment of Educational Psychology, School Psychology, and Special EducationThe Pennsylvania State UniversityUniversity Park, PA 16802(814) 863-2285 [email protected]
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