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Social Values Associated with Cross-national Differences in Mathematicsand Science Achievement: A cross-national analysisCe ShenPublished online: 09 Jun 2010.

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Assessment in Education, Vol. 8, No. 2, 2001

Social Values Associated withCross-national Differences in Mathematicsand Science Achievement: a cross-nationalanalysisCE SHENInternational Study Center, Lynch School of Education, Boston College, Chestnut Hill,MA 02467, USA

ABSTRACT This study explores several factors that account for cross-national differences inmathematics and science achievement for middle-school students from 39 countries based onthe Third International Mathematics and Science Study. The results suggest that economicdevelopment level, as measured by GNP per capita, has a positive but relatively weakassociation with mathematics and science achievement. In contrast, variables re� ecting asociety’s value on education, speci� cally the education of mathematics and science, demon-strates strong effects on students’ achievement. These variables include students’ perceivedrigour of mathematics and science—a proxy of academic standards of mathematics andscience, students’ school attendance, the length of a school year, students’ educationalaspiration, and the average number of parents living with the student. The evidencepresented in this study supports the argument that education reform aiming at improvingmathematics and science achievement can hardly be successful without the efforts of thewhole society.

Introduction

The years after World War II have seen uneven economic and social developmentacross the world. School systems that perform vital roles in every society have beenboth causes and results of the uneven development cross-nationally. It is widely heldthat improved educational achievement is a key to improving global competitivenessbecause the ultimate foundation of a nation is the quality of its people (Rohlen,1983). Policymakers are inspired to inquire about the standing of their countryrelative to other countries with respect to students’ achievement. As Postlethwaite(1987) claimed, comparative education achievement research provides two kinds of

ISSN 0969-594X print/ISSN 1465-329X online/01/020193-31 Ó 2001 Taylor & Francis LtdDOI: 10.1080/09695940120062656

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comparisons: (1) straight comparisons of total scores or subscores on a commoninternational test and (2) comparisons of how well a country’s intended curriculumis implemented and achieved. Once the differences are identi� ed in achievement,standards and other aspects, the effects of such studies will gradually permeate andbe absorbed by a given educational system through consideration of what seems tobe working elsewhere that can be adopted or adapted to one’s own country so as toimprove the academic performance (Howson, 1999). Therefore, interest in compar-ative education has experienced continued growth.

Under the auspices of the International Association for the Evaluation of Educa-tional Achievement (IEA), the Third International Mathematics and Science Study(TIMSS) provides unprecedented opportunities for cross-national analyses of edu-cational systems all over the world. TIMSS has compared the mathematics andscience achievement of students in 41 countries/school systems at � ve levels—thethird, fourth, seventh and eighth grades, and the � nal year of secondary school, in1994–95. Information was also collected about students’ home background, schoolcharacteristics and instructional practices for participating countries (Gonzalez &Smith, 1997). TIMSS results have provided invaluable data to researchers anddecision-makers around the world. With rigorous methodology, TIMSS providedhigh quality and comprehensive data on students’ achievement, which revealssubstantial differences in mathematics and science achievement between top- andbottom-performing countries. The broad range of achievement both across andwithin countries is illustrated in TIMSS publications (Beaton et al., 1996a,b; Martinet al., 1997; Mullis et al., 1997, 1998). Appendix Table A-I presents the distributionof mathematics and science achievement for eighth-grade students for the 39 schoolsystems included in this study.

Identifying the cross-national differences in various � elds of mathematics andscience, and estimating the magnitude of cross-national differences in mathematicsand science attainment are important accomplishments of the TIMSS project. Thesubstantial differences found among the participating TIMSS countries make poli-cymakers, as well as the public, ponder what factors contributed to the cross-national differences, especially the big gap between the top- and bottom-performingcountries in mathematics and science teaching and learning. However, identifyingthe underlying causes of the substantial differences between countries is a morechallenging task. Even though the data provided by TIMSS, including backgroundinformation on students, teachers and schools, are extensive, the effort to seekexplanations for the cross-national variance in achievement is constrained by anumber of factors. These factors include the tremendous diversity in terms ofeducational systems, de� ned curriculum, instructional practices, social and culturalcontexts and tradition, and economic development level among these countries.Nonetheless, these constraints should not preclude our utilising the data from suchan unprecedentedly large-scale study to explore the possible factors that mayaccount for the cross-national variance in students’ achievement. This paper pre-sents the results of an exploratory analysis of possible factors associated withcross-national differences in mathematics and science achievement for 8th graders ofparticipating TIMSS countries.

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Cross-national Differences in Mathematics and Science Achievement 195

Countries/School Systems Included in the Study

Out of the � ve levels of students involved in TIMSS, this study only presents theanalysis of results for eighth grade students since the largest number of countries(41) participated at this grade in the TIMSS project. When the country is used asthe unit of analysis, as in this study, a small number of countries makes multivariateregression analysis dif� cult and the results unreliable. Bulgaria and South Africa areexcluded from this study because the student and school background data areunavailable (Beaton et al., 1996a,b; Martin et al., 1999). Therefore, 39 schoolsystems were included in the analysis.

Data and Variable Measurements

The dependent variables of this study are international mathematics and scienceachievement scores of students in the two adjacent grades that contain the largestproportion of 13-year-old students at the time of testing—the seventh and eighthgrades in most participating countries. On occasion, the selected target grades led tothe sampling of students older than expected. This was the case for Colombia,Germany, Kuwait, Romania and Slovenia. For the speci� c grades, participatingcountries identi� ed as their target population for TIMSS and the coverage of13-year-old students across the two grades tested in each country, see the TIMSSTechnical Report (Martin & Kelley, 1997). The national average scores of math-ematics and science and standard errors are listed in Appendix Table A-I for grade8. Grade 7 data were also analysed, but are not reported in the paper because theresults were quite similar for the two grades. Apparently, using the aggregated datafor this analysis to represent the achievement level of a country may have bothvalidity and reliability constraints. The average scores are aggregated over a con-siderable amount of subject areas. They do not take into account the variationamong various areas within the subject. For mathematics, the test items for grades7 and 8 cover the following six areas:

· fractions and number sense;· measurement;· proportionality;· data representation, analysis and probability;· geometry;· algebra.

Similarly, science test items cover the following six areas:

· earth science;· life science;· physics;· chemistry;· environmental issues;· the nature of science.

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In addition, the aggregated data, including both the dependent and independentvariables, do not take into account the variation among the sizeable number ofstudents and schools within a participating school system. These constraints ofaggregated comparisons of educational achievement have long been recognised inearlier IEA studies (Robitaille & Garden, 1989; Burstein, 1992). Burstein suggestedthat in aggregate data, one is not simply trying to measure differences betweendistinct points (the national averages), but rather is interested in differences amongthe ‘swarms or scatters’ of points (within-system distributions) that each single pointinherently inadequately represents.

