Mathematical performance predicts progress in reading comprehension among 7-year olds

European Journal of Psychology of Education2005. yol.XXn"2. 121-137^ 2005.1.S.P.A.

Mathematical performance predicts progressin reading comprehension among 7-year olds

Marja-Kristiina LerkkanenHelena Rasku-PuttonenKaisa AunolaJari-Erik NurmiUniversity ofJyvdskyld, Finland

The aim of this longitudinal study was to investigate cross-laggedrelationships between tnathematical performance and readingcomprehension during the first and second years of primary school.114 Finnish-speaking children were examined six times on mathematicsand reading comprehension during Years I and 2. At the beginning ofYear I. they were also tested on initial mathematics and reading skill,general concept ability and visual-motor skills. The results showed,firstly, that mathematics and reading comprehension were highlyassociated with each other across both years. Secondly, mathematicalperformance predicted subsequent reading comprehension during thefirst year rather than vice versa. The results suggest that it is importantto pay more attention to the role of mathematical knowledge whenchildren are entering to school.

There is a growing interest in the relationship between mathematics and reading. Previousstudies have shown that mathematical skills and reading skills are associated and may sharesome basic cognitive components, such as working memory, auditory and visual perception, andphonological skills (Bull & Johnston, 1997; Hecht, Torgesen, Wagner, & Rashotte, 2001; Kail& Hall, 1999; Macaruso & Sokol, 1998; Muth, 1984; Swanson, Cooney, & Brock, 1993).However, most of the previous studies concerning the relationship between mathematics andreading skills have been carried out among learning-disabled students (Bull & Johnston, 1997;Geary, 1990, 1993; Jordan, Kaplan, & Hanich, 2002; Jordan, Hanich, & Kaplan, 2003;Macaruso & Sokol, 1998; Share, Moffitt, & Silva, 1988), with only a few studies usingunselected samples of primary school students (Dowker, 1998; Hecht et al., 2001; Muth, 1984;Tymms, 1999). Moreover, little research has focused upon prospective relationships between

We would like to thank Molla Walamies for her help in data collecting, Jenny Thomson for her advice on language,

and the children and the teachers who so kindly parlJcipaied in this study.

122 M.-K. LERKKANEN, H. RASKU-PUTTONEN, K. AUNOLA. & J.-E. NURMI

mathematical performance and reading conipreliension using cross-lagged longitudinal data.In addition, few studies have focused on the time children start to have formal instruction inboth skills. To overcome thi.se limitations the purpose of this longitudinal study was toexamine the relationships be:-/een mathematics and reading comprehension at the beginningof formal schooling by use of a cross-lagged longitudinal design.

Mathematical performance involves many components. For example, arithmetical skillsinclude basic number knowledge (recognising numbers and the ability to order them), memoryfor arithmetical facts {e.g., addition, subtraction), conceptual understanding (e.g.,understanding the effects of arithmetical operations, semantic understanding of verbalproblems), and procedural knowledge (e.g., the ability to count accurately) (Dowker, 1998;Donlan & Gourlay, 1999; Fazio, 1996; Rittle-Johnson & Sicgler, 1998). Mathematical skillsdevelop from small units of information (e.g., counting) to larger units (e.g., arithmetic facts).Achieving automaticity in arithmetical operations is important, because it releases cognitiveresources for tasks that require more complex processing, such as solving verbal problems(Bull & Johnston, 1997; Kail & Hall. 1999; Kaye, Post, Hall, & Dineen, 1986; Kulak, 1993).Previous studies have shown that, although young children's mathematical skills developrapidly during formal instruction (Geary, 1990; Jordan, Kaplan, & Hanich, 2002; Jordan,Hanich, & Kaplan, 2003), individual differences in performance are relatively stable duringthe early school years (Davies & Bremher, 1999).

Reading performance clearly includes two basic components: word reading and readingcomprehension. As in mathematics, the development of basic reading skills grows from smallunits (e.g., letter knowledge, phonemic awareness) to larger units (e.g., visual wordrecognition) (Adams, 1990; Seymour &. Evans, 1994, 1999). Moreover, achievingautomaticity in word reading frees up resources for reading comprehension (Perfetti, 1985).Reading comprehension requires advanced cognitive and linguistic skills, which provide abasis for the understanding of specific words and facts or the full meaning of a text (Yuill &Oakhill, 1991). Reading itself supports children's development of vocabulary knowledge andlanguage comprehension (Stanovich, 1986) but other abilities, such as listeningcomprehension and inference-making skills, are also relevant to the development of readingeotnprehension (de Jotig & van der Leij, 2002; Juel, 1994; Oakhill & Yuill, 1996; Stothard &Hulme, 1996; Vellutino & Scanlon. 1991; Yuiil Sc Oakhill, 1991). Existing studies haveshown that, although reading performance (i.e., word reading and reading comprehension)develops rapidly from the first to the sixth year of schooling (Phillips, Norris, Osmond, &Maynard, 2002), individual differences in reading achievement, especially readingcomprehension, are stable (Juel, 1988; de Jong & van der Leij, 2002; Smith, 1997).

Previous studies suggest that mathematics and reading may depend upon similar cognitivepredictors (Bull & Johnston, 1997; Geary, 1993; Hecht et al., 2001; Kulak, 1993; Tymms,1999). It is well known, for example, that phonological awareness predicts reading skill(Bradley & Bryant, 1983; Lundberg, Olofsson, & Wall, 1980; Stanovich, West, & Cunningham,1991; Wagner, Torgesen, & Rashotte, 1994). Similarly, Hecht et al. (2001) found thatphonological memory and phonological awareness predicted also the development ofcomputation skills from the second to the fifth year of school. Bull and Johnston (1997) reportedcotnparable results. Geary (1993) showed that learning-disabled children had cognitivedifficulties in the representation and retrieval of semantic information from long-term memorywhich then caused weaknesses in both maths and reading. Further, Jordan et al. (2002) foundthat the same linguistic abilities are needed for both mathematical problem solving and readingtasks. Tymms (1999) also recently demonstrated that the digit and letter identification skills of4-year-olds predicted both mathematical and reading achievement three years later. Moreover,number recognition was found to predict literacy as much as letter identification.

