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 paulmorgan@psu.edu

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