Journal of Experimental Child Psychology 110 (2011) 647–658

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Journal of Experimental ChildPsychology

journal homepage: www.elsevier .com/locate/ jecp

Early literacy and early numeracy: The value of includingearly literacy skills in the prediction of numeracydevelopment

David J. Purpura a,⇑, Laura E. Hume b, Darcey M. Sims b, Christopher J. Lonigan b

a College of Education, University of Illinois at Urbana – Champaign, Champaign, IL 61820, USAb Department of Psychology, Florida State University, Tallahasee, FL 32306, USA

a r t i c l e i n f o

Article history:Received 10 February 2011Revised 8 July 2011Available online 9 August 2011

Keywords:NumeracyMathematicsEarly literacyVocabularyPrint knowledgePhonological Awareness

0022-0965/$ - see front matter � 2011 Elsevier Indoi:10.1016/j.jecp.2011.07.004

⇑ Corresponding author.E-mail addresses: dpurpura@illinois.edu (D.J. Pu

a b s t r a c t

The purpose of this study was to examine whether early literacyskills uniquely predict early numeracy skills development. Duringthe first year of the study, 69 3- to 5-year-old preschoolers wereassessed on the Preschool Early Numeracy Skills (PENS) test andthe Test of Preschool Early Literacy Skills (TOPEL). Participantswere assessed again a year later on the PENS test and on theApplied Problems and Calculation subtests of the Woodcock–Johnson III Tests of Achievement. Three mixed effect regressionswere conducted using Time 2 PENS, Applied Problems, and Calcu-lation as the dependent variables. Print Knowledge and Vocabularyaccounted for unique variance in the prediction of Time 2 numer-acy scores. Phonological Awareness did not uniquely predict any ofthe mathematics domains. The findings of this study identify animportant link between early literacy and early numeracydevelopment.

� 2011 Elsevier Inc. All rights reserved.

Introduction

The preschool and kindergarten years represent a critical juncture in children’s academic develop-ment. Research has shown that academic achievement at early ages is highly related to later academicachievement (Butler, Marsh, Sheppard, & Sheppard, 1985; Krajewski & Schneider, 2009; Stevenson &Newman, 1986). The two central domains of children’s early academic achievement are reading andmathematics. These two domains not only are important individually but also are necessary for the

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rpura), lonigan@psy.fsu.edu (C.J. Lonigan).

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acquisition of knowledge in other domains (Anders, 1986; Brown & Murray, 2005; Snow, Burns, &Griffin, 1998). Furthermore, mathematics and reading may be important in the development of eachother. From very early ages, these two domains are related (McClelland et al., 2007; Welsh, Nix, Blair,Bierman, & Nelson, 2010) and are predictive of each other over the long term (Duncan et al., 2007; Juel,1988). However, the specific nature of this relation, particularly at school entry, is unclear. In thisstudy, we examined how specific early literacy skills predict later numeracy skills beyond initialnumeracy skills.

Early literacy skills

Although most children do not often receive formal instruction in reading until they enter kinder-garten or first grade, skills that are developed prior to formal instruction have been shown to beimportant to the development of reading proficiency. The skills, knowledge, and attitudes towardreading and writing that develop before formal instruction are called early literacy skills (Whitehurst& Lonigan, 1998). The three primary early literacy skills are oral language, phonological processingabilities, and print knowledge. Oral language skills include word knowledge, vocabulary, understand-ing grammatical rules (Storch & Whitehurst, 2002). The aspect of phonological processing abilitiesmost often linked to reading development is phonological awareness (Adams, 1990; Cunningham &Stanovich, 1997; Wagner & Torgesen, 1987). Phonological awareness refers to a child’s ability to detectand manipulate language through tasks such as matching, blending, and deleting parts of words(Wagner & Torgesen, 1987). The third early literacy skill, print knowledge, is a child’s knowledge ofletter names and sounds, words, and basic conventions about books and print such as how to holdand use books and the directionality of print (Whitehurst & Lonigan, 1998).