Numerous correlational studies have shown that achievements in maths and readingare associated in many ways (Geary, 1993; Heeht et al., 2001; Jordan et al., 2002; Muth, 1984;Share et al., 1988; Sovik, Frostrad, & Heggberget, 1999; Tymms, 1999) and theserelationships have been explored in both learning-disabled as well as typically-developingpopulations. Studies carried out amongst learning-disabled populations have shown that

MATHEMATICS AND READING COMPREHENSION 123

children who have difficulties in reading are also likely to have difficulties in mathematics (Bull& Johnston, 1997; Geary, 1993; Jordan, Kaplan, & Hanich, 2002; Jordan, Hanich, & Kaplan,2003; Macamso & Sokol, 1998; Share et al., 1988). Jordan, Kaplan, and Hanich (2002), forexample, fotind that reading skills predicted learning-disabled children's progress inmathematics. In temi.s of typically-developing children, several studies have shown that readingskills play a major role in the solution of arithmetic word problems (Hecht et al., 2001; Kail &Hall. 1999; Muth, 1984; Sovik et al., 1999; Swanson, Cooney, & Brock, 1993). For example,Muth (1984) demonstrated the importance of reading skills in mathematical word problemsolving amongst Year 6 students. A study by Kail and Hall (1999) also showed thatperfonnancc in mathematical word problems was predicted by word reading skills in 8-12-year-olds. Swanson, Cooney and Brock (1993) reported that reading comprehension skills predictedsuccess in solving arithmetic word problems at Years 3 and 5. Moreover, Hecht, Torgesen,Wagner, and Rashotte (2001) showed that phonological awareness and reading skills predictedthe development of basic computaiion skills, although the reverse was not true.

Studies with specific clinical samples have also shown distinctive relationships betweenmathematical and reading difficulties. Geary and Hoard (2001) have discussed the relationbetween dyscalculia (i.e., difficulties with solving complex arithmetic problems and withremembering basic arithmetic facts) and dyslexia. People with a genetic disorder, such asWilliam syndrome (Ansari, Donlan, Thomas, Ewing, Peen, & Karmiloff-Smith, 2003) orTurner syndrome (Bruandet, Molko, Cohen, & Dehacne, 2004), show much more severedisability in mathematics than in language skills. Additionally, children with specific languageimpairment (SLI) tend to show deficits in some aspects of mathematics, such as tasks thatrequire rapid retrieval of declarative knowledge (Fazio 1996, 1999), but not with aspects ofmaths that are based on non-verbal abilities, such as place-value knowledge (Donlan &Gourley, 1999).

Previous research on relationships between mathematics and reading skills has severallimitations. Firstly, most of the previous studies have been cross-sectional (Bull & Johston,1997; Muth, 1984; Sovik et al., 1999); only a few studies have investigated cross-laggedlongitudinal relationships between mathematics and reading comprehension. Secondly, themajority of previous studies have focused on word reading, whereas reading comprehensionhas rarely been examined. Thirdly, a major emphasis of earlier research has been upon therelative importance of reading comprehension in mathematical word problems. However, theconverse relationship has seldom been studied. Fourthly, there is a lack of research onmathematical performance and reading comprehension in the early school years. Finally, mostof the earlier studies in this research field are carried out with learning-disabled children (e.g.,Fazio 1996, 1999; Share et al., 1988). Consequently, in the present study we will examine therelationships between mathematical pertbrmancc and reading comprehension by use of across-lagged longitudinal dataset with several measurements during Years 1 and 2.

The following research questions were examined (see Figure 1):

1) To what extent does mathematical performance predict subsequent readingcomprehension during the first and the second school years? Our hypothesis was (I)that mathematical skills would predict children's subsequent reading skills. Thisassumption was based on two rationales. First, both math and reading skills partlydepend on the same cognitive and language-based processes, such as working memory,auditory and visual perception, and phonological awareness. Second, there is alsosome previous evidence suggesting that a low level of mathematical skills, likeproblems in number identification or the ability to count dots, correlate strongly withsubsequent reading skills (Share etal., 1988;Tymms, 1999).

2) To what extent does reading comprehension predict the development of mathematicalperformance during the first and the second school years? Our hypothesis was (II) thatreading skills would predict children's subsequent mathematical skills. Thisassumption was based on some previous findings suggesting that reading abilityincreases child's vocabulary and language comprehension (Stanovich, West,

124 M,-K. LERKKANEN, H. RASKU-PUTTONEN, K. AUNOLA, & J.-E. NURMI

Cunningham, Cipielewski, & Siddiquil996), which then contributes to some aspectsof math performance, for example word problem solving and number combinations(Geary, 1993; Hecht t̂ al., 2001; Jordan et al., 2002; Muth, 1984; Sovik et al., 1999;Swanson et al., 1993).

TimeO

August

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Time 2

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January

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The first school week Year I Year 1 Year 1 Year I Year 2 Year 2

Figure I. Schematic representation of the tested model

Method

Participants and procedure

One-hundred and fourteen children (61 boys, 53 girls) from six classes and four schoolsparticipated in the study. The schools were situated in an urban district of central Finland. Thechildren were examined while they were in Year I and Year 2. At the beginning of Year 1, theparticipating children were 6-7 years-old (M=7.30, SD=.32). In Finland children start school inthe year they tum seven years of age. All children were native Finnish speakers. A total of30% of their mothers and 35% of their fathers had a degree from an institute of universitystanding, 64% of mothers and 59% of fathers had a degree from an institution of professionalor vocational education, and 6.5% of parents had no occupational education. The educationallevel of the parents was representative of the distribution in the Finnish population aged 25-49years (Statistics and Indicators, 2003).

