effects of background and school factors on the mathematics achievement

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Effects of Background and SchoolFactors on the MathematicsAchievementConstantinos PapanastasiouPublished online: 09 Aug 2010.

To cite this article: Constantinos Papanastasiou (2002) Effects of Background and SchoolFactors on the Mathematics Achievement, Educational Research and Evaluation: AnInternational Journal on Theory and Practice, 8:1, 55-70

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Educational Research and Evaluation 1380-3611/02/0801±055$16.002002, Vol. 8, No. 1, pp. 55±70 # Swets & Zeitlinger

Effects of Background and School Factors onthe Mathematics Achievement

Constantinos PapanastasiouUniversity of Cyprus, Nicosia, Cyprus

ABSTRACT

Using a structural equation model, this research study investigated the mathematics achieve-ment of 8th grade students in Cyprus enrolled in the year 1994±1995. The model contained 2exogenous constructs ± the educational background of the family and the reinforcement frommother, friends and the individual himself; and 5 endogenous constructs ± socioeconomicstatus (SES), and student attitudes toward mathematics, teaching, school climate, and beliefsrelated to success in mathematics. The study demonstrated that although attitudes, teaching,and beliefs had direct effect on mathematics outcomes, they were not statistically signi®cant. Itwas also found that family educational background directly affected SES, attitudes towardmathematics, school climate and beliefs related to success in mathematics. Reinforcementexerted a direct effect on attitudes, teaching and beliefs regarding success. There was alsoevidence that SES directly affects school climate and that teaching directly affects attitudestoward mathematics.

INTRODUCTION

The realization that mathematical skills are vitally important to economicprogress, especially now in the 21st century, has prompted many nations toinvestigate the validity of their educational curricula in mathematics (Beatonet al., 1996). Moreover, there is widespread interest and concern to determinemore speci®cally what measures can be taken to improve students' abilitiesand attitudes towards mathematics.

The Third International Mathematics and Science Study (TIMSS),sponsored by the International Association for the Evaluation of EducationalAchievement (IEA), had as its stated aim the measurement of student

Address correspondence to: Dr Constantinos Papanastasiou, University of Cyprus, P.O. Box20537, 1678 Nicosia, Cyprus. E-mail: [email protected]

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achievement in mathematics and science and the assessment of certain factorsin¯uencing student learning in these subjects (Schmidt, McKnight, Valverde,Houang, & Wiley, 1997). TIMSS focused on three populations: population1 included students of the two adjacent grade levels comprising the most 9-year-olds; population 2 comprised students of two adjacent grade levels withthe most 13-year-olds; population 3 included students in their ®nal year ofsecondary school (Robitaille & Garden, 1996). The information collected andanalyzed was based on over half a million students of ®ve grades, in more than15,000 schools and in more than 40 countries around the world (Mullis et al.,1997).

Since its accession to IEA membership, Cyprus has been a regular partic-ipant in IEA research projects in an effort to compare the standards of Cypriotpupils with those of their counterparts in other countries. One of the projects inwhich Cyprus participated was TIMSS, the results of which indicated thatamong the participating countries Cyprus occupies one of the lowest positionsin both mathematics and science. Cypriot society was unwilling to acceptthis result because until recently the prevailing opinion ± an impressionnever supported by research ± was that the Cypriot educational system wasvery good. The various discussions ± in the House of Representatives, ontelevision, radio and in the press following in the wake of the publication ofthe results were indicative of the great shock suffered by both the Ministry ofEducation and public opinion. The question now is: What are the factorscontributing to the low scores achieved by the pupils of Cyprus? If thesefactors could be identi®ed and juxtaposed against relevant factors of otherparticipating countries that have achieved high scores, we would be able to saythat we have made a good start toward taking measures that would bene®t low-scoring countries.

This study will examine predictors of mathematics outcomes, focusing onthose related to school, family and student. The goal of the present study is toadvance a conceptual model based on the previous concepts, and to test thismodel empirically using of data collected as part of the TIMSS project.