Early numeracy skills

Similar to reading, children begin to develop their mathematics skills at an early age. Some evi-dence suggests that children are born with a degree of informal mathematical competence such asthe ability to recognize changes in magnitude (Starkey & Cooper, 1980; Wood & Spelke, 2005). Thisinformal knowledge develops as children explore their natural environment (Ginsburg, 1975), butcan also be improved through instruction (Baroody, Eiland, & Thompson, 2009; Clements & Sarama,2008; Lai, Baroody, & Johnson, 2008; Ramani & Siegler, 2008; Starkey, Klein, & Wakeley, 2004). Theevaluation of the early numeracy skills of preschoolers centers around three highly related, but dis-tinct, domains: numbering, numerical relations, and arithmetic operations (Jordan, Kaplan, Locuniak,& Ramineni, 2007; Purpura, 2009). Numbering entails knowledge of the standard verbal counting se-quence, knowledge of counting principles, and the ability to determine the total number of items in aset (cardinality) by immediately recognizing it (subitizing) or by counting the set. Numerical relationsinvolves knowledge of how two or more items (collections or numbers) are connected or relevant toeach other and the association between the numbers on the mental number line. Arithmetic opera-tions is a child’s ability to understand changes in quantity and obtain new quantities from the changein the size of sets. These domains, or aspects of these domains, are the most studied aspects of earlymathematics (Baroody, Gannon, Berent, & Ginsburg, 1984; Ginsburg, Klein, & Starkey, 1998; Jordan,Kaplan, Olah, & Locuniak, 2006) and the concepts and skills most necessary for the development ofbasic formal mathematics skills such as addition and subtraction (Jordan, Kaplan, Ramineni, &Locuniak, 2009).

Relations between early literacy skills and early numeracy skills

Reading and mathematics skills are related over time (Duncan et al., 2007; Hecht, Torgesen, Wagner,& Rashotte, 2001; Juel, 1988), and children who have difficulties in one area have a high likelihoodof having difficulties in the other area (Barberisi, Katusic, Colligan, Weaver, & Jacobsen, 2005). Corre-lations between mathematics and reading scores generally average approximately .60 in elementaryschool and adolescence (Fuchs et al., 2006; Hecht et al., 2001; Lee, Ng, & Ng, 2009) and can be evenhigher in preschool (McClelland et al., 2007; Welsh et al., 2010). In addition, early mathematics and

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reading skills are predictive of each other over time, even as late as middle school and high school(Hooper, Roberts, Sideris, Burchinal, & Zeisel, 2010). Potential explanations for the significant relationsbetween these domains include genetic, cognitive, and environmental links (Farrington-Flint,Vanuxem-Cotterill, & Stiller, 2009; Gathercole, Pickering, Knight, & Stegmann, 2004; Hart, Petrill,Thompson, & Plomin, 2009; Rohde & Thompson, 2007; Spinath, Spinath, Harlaar, & Plomin, 2006;Swanson & Beebe-Frankenberger, 2004). However, one understudied reason for this connection is thatskills in each domain reciprocally influence the development of skills in the other domain.

There is evidence for a unique role that specific early literacy skills play in the development of latermathematics abilities. Notably, children with both reading and mathematics difficulties appear to de-velop specific mathematics skills at a slower rate than children with only mathematics difficulties(Jordan, Hanich, & Kaplan, 2003). Of the three early literacy skills, the one most often connected tomathematics skills is phonological awareness (Fuchs et al., 2006, 2010; Hecht et al., 2001;Krajewski, Schneider, & Niedling, 2008; Krajewski & Schneider, 2009; Krajewski et al., 2008). Severaltheories propose a direct or indirect relation between phonological awareness and mathematics skills(Krajewski et al., 2008; Simmons & Singleton, 2008). Notably, the isolated number words hypothesis(Krajewski et al., 2008) indicates that the relation between reading and mathematics is focused on theapplication of phonological awareness principles to the learning of number words. Krajewski and col-leagues (2008, 2009) noted that phonological awareness skills enable children to differentiate andmanipulate individual words in the number sequence. However, their research also indicates that thisrelation is primarily found at the base level of mathematics skills (i.e., number word learning) and thatphonological awareness is related to later mathematics skills only indirectly through its relation toearly mathematics skills.