Children's formal instruction in reading and mathematics was started at school, but mostchildren had attended a year in pre-school before this. In Finnish preschool there is no formalinstruction in mathematics or reading, but the play-centered activities support children'slanguage and computational skills. Due to the regularity of the Finnish language, 27% ofchildren could read when they entered school (in August) and in October, 86% of childrenwere already getting the maximum score on word reading tasks, with the remainder able todecode most words (Lerkkanen, Rasku-Puttonen, Aunola, & Numii, 2004).

The children were examined 7 times. All children were tested in the first school week ofYear I (Time 0, August) on general concept ability, visual-motor skills, initial mathematical


skills and initial reading skills. Besides this, they were tested four times at seven weekintervals (Time 1, 2, 3, and 4) during the first year (at the beginning of October, the beginningof December, the end of January, and March) on mathematics and reading. The assessmentschedule reflected the seven week periods of maths and reading instruction at the participatingschools. During Year 2 the children were tested in December, and March (Time 5 and 6).Because of some children's absenteeism at some measurement points, the final sampleconsisted of 111 children at Time 1, 107 at Time 2, 105 at Time 3, 107 at Time 4, 107 at Time5, and 90 at Time 6. The assessments lasted approximately two school hours each, includingone 15-minute break. Reading comprehension was always assessed before mathematicalperformance.

Measurements

General concept ability. The general concept ability test (Liikanen, 1994) consisted ofeight drawing tasks which the tester read aloud one at a time ("Draw three lines, not of equallength"; "Draw three triangles with the smallest in the middle"; "Draw four circles with twoequal in size"). Scoring for the General Concept Ability variable was based on the number ofcorrect items (maximum value of 8).

Visual-motor skills. Visual-motor skills were tested by a paper and pencil test whichconsisted of 16 copying tasks (Liikanen, 1994). Children were asked to copy dot-to-dotfigures alongside a model. The number of correctly copied models comprised the child's scorefor the Visual-motor Skills variable (maximum value of 16).

Initial mathematical skills. Mathematical skills at the beginning of primary school weretested using the Mathematical Concept Test (Liikanen, 1994). The tasks were similar to thoseof the Morales, Shute, and Pellegrino (1985) study. The test consisted of 24 word problemsread aloud one at a time, with the child selecting the answer from a separate answer sheetfeaturing several alternative pictures. The test assessed three kinds of knowledge related tomathematics: (a) conceptual knowledge (relational concepts, such as last, middle, nearest,between, before, and furthest e.g., "Draw a line over the picture which is furthest from theboat."); (b) declarative knowledge (ordinal- and cardinal numbers e.g., "Draw a line over thesecond fish."); (c) procedural knowledge (addition, subtraction, division and multiplicationskills e.g., "You have four pears. You get an equal amount more. Draw a line over the numberof pears you now have"; "Eeva has five balls. Kirsti has twice as many balls as Eeva has.Draw a line over the number of balls Kirsti has."). The Initial Mathematical Skills scoreconsisted of the number of correct answers (maximum value of 24). The Cronbach alphareliability for this test has been shown to be .82 (Liikanen, 1994).

Initial reading skills. Initial reading skills were tested individually using the Beginner'sReading Test (Airo, Roman, & Tuononen, 1985), which consisted of two subcomponents. Thefirst subcomponent was letter naming where the experimenter showed 21 uppercase letters,one at a time and in random order, whilst the rest of the letters were covered. The child wasasked to the name the letters they were shown. The second subcomponent consisted of readinga list of 20 increasingly difficult words and two sentences (written in uppercase letters) whichwere shown one at a time. The child was asked to read them aloud whilst the rest of the wordswere covered. Individual assessments were finished after four consecutive incorrect responses.At the very beginning of school, 52% of these children correctly named all 21 letters{M-18.29, SD^AM), and 27% of children accurately read the word list (A/=9.39, SD=9.77).In the later analysis we used the sum of all correct answers (maximum value of 43).

Mathematical performance. Mathematical performance was assessed by theMathematical Skill Test (Aunola, Nurmi, Lerkkanen, & Rasku-Puttonen, 2003). The tasks

126 M.-K. LERKKANEN, H. RASKU-PUTTONEN, K. AUNOLA, & J.-E. NURMI

were modified from the Diagnostic Tests 3; Motivation, metacognition and mathematics(Salonen, Lepola, Vauras, Rauhanummi, Lehtinen, & Kinnunen, 1994). The structure of thetest was similar at all measurement points, however, the tasks included in the test becameprogressively more difficult as children become more mathematically skilled. The testconsisted of three subcomponents:

1) Conceptual knowledge and mathematical-logical reasoning. This subcomponentconsisted of four or five orally-described problems, which each assessed differentaspects of reasoning: transitive reasoning, number conservation, class inclusion, andlogical reasoning (e.g., "Here you can see a group of animals. There are 15 cats and 6dogs. Which one is more: cats or animals?"), In Year 1 the problems were read aloudto the participants twice. After each problem, the participants were asked to chooseand mark the right solution on a piece of paper. In Year 2 children read the tasks fromthe paper and were then asked to choose the right solution. Scoring was based on thenumber of correct answers (maximum value of 4 in Year 1 and 5 in Year 2).

2) Declarative knowledge. This subcomponent consisted of four tasks assessingchildren's knowledge of ordinal aspects of numbers forwards and backwards. At TimeI and 2 children were read aloud four questions (e.g., "What number is after numberfive?"; "What number do you get when you count five numbers backward fromnine?") and asked to write their answers down. For the rest of the measurements, thechildren's task was to complete four rows of printed numbers (e.g., "2, 4, 6, _, 10,12"; "18, 17, _, 15, 14, 13"). Scoring was based on the number of correct answers(maximum value of 4).

3) Procedural knowledge. This subcomponent included basic arithmetic skills andconsisted of a set of addition (e.g., "9+5=_"; "7+_=14") and subtraction (e.g.,"17-9="; "15-_=9") tasks on paper. Scoring was based on the number of correctanswers (maximum value of 12 at Time 1, and 16 at time 2 to 6).