DATA SOURCE

In this article we focus on the higher grade of population 2, de®ned as allstudents enrolled in the two adjacent grades containing the largest proportionof 13-year-old students (Martin & Kelly, 1996). Because home, school and

56 CONSTANTINOS PAPANASTASIOU

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national contexts within which education takes place can play important rolesin how students learn mathematics, TIMSS collected extensive information onsuch background variables. The participating students completed question-naires on home and school experiences related to learning mathematics, andschool administrators and teachers answered questionnaires regarding instruc-tional practices (Beaton et al., 1996). This study examined data from thestudent questionnaire and student tests in mathematics.

One objective of the TIMSS project was to ascertain the varying impor-tance of attitudes toward mathematics, the home environment, instructionalcontexts and practices in relation to mathematics achievement. In Cyprus, thedata were collected in 1995. All 55 gymnasia (the secondary junior schools)participated in this project, each school selecting four classes: two from theupper grade and two from the lower grade. Altogether, 5,852 studentsparticipated in the study (about 31% of the entire population).

The subset of students used in this research project was obtained as follows.Of the 5,852 students in the population 2 sample from Cyprus, only 8th gradestudents were selected, and from among those students, only those who hadcompleted the entire students' questionnaire and participated in the mathema-tics test were eligible. Next a subset of variables was chosen from the studentsurvey, so that any missing data or multiple responses led to listwise deletionof the subjects from the data set. This led to a ®nal sample of N� 1026.

Student IndicatorsThe student indicators included in the model were determined on the basis offactor analysis. The 35 questions used in this study were grouped into separatecategories, and are related to the following:

1. teaching ± initiated activities in the mathematics class especially thoseoccurring at the beginning of a new topic;

2. school ± the general climate of the school;3. student views and attitudes on mathematics, and mother's and friends'

opinion on the importance of mathematics;4. the SES and educational background of the family.

Based on the above grouping and running separate factor analysis, 12 factorswere extracted. The observed variables `̀ Work on projects,'' `̀ Problems relatedto everyday life things,'' `̀ Teacher checks homework,'' `̀ Discuss completedhomework'' are assumed to be indicators of the factor a1. The observedvariables `̀ Discuss practical problems,'' `̀ Teacher asks what student knows''

EFFECTS OF BACKGROUND AND SCHOOL FACTORS 57

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are assumed to be indicators of the factor b1, and so on. Both factors a1 and b1are related to teaching and consequently all 6 variables are assumed to beindicators of the latent variable `̀ Teaching.'' Also, the factors h1, i1 are relatedto reinforcement, and the variables `̀ Mother thinks it is important to be placedwith high achieving students,'' `̀ Friends think it is important to be placedwith high achieving students,'' and `̀ I think it is important to be placed withhigh achieving students'' belonging to these two factors are assumed to beindicators of the corresponding latent variable reinforcement. The observedvariables `̀ Highest education-mother,'' `̀ Highest education level-father,''`̀ Number of books in student home,'' `̀ Home possess-calculator,'' `̀ homepossess-dictionary,'' and `̀ Home possess-video'' are assumed to be indicatorsof family. The two factors related to family are: `̀ educational background''and `̀ SES''. The observed variables related to the factors `̀ attitudes,''`̀ beliefs,'' and `̀ climate'' are presented in Table 1.

The measures used to de®ne the conceptual areas are now brie¯y described.SES measures included: items that students have at home, such as calculators,dictionary, and video recorder (1� yes, 2� no). Educational background ofthe family measures included the highest level of parents' education(1� primary, 2� some secondary, 3� secondary, 4� vocational / technicalafter secondary, 5� some university and 6� university), and size of the homelibrary excluding student textbooks (1� 1±10 books, 2� 11±25 books,3� 26±100 books, 4� 101±200 books and 5�more than 200). Attitudesmeasures included questions to determine whether students like mathematics(1� dislike a lot, 2� dislike, 3� like, 4� like a lot) and if they enjoymathematics, do not ®nd it boring and think it is an easy subject (1� stronglyagree, 2� agree, 3� disagree, 4� strongly disagree). Beliefs regardingsuccess in mathematics included questions on the need for natural ability /talent, hard work studying at home and memorization of textbooks and notes(1� strongly agree, 2� agree, 3� disagree, 4� strongly disagree). Reinfor-cement measures included questions related to whether mother, friends andthe student himself think placement in a class with high achieving students isimportant (1� strongly agree, 2� agree, 3� disagree, 4� strongly disagree).Teaching measures included questions on activities related to the mathematicslesson; that is, do they work on mathematics projects, do they use things fromeveryday life in solving mathematics problems, does the teacher check anddiscuss homework, do they begin the lesson discussing a practical problem,and does the teacher ask questions related to the new topic (1� almost always,2� pretty often, 3� once in a while, 4� never). And ®nally climate measures


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included questions related to the school environment, that is, did they thinkthat another student might hurt them, if some of their friends skipped a class, ifsomething was stolen from school and if friends were hurt by other students(1� almost always, 2� fairly often, 3� once in a while, 4� never).