Although less studied than phonological awareness, language skills have also been found to be re-lated to concurrent mathematics performance and predictive of later mathematics performance (Hoo-per et al., 2010; Romano, Babchishin, Pagani, & Kohen, 2010). Much of the application of mathematicalknowledge to basic computational and comparative skills is inherently dependent on children’sunderstanding of language. For example, language skills may be important for understanding the con-cepts of ‘‘more’’ and ‘‘less’’ as well as understanding that a range of mathematical words can mean thesame thing and can often be used interchangeably (e.g., plus, and, add, together). These language-re-lated mathematics terms are often found in mathematics assessments, interventions, and curricula.

Most research regarding the relation between language skills and mathematics skills has focusedon two areas: children’s language skills in relation to word problem performance in elementary school(Fuchs et al., 2005, 2008, 2010) and mathematics performance differences between native Englishspeakers and English language learners (Chang, Singh, & Filer, 2009; Bautista, Mitchelmore, & Mulli-gan, 2009; Johnson & Monroe, 2009; Martiniello, 2009). These studies generally indicate that childrenwith low language skills—as a function of either ability or English language learner status—performmore poorly than higher ability peers on mathematics word problems, but these differences do notextend to general nonverbal calculation skills. Little research has been conducted to examine the rela-tion between language and mathematics at school entry.

Even though print knowledge is often a strong predictor of children’s later reading skills (Compton,2000; Furnes & Samuelsson, 2009; Lonigan, Burgess, & Anthony, 2000; Stevenson & Newman, 1986;Tunmer, Herriman, & Nesdale, 1988), the relation between children’s print knowledge and mathemat-ics skills is not well studied. Knowledge of the base concepts of print knowledge and mathematics(number identification and letter identification) are highly related in preschool (Piasta, Purpura, &Wagner, 2010) and kindergarten (Matthews, Ponitz, & Morrison, 2009). Understanding the functionsand nature of print can logically be connected to early mathematics skills because many aspects ofinformal and formal mathematics rely on printed numbers or symbols. For example, both lettersand numbers serve similar functions as labels applied to base structures of their respective domains.When combined with other letters or numbers, they result in a new symbol with a different meaning.

The current study

Although each early literacy domain is correlated to and predictive of numeracy skills, it is unclearwhether each early literacy skill is uniquely related to numeracy skills development. As of yet, no study

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has evaluated the relation between these domains at the same time. Understanding the concurrentand predictive relations each early literacy skill has with numeracy development can provide informa-tion for the enhancement of preschool curriculum and intervention development. The purpose ofthe current study was to examine how and which early literacy skills in preschool uniquely predictlater numeracy skills. Based on prior research, it was hypothesized that all three early literacy skillswould uniquely predict later numeracy performance even after initial mathematics skills werecontrolled.

Method

Participants

As part of a larger study on children’s mathematics development involving 393 preschoolers, 91children were also assessed on their early literacy skills during the first year of this study. Of thesechildren, a total of 69 were assessed on their mathematics abilities a year later. Those children whodid not complete the second assessment had either moved out of district during the course of the yearor changed schools and could not be located. At the start of the study, 40 of the children who com-pleted both assessments were in their first year of preschool and 29 were in their second year of pre-school. Participants were from 10 preschools serving children from families with low to middlesocioeconomic status (SES) living in northern Florida. Family SES was obtained through parent reports.Of the 69 children who completed this study, 19 of their parents did not complete SES information.Because there was only minimal variation in SES within schools, the missing SES data were replacedby the school median SES. Family SES for participants was broken down into four SES brackets (rep-resenting annual income): less than $30,001 (7 children), $30,001 to $50,000 (23 children), $50,001 to$75,000 (18 children), and more than $75,000 (21 children). Participants were evenly split by sex(52.2% female and 47.8% male) and were predominantly White (81.2% White, 10.1% African American,and 8.7% other race/ethnicity). Children ranged in age from 3.18 to 5.70 years (M = 4.41, SD = 0.64) atinitial testing. All children were primarily English speaking and had no known developmental disor-ders. Parental consent was obtained for each participating child.