Because of the degree of skew present for each of these individual subcomponents (i.e.,conceptual knowledge, declarative knowledge and procedural knowledge) sum-scores formathematical performance were employed rather than separate variables for eachsubcomponent (maximum scores: 20 at Time 1, 24 Et Time 2 to 4, and 25 at Time 5 and 6).The internal consistency for mathematical performance at the different measurement points,assessed with the Cronbach alpha coefficient, was .51, .61, .80, .75, .69 and .57, respectively.Split-half reliability (Unequal-length Speannan-Brov/n) for mathematical performance at thedifferent measurement points ranged from .68 to .76. The low internal consistency of the scaleat the some of the measurement points was due to the skewed distributions of the individualsubcomponents. The test-retest correlation for Mathematical Performance betweenmeasurements 1 and 2 was .57, between measurements 2 and 3, .76, between measurements 3and 4, .74, between measurements 4 and 5, .60, and between measurements 5 and 6, .73. Thetest scores were also shown to be highly correlated with teacher ratings of mathematical skills,on a scale of 1 (poor) to 10 (excellent) and at measurement points I to 4 (.59, .62, .64, and .61).

Reading comprehension. In the first year, the tasks for the Reading Comprehension Test(Lerkkanen et al., 2004) were adapted from teacher resources for first year literacy lessons andwere similar to those used eariier by Yuill and Oakliill (1991). Children had two tasks eachtime: a literal text comprehension task (requiring an understanding of exact words from thetext) and an inferential text comprehension task (requiring an ability to understand the fullliteral meaning of the text as well as to go beyond the level of direct sentence meaning). Forthe literal task the child read a text (27-55 words) and then completed a picture by colouringor drawing on the basis of the text. A sample test item at Time 1 was, for example, to colourthe hippo's clothes according to the text, (e.g., "Hippo's trousers has three patches. Thetrousers are blue and the patches are red. Hippo's jacket has two pockets. The jacket is greenand the pockets are blue. Hippo has a red bowtie around his neck..."). In the inferential task


the child read a story (45-51 words) and chose answers to the questions, Sample test itemswould be, for example, to decide who was who in a picture according to the text (e.g., "Alinahas a white blouse with green stripes. Furthest on the left is Susanna. She has a red blouse.Beside Alina is Olli...'").

In the second year, the standardized Finnish Reading Test for Primary School (Lindeman,1998) was used to test reading comprehension. The first version of the test was a fictionalstory (203 words Time 5) and the second one was a folktale (143 words Time 6). Both hadtwelve questions which required literal text comprehension (six questions e.g., "Rex is (a) aboy, (b) a man, (c) a dog, (d) a cat") and inferential text comprehension (six questions e.g.,"Rex needs his owner (a) to find his yellow nibber hedgehog, (b) to release Rex from Outi'scabin, (c) to find his decomposed bone, (d) to clean up the house"), with four alternativeanswers for each.

The structure of the Reading Comprehension Tests was similar at all measurement pointsbut the texts became longer across the measurement points as children became more skilled asreaders. The texts were available at the child's table and there was no time limit.

Sum-scores for the reading comprehension variable were based on the number of correctitems (maximum value of 22 at Time I, 30 at Time 2, 11 at Time 3. 19 at Time 4, 12 at Time5, 12 at Time 6). Intenial consistency assessed with the Cronbach alpha coefficient for readingcomprehension at the different measurement points was .94, .87, .82, .69, .78 and .66,respectively. The test-retest correlation for Reading Comprehension between measurements 1and 2 was .88, between measurements 2 and 3, .69, between measurements 3 and 4, .72,between measurements 4 and 5, .63, and between measurements 5 and 6, .65. The test scoreswere also shown to be highly correlated with teacher ratings of reading, on a scale of I (poor)to 10 (excellent) and at measurement points 1 to 4 (.87, .88, .76, and .66).

Analysis strategy

In order to investigate the prospective relationships between Mathematical Performanceand Reading Comprehension, simplex models were constructed and carried out using theMplus statistical package (Muthen & Muthen, 1999). Model construction proceeded in foursteps. First, simplex models were constructed separately for Mathematical Performance andReading Comprehension. Second, these models were combined and a model including cross-lagged paths between Mathematical Performance and Reading Comprehension was tested.Third, this complete model with cross-lagged paths was tested against an alternative modelwhich included only intercorrelated factors for each measurement point instead of cross-lagged paths. Fourth, initial skills in mathematics and reading were added to the model ascovariates. The parameters of the models were estimated using a missing data method with theMLR procedure. The missing data method uses all observations in the data set that areavailable to estimate the parameters of the model. The MLR estimator has maximumlikelihood estimates and non-normal robust standard errors (Muthen & Muthen, 2002). The fitof the models was estimated using various goodness-of-fit measures: chi-square iX'^df),Bentler's (1990) Comparative Fit Index {CFl), Root Mean Square Error of Approximation(RMSEA) and Standardized Root Mean Square Residual (SRMR).

Results

The Pearson's Product Moment correlations for the measured variables are presented inTable 1. The correlations clearly indicate a strong relation between the MathematicalPerfomiance and Reading Comprehension variables at every measurement point. Also, initialskills In mathematics and reading correlated with Mathematical Performance and ReadingComprehension during the first and the second years.

128 M.-K. LERKKANEN, H. RASKU-PUTTONEN, K. AUNOLA. & J.-E. NURMI

Table 1

The Pearson's product moment correlations between variables

Variables l. 2. 3. 4. 5. 6. 1 s. 9. 10, 11. 11 n. i4.