Table 1. Factors, Items, Item Means, SD, and Factor Loadings.

Factors Items Loading X SD

a1, b1 a11- Work on projects .57 3.03 1.44Teaching a12- Problems related to everyday life things .57 2.65 1.47

a13- Teacher checks homework .60 2.16 1.55a14- Discuss completed homework .63 2.16 1.49b11- Discuss practical problems .52 2.41 1.49b13- Teacher asks what student knows .53 2.41 1.55

c2 c22- Student thought might get hurt .63 1.83 1.46Climate c23- Friends skipped a class .61 2.65 1.56

c24- Friend had something stolen .75 2.02 1.44c25- Friend thought might get hurt .65 2.39 1.40

e1, e2, e3 e11- Highest education-mother .87 4.76 3.46Family e12- Highest education level-father .87 5.11 3.41(edbackgr- e13- Number of books in student home .55 3.49 1.50ses) e21- Home possess-calculator .69 1.12 0.80

e23- home possess-dictionary .69 1.11 0.79e31- Home possess-video .75 1.17 0.83

h1, i1 h12-Mother thinks it is important to beReinforce- placed with high achieving students .76 2.45 1.87ment h14- Friends think it is important to be

placed with high achieving students .79 2.51 1.59i12- I think it is important to be placed

with high achieving students .82 2.38 1.69

b1, j1, j2 j11- To do well in mathematicsBeliefs you need natural talent .86 2.67 1.64

j21- To do well in mathematicsyou need hard work .86 1.60 1.31

j22- To do well in mathematics youneed to memorize notes .77 2.36 1.72

b14- To look at textbooks .63 2.85 1.52

k1 k11- I like mathematics .86 3.02 1.33Attitudes k12- I enjoy learning mathematics ÿ.83 2.07 1.48

k13- Mathematics is not boring .72 3.13 1.55k14- Mathematics is an easy subject ÿ.69 2.91 1.64


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Throughout the process of building the model, certain variables which hadbeen assumed as valid, proved not to ®t. These were thus excluded fromfurther analysis so that of the 35 observed variables, only 27 remained in themodel. Table 1 presents the factors, the items that were used in this study, thefactor loadings, the means and standard deviations. Eight variables wereexcluded from the hypothetical model.

The covariance matrix based on the 27 items and on the three mathematicsoutcomes that were used in the model is presented in the Table 2.

MODEL

Most educational models emphasize basically two kinds of variables:environmental and learner-related (Leder, 1992). Environmental variablesare those related to teachers, parents, peer groups and society in general.Learner-related variables comprise con®dence, attribution of success andpersistence (Vanayan, White, Yuen, & Teper, 1997). Some researchers em-phasize the role of ability-related self-perceptions in motivating achieve-ment behavior, while others attribute equal importance to subjectivetask values ± such as interest in mathematics and belief in the importanceof doing well ± in predicting behavior (Eccless, Wig®eld, Harold, &Blumenfeld, 1993).

Analysis of the TIMSS data used in this study, revealed statistical differences inachievement between students receiving high versus low reinforcement, andbetween students whose parents have high versus low educational background.Thus these two factors were selected as the two exogenous constructs (forindependent variables) of the proposed, which assumed that mathematics out-comes of the students were initially affected by the characteristics of the twofactors. The two factors are included in the model as partial explanation ofstudents' mathematics achievements, and represent variables brought into theschool learning environment, which in¯uence attitudes, beliefs, teaching andschool climate.

Many studies have examined students' attitudes and beliefs toward mathe-matics (Vanayan et al., 1997). As used in this study, an attitude is a mentalconcept that depicts favorable or unfavorable feelings toward an object(Koballa, 1988). Thus, statements such as `̀ I like mathematics'' or `̀ I enjoymathematics,'' are de®ned as attitudes. Beliefs represent information about anobject that is known or perceived by the individual (Fishbein & Ajzen, 1975),


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Table 2. Covariance Matrix of the Variables in the Model.