The selection of independent variables was based on both theoretical and empiri-cal considerations, including hypotheses based on previous research, data compara-bility and availability. Two measures of country-level data external to TIMSS datawere included: economic development level as measured by real GNP (GrossNational Product) per capita, and public expenditure on primary and secondaryeducation as percentage of GNP. The choice of predictor variables from the TIMSSdatabase for this study was made after extensive exploratory analyses of the dataavailable, including correlation analysis, factor analysis and regression analysis. TheTIMSS database provides data for hundreds of variables measuring school andteacher characteristics. Instructional practices including school and class size, schoollocation, organisation of classroom instruction, school resources, teachers’ educa-tional background, school and classroom environment, how teachers and principalsspend their time at school, responsibilities of principals and how often teachersassign homework and so on. Unfortunately, the majority of these variables fail todemonstrate consistent effects on mathematics and science achievement for mostschool systems. Even fewer show signi� cant effects on students’ achievement forcross-national analysis.

Some potential relevant predictors were rejected because they were not interna-tionally comparable or because of missing data. As a result, the number of predictorschosen for this study is quite limited. Because the model is under-speci� ed, substan-tive conclusions are made with extreme caution. However, as we shall see, theexploratory analysis results do provide at least some insightful suggestions inaccounting for the cross-national variance in students’ achievement among partici-pating TIMSS countries. The predictor variables chosen fall into the followingcategories:

· Economic development level.· Society’s commitment to education and literacy environment.· Place of schooling in adolescents’ life.· Students’ educational aspiration.· Students’ perceived dif� culty level of mathematics and science.· Students’ family structure.

The variables used in each category and the rationale for including these variablesfollow.

1. A country’s economic development level directly or indirectly affects the educa-

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tional processes and outcomes of the society by providing the material, informa-tional and human resources needed for educational attainment. GNP per capita in1994 converted at purchasing power parity (ppp) was included as an indicator ofeconomic development level in this study. GNP per capita for each participatingcountry/school system is listed in Appendix Table A-II, column 1. The 39 countries/school systems include almost all high-income economies in the world and somemiddle-income economies de� ned by the United Nations Development Programme(UNDP, 1997). As shown in Table A-II, 12 countries have GNP level above 20,000international dollars per capita, with the United States as the wealthiest, 17 countrieshave GNP level between 10,000 to 20,000, and 10 countries have GNP level under10,000 per capita. The three countries with the lowest GNP are Iran, Lithuania andRomania. Even though the 39 economies did not include low-income countriesde� ned by the United Nations, they do show a wide range of differences in wealth.

2. Society’s commitment to education and a literacy environment could be mea-sured by many things. Public expenditure on education (primary and secondaryschool levels) as a percentage of a country’s GNP was included in this study as ameasure of a society’s commitment to education. The distribution of this variable foreach country is listed in Appendix Table A-II, column 2. When governments canafford to spend extensive funds on schools, teacher training, and school facilities, wewould assume they should produce high-achieving students.

Another measure—the average educational level of teachers of a country—couldre� ect the extent of a society’s commitment to education. The TIMSS teacherquestionnaire did ask teachers about their educational background and teachertraining experience. However, it was noted that there is a tremendous heterogeneityin terms of educational system and structure for TIMSS countries, especially atpost-secondary and tertiary levels, including teacher training programmes (seePostlethwaite, 1995). This made it dif� cult to de� ne various educational levels in aninternationally comparative way. In addition, a few countries did not administer thisquestion. Therefore, this variable was not included in this study.

It is often assumed that smaller class size may enhance academic attainment andis regarded as a re� ection of society’s commitment to education. The IEA ReadingLiteracy Study found that countries with generally smaller classes produced betterscores in reading, on average (Elley, 1994, p. 227). However, cross-national analysisbased on TIMSS data does not demonstrate this association at the country level andthe analyses based on within-country data even revealed an opposite pattern formost TIMSS countries. Therefore, average class size was not included in the study.The length of the school year may re� ect the commitment to education in a society.TIMSS data show that the average number of instructional days in a school yearvaries from 162 in Iceland to 231 in Japan (Martin et al., 1999, pp. 66–67). This gapmay contribute to the cross-national variance in academic attainment. The TIMSSschool questionnaire asked the principal to provide the number of instructional daysin a school year. This variable was included in the study.

A society’s literacy environment exerts signi� cant in� uence on students’ educa-tional aspiration and facilitates potential for students to learn. Literacy environment

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of a society could include the average literacy level of the population. The TIMSSstudents’ questionnaire asked students to provide their parents’ estimated educa-tional background. However, this variable was not included in this study for tworeasons. First, as noted earlier, there is a tremendous diversity in educationalstructures cross-nationally (for detailed country modi� cation of educational level ofparents, see Beaton et al., 1996b, p. 104). Secondly, initial analysis revealed thecorrelation between parent’s education, and mathematics and science achievementat the country level is pretty weak. A few high performing countries such asSingapore and Hong Kong had parents’ educational level lower than that for themajority of other TIMSS countries (Beaton et al., 1996b, p. 103).

The IEA Reading Literacy Study revealed that countries with many books inhomes and higher newspaper circulation were mostly high-performing countriesbecause homes with plentiful source books and newspapers apparently providedmore advantages for children’s literacy development in all countries. The correlationwith reading achievement across countries was close to 0.40 (Elley, 1994, p. 226).The TIMSS student’s questionnaire also asked students to provide the estimatednumber of books at home. The average number of books at home at the countrylevel is included as a predictor in this study. It is a 5-point-Likert scale measure,ranging from 1 5 less than 10 books; 2 5 11–25 books; 3 5 26–50 books; 4 5 51–200books; to 5 5 more than 200 books.

3. The place or importance of schooling in adolescents’ life within a society isassumed to have great in� uence on student academic achievement (Stevenson &Stigler, 1992; Stevenson, 1999). This category could ideally include measuresprovided by the TIMSS questionnaire, such as students’ perceived importance ofdoing well in mathematics and science, and the average amount of out-of schooltime spent on studying mathematics and science. However, for the former, it wasfound that all TIMSS countries had a high percentage of students responding ‘agreeor strongly agree’ that it was important to do well in the two subjects (Beaton et al.,1996a, pp. 100–102, 1996b, pp. 106–108). Due to the lack of variance, this variablewas not included in this study. For the latter, there was an international comparabil-ity issue. For example, in Singapore, most schools have double-sessions, withstudents attending either the morning session from 07.30 to 13.00 hours or theafternoon session from 13.00 to 18.30 hours (Robitaille, 1997, p. 332). Therefore,they have more out-of-school time than students in many other countries. Incontrast, Japanese students have a long school day, usually arriving at school shortlyafter 08.00 and leaving at 18.00 hours or even later in the evening (Stevenson,1999). They spend fewer hours on out-of-school study than students in many othercountries. Due to the incomparability, this variable was not included in this study.The school questionnaire asked school principals the average percentage of absen-teeism, students arriving late at school and students skipping classes. If schooling isregarded as very important in students’ life, the percentage of these occurrencesshould be low. An index of ‘poor school attendance’ created to compute the meanof the three variables, was included in this study as an indicator of the place ofschooling in adolescents’ life.