1. Initial mathematical skills (0) 1.002. Initial reading skill (0) 31^ 1,003. Mathematical performance (1) .Sl<^ .38"^ 1,004. Mathematical performance (2) .5'/ 37̂ ^ .57*̂ 1.005 . Mathematical per formance (3) .53= 33"^ .55*^ .76'^ 1,006. Mathematical performance (4) ,57^ ,2')'' .si*^ .65'= ,74'-" i.oo7. Mathematical performance (5) ,49= ,2a'' .46= ,S7>: .62^ .60= 1.008. Mathematical per formance (6) 43= .19» A(f .60<= .63'̂ .58̂ .73*̂ i.oo9. Reaclingcomprehension(t) 44= 79« .34= .vf .38'" Je-^ .3')'̂ .30*' 1.00

10. Reading comprehens ion (2) 50<̂ 77= .41= .46= .38'- .41'^ .39= .35= .88= 1.0011. Reading comprehens ion (3) 4g= .51= .42= .49= .37*̂ .37= .38= ,27^' ,58= ,69= 1,0012. Reading comprehension (4) ss'̂ 44= 42= .44= .40^ .38= .34= ,4i= .50= .62= ,72= i.oo13. Reading comprehens ion (5) 4S= ,43= ,34= .36= ,40= ,30'' .41= .37= .56= .64= .64= .63= 1.00

14. Reading comprehens ion (6) ,43= ,35= ,25^ .40= .24^ .22^ .36= .36= .39= .46= .49= .49= .65= 1.00

M 19.78 26,44 15,68 14.76 14.59 16.36 21.10 18J6 8.74 16.61 8.22 14.98 7.62 9.29

SD 3 93 1240 2 % 4,62 4.86 4,72 3,12 4,26 9,65 11.78 3.78 4.93 3.21 2.01

Note. O=Pre-measuremeiit, l^Measaremeiil I, 2=Measurement 2, 3=Measurement 3, 4=Measurement 4,5=Measurement 5. 6=Measuretnent 6; ^

Simplex model for mathematical performance

First, to test stability of mathematical performance and that of reading comprehension asimplex model was carried out separately for both variables. The results of these models arepresented in Table 2.

Table 2

Estimated simplex models for maths performance (Model I) and reading comprehension(Model 2), unstandardized solutions (standard errors in parentheses)

Maths performance Reading comprehension

Parameters Model I Model 2

^21 2.07(0.29) 1.07(0.05)^32 1.08(0.10) 0.21 (0.02)^43 0.8 i (0.07) 1.27(0.15)^54 0.56(0.08) 0.61 (0.08)5g5 1.37(0.15) 0.53(0.06)¥ , l 3.81(1.28) 91.12(4.31)^22 0" 31.45(8.05)* 2 2.01(1.78) 3.90(0.87)%A 1.03(1.24) 0.34(1.73)V55 2.11(0.56) 2.17(0.84)ifL 2.19(1.79) 0*e , ^ 4.97 (0.99) 0*^3 3.40(1.22) 3.66(0.88)$^ 7.08(1.78) 7.90(1.84)

2.66(0.70) 1.94(0.32)1.00 0.880.95 0.78

^rj'A 0.96 0.99R(n5) 0.84 0.86

0.93 LOO

Note. •=fixed;^21 to/?^5=unstandardized/3 values. * ipvariance of the latent variable at Time 1, ^22 ' ° '^66^''^^residuals of the latent variables from Time 2 to Time 6, 6 | to fl^=measurement error variances of the observedvariables, R{ri2) to R(f?6)=stability estimates of the latent variables.


In the model for mathematical performanee, the latent Mathematical Performanceconstructs each consisted of one indieator, i.e., the observed mathematical performancevariable at different time-points. Consequently, their loadings were set equal to I. In order toend up with an identifiable model, the measurement error variances of the observedmathematical performance variables at Time 1 and Time 2 were estimated as equal and,similarly, the measurement error variances of observed mathematical performance at Time 5and Time 6 were estimated as equal (standardized estimates for the error terms at differenttime points were .57, .23, .14, .33, .27, .15, respectively). Because the residual variance of thelatent Mathematical Performance construct at Time 2 was found to be negative (indicatingperfect stability for mathematical performance from Time 1 to Time 2), this parameter wasfurther fixed to 0. The fit of the final model was: ^^(7)=2.98,/P-0.89; CFl=\.OO; 77.7=1.03;RMSEA=Om\ SRMR=0.02.

The results (see Table 2) showed high stability for Mathematical Performance throughoutthe study period, Statistically significant residual variance, i.e., unexplained variance, forMathematical Performance was evident only at Time 5 (at the beginning of Year 2).

Simplex model for reading comprehension

Next, a simplex model for Reading Comprehension was constructed. Again, the latentReading Comprehension constructs each consisted of one indicator. In order to end up with anidentifiable model, the measurement error variances of the observed reading performancevariables at Time 1 and Time 2 were first estimated as equal and, similarly, the measurementerror variances of observed reading comprehension at Time 5 and Time 6 were estimated asequal. However, because the measurement error variances for observed readingcomprehension variables at Time 1 and Time 2 were found to be negative, these parameterswere further fixed equal to zero (standardized estimates for the error terms at different timepoints were 0 (fixed), 0 (fixed), .27, .33, .19, .45, respectively). Moreover, because theresidual variance of the latent Reading Comprehension construct at Time 6 was found to benegative (indicating perfect stability for reading comprehension from Time 5 to Time 6), thisparameter was further fixed to 0. The fit of the final model was: /-(8)=4.06, p~0.S5;CF/=I.OO; 77,/=1.02; RMSEA=O.OO; SRMR=Om. The results are presented in Table 2.

The results (see Table 2) showed high stability for Reading Comprehension throughoutthe study period. However, there was statistically significant residual variance, i.e.,unexplained variance, for Reading Comprehension at Time 2, Time 3 and at Time 5.