A11 A12 A13 A14 B11 B13 B14 C22 C23 C24 C25 E11 E12

A11 1.000A12 0.201 1.000A13 0.234 0.276 1.000A14 0.306 0.199 0.319 1.000B11 0.281 0.424 0.340 0.287 1.000B13 ÿ0.314 0.198 0.303 0.233 0.298 1.000B14 0.162 0.101 0.002 0.041 0.022 0.216 1.000C22 0.015 ÿ0.049 0.039 0.100 0.025 ÿ0.007 ÿ0.017 1.000C23 0.017 0.050 0.121 0.082 0.069 ÿ0.032 ÿ0.059 0.279 1.000C24 0.074 0.094 0.166 0.095 ÿ0.111 0.017 ÿ0.034 0.284 0.384 1.000C25 0.042 0.061 0.147 0.106 0.079 0.005 ÿ0.064 0.348 0.405 0.410 1.000E11 0.185 0.077 0.019 0.088 0.135 0.194 0.093 0.024 0.025 0.053 0.033 1.000E12 0.150 0.018 0.004 0.034 0.060 0.137 0.077 0.024 0.020 ÿ0.009 0.027 0.817 1.000E13 0.113 ÿ0.025 ÿ0.081 ÿ0.048 0.002 0.054 0.098 0.030 0.005 0.068 0.037 0.401 0.395E21 ÿ0.230 0.069 ÿ0.201 0.022 0.062 ÿ0.062 ÿ0.114 0.130 0.159 ÿ0.054 0.101 ÿ0.208 ÿ0.228E23 0.102 ÿ0.205 ÿ0.033 ÿ0.092 0.110 0.021 0.203 0.225 0.091 0.070 0.101 ÿ0.208 ÿ0.227E31 ÿ0.014 0.018 ÿ0.022 0.089 0.051 0.031 0.076 0.045 ÿ0.066 ÿ0.075 ÿ0.096 0.012 ÿ0.084H12 0.199 0.035 0.100 0.093 0.089 0.144 0.068 0.032 0.071 0.020 0.011 0.058 0.063H14 0.220 0.051 0.114 0.133 0.071 0.188 0.125 0.019 0.082 0.039 0.014 0.093 0.080I12 0.212 0.121 0.124 0.164 0.115 0.192 0.077 0.042 0.075 0.041 0.007 0.038 0.033J11 0.075 0.057 0.033 0.074 0.097 0.037 0.105 ÿ0.073 0.014 ÿ0.012 ÿ0.026 0.052 0.070J21 0.135 0.053 0.145 0.105 0.066 0.143 0.120 0.086 0.025 0.032 0.044 0.077 0.039J22 0.247 0.069 0.030 0.113 0.104 0.191 0.211 0.019 ÿ0.022 0.004 0.033 0.166 0.169K11 ÿ0.071 ÿ0.130 ÿ0.204 ÿ0.174 ÿ0.134 ÿ0.154 0.066 ÿ0.058 ÿ0.182 ÿ0.097 ÿ0.112 0.061 0.055K12 ÿ0.092 0.161 0.191 0.216 0.185 0.124 ÿ0.025 0.065 0.166 0.037 0.084 ÿ0.064 ÿ0.081K13 ÿ0.099 ÿ0.131 ÿ0.184 ÿ0.144 ÿ0.144 ÿ0.118 0.086 ÿ0.006 ÿ0.148 ÿ0.079 ÿ0.144 0.055 0.042K14 0.099 0.085 0.104 0.121 0.136 0.065 0.005 0.030 0.130 0.000 0.024 ÿ0.086 ÿ0.088MATH 0.218 ÿ0.009 ÿ0.021 ÿ0.013 ÿ0.001 0.110 0.190 0.024 ÿ0.063 0.021 ÿ0.012 0.298 0.301MS 0.246 ÿ0.020 ÿ0.047 ÿ0.017 ÿ0.007 0.117 0.203 0.017 ÿ0.087 ÿ0.004 ÿ0.017 0.318 0.314MR 0.249 ÿ0.020 ÿ0.047 ÿ0.021 ÿ0.007 0.117 0.204 0.023 ÿ0.080 0.009 ÿ0.011 0.322 0.315