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Cross-national Differences in Mathematics and Science Achievement 199

4. It is widely assumed that students’ educational aspiration is positively related totheir motivation and academic achievement. A sizeable body of research in recentyears, especially research related with Bandura’s self-ef� cacy theory, has addressedthe relationship among self-ef� cacy of capabilities, goal-setting, aspiration, motiv-ation and accomplishment (Bandura, 1994). Many studies have tested their rela-tionship, and generally support the hypothesised continuous feedback loop amongpeople’s self-ef� cacy beliefs, educational aspiration and accomplishment (Schunk,1984, 1989, 1991; Brown et al., 1989; Locke & Latham, 1990; Multon et al., 1991;Zimmerman et al., 1992; Zimmerman & Bandura, 1994). Empirical studies showthat students with high academic goals usually display greater persistence, effort,and intrinsic interest in their academic learning and performance. The TIMSSstudent questionnaire asked students how far they expected to go including ‘� nishsome secondary school’, ‘� nish secondary school’, ‘some vocational/technical edu-cation after secondary school’, ‘some university’ and ‘� nish university’. This variablewas included in this study. Considering the diversity of educational systems amongTIMSS countries, especially education after secondary school, as noted above, thisvariable was collapsed into three broad categories so as to be more comparable forall TIMSS countries:

· � nish some secondary school;· � nish secondary school;· beyond secondary school.

5. Many comparative studies have shown that high academic standards at the countrylevel are crucial for high achievement (cf. Stigler et al., 1985; Stevenson & Stigler,1992; Becker et al., 1999; Stevenson, 1999; Kawanaka et al., 1999). However, tocompare the challenging level of academic standards for all TIMSS participatingcountries is a formidable task and beyond this study. However, measuring students’perception of a challenging level of mathematics and science may provide someindication of academic standards and expectations of a school system. For example,Stigler et al. (1985) and Stevenson & Stigler (1992) compared students’ achievementfrom the USA, Japan and China. They found that American students performedpoorly in relation to their Chinese and Japanese counterparts, but tended to thinkmathematics and science were easy, and felt that they did well in these subject areas.Conversely, Japanese and Chinese students tended to ‘downgrade’ themselves inrelation to others, and thought these subjects were hard and felt they were not goodat them. Using TIMSS data, Shen & Pedulla (2000) found that for within countrydata, those students who perceived mathematics and science as being easy usually didbetter than those who perceived the two subjects as being dif� cult. However, forcross-national data, the pattern was opposite, that is, countries with a high proportionof students perceiving mathematics and science as being easy usually performedpoorly on the TIMSS tests, and countries with a high proportion of studentsperceiving mathematics and science as being dif� cult usually performed well onthe TIMSS tests. They found this pattern existed for both mathematics and science,at grades 3, 4, 7 and 8. The authors suggested that this pattern may re� ectlow academic expectations and standards in low performing countries, and high

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academic expectations and standards in high performing countries. In this study, thesame variable was used as a predictor of achievement for cross-national analyses.Students’ perceived dif� culty level of mathematics and science was measured by theaverage response on a 4-point Likert scale for ‘Mathematics (or Science) is an easysubject’ (1 5 strongly agree, 2 5 agree, 3 5 disagree, and 4 5 strongly disagree).

6. Findings from previous research pointed to the strong effects of the students’home background on both individual and school level performance (Coleman et al.,1966; Peaker, 1967, 1971). Much research has also found that family structure inparticular has signi� cant in� uence on children’s educational achievement (Moyni-han, 1965; Dawson, 1991; Popenoe, 1996; Biblarz & Raftery, 1999). Most studiesagree that children from alternative families (single father or single mother families,father/stepmother families, and mother/stepfather families) had lower attainmentsthan children from two-biological-parent families. According to almost all existingsociological and psychological theories—socialisation, learning and control theory—children from alternative families get fewer economic, social and cultural resources,which help facilitate educational success (Biblarz & Raftery, 1999).

As children’s � rst teachers, parents have a profound impact on children’s educa-tional attainment. In a single-parent family, children will lack a male or femalemodel of how successfully to achieve their academic and occupational goals (Powell& Parcel, 1997). The death of a father or mother, or the divorce of parents may havethe potential long-term negative impact on children in many ways (Wallerstein,1989; Amato & Booth, 1997). Research has also found that many children’sbehavioural problems are associated with family dysfunction and divorce (Cherlin etal., 1998). Children of divorce have lower attainments than children from two-parent families because they have had sustained exposure to their parents’ discord[Amato & Booth, 1997; see Biblarz & Raftery (1999) for a detailed discussion ofvarious theories on the effects of family structure on children’s well-being andeducational attainment]. However, no comparative study has ever used a measure offamily structure to predict academic achievement in cross-national analyses. TheTIMSS student questionnaire asked students whom they were living with at home.An index was created to compute the average number of biological parents livingwith the student at home for each of the TIMSS countries. It is assumed that asociety with high percentage of students living with both biological parents maydemonstrate a higher academic achievement than a society with a lower percentageof students from such family structure.

In summary, nine variables/indices at the country level were chosen as predictorsof mathematics and science achievement for this cross-national study. However, foreach subject, there are only eight predictors because students’ perceived dif� cultylevel of mathematics and science were used as two separate variables. If onlycountries with complete data for the nine predictors were included in this study, sixcountries would be excluded. The ‘sample size’ would drop to 33 for grade 8. Fiveof the six countries had missing data for only one variable. They are Greece,Switzerland, England, Scotland and Kuwait. One country—Japan—had missingdata for two variables. The following measures were taken to solve the missing data

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Cross-national Differences in Mathematics and Science Achievement 201

problem so as to retain the six countries in this study. Greece and Kuwait did notprovide instructional days in a school year and Switzerland’s data of this variable wasnot internationally comparable. The international mean for instructional days (187days) was used for these three countries. England did not have internationallycomparable data for the variable of student’s educational aspiration. The data ofScotland were used for England for this measure. Scotland did not ask aboutstudents’ perceived dif� culty level of mathematics. English data for this measurewere used for Scotland. Japan did not ask students’ about the number of books athome and the number of parents living with the student. For the former variable,again, international mean substitution for average number of books was used and forthe latter, the average of the other four Asian school systems (Hong Kong, SouthKorea, Singapore and Thailand) was used due to the consideration of culturalsimilarities.