Cross-lagged relationships between mathematical performance and reading performance

Next, to examine the research questions, the previous models were combined and cross-lagged paths between the constructs were investigated. Besides of stability coefficients forlatent Mathematical Performance and Reading Comprehension, the model included cross-lagged paths from previous Mathematical Performance (t-\) to subsequent ReadingComprehension (0 and from previous Reading Comprehension ( M ) to subsequentMathematical Performance (?)• Because after taking into account the stabilities there was noresidual variance in the latent Mathematical Perfoniiance at Time 2, the cross-lagged pathfrom Reading Comprehension at Time 1 to Mathematical Performance at Time 2 was fixed tozero. Similarly, because there was no residual variance in the latent Reading Comprehensionat Time 6, the cross-lagged path from Mathematical Performance at Time 5 to the ReadingComprehension at Time 6 was fixed to zero. All other cross-lagged paths were estimated. Theassociations between the residual variances of the two constructs were also allowed at Time 1,Time 3, Time 4, and Time 5. The fit of the model was good: ;}'-'(39)=45.99, p=0.21; Cf/=0.99;TLI=OM\ RMSEA=Q.04\ SRMR=Q.Q3. After excluding non-significant paths, the fit of themodel was:/-^(45)=46.94,/7=0.39; CF/=1.00; 7-L/=1.00; RMSEA^0.02\ SRMR^OM.

The results yielded two statistically significant cross-lagged paths between MathematicalPerformance and Reading Comprehension. First, Mathematical Performance at Time 1

t30 M.-K. LERKKANEN, H. RASKU-PUTTONEN, K. AIJNOLA, & J.-E. NURMI

predicted Reading Comprehension at Time 2: the higher the level of mathematical skillschildren showed in October, the higher the level of reading eomprehension they exhibited inDecember. Second, Mathematical Performance at Time 2 predicted Reading Comprehensionat Time 3: the higher the level of mathematical skills children showed in the beginning ofDecember, the higher the level of reading comprehension they demonstrated in the end ofJanuary. In Year 2, Mathematical Performance did not predict Reading Comprehension.However, Reading Comprehension also did not show a unique impact upon MathematicalPerformance.

Next, we investigated whether an alternative and more simple model, which includedonly correlations between the residuals of Reading Comprehension and MathematicalPerformance constructs at Time 1, Time 3, Time 4, and Time 5, would explain the correlationalpattern between the variables | / - ' (47)^65.8! , /J=0.04] as well as the more complex modeldescribed above. To examine this, the significance of the difference between^-' values of thetwo alternative models was tested. The results showed that the model including cross-laggedpaths was significantly superior to the model without the cross-lagged paths [the differencebetween ^-(2)= 18.87, p< 0.00! ].

Finally, prerequisite skill.s were added to the previous model with cross-lagged paths ascovariates. After adding paths from initial skills in reading and maths to MathematicalPerformance and Reading Comprehension at the first measurement point, the fit of the modelwas:/-'(67)=8t.86,/?=0.10; CF/=.98; 71/-.98; RMSEA=^.Q^; SRMR=0.04. The results of thisfinal model are presented in Figure 2.

TimeO

August

. . . "

Time 1

Oclober

1 RMduig \

/ ^ CDinireliein™i 1

Time 2

December

• " /^ " ^ .SB*"

~ H Coinirtheiiiloii 1 *

\ R'-.9O /

Time 3

January

\T 7

Time 4

March

/ Riading \

—fci L

^ n Coiujtebenuoo 1

\ R'- 1.00 /

Time 5

December

\ R'-,7S /

Time 6

March

' Rnduig

V R"- 1.00

The firsi school week Year 1 Year I Year I Yearl Year 2 Year 2

Figure 2. Significant path coefficients between Initial Mathematical Skills, Initial ReadingSkills, Mathematical Performance and Reading Comprehension during the first andthe second school years.Note. Tlie model included also correlalions between ilie residuals oT Reading Compreliension and

Malliemalical Perlbmiance at time points 1, 3, 4 and 5. Only statistically signiHcant correlationsbetween the residuals are sliown in ihc Figure.

The results showed (see Figure 2) that the initial level of Mathematical Skills predictedMathematical Performance at Time 1: the higher the level of mathematical skill children


displayed in August, the higher the level of mathematical performance they were able to reachby October. Similarly, Initial Reading Skills predicted Reading Comprehension at Time 1: thehigher the level of reading skill children displayed in August, the higher the level of readingcomprehension they were able to reach by October. Interestingly, Initial Mathematical Skillsalso predicted Reading Comprehension at Time 1: the higher the level of mathematical skillsupon school entrance, the higher the level of reading comprehension children were able toachieve by October. In addition, Initial Reading Skills also predicted MathematicalPerformance at Time 1.

Adding these covariates to the model did not change any of the cross-lagged associationsbetween Mathematical Performance and Reading Comprehension. This result suggested thatthe results concerning cross-lagged impacts between the two skills remain same aftercontrolling for the skill level before entrance into school. In other words, the impact ofmathematical performance upon reading comprehension was not due to the initial levels ofmathematical skills and reading skills.

Because it is possible that the relations between mathematical performance and readingcomprehension were due to the overall ability or nonverbal comprehension, all the modelswere also re-rim controlling for general concept ability and visual-motor skills. However,cross-lagged paths between Reading Comprehension and Mathematical Performance, as wellas the effects of anteceding variables, remained the same in these models compared to originalcross-lagged models.

Discussion

There are a substantial number of cross-sectional studies showing that mathematicalperformance and reading skills are associated (Geary, 1993; Hecht et al., 2001; Jordan,Kaplan, & Hanich, 2002; Jordan, Hanich, & Kaplan, 2003; Muth, 1984; Share et al., 1988;Sovik et al., 1999), The present cross-lagged longitudinal study examined prospectiverelationships between mathematical performance and reading comprehension during the firstand second years of primary school As stated in our first hypothesis, the results showed thatmathematical performance predicted subsequent development of reading comprehension,whereas no evidence was found for the reverse pattern. This result was true even aftercontrolling for general concept ability and nonverbal skills. Importantly, however, the resultthat mathematics predicted reading comprehension was true only in Year 1.