EF

FE

CT

SO

FB

AC

KG

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ND

SC

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Table 2. (continued)

E13 E21 E23 E31 H12 H14 I12 J11 J21 J22 K11 K12 K13 K14 MATH MS MR

E13 1.000

E21 ÿ.467 1.000

E23 ÿ.562 .597 1.000

E31 ÿ.092 .118 .217 1.000

H12 ÿ.074 .075 .080 .060 1.000

H14 ÿ.034 ÿ.067 ÿ.105 .030 .701 1.000

I12 ÿ.048 .070 .035 ÿ.039 .804 .790 1.000

J11 .063 ÿ.106 ÿ.065 ÿ.004 .150 .140 .188 1.000

J21 .016 .118 ÿ.020 ÿ.017 .224 .330 .282 .021 1.000

J22 .171 ÿ.052 ÿ.057 .063 .144 .215 .171 .134 .348 1.000

K11 .080 ÿ.134 ÿ.054 .076 ÿ.156 ÿ.187 .232 ÿ.028 .043 .034 1.000

K12 ÿ.090 .304 .007 .034 .197 .260 .275 .066 .071 .034 ÿ.805 1.000

K13 .043 .022 .078 ÿ.011 ÿ.103 ÿ.182 ÿ.175 .014 ÿ.036 .044 .670 ÿ.591 1.000

K14 ÿ.055 .165 .335 .022 .176 .161 .249 ÿ.014 ÿ.094 ÿ.036 ÿ.585 .586 ÿ.392 1.000

MATH .210 ÿ.253 ÿ.095 .035 .047 .108 .005 .027 .138 .236 .320 ÿ.270 .246 ÿ.221 7279.389

MS .246 ÿ.231 ÿ.134 .037 ÿ.023 .096 ÿ.012 .036 .134 .263 .361 ÿ.311 .262 ÿ.236 777.944 97.905

MR .246 ÿ.228 ÿ.121 .042 .026 .097 ÿ.005 .025 .148 .267 .365 ÿ.310 .266 ÿ.233 797.686 98.530 103.864

62

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and so student statements such as `̀ need hard work'' and `̀ natural talent'' todo well in mathematics are de®ned as beliefs.

Research in this area, has led mathematics educators to study affectivedifferences in conjunction with student achievement (Fennena, 1980; Leder,1990), and it has been found that attitudes play important roles in both learn-ing mathematics (Lester, Garofalo, & Kroll, 1989; Shaughnessy, Haladyna, &Shaughnessy, 1983) and in maintaining a continued interest in the subject(Eccless et al., 1985). Tocci and Engelhard (1991) argue that affectivevariables are as important as cognitive variables in their impact on learningoutcomes, and Oliver and Simpson (1988) found that affective behaviors inthe classroom are strongly related to achievement. The belief that positiveaffect might lead to positive achievement outcome is fairly widespread(McLeod, 1992).

Opposing these views, Fraser and Butts (1982), reviewed a meta-analysisby Willson (1981) and concluded that the empirical evidence is insuf®cient tosupport the claim that attitudes and achievement are highly related. AndEisenhardt's (1977) research indicated that achievement in¯uenced attitudemore than attitude in¯uenced achievement in mathematics.

Structural equation models are often used to analyze relationships amongvariables, and in many different ®elds, such as sociology (Alsup & Gillespie,1997), psychology (Raykov, 1997), medicine (Papa, Harasym, & Scumacher,1997), economics (Kaplan & Elliot, 1997), and education (Dauphinee, Schau,& Stevens, 1997). While structural equation modeling supposes that cross-product covariances or Pearson correlations have been derived from variablesthat are continuous and measured on interval scale, this is rarely the case forsurvey data (Coenders, Satorra, & Saris 1997). Data collected throughquestionnaires or interviews are usually based on ordinal observed variables,that is, the responses are classi®ed into different ordered categories, althoughthey are conceptually continuous. An ordinal variable Zi may be regarded as ameasurement of an underlying unobserved continuous variable Z�i , andtherefore Zi would be related to Z�i through the step-function:

Zi � m when �i;mÿ1 < Z�i <� �i;m;

for m � 1; . . . ; ni; where �i;0 � ÿ1; �i;m < �i;m�1; �i;mi � 1 :

The parameters �i;1; . . . �i; niÿ1 are called thresholds of the ith variable. Thismethod appears most suitable for the social sciences (Coenders et al., 1997),where many variables are conceptually continuous, and measurement instru-ments may be discrete and have only ordinal properties. In this study three


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variables were interval; three were categorical, with two levels which areregarded as ordinal; and the remaining 24 were ordinal.