Descriptive statistics (mean and standard deviation) of the seven predictors fromthe TIMSS database of grade 8 for each country are presented in Appendix TableA-III.

Methods, Signi� cance Testing and In� uential Cases

Ordinary least square (OLS) regression analysis was used to estimate the relativeimportance of predictors in accounting for cross-national variance of achievement inmathematics and science. In constructing regression models, following the conven-tional rule to keep the ratio of cases to predictors to the suggested limit (Tabachnick& Fidell, 1996), in one regression equation, no more than four predictors wereincluded. The number of school systems varies between 37 and 39 for regressionmodels. The resulting variation in the sample should be taken into considerationwhen interpreting differences between models.

Original data analyses were conducted for both seventh and eighth grades. Exactlythe same variables were used for analyses of both grades. If the results are similar forthe two grades, the robustness and reliability of the � ndings will be enhanced. Ifsigni� cant discrepancies are found between the analyses of the two grades, cautioncould be taken in drawing conclusions. Because the results were similar, to savespace, only eighth grade analysis results are presented in the paper.

Given that none of our samples are simple random samples, the use of tests ofsigni� cance and t-statistics are presented for heuristic purposes. Bollen et al. (1993)assert that statistical signi� cance tests can be justi� ed with samples such as this studyin terms of a hypothetical ‘super-population’ where the observed sample is treatedas one possible sample that could be drawn from that hypothetical population.Messner (1989) also argued that signi� cance tests could still be used as a criterionfor identifying nontrivial relationships. The signi� cance levels based on t-statisticswere used to indicate the relative strength of a variable in accounting for thecross-national variation of mathematics and science achievement.

The ratio of the regression coef� cient to its standard error was used as a measureof the level of signi� cance. Following some previous sociological studies (Bradshaw& Tshandu, 1990; London & Williams, 1990) coef� cients are considered signi� cant

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if the coef� cient is at least 1.5 times the size of its standard error. According toPedhazur (1982), in analysis of this type, where the units of analysis are largeaggregates and where the number of cases is relatively small, this measure is themost reliable guide to interpreting the ‘signi� cance level’ of coef� cients.

Bollen & Jackman (1985) pointed out that with small samples, the sensitivity ofestimates to one or two in� uential outliers is more likely to be a problem than it isin studies based on larger samples. Outliers are cases with such extreme values onone variable or a combination of variables that they unduly in� uence statistics. Inthis study, a few multivariate outliers—cases with an unusual combination of two ormore variable values—demonstrated a large impact on the estimates of regressioncoef� cients. Their presence may be a signal, either that the data fall out of theexpected ranges for the outlier countries or that an important predictor has beenomitted; that is, that the model is mis-speci� ed. Considerable efforts have beenmade to check for in� uential outliers and, where appropriate, to remove them so asto ensure the robustness of the � ndings. Outliers were sought using both statisticalmethods such as Mahalanobis distance or modi� ed Cook’s distance, DFFITSand DBETAS, and graphical methods such as histograms looking at studentisedresiduals. Statistical results are discussed whenever the deleting of outlier(s) exertsa large impact on the results.

Results

Table I presents the Pearson’s zero order correlation coef� cients among the vari-ables involved in the study for eighth grade data for 39 participating TIMSScountries. On the right hand side of the table, the mean values of all the dependentand predictor variables based on the 39 school systems are listed.

A few points are noted from Table I. First, it is not surprising that at thecountry-level the scores of the two subjects are highly correlated with each other(r 5 0.86, P , 0.01), indicating that countries that did well in mathematics usuallyalso did well in science. However, there are discrepancies. For example, high-performing Hong Kong ranked 4th for mathematics, but dropped to about themiddle in science, and the Czech Republic, ranked sixth in mathematics, was secondin science (see Beaton et al., 1996a, p. 22, 1996b, p. 22).

The correlation of GNP per capita and mathematics and science achievementscores are 0.24 and 0.18, respectively—a weak positive correlation. This issue will beaddressed in more detail later. The percentage of public expenditure on educationshows a very weak correlation with achievement. Average length of a school year hasa moderate positive correlation with the achievement. The average number of booksat home at the country-level has a slightly weaker correlation with achievement thanschool year length. The index of poor school attendance demonstrates a signi� cantand negative correlation with academic achievement for both mathematics andscience, indicating a tentative con� rmation of the hypothesis that countries withpoor school attendance are likely to be poor performing countries. Educationalaspiration based on the response to the question ‘How far do you expect to go (interms of schooling)?’ has a signi� cant positive correlation with achievement.

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Cross-national Differences in Mathematics and Science Achievement 203

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204 C. Shen

A very strong correlation is found between achievement and students’ perceiveddif� culty level of mathematics and science at the country level. Consistent with� ndings from Shen & Pedulla (2000), countries where students are likely to perceivethe two subjects as being hard are usually countries with high performance and viceversa. The last variable—the average number of biological parents living withstudents—demonstrates a moderate positive correlation with academic achievement.

The correlation coef� cients of the same variables for seventh grade were com-puted, but are not presented here. The results are similar to those presented inTable I with the exception of the correlation with GNP per capita. The correlationcoef� cients of GNP with the international scores of mathematics and science are0.40 and 0.33, higher than those for grade 8. The possible reason will be discussedbelow.

It is often argued that countries should be compared with respect to academicachievement only if those countries have similar resources as indicated by the GNPper capita (Raudenbush et al., 1995). The IEA Reading Literacy Study found thatthe correlation between GNP and reading achievement scores for 14-year-oldstudents at the country level is 0.64 (n 5 32 school systems). As noted above, weakercorrelation coef� cients were found in this study—0.24 and 0.18—for mathematicsand science, respectively, at grade 8. Figure 1 presents a graph plotting GNP percapita versus mathematics scores at grade 8 for the 39 school systems in this study.We can identify some in� uential outliers from the graph. For example, Kuwait(located at the bottom-right corner) has a high GNP level, just next to that of UnitedStates (see Appendix Table A-II), but its mathematics (and science) achievement

FIG. 1. Scatterplot of mathematics score versus GNP per capita for grade 8 TIMSS participatingcountries. Pearson correlation 5 0.24 (n 5 39).

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Cross-national Differences in Mathematics and Science Achievement 205

scores are almost at the bottom (see Appendix Table A-I). When Kuwait wasremoved from the sample, the correlation coef� cients increased to 0.37 (P , 0.05)and 0.29 for mathematics and science, respectively. This also explains whyfor seventh grade the correlations between GNP, and mathematics and scienceachievement are higher than those for grade 8, because Kuwait did not par-ticipate in the TIMSS study at the seventh grade. In the graph, if a regressionline was drawn, we could see that certain school systems achieved about asexpected given their GNP level. However, at the same time, we could tell that quitea few school systems achieved much above what would have been expectedaccording to their GNP level, including Singapore, South Korea, Japan, HongKong, Czech Republic, Slovak Republic, Slovenia, Russia and Thailand. On theother hand, some school systems achieved much below what would have beenexpected according to their GNP per capita, including Kuwait, Colombia, Iran, andPortugal.