These findings are in accordance with some of the existing literature. For example,Tymms (1999) found that number recognition contributed to literacy even more than letteridentification did. Ball (2003) suggested that number literacy and word literacy are closelyassociated, partly because number reading for children may be an initial and easy introductionto the relationship between print and language. This may also explain why in the present studymathematical skills predicted reading comprehension.

One further explanation for the results of the present study is that the performance on themathematical skill tests was significantly influenced by language comprehension and theability to follow verbal instructions. Most mathematical knowledge requires specificmathematical vocabulary and knowledge of certain mathematical concepts. Moreover, themaths tests here were introduced orally to the children in Year I. Consequently, the taskrequired both mathematical knowledge and listening comprehension. Previous studies haveshown that listening comprehension skills predict reading comprehension in the primaryschool years (Juel, 1994; Stothard & Hulme, 1996; Vellutino & Scanlon, 1991). For example,de Jong and van der Leij (2002) found that listening comprehension affected readingcomprehension from the first through to the third year of school.

Previous studies have showed that there are common cognitive skills behind mathematicsand reading (Bull & Johnston, 1997; Hecht et al., 2001; Kail & Hall, 1999; Muth, 1984;Swanson et al., 1993). For example, Jordan et al. (2002) showed that the same linguistic


abilities are needed in mathematics and reading. The results of the present study also showedthat maths and reading comprehension were associated at every measurement point. Theseresults are in accordance with earlier studies suggesting a strong relationship betweenmathetnatics and reading comprehension (Hecht et al., 2001; Muth, 1984; Sovik et al., 1999;Swanson etal,, 1993).

The results of the present study were also contradictory with some previous researchfindings. It has been shown, for example, that reading comprehension predicts mathematicalperformance (Hecht et al., 2001; Kail & Hall, 1999; Muth, 1984; Sovik et al., 1999; Swansonet al,, 1993). Jordan, Kaplan, and Hanich (2002) showed that reading skills predictedmathematically-disabled children's development in mathematical performance butmathematical skills did not contribute to reading performance. However, this was not true inthe present study.

Finally, the results of the present study showed that individual differences in bothmathematical performance and reading comprehension were very stable across the first andthe second school years. Those who already have good skills in mathematics upon schoolentry continue to demonstrate good skills later on. This result is in accordance with the studyof Davies and Brember (1999) who showed likewise that individual differences inmathematical performance were stable during the primary school years. An additionalobservation made in the present study was that those children who had good reading skills atthe beginning of Year 1 performed well on reading comprehension tasks during the first andsecond school year. This is in accordance with the de Jong and van der Leij (2002) studywhich found that individual differences in the development of reading comprehension arestable from the first until the third school year. Because the high stability of both mathematicalperformance and reading comprehension skills there was not much to left to be explained withother variables.

This study has some limitations that should be taken into consideration when making anygeneralizations. First, the results may be infiuenced by the fact that the study was carried outin the context of the highly transparent Finnish language. The regularity of the Finnishlanguage supports children's rapid learning of basic word reading and allows children to focuson reading comprehension earlier than in most languages (Lerkkanen et al,, 2004; Seymour,Aro, & Erskine, 2003), When Finnish-speaking children learn the idea of letter-soundcorrespondence they rapidly become fluent readers. Therefore, Year 1 word reading skill inFinnish is more of a dichotomous 'oii-off skill, not at all resembling a normal distribution.For this reason, the results may have turned out differently in orthographically more opaquelanguages, such as English, where mastery of adequate word reading skills usually takeslonger to develop (Seymour et al., 2003),

Second, sum-scores of mathematical performance consisting of three differentsubcomponents, i,e., conceptual, declarative and procedural knowledge, were used in thepresent study. This was done because we were interested in examining overall mathematicalperformance rather than its subcomponents. However, because a ceiling effect was present forconceptual knowledge, the differences in the sum-scores would have mainly been driven byprocedural and declarative knowledge.

Third, partly because we examined rapidly developing skills, we were not able to use fullmeasurement models for math and reading performance. Moreover, the reliabilities of some ofour measurements were somewhat low. This may have influenced our results. Consequently,there is an evident need to replicate the findings of the present study in future research.

Finally, although mathematical skills were found to predict reading comprehension, theremay be other cognitive abilities which also influence both maths and reading performance. Infuture research, there is an evident need for more specific measures of nonverbal reasoning(e,g.. Raven Matrices or Block Design) in order to more effectively control for variation in IQ.

In conclusion, the findings of the present study indicate that mathematical performancecontributes subsequent development of reading comprehension but only during Year I,However, no evidence was found for a revised pattern.


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Le hut de cette ctiule a long ternie etait de rechercher les relationsentre la performance mathematique et la comprehension ecrite pendantla premiere et la seconde annee de I'ecole pritnaire. La performancemathematique et la comprehension ecrite de ! 14 enfants parlant leftnnois comme langue maternelle ont ete etudiees six fois pendant lesdeux premieres annees a I'ecole. Les connaissances tnathetttatiquesitiueraires et la competence ecrite, I'habilete generate deconceptualisation et les competences visuelles et motrices ont etesetudies^ au debut de la premiere annee scolaire. Les resultats ontmontre que premietement les mathematiques et la comprehensionecrite s'associaient pendant les deux premieres annees scolaires.Deuxiemement, la performance mathematique predit la comprehensionecrite utterieure pendant la premiere annee scolaire phitot que viceversa. Les resultats suggerent qu'il est important d'accorder deI'interet dans une plus grande mesure au role des connaissancesmathematiques qtiandles enfants commencent I'ecole.

Key words: Ar i thmet ic ski l ls , Mall iematical knowledge , Mathemat ica l ski l ls , Readingcomprehension.

Received: September 2003

Revision received: October 2004


Marja-Kristiina Lerkkanen. University of JyvSskylS, Department of Teacher Education, P.O. Box 35,FIN-40014, Jyvaskyia, Finland; Tel.; +358142601785, Fax; +358142601701; E-mail:[email protected], Web site: www.jyu.fi

Current theme of research:

Developmental processes of reading, writing and mathematics at early school years.