Measures

Preschool early numeracy skills testChildren were assessed using the Preschool Early Numeracy Skills (PENS) test (Purpura, 2009) at

both Time 1 and Time 2. This measure consists of three separate subtests: Numbering, Numerical Rela-tions, and Arithmetic Operations. Each subtest consists of 7 to 9 tasks. The tasks are representative ofthe range of skills assessed by previously developed numeracy measures and were developed by mod-ifying and revising those measures (Clements, Sarama, & Liu, 2008; Ginsburg & Baroody, 2003; Griffin& Case, 1997; Jordan et al., 2007; Klein, Starkey, & Ramirez, 2002; van de Rijt et al., 2003). The Num-bering subtest consists of the following tasks: verbal counting, counting forward/backward from anumber other than 1, counting error identification, structured counting, cardinality, resultative count-ing, counting a subset, subitizing, and estimation. The Numerical Relations subtest consists of the fol-lowing tasks: ordinality, relative size, number comparison, set comparison, number order, sequencing,set reproduction, number identification, and numerals. The Arithmetic Reasoning subtest consists ofthe following tasks: addition/subtraction with objects, story problems, initial equivalence, two-setaddition/subtraction, equivalent sets, number composition/decomposition, and number combina-tions. This measure was designed as a research tool to assess numeracy at both broad (many taskswere assessed) and deep (a range of items for each task was assessed) levels.

Items on the PENS test were selected from a larger item pool using item response theory. This pro-cess ensured that each item was related to its intended construct, had adequate discrimination (aparameter), and did not duplicate the difficulty level (b parameter) of other items on the same task.Through this process, 25 distinct tasks were developed (9 for Numbering, 9 for Numerical Relations,and 7 for Arithmetic Operations), each with 3 to 9 items that spanned the developmental continuumfor each skill. To calculate children’s overall early numeracy ability, a latent factor score was created in

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Mplus version 6.1 (Muthén & Muthén, 2010) separately for each time point.1 At Time 1, data from theoriginal sample of 393 children were used to calculate scores. At Time 2, data from the 213 children whocompleted the full follow-up testing were used to calculate the Time 2 PENS factor scores. To obtain thefactor scores, items on each task were summed to create 25 task scores. The 25 tasks were then enteredinto a three-factor (Numbering, Numerical Relations, and Arithmetic Operations) confirmatory factoranalysis model with a one-factor higher order level (Numeracy). This analysis provided a latent factornumeracy score for each child that subsumed the common variance from all tasks. Age was then re-gressed out of the latent factor scores separately for each time point, and the resultant scores were trans-formed to create age-standardized scores with a mean of 100 and a standard deviation of 15.

Woodcock–Johnson III Tests of AchievementDuring the spring of the second year of the study, children were also assessed on the Applied Prob-

lems and Calculation subtests of the Woodcock–Johnson III Tests of Achievement. These subtests arenationally normed measures of mathematics ability. The Applied Problems subtest is an untimedmathematics test where problems are visually and/or orally presented to children and has been shownto have a median reliability of .85 (Woodcock, McGrew, & Mather, 2001). The Calculation subtest is apaper-and-pencil arithmetic test where children are asked to solve addition and subtraction problemsand has been shown to have a median reliability of .92 for 5- to 19-year-olds (Woodcock et al., 2001).Because the Calculation subtest is standardized only down to 5 years of age, a sample-specific agestandardization was conducted on the portion of the full sample assessed at Time 2 (N = 213) fromthe larger project. The age standardization process resulted in a full sample mean of 100 and a stan-dard deviation of 15.