Because the overall pattern of the scatterplot for science score versus GNPper capita is similar to Figure 1, it is omitted here. The cases well above or belowthe predicted values based on GNP level may be in� uential outliers. Due to themoderate number of countries in the study, one or two cases may have a largeimpact on the correlation coef� cient. This can be better explained by usingHong Kong and the Czech Republic as an example. As mentioned earlier, HongKong did better in mathematics than in science, while the Czech Republic didbetter in science than in mathematics. On the other hand, Hong Kong’s GNPlevel is about three times as high as that of the Czech Republic. The fact that GNPlevel has a stronger positive effect on mathematics than on science (as shown inTable I) is partly due to the switch of positions of Hong Kong, and the CzechRepublic in mathematics and science. The Czech Republic performed far betterthan what would be expected given its GNP, while Hong Kong is just about asexpected for the science score, based on its GNP. When Hong Kong and the CzechRepublic are removed, the correlation of GNP with the science score rises from0.18 to 0.23.

Table II presents standardised coef� cients for the eight predictors of mathematicsachievement in TIMSS based on OLS regression analyses. The table summarisesthe results based on 10 models (regression equations) with an attempt to allow allthese predictors to have maximum opportunities to compete with each other. In theregression analyses, residual analysis was conducted throughout the process, includ-ing requesting the statistics to measure the in� uence of each country on theparameter estimates. For each regression model, multivariate outliers—cases with anunusual combination of values from two or more variables—were checked forauthenticity. Some outliers were removed and the statistics were compared with andwithout the outlying cases in regression models.

As shown in Table II, each predictor was included in at least three models,because the parameter estimate of a variable may vary from model to model,depending partly on (1) what other predictors are in the model and (2) whetherthere are in� uential outliers in the model. The relative importance of a predictor inaccounting for cross-national achievement variance can be claimed only when the

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Cross-national Differences in Mathematics and Science Achievement 207

predictor demonstrates a relatively stable effect on the dependent variable in most ofthe models in which it was included. We should also keep in mind that a strongpredictor in the model may prevent other predictors from achieving signi� cance inthe same model.

Equation 2.1 includes three predictors: GNP per capita; percentage of educationexpenditure; length of a school year.

With Kuwait and Colombia removed from the model, the adjusted R2 is 0.18,indicating that 18% of the cross-national variance in mathematics achievement isaccounted for by the model. Both GNP and school year length have signi� cantpositive effects on mathematics achievement. When Kuwait and Colombia wereincluded, the effect of GNP was no longer signi� cant though still in the expecteddirection, but the school year length still had a signi� cant positive effect onmathematics achievement. In equation 2.2, one more predictor was added: theaverage number of books at home—an indicator of a society’s literacy environment.Two in� uential cases were removed: Kuwait and Singapore. When they were in themodel, the effect of GNP lost signi� cance and the coef� cient of number of booksdropped a little, but was still signi� cant. Equations 2.1 and 2.2 reveal that bothschool year length and average number of books at home have greater impact thanGNP per capita on mathematics achievement.

As shown in Table II, from Equations 2.3 to 2.6, each model drops a variable atthe top and adds a new variable at the bottom. Due to the very weak effect of publicexpenditure on education as percentage of GNP, it was excluded from furtheranalyses from Equation 2.4 on.

In Equation 2.7, as usual, the index of poor school attendance was dropped andGNP per capita was put back because it did not have an opportunity to compete withthe last few predictors. As shown, perceived dif� culty level of mathematics still hasa strong effect, though a little weaker than in Equation 2.6. The number of parentsat home shows signi� cant positive effect on mathematics achievement. Its effect isstronger than that of GNP per capita. With the presence of the three strong variables,the regression coef� cient of education aspiration became weaker and no longersigni� cant. Equation 2.8 offers an opportunity for the last two predictors to competewith the � rst two predictors (after dropping public expenditure of education aspercentage of GNP). As in Equations 2.6 and 2.7, perceived dif� culty level has thestrongest effect, followed by GNP, number of parents at home, and the length of aschool year.

So far, we have acquired pretty reliable estimates for the relative importance ofsome variables. To gain more con� dence in these estimates, we need to test furtherthe effects of predictors which have shown unstable parameter estimates, especiallythe average number of parents and the students’ educational aspiration. Equation2.9 includes these two variables and the number of books at home and the index ofpoor school attendance. The adjusted R2 is 0.56 with Kuwait removed as anin� uential outlier. Among these four predictors, average number of biologicalparents has the strongest effect, followed by index of poor school attendance andeducation aspiration. The average number of books at home lost its signi� cance.The last model includes number of parents, educational aspiration, school length

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208 C. Shen

and real GNP per capita. Two cases were identi� ed as in� uential outliers andremoved: Kuwait and Iran. The adjusted R2 is 0.56, with the number of biologicalparents at home as the strongest predictor, followed by school year length andeducational aspiration, and GNP having no signi� cant effect. When the two out-lying cases were included, the three signi� cant predictors were still signi� cant, butthe standardised coef� cient for educational aspiration increased from 0.18 to 0.33,while the coef� cient for number of parents dropped somewhat, but was stillsigni� cant.

The results of OLS regression analyses based on the ten models enable us toobtain an overall evaluation of the relative importance of the eight predictors.Cross-nationally, students’ perceived dif� culty level of mathematics has thestrongest association with the dependent variable—mathematics achievement score.Its effect is far greater than economic development level as indicated by GNP percapita. The next strong and stable predictor is the index of poor school attendance—an indicator of the place of schooling in adolescents’ life. Other strong predictorsare: the average number of biological parents living with the students, school length,and the indicators of economic development level as measured by GNP per capitaand social literacy environment—average number of books at home. Average stu-dents’ educational aspiration demonstrates a positive effect, too, but the strength issomewhat weaker than other predictors noted above.

To what extent can the � ndings shown in Table II be replicated when scienceachievement score is used as the dependent variable? The results are presented inTable III. As mentioned earlier and shown in the correlation table (Table I), thereare some discrepancies between mathematics and science results. As shown in TableI, the correlations are somewhat stronger for science achievement with the numberof books, but weaker for science achievement with GNP per capita, index of poorschool attendance and educational aspiration. Some of these discrepancies arere� ected in regression analyses. Table III presents the results with the same numberof equations and the same variables for each equation as for mathematics analyses,but the in� uential outliers are somewhat altered.