Most relevant publications in the field of Psychology of Education:

Aunola, K., Leskitien, E., Lerkkatien, M.-K., & Nurmi, J.-E. (2004). Developmental dynamics of math performance

from preschool to grade 2. Journal of Educational Psychology. 9(5(4), 699-713.

Lerkkanen, M.-K., Rasku-Puttonen, H., Aunola, K., & Nurmi, J.-E;. (2004). Predicting reading performance dtiritig thefirst and the second year of primary school. British Educational Research Journal. 30(1), 61-92.

Lerkkanen, M.-K., Rasku-Puttonen, H,. Aunola, K., & Nurmi, J.-E. (2004). Developmental dynamics of phonemicawareness and reading performance during ihe first year of primary school. Journal of Early Childhood Research.2(2), 139-156.

Lerkkanen, M.-K., Rasku-Puttonen, H., Aunola, K., & Nurmi, J.-E. (2004). Reading performance and its developmentaltrajectories during the first and ihe seeond grade. Learning and Instruction. 14(2). 111-130.

Lerkkanen, M.-K., Rasku-Puttonen, H., Aunola, K., & Nurmi, J.-E. (2004). The developmenlal dynamics of literacyskills during the first grade. Educational Psychology. 24(6), 793-810.

Helena Rasku-Puttonen. University of JyvSskyia, Department of Teacher Education, P.O. Box 35,FIN-40014, Jyvaskyla, Finland; Email; [email protected]. Web site; www.jyu.fi


Learning communities and teacher-student interaction, learning processes and teacher's insltuclional scafTolding.

Most relevant pubiications in the field of Psychology of Education:

Arvaja, M., Rasku-Putlonen, H., Hakkinen, P., & Eteiapelto, A. (2003). Constructing knowledge through a role-play in aweb-based \earn\n^ environment Journal of Educational Computing Research. 28(4), 319-341.

Lerkkanen, M.-K., Rasku-Puttonen, H., Aunola, K., & Nurmi, J.-E. (2004). Reading performance and its developmentaltrajectories during the first and the second grade. Learning and Instruction. 14(2), 111-130.

Lerkkanen. M.-K., Rasku-Puttonen. M., Aunola, K., & Nurmi, J.-E. (2004). The developmental dynamics of literacyskills during the first grade. Educational Psychology. 24(6), 793-810.

Rasku-Puttonen, H., ElelSpelto, A., Arvaja, M., & Hakkinen, P. (2003). Is successful scafTolding an illusion? - Shiftingpatterns of responsibility and control in teacher-student interaction during a long-term learning project.Instructional Science. 31, 377-393.

Rasku-Puttonen, H., Eteiapelto, A., Lehtonen, 0., Nummila, L., & Hakkinen, P. (2004). Developing teachers' professionalexpertise through collaboration in an innovative lCT-based learning environment. European Journal of TeacherEducation. 27(1), 41-60.

Kaisa Aunota. University of Jyvaskyla, Depatiment of Psychology, P.O. Box 35, FIN-40014, JyvSskyia,Finland; E-mail: [email protected]. Web site: www,jyu.fi/psychology


Children's and adolescents' underachievement and related developmental processes at school and in family environment.

Most relevant publications in the field of Psychology of Education:

Aunola, K., & Nurmi, J.-E. (2004). Maternal affection moderates the impact of psychological conirol on a child'smathematical performance. Developmental Psychology. 40, 96.5-978.


Aunola. K,. Stallin. l[.. & Nurmi. J.-E. (2000), Parenting styles and adolescents' achievement strategies. Journal ofAdolescence, 2i, 205-222.

Aunola, K,. Leskinen, E.. Lerkkanen, M.-K., & Nurmi, J.-E. (2004). Developmental dynamics of math performancefrom preschool to grade 2. Journal of Educational Psychology. 96. 699-713.

Aunola. K., Leskinen. E., Onatsu-Arvilommi. T., & Nurmi, J.-E. (2002). Three methods for studying developmentalchange: A case of reading skills and self-concept. British Journal of Educational Psychology'. 72,343-364.

Aunola. K., Nurmi, J.-E.. Niemi, P., Lerkkanen, M.-K., & Rasku-Puttonen, H. (2002). Developmental dynamics ofachievement strategies, reading performance, and parental beliefs. Reading Research Quarterly, 370), 310-327.

Jari-Erik Nurmi. University of Jyvaskyla, Department of Psychology, P.O. Box 35, FIN-40014,Jyvaskyla, Finland; E-mail: [email protected], Web site: www.jyii.fi.


Educational planning, learning nioiivaiion, life-span development, socialization.

Most relevant puhlicalions in thefteld of Psychology of Education:

Leppanen. U.. Niemi , P., Aunola, K,, Nurmi , J.-E. (2004), Development of reading skills among preschool and primary

school pupils. Reading Research Quarterly. 39. 72-93.

Nurmi , J.-H,, & Aunola , K, (in press). Task-motivat ion during Ihe first school year: A person-oriented approach to

longitudinal data. Learning and Instruction.

Numii, J.-E,, Aunola, K.. Salmela-Aro, K., & Lindroos, M. (2002). The role orsuccess expectation and lask-avoidantein academic achievement and satisfaction: Three studies on antecedents, consequences and correlates.Contemporuiy Educational Psychology, 28, 59-90.

Onatsu-Arvolommi, T., Nurnii, J.-E., & Aunola, K. (2002). The development of achievement strategies and academicskills during ihe first year of primary school. Learning and Instruction. 12, SO'i-ill.

Rytkftnen. K.M., Aunola, K., & Nurmi, J.-E. (in press). Parents' causal attributions concerning their children's schoolachievement: A longitudinal study. Merrill-Palmer Quarterly.

Mathematical performance predicts progress in reading comprehension among 7-year olds

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