Test of Preschool Early Literacy SkillsThe Test of Preschool Early Literacy Skills (TOPEL) (Lonigan, Wagner, Torgesen, & Rashotte, 2007) is

a standardized measure of early literacy skills. This measure consists of three subtests: Print Knowl-edge, Vocabulary, and Phonological Awareness. The Print Knowledge subtest measures print concepts,letter discrimination, word discrimination, letter name identification, and letter sound identification.The Vocabulary subtest measures children’s single-word spoken vocabulary and their ability to formu-late definitions for words. The Phonological Awareness subtest includes both multiple-choice andfree-response items along the developmental continuum of phonological awareness from wordawareness to phonemic awareness. The internal consistency for each of the three subtests was be-tween .86 and .96 for 3- to 5-year-olds. The standard scores for each subtest have a mean of 100and a standard deviation of 15.

Nonverbal cognitive abilityThe Copying subtest of the Stanford–Binet (Thorndike, Hagen, & Sattler, 1986) was used as a proxy

measure of nonverbal cognitive ability and served as a control variable. This test is composed of 28items. The first 12 items require children to duplicate the examiner’s design made from single-colorblocks. The latter 16 items require children to copy designs from drawings in the administration book.Overall, nonverbal subtests of the Stanford–Binet have been shown to have high reliability (coeffi-cients >.90) for 2- to 5-year-olds. The age-standardized scores have a mean of 50 and a standard devi-ation of 8.

Assessment procedure

Children were assessed on the PENS test, the TOPEL, and the Copying subtest during the spring ofthe first year of the study and were assessed on the PENS test and the Woodcock–Johnson III AppliedProblems and Calculation subtests during the spring of the second year. Assessments were conductedby individuals who either had completed or were working toward completion of a bachelor’s degree.

1 Results were first evaluated for all three early numeracy factors separately. However, no differences were found between thefactors, so only the results related to the overall mathematics score are reported.

Table 1Means, standard deviations, and correlations for measures at Time 1 and Time 2.

Task Mean SD 1 2 3 4 5 6 7 8

1. Time 1 PENS 104.12 12.87 –2. Print Knowledge 106.69 11.64 .43** –3. Vocabulary 101.00 9.89 .24* .23 –4. Phonological Awareness 100.12 14.80 .26* .42** .60** –5. Nonverbal problem solving 41.39 4.13 .21 .06 .12 .05 –6. Time 2 PENS 106.21 11.64 .63** .47** .40** .28* .18 –7. Applied Problems 111.91 11.75 .56** .48** .55** .44** .05 .57** –8. Calculation 103.57 15.71 .36** .28* .14 .28* .02 .29* .55** –

* p < .05.** p < .01.

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Assessments took place in the local preschools or kindergarten classrooms (in the second year of thestudy, the 29 older children were in kindergarten) during noninstructional time in a quiet room des-ignated by the individual school directors or teachers.

Results

Preliminary analyses

Children who completed both assessments were not significantly different from those who did notcomplete the posttest on their Time 1 mathematics, F(1, 90) = 0.28, p = .596, Print Knowledge,F(1, 90) = 0.14, p = .706, Vocabulary, F(1, 90) = 1.00, p = .320, Phonological Awareness, F(1, 90) = 0.74,p = .393, or nonverbal cognitive ability, F(1, 86) = 1.51, p = .222. Means, standard deviations, and cor-relations between tasks are presented in Table 1.2 No tasks exhibited significant skew or kurtosis. Dif-ferences by sex on each task were examined. On the Print Knowledge and Phonological Awareness tasks,boys performed significantly better than girls; however, when the Benjamini–Hochberg correction wasapplied to correct for Type I error, this effect was no longer significant. There were no other statisticallysignificant differences by sex.