To save space, a brief general discussion follows. Students’ perceived dif� cultylevel of science demonstrated a strong and stable positive effect as expected. Theeffects of the index of poor school attendance, the average number of biologicalparents at home and the length of a school year are also strong, and similar towhat we have seen from Table II for mathematics achievement. Similarly, as inTable II, public expenditure on education has no signi� cant effect on scienceachievement.

The differences between Tables II and III are found in two predictors—GNP percapita and educational aspiration. Their effects on science achievement are weakerthan those demonstrated in Table II for mathematics. As mentioned earlier, theswitches of ranking positions of a couple of cases, such as Hong Kong and the CzechRepublic, exert a large impact on the overall correlation with GNP. The unstableeffect of educational aspiration may be due to the collapse of the original � vecategories into three general and broad categories to ensure international compara-bility. Moreover, this variable may not be a valid measure of students’ educational

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Cross-national Differences in Mathematics and Science Achievement 209

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210 C. Shen

aspiration. This validity issue will be addressed in the section on limitations of thestudy.

As a useful check on the validity of the � ndings from the grade 8 analysis, analyseswere also conducted for grade 7 data with exactly the same variables. The resultswere quite similar to the results for grade 8 except for the difference due to theabsence of Kuwait as discussed earlier. To save space, the analysis results for grade7 are omitted.

Summary and Implications

Summary of Findings

This study found that students’ perceived dif� culty level of mathematics and scienceat the country level is a strong predictor of their achievement cross-nationally.From students’ perceived dif� culty level of mathematics and science, we couldpostulate that countries with high academic standards (such as Japan) are alsolikely to have high academic achievement. This � nding is consistent with previousresearch � ndings. Research since the 1970s (e.g. Comber & Keeves, 1973;Cummings, 1980; Rohlen, 1983) points to the demanding standards and highattainment of Japanese students in mathematics and science. Research in recentyears has recon� rmed these � ndings (Stevenson & Stigler, 1992; Stevenson, 1999;Shen & Pedulla, 2000).

As one of many possible variables measuring the place of schooling in adolescents’life, the index of poor school attendance measured by the average percentage ofabsenteeism, arriving late at school and skipping classes, demonstrated a signi� cantnegative effect on students’ achievement. This variable re� ects the extent of stu-dents’ dedication to education. Similarly, the length of the school year—averageinstructional days per school year—also indicates the place of schooling in adoles-cents’ life. More importantly, it is an indicator of a society’s commitment toeducation. Japan has an average of 231 school days per year, while the internationalaverage is 187 days. The difference is 44 days—about 9 weeks a year. We canimagine how much more Japanese children can learn in those 9 weeks, especiallyconsidering their long school hours per day and demanding standards as notedearlier.

This study also found that the average number of books at home had a positivecorrelation with achievement in mathematics and science, even when GNP per capitawas controlled. It implies the importance of a literacy environment for students’learning. Another � nding of this study is the importance of family structure onstudents’ academic attainment at the country level. It is the � rst time that thisvariable has been used to predict students’ achievement in a cross-national analysis.This � nding tells us that despite cultural differences, as aggregate data, the averagenumber of parents living with the students has a positive effect on students’academic achievement.

Regarding the effect of economic development level, this study found that al-though economic development level, as indicated by GNP per capita, is positively

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Cross-national Differences in Mathematics and Science Achievement 211

associated with students’ achievement in mathematics and science, its overall effectis neither strong nor stable. A number of countries, such as South Korea, the CzechRepublic, Hungary, Slovenia, the Slovak Republic, Russia and Thailand, withmoderate or even relatively low GNP levels, out-performed some high-incomecountries. The different effect of GNP on achievement for the IEA Reading LiteracyStudy and TIMSS may be due to two reasons. One is due to the different samplesfor the two studies. The other may re� ect the different prerequisites for acquiringskills in reading on one hand and in mathematics and science on the other. Theenvironment of a wealthy society may be more conducive to producing good readersthan to producing students with high-pro� ciency in mathematics and science.

Students’ educational aspiration in this study demonstrated a positive effect onachievement in mathematics, but its effect on science is weak and unstable. Theseinconsistent results do not mean that the effect of educational aspiration on aca-demic achievement is questionable. It only reminds us that at the country level, theaverage student’s educational goal is affected by a number of societal factors andmay not be an appropriate predictor of students’ achievement for cross-nationalanalysis.

National Characteristics of Selected School Systems

To have a better understanding of the relative importance of all the variablesincluded in the study, it will be helpful to look at a few successful school systems byexamining them brie� y in their economic, social and cultural contexts:

· Singapore ranks � rst on the seventh and eighth grade TIMSS tests in bothmathematics and science. It is a newly industrialised country with relatively highGNP per capita. Singapore has a relatively high number of instructional days ayear (about 200), a relatively lower number of books at home (2.9), a very lowpercentage of absenteeism, arriving late and skipping classes (1.82%) comparedwith the international mean of 3.74%, and the highest average educationalaspiration (2.97) among the 39 TIMSS countries. Singapore’s average class sizeis 36 and school enrolment is over 1200, larger than most other TIMSS countries.

· Japan has been included in a number of comparative studies since the 1960s (e.g.Husen, 1967). As shown in Table A-III, among the 39 school systems, Japanesestudents perceived both mathematics and science the hardest. This is consistentwith previous � ndings that Japan has high academic standards. As mentionedabove, it also has the longest school year and possibly the longest school dayamong participating TIMSS countries. Although it is the second economic powerin the world, the enrolment rate for tertiary level education was only 30% in 1993(World Bank, 1996a), implying a tough selection and examination system.

· South Korea may be the most appealing case among TIMSS countries, consider-ing its moderate income level and excellent performance on TIMSS tests. SouthKorea’s GNP level is about half of that of approximately 10 high-income coun-tries (Appendix Table A-II) and its public expenditure on education is 3.43% ofGNP—at the middle range of the 39 participating TIMSS countries. However, it

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212 C. Shen

is a top-performing country on TIMSS tests for both Population 1 (grades 3 and4) and Population 2 (grades 7 and 8). How did the South Korean peopleaccomplish this? According to a United Nation’s report (UNICEF, 1992, p. 42),South Korea succeeded in wringing more education out of every governmentdollar than any other country. The report listed the following factors explaininghow it was achieved. First, due to the more than 2000-year-old Confuciantradition of respect for the educated person, a massive social demand for edu-cation was translated into a willingness of parents to pay for their children’seducation. Secondly, South Korean policy subsidised education less and less ateach successive level, letting the private sector pick up an increasing share of thebill for secondary and higher education. Thirdly, large class size and low teachersalaries have kept the cost of education low. South Korea has the largest averageclass size in TIMSS countries (46 at eighth grade). Teachers are compensated forlow salaries by high social status. Fourthly, due to the high value of education inSouth Korea, there are almost no ‘repeaters’ or drop-outs. All students areexpected to progress. Finally, parental pressure to pass examinations has led to thewidespread practice of extra-curricular private tutoring. This raises academicachievement and supplements teachers’ salaries, while costing the governmentnothing. Given such a social context, it is not surprising that South Korea has thelowest percentage of absenteeism, students arriving late and students skippingclasses among the 39 TIMSS school systems (Appendix Table A-III).