One of the easiest ways to communicate a structural equation model is todraw a picture of it. Pictures of structural equation models are called pathdiagrams (Raykov & Marcoulides, 2000). Latent and observed variables areconnected in order to re¯ect a set of theoretical propositions about a studiedphenomenon. These relationships are represented graphically in a pathdiagram by one- and two-way arrows. The structure coef®cients indicate thestrength (i.e., weak or strong) and direction (i.e., positive or negative) of therelationships among the latent variables.

Despite the prediction that the effects of attitudes (0.03, (0.05), t� 0.68),teaching (0.01, (0.06), t� 0.18) and beliefs for success in mathematics (0.03,(0.06), t� 0.47) would have signi®cant effects on mathematics outcomes, this

Table 3. Lisrel Estimates (Maximum Likelihood).

Observed Lambda-x s.e t Observed Lambda-y s.e. tvariables variables

e11 .43 .06 6.97 e21 .71 .09 7.81e12 .43 .06 7.02 e23 .85 .11 7.47e13 .93 .09 10.78 e31 .18 .06 3.00

h12 .82 .05 15.81 k11 .92 .06 16.30h14 .85 .05 16.19 k12 ÿ.89 .06 ÿ16.01i12 .95 .05 17.78 k13 .68 .05 12.73

k14 ÿ.64 .05 ÿ11.99

a11 .50 .06 8.07a12 .48 .06 7.73a13 .57 .06 9.11a14 .52 .06 8.40b11 .61 .06 9.61b13 .50 .06 8.10

c22 .50 .07 7.36c23 .60 .07 8.49c24 .60 .07 8.50c25 .69 .07 9.15

b14 .28 .07 3.83j11 .24 .07 3.38j21 .55 .09 6.20j22 .58 .09 6.27


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was not proven in the structural model. As Figure 1 shows, however, the pathsfrom educational background to SES (ÿ0.69, (0.13), t�ÿ5.20), to attitudes(0.15, (0.05), t� 2.84), to beliefs (0.22, (0.08), t� 2.78), and climate (0.36,(0.16), t� 2.25) were signi®cant.

The paths from reinforcement to attitudes (ÿ0.18, (0.05), t�ÿ3.52), tobelief for success in mathematics (0.48, (0.09), t� 5.27), and teaching (0.29,(0.06), t� 5.16) were also signi®cant, as were the paths from climate toteaching (0.21, (0.06), t� 3.20), the path from teaching to attitudes (ÿ0.30,(0.06), t�ÿ4.88) , and the path from SES to climate (0.43, (0.15), t� 2.98).

FIT STATISTICS

A variety of ®t statistics were applied to assess the `̀ goodness of ®t'' of themodel. Measures of ®t included chi-square� 401.71 (df� 390, p� 0.33), thegoodness-of-®t index (GFI� 0.97), adjusted goodness-of-®t index (AGFI�0.97), comparative ®t index (CFI� 1.0) and the root mean square of

Fig. 1. Model of mathematics outcomes process.


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approximation (RMSEA� 0.0054). The three ®t indexes GFI and AGFI andCFI with values above 0.9 (in general) represent reasonable ®t (Broome,Knight, Joe, Simpson, & Cross, 1997). The CFI is the least affected by samplesize (Hu & Bentler, 1995), and the RMSEA index with its value less than 0.05,re¯ects a close ®t. Browne and Cudeck (1993) believe that RMSEA valuesbetween 0.0 and 0.05 re¯ect a close ®t, less than 0.08 re¯ect reasonable ®t, andgreater than 0.08 re¯ect poor ®t. All remaining goodness of ®t indices alsodemonstrated an acceptable ®t.