Mixed effect regression analyses

OverviewTo test the unique contribution of early literacy skills in the prediction of the three mathematics

measures at Time 2, three separate mixed-effects regression analyses (Raudenbush & Bryk, 2002) wereconducted. In each of the analyses, children’s preschool was included as a random effect to account forvariance due to preschool center. There were a total of 10 preschools with an average of 6.9 childrenper preschool. Time 1 PENS scores, nonverbal cognitive ability scores, and SES were included as fixedeffects covariates. Grade (a dichotomous variable indicating whether children began the study in theirfirst or second year of preschool) was also included as a fixed effect covariate to account for instruc-tional differences between grade levels. Print Knowledge, Vocabulary, and Phonological Awarenesswere included in the model as fixed effect predictors. The amount of variance explained by the fullmodels is presented as pseudo-R2, and the amount of unique variance explained by individual predic-tors is presented as pseudo-sr2 (pseudo-squared semipartial). Pseudo-sr2 values, in contrast to stan-dard sr2 values, can be negative due to chance variability. According to Snijders and Bosker (1999),only negative sr2 values that are greater than �.05 are indicative of model misspecification. All othervalues (those close to zero) are trivial and should be considered to be effectively zero. In this study,although some of the sr2 values were negative, all were in the trivial range.

2 The copying task items were consistently scored more stringently than is typical, resulting in children reaching the ceilingssooner than they typically would.

Table 2Mixed effects regression predicting PENS total standard score at year follow-up assessment.

Estimate SE Pseudo-sr2 F p

Nonverbal problem solving 0.11 0.28 �.01 0.16 .688SES �1.58 0.53 .01 2.00 .163Grade 0.12 2.42 �.01 0.00 .962Time 1 PENS 0.44 0.10 .14 20.83 .000Print Knowledge 0.23 0.09 .05 6.25 .015Vocabulary 0.30 0.13 .03 5.04 .028Phonological Awareness �.07 0.09 �.01 0.63 .429

Note. N = 69.

Table 3Mixed effects regression predicting Woodcock–Johnson III Applied Problems standard score at year follow-up assessment.

Estimate SE Pseudo-sr2 F p

Nonverbal problem solving �0.01 0.28 �.01 0.00 .964SES �1.32 1.05 .01 1.59 .215Grade 4.61 2.37 .03 3.80 .057Time 1 PENS 0.31 0.09 .07 11.23 .001Print Knowledge 0.23 0.09 .05 6.27 .015Vocabulary 0.50 0.13 .09 15.37 .000Phonological Awareness �0.02 0.09 �.01 0.07 .798

Note. N = 69.

Table 4Mixed effects regression predicting Woodcock–Johnson III Calculation standard score at year follow-up assessment.

Estimate SE Pseudo-sr2 F p

Nonverbal problem solving 0.46 0.48 �.01 0.91 .343SES 0.59 1.87 �.01 0.10 .752Grade 10.59 4.16 .02 6.48 .014Time 1 PENS 0.15 0.16 .00 0.92 .343Print Knowledge 0.13 0.16 �.01 0.65 .423Vocabulary �0.17 0.22 .01 0.63 .430Phonological Awareness 0.23 0.16 .04 2.27 .137

Note. N = 69.

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PENS testThe intraclass correlation coefficient (ICC) for preschool in the unconditional model indicates that

preschool accounted for 10% of the explained variance. The full model accounted for 43% of the vari-ance in the Time 2 PENS score based on pseudo-R2, Dv2(7) = 40.99, p < .001. Time 1 PENS, Print Knowl-edge, and Vocabulary were significant predictors of the Time 2 PENS test, but Phonological Awarenesswas not a significant predictor (see Table 2). All significant findings retained their statistical signifi-cance when the Benjamini–Hochberg correction was applied.

Applied problemsThe ICC for preschool in the unconditional model indicated that preschool accounted for 11% of the

explained variance. The full model accounted for 49% of the variance in the Applied Problems subtestscore based on pseudo-R2, Dv2(7) = 48.85, p < .001. Both Print Knowledge and Vocabulary were signif-icant predictors of the Time 2 Applied Problems subtest, but Phonological Awareness was not a signif-icant predictor (see Table 3). All significant findings retained their statistical significance when theBenjamini–Hochberg correction was applied.

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CalculationThe ICC for preschool in the unconditional model indicated that preschool accounted for 10% of the

explained variance. The full model accounted for 26% of the variance in the Calculation subtest scorebased on pseudo-R2, Dv2(7) = 18.25, p < .001. PENS scores at Time 1 and the early literacy skills werenot significant predictors of the Time 2 Calculation subtest (see Table 4), and grade was the only sig-nificant predictor in the model.