· The Czech Republic has a GNP per capita of 7910 international dollars, aboutone-third of that for high-income countries. However, it is a high-performingcountry, especially in science at both grades 7 and 8. The Czech Republic has arelatively long average school year—198 days a year and a relatively high literacyenvironment as indicated by the average number of books (3.9). In addition toits long tradition of literacy, the Czech Republic has well-trained teachers.The Czech Republic requires all primary and secondary school teachers tohave a university degree, and admission to universities is quite competitive(Postlethwaite, 1995, pp. 261–263).

Limitations of the Study

As mentioned earlier, the tremendous diversity of participating school systems interms of educational, social and cultural contexts constitutes some of the majorlimitations of this kind of study. Based on the analysis of the Second InternationalMathematics Study (SIMS), Robitaille & Garden (1989) observed that such differ-ences complicate the process of drawing valid conclusions and generalise the� ndings. The participating countries were not randomly sampled. They voluntarilyparticipated. Furthermore, the number of participants is small and, for the mostpart, from high-income and upper-middle-income countries. The correlation be-tween GNP and achievement found in this study might be different if anothercombination of school systems were examined.

In doing cross-national analysis and using the country as the unit of analysis, somehypothesised relationships established by analysing within-country data may not

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Cross-national Differences in Mathematics and Science Achievement 213

hold. For example, we all know the importance of parents’ education on children’sacademic achievement. TIMSS data reveal that high percentages of students fromCanada (37%) and the United States (33%) reported that at least one parent� nished university, while Singapore and Hong Kong reported only 8 and 7%,respectively (Beaton et al., 1996a, p. 97). However, Singapore and Hong Kongoutperformed Canada and the United States in students’ achievement at the countrylevel. Each country’s average educational level has been determined by speci� csocietal and historical factors of that country. Caution should be taken when usingthis measure to predict students’ achievement for cross-national comparison.

Another example is students’ educational aspiration (usually measured by whateducational level they plan or expect to reach), which is also constrained by societalfactors, such as the labour force structure and the enrolment rate for various levelsof educational institutions in each country. This, at least partly, explains why theeffect of this variable at the country level is relatively weak and unstable in this study.In some cases, this measure re� ects the aggregate level of the nation’s educationalaspiration, but not always. For example, according to the data in Appendix TableA-III, the average student’s educational aspiration is 2.74 and 2.47 for Canada andthe United States, respectively (1 5 � nish some secondary school, 2 5 � nish second-ary school, and 3 5 beyond secondary school), compared with 2.56 and 2.97 forHong Kong and Singapore, respectively. Considering the enrolment rate for tertiarylevel of 20–25% for Singapore and Hong Kong (Postlethwaite, 1995, p. 866), incontrast to 90 and 81% for Canada and the United States (World Bank, 1996a), itis safe to say that students in Singapore have relatively high aspirations. However, wecannot say Canadian students have higher aspirations than students from HongKong. Linking to parents’ educational level, the contrast implies that even thoughthe parental educational level of students from Singapore and Hong Kong is muchlower than that of the United States and Canada, a greater percentage of studentsfrom Singapore and Hong Kong intend to surpass their parents’ education than theircounterparts in Canada and the USA. Apparently, the chances for students to beenrolled in higher education are much smaller for students from Hong Kong andSingapore than for their counterparts in Canada and the USA. The combination ofhigh aspiration and low enrolment rate means strong competition. The toughselection and examination system in Asian countries is another driving force onstudents’ motivation for attaining high academic achievement. Therefore, for cross-national analyses, the average level of students’ educational goal may not be anappropriate measure for educational aspiration.

Implications

This study reveals that predictors re� ecting societies’ values in education, especiallyin mathematics and science education, play important roles in accounting forcross-national variance in mathematics and science achievement. Meanwhile, asmentioned earlier, in the process of screening hundreds of variables of backgrounddata from student, teacher and school questionnaires, the author found that aftercontrolling students’ home background variables, a majority of those variables did

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not demonstrate consistent and signi� cant effects on mathematics and scienceachievement, even for within country data analyses for most school systems. Theeffects of the aggregates of those variables at the country level became even weakerin accounting for cross-national variance in achievement. The seemingly weakimpact of these variables does not mean they are unimportant. Rather, it reveals theimportant fact that learning and teaching are cultural activities (Kawanaka et al.,1999) and pedagogical methods are culturally embedded (Serpell & Hatano, 1997).We can hardly say what class size and what teaching methods are ideal for allcultural contexts. A method effective in one culture may be a disaster in another.However, it is safe to say that a universal prerequisite for high achievement inmathematics and science is a social environment, where education in mathematicsand science is highly valued.

Recent years have seen a great increase in comparative education research andeducational reforms in many countries. Policymakers and even the public are likelyto blame schools and teachers for the poor performance of students, and reformefforts often pinpoint how to improve pedagogy. Researchers and educators haveattempted to � nd out how teachers in top-performing countries (such as Japan)teach, including what percentage of the instruction time is based on the textbook,how often teachers assign students homework, how they begin a new topic in class,how they organise their classes, how the principals and teachers spend their time atschool, and so on. This approach to educational reform is likely to neglect animportant premise: instructional practices and teaching methods are embedded incertain cultural and social contexts. It is helpful for teachers and researchers tocompare how the instructional pedagogy differs, and to learn from other schoolsystems and cultures. However, transplanting pedagogical methods without under-standing the social and cultural contexts is unlikely to succeed in improvingstudents’ achievement.

Similarly, previous research based on the Second International MathematicsStudy (SIMS), Robitaille & Garden (1989) also found that countries even with verysimilar curricula performed very differently. One possible explanation is the exist-ence of the gap between intended and implemented curricula within many schoolsystems (Travers & Westbury, 1989). More importantly, without a consensusunderstanding of the importance of education in general, and mathematics andscience in particular from students, teachers and parents and appropriate measuresto implement high standard curricula, raising the standards alone will not bringabout the expected success. For example, many states and cities in the USA haverecently embraced tougher academic standards. However, these attempts haveencountered strong resistance including protests from students’ parents. People havediscovered that putting the new school reform into practice is not easy and somestates are beginning to retrench, by lowering the raised bar, fearing that too manystudents would drop out or fail to earn diplomas (Wildavsky, 1999). Educationreform and the attempt to improve students’ achievement should be addressed as aholistic issue, and requires the effort and commitment of the whole society. In asociety where all its citizens believe the country’s future depends on the educationalattainment of the younger generation, especially the education of mathematics and

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science, dedicated teachers and educators will develop a high-standards curriculum,and � nd the pedagogy appropriate for its own cultural and social contexts.