DISCUSSION

The present study explored how mathematics outcomes are stimulated bypredictors related to family and schools. For initial analyses we decided touse only the student questionnaire data, although the teacher and schoolquestionnaire data could prove informative for subsequent research. For thisstudy we begun by posing a simple question: How can we best explain studentachievement (based on the TIMSS data) in relation to attitudes and beliefs ofthe students, teaching, SES, and environmental support? To answer this, wechose to elaborate on a model comparing various background factors(educational background of the family, what mother and friends believe that isgood for a student to be in a high achievement class, and the school climate) interms of their effect on student attitudes and beliefs related to mathematics andthe teaching of the subject.

Our model (Fig. 1) seems to indicate that the strongest direct in¯uence onattitudes toward mathematics was teaching, followed by reinforcement of thestudents from their near surroundings. The weakest effect was exerted by theeducational background of the family. The strongest direct effect on studentbeliefs about mathematics was exerted by the reinforcement given by mothersand friends, followed by the educational background of the family. Finally, theclimate of the school is most directly in¯uenced by SES followed by theeducational background.

The results of this study indicated that two exogenous factors ± educationalbackground of the family, and student reinforcements ± de®ne a second-orderfactor structure which includes endogenous predictors, SES of the family,student attitudes toward mathematics, beliefs regarding success in mathe-matics, the kind of teaching and the school climate. These results indicate thatthe problem of mathematics achievement is multidimensional in nature.


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This model also seems to indicate that attitudes, beliefs and teaching cannotbe used to predict student outcomes in mathematics. This ®nding concurs withthe research of Eisenhardt (1977), which showed achievement to be a morein¯uential factor to attitude, than attitude to achievement, and with that ofFraser and Butts (1982) which showed little correlation between achievementand attitude. However, there are many researchers who nevertheless contendthat attitudes are important factors (Lester et al., 1989; Meyer & Koehler,1990; Shaughnessy et al., 1983), and Seegers and Boekaerts (1993) arguedthat learners' beliefs about their capacities exert a strong in¯uence on taskperformance. Volet (1997) has found evidence that achievement in academicperformance can be attributed to a complex and dynamic interaction betweencognitive, affective and motivational variables.

The contradictions among research ®ndings leave the basic questionunanswered. Why did attitudes and beliefs in relation to mathematics do notsatisfactorily predict mathematics outcomes among Cypriot students? The resultsof the TIMSS study (Beaton et al., 1996) show that the great majority of studentsin Cyprus, about 80%, have positive attitudes toward mathematics; in fact this isone of the highest percentage compared with other countries participating in theTIMSS study. On the other hand the level of student achievement fell between165 and 769, with an average of 474 and SD� 88. Therefore, although attitudeswere positive for the majority of the students, achievements did not follow thesame pattern. One possible explanation is that teachers have low expectationswhich students can easily satisfy. Another possible reason is that students use nosystematic planned approach in their attempts to solve problems. It would beinteresting to see if the model can be applied to other countries with varyingpercentages of students with positive attitudes and beliefs. Japan for exampleshows only 52% of its students with positive attitudes but shows a very highaverage of achievement (605). The United States have an extremely highpercentage of students with positive attitudes (70%), but an achievement averageof only 500. Remaining the model on these countries, and comparing results withCyprus (positive attitudes 79%; achievement 474) may prove insightful.

Although attitudes, beliefs and teaching, were not found to be predictorsof student achievement in mathematics in Cyprus, attitudes are learned, andtherefore can be taught in such a way to make them important educationalobjectives. Beliefs can also be educational objectives and should be of concernto mathematics educators (Weinburgh & Englehard, 1994). The ®ndings ofthis study indicate that more should be undertaken to examine the in¯uence ofattitudes and beliefs and teaching on mathematics outcome.


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The model presented has implications for future research in the modelingof mathematics achievement. First, as with any modeling approach, cross-validation and replication are required (Bollen, 1989). The ®ndings of thisstudy are based on a single sample. Second, generalization of the model wouldprovide considerable support for the impact of mathematics achievement.Third, to further investigate the process of mathematics achievement, thecompatibility of the present model with other models for different countriescould be explored. Finally, the elements of the present model may provideempirical measures for a broad conceptualization of mathematics outcomes inthe developmental model.

ACKNOWLEDGEMENTS

I would like to express my gratitude to George Marcoulides at California StateUniversity, Fullerton, for his help and invaluable comments on earlier drafts ofthis article.

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effects of background and school factors on the mathematics achievement

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