Discussion

The results of this study indicate that all three early literacy skill domains were individually relatedto, and predictive of, young children’s general numeracy knowledge. However, only two of these threeskills—vocabulary and print knowledge—were uniquely predictive of later numeracy performancewhen accounting for initial numeracy performance and nonverbal cognitive ability. Although initialphonological awareness was correlated with later numeracy development, the predictive relation be-tween these variables was fully accounted for by the other two early literacy skills. Interestingly, thispattern of relations was found only for the two general measures of numeracy ability (PENS test andApplied Problems subtest) and not for the Calculation subtest. None of the early literacy skills ac-counted for a significant amount of unique variance in the prediction of the Calculation subtest. Onlychildren’s grade was significantly predictive of variance in children’s Calculation subtest. These find-ings follow with past research that has identified links between early literacy skills and early mathe-matics development (Duncan et al., 2007; Hecht et al., 2001; Hooper et al., 2010; Lee et al., 2009;Matthews et al., 2009) and fill a gap in this research domain by identifying the unique relations be-tween early literacy and early numeracy skills.

Most notable of the findings from this study was that phonological awareness did not uniquely pre-dict numeracy development when accounting for the other early literacy skills. This finding stands incontrast to prior research that has indicated significant relations between early literacy skills andnumeracy skills and that is most frequently focused on the relation between phonological awarenessand numeracy skills (Alloway et al., 2005; Bradley & Bryant, 1985; Fuchs et al., 2006, 2010; Hechtet al., 2001; Leather & Henry, 1994; Krajewski & Schneider, 2009; Krajewski et al., 2008; Simmons& Singleton, 2008). The past focus on the relation between numeracy and phonological awarenesswas likely due to the prominence that phonological awareness skills has taken in the field of earlyreading development and reading disability identification (Adams, 1990; Cunningham & Stanovich,1997; Wagner & Torgesen, 1987). A general correlation would be expected to be found betweennumeracy and phonological awareness because both domains are influenced by a range of commonfactors, including aspects of both genetics and environment (Petrill & Plomin, 2007; Plomin & Kovas,2005). However, the specific relation between phonological awareness and numeracy may have beenoverestimated because past studies failed to account for common relations between phonologicalawareness and the other early literacy skills or between phonological awareness and children’s gen-eral academic capabilities.

The identification of the unique relations between early numeracy skills and print knowledge andvocabulary can lead to greater understanding of how early mathematics skills develop and help toidentify potential barriers to successful acquisition of these skills. Language and early numeracy skillsmay be linked because the understanding of certain specific language terms is inherently necessary forthe completion of basic mathematical tasks. Children’s ability to understand a mathematical concept(e.g., discriminating that one set has fewer or more objects than another set) may develop at a differ-ent time than their ability to comprehend the applicable language skills necessary to understand thequestion (e.g., know the meaning of fewer; Lansdell, 1999). Furthermore, certain mathematics tasks,such as basic arithmetic reasoning, often are couched in story problems, necessitating an ability toread or have adequate language development to comprehend spoken story problems. Similarly, duringthe transition phase from informal to formal mathematics development, children’s mathematicalknowledge must be applied to the written symbolism associated with formal mathematics. For exam-ple, children must know that each Arabic number is unique and has a distinct meaning, the combina-tion of two numbers (e.g., placing a 1 and a 4 together) represents a wholly new number (14), and

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other non-numerical symbols have distinct meanings for mathematical operations (e.g., +, �, =). Eventhough some children may conceptually grasp the informal mathematical concepts, without a deepknowledge of language and the mathematical print system, it is unlikely that they can apply theirknowledge in a formal mathematical context.