This study also reveals that high economic development level does not automati-cally raise students’ achievement in mathematics and science. If the value ofeducation is eroded in general and the importance of mathematics and scienceeducation in particular is ignored, the power of social wealth is severely con-strained. This study shows that societies with moderate income levels, butstrong ‘social will’ and social value for mathematics and science education, cando better than high- income countries in terms of mathematics and scienceachievement.

Can cultures and values change? The answer is Yes. They change, for good andfor bad (Harrison, 1992). Can people borrow values and cultures from othercountries? The answer is also Yes. Japanese culture today embraces traditionsdeveloped elsewhere in highly diverse times and places—the language and Confu-cianism from China, Buddhism from India, China and Korea, and the institutions,arts and philosophies of China, and later from the Western world (Smith, 1983,p. 10). ‘Modernization and cultural diffusion in an increasingly interdependentworld diminish regional differences. Building on the best in one country’s past is notsuf� cient; the ability to borrow and adapt the best of all regions is becoming morevital to success in world competition …’ (Rozman, 1991, p. 36). We should alsoremember that much of the current educational systems, including the division ofeducational levels, course designs, curriculum, pedagogy, and even mathematics andscience textbooks in most Asian countries were basically transplanted and translatedfrom the Western industrialised countries around a century ago or even earlier.Such transplantation requires inventiveness and consideration of cultural andsocial contexts. Pedagogical methods, curricula and even beliefs should be ‘trans-planted’ so that they can be harmonious with indigenous practices (Hatano &Inagaki, 1998).

Acknowledgements

The author gratefully acknowledges the technical support of Eugenio Gonzalez forensuring data integrity, the editing of Kathleen O’Connor, as well as the helpfulcomments from two anonymous reviewers. The views expressed are those of theauthor alone and do not represent the views of the International Study Center atBoston College.

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Appendix I

TABLE A-I. National average scores and standard errors(grade 8, n 5 39 countries/school systems)

Country Mathematics Science

Singapore 643 (4.9) 607 (5.5)Korea (South) 607 (2.4) 565 (1.9)Japan 605 (1.9) 571 (1.6)Hong Kong 588 (6.5) 522 (4.7)Belgium-Flemish 565 (5.7) 550 (4.2)Czech Republic 564 (4.9) 574 (4.3)Slovak Republic 547 (3.3) 544 (3.2)Switzerland 545 (2.8) 522 (2.5)(Netherlands) 541 (6.7) 560 (5.0)(Slovenia) 541 (3.1) 560 (2.5)(Austria) 539 (3.0) 558 (3.7)France 538 (2.9) 498 (2.5)Hungary 537 (3.2) 554 (2.8)Russia Federation 535 (5.3) 538 (4.0)(Australia) 530 (4.0) 545 (3.9)Canada 527 (2.4) 531 (2.6)Ireland 527 (5.1) 538 (4.5)(Belgium-French) 526 (3.4) 471 (2.8)Israel 522 (6.2) 524 (5.7)(Thailand) 522 (5.7) 525 (3.7)Sweden 519 (3.0) 535 (3.0)(Germany) 509 (4.5) 531 (4.8)New Zealand 508 (4.5) 525 (4.4)England 506 (2.6) 552 (2.3)Norway 503 (2.2) 527 (1.9)(Denmark) 502 (2.8) 478 (3.1)United States 500 (4.6) 534 (4.7)(Scotland) 498 (5.5) 517 (5.1)Latvia (LSS) 493 (3.1) 485 (2.7)Iceland 487 (4.5) 494 (4.0)Spain 487 (2.0) 517 (1.7)(Greece) 484 (3.1) 497 (2.2)(Romania) 482 (4.0) 486 (4.7)Lithuania 477 (3.5) 476 (3.4)Cyprus 474 (1.9) 463 (1.9)Portugal 454 (2.5) 480 (2.3)Iran 428 (2.2) 470 (2.4)(Kuwait) 392 (2.5) 430 (3.7)(Colombia) 385 (3.4) 411 (4.1)

1 Nations shown in parentheses not meeting inter-national guidelines for sampling procedure or partici-pation rates.2 Latvia is designated LSS because only Latvian-speaking schools were tested, which represents less than65% of the population.Source: Beaton et al. (1996a,b).

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Appendix II

TABLE A-II. GNP per capita and public expenditure on education as percentage ofGNP (n 5 39 countries/school systems)

Public expenditure onGNP per capita education (levels 1 and 2)

Country (international dollars)1 as % of GNP2

United States 25860 4.02Kuwait 24500 3.46Switzerland 24390 3.72Hong Kong 23080 1.34Singapore 21430 3.38Japan 21350 2.82Canada 21230 4.62Norway 21120 5.26Denmark 20800 4.80Belgium (Flemish) 20450 3.70Belgium (French) 20450 3.70Austria 20230 4.24Germany 19890 2.43France 19820 3.61Australia 19000 3.69Iceland 18900 4.77England 18170 3.57Scotland 18170 3.57Netherlands 18080 3.30Sweden 17850 4.92New Zealand 16780 3.15Israel 15690 3.72Ireland 14550 4.21Spain 14040 3.17Cyprus 130713 3.60Portugal 12400 2.98Greece 11400 2.27Korea (South) 10540 3.43Slovenia 104043 4.20Czech Republic 7910 3.75Thailand 6870 3.00Slovak Republic 6660 2.69Hungary 6310 4.31Colombia 5970 2.83Russia Federation 5260 4.404

Latvia 5170 2.85Iran 4650 3.93Lithuania 3240 2.18Romania 2920 1.89

1 Source: World Bank 1996b. Converted at purchasing power parity (PPP). PPP isde� ned as number of units of a country’s currency required to buy same amountsof goods and services in domestic markets as one dollar would buy in the UnitedStates.2 Source: UNESCO Statistical Yearbook, 1995. Calculated by multiplying thePublic Expenditure on Education as a percentage of GNP by the percentage of publicexpenditure on the � rst and second levels of education. Figures represent the mostrecent � gures released.3 Source: UNDP, 1997, p. 146.4 Source: UNDP, 1997, p. 208.

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Appendix III

TABLE A-II. (i) Descriptive statistics for predictor variables in TIMSS data (grade 8,n 5 39)

Instructional Number of books Index of poordays a year at home school attendance

Country Mean SD Mean SD Mean SD

Australia 197 7.1 4.0 1.1 4.56 2.48Austria 2001 — 3.3 1.3 3.96 2.19Belgium (Flemish) 1821 — 3.2 1.3 2.81 1.58Belgium (French) 1821