The nature of the numeracy tasks in this study—which were similar to those commonly presentedto young children and representative of the key early numeracy skill domains—likely contributed tothe significance of the specific relations identified in the study. Recalling that the numeracy taskson the PENS test included story problems, ‘‘most’’ and ‘‘least’’ problems, and items that required chil-dren to know other mathematical terms and concepts, it was reasonable to expect that vocabularywould account for unique variance in the analyses. The same is true for the Applied Problems subtestbecause it contains many of the same types of problems. In terms of print knowledge, both the PENStest and Applied Problems subtest required children to be able to identify printed numbers, mathe-matical symbols, and the meanings behind the numbers and symbols. It was surprising that printknowledge was not uniquely predictive of the Calculation subtest given that knowledge of printednumbers and symbols was necessary to complete the items on that measure. One explanation for thisfinding was that the Calculation subtest items were generally too advanced for the younger children inthe study and their lack of conceptual or procedural formal mathematical knowledge overrode anylinkages to early literacy skills. Furthermore, the older children in this study—those who were in kin-dergarten at Time 2—likely received more standardized and focused instruction on computationalskills during their kindergarten year. This differential instruction is reflected by grade being the onlysignificant predictor of children’s scores in the Calculation subtest.

The unique relations identified in this study provide important foundational information for under-standing the interactional development of early academic skills. However, it must be noted that thesefindings are not causal in nature. Further research is needed to identify and evaluate the causal rela-tions between these domains. Causal research in this area can enable researchers and educators tobetter understand how these skills develop individually and affect the development of one another.It is important, from both research and practical educational perspectives, to determine whether ornot intervening in one of these early literacy skills has either a direct or indirect impact on mathemat-ics development. For example, if a print knowledge (or language) intervention has a direct impact onchildren’s mathematics development, then such an intervention could (and should) be used as an inte-gral part of remediating specific mathematics difficulties. However, if there is no direct and immediateimpact on children’s mathematics performance, then it may be possible that there is an indirect rela-tion where improving children’s print knowledge (or language skills) may enhance the effects of a pro-ceeding mathematics intervention. In the absence of direct or indirect relations between thesedomains, third variables such as children’s behavior, classroom instructional techniques, and parentalfactors should be evaluated to explain the relations.

The relation between the early literacy skills and specific early numeracy skills (e.g., cardinality, setcomparison) also needs to be examined through further research. Because the development of eachaspect of early mathematics skills is likely to be affected by different early literacy skills, it is impor-tant to identify which numeracy skills have vocabulary components, print components, or both. Forexample, a verbal counting task may be related to vocabulary but not to print knowledge, whereasa number identification task may be related to print knowledge but not to vocabulary. This informa-tion, combined with the previously mentioned causal research, can be used to guide educators in theirselection of appropriate interventions for struggling children so as best to remediate specific mathe-matics problems. Furthermore, broader evaluation of ‘‘vocabulary-related’’ and ‘‘print-related’’ numer-acy skills could be used to identify whether or not the specific early numeracy skills cluster based ontheir relations to early literacy skills. Investigations of these relations should also be extended to lon-gitudinal prediction of more formal mathematical concepts.

Overall, the findings from this study provide a unique framework for the evaluation of early numer-acy skills that can be used to enhance both research and practical aspects of early numeracy develop-ment. However, two limitations to this study should be noted. First, given the relatively small numberof participants, it was not feasible to examine whether there were more detailed differences based ongrade (e.g., between those children who started the study in their first or second year of preschool).Additional research examining grade- or age-related differences in these relations should be

656 D.J. Purpura et al. / Journal of Experimental Child Psychology 110 (2011) 647–658

conducted to identify important developmental or instructionally based factors that affect numeracydevelopment—particularly regarding children’s calculation skills. Second, early literacy skills were notassessed at Time 2, and thus it could not be determined whether numeracy skills also uniquely pre-dicted individual early literacy skill development and whether there was a transactional relation be-tween these domains. Further investigation may be needed to determine whether early numeracyskills also affect the development of early literacy skills or whether both areas are affected by thirdvariables such as cognitive or behavioral factors.

Acknowledgments

This work was supported by grants from the Institute of Education Science, US Department of Edu-cation (R305B04074 and R305B100017). Views expressed in this article are solely those of the authorsand were not reviewed or cleared by the grantors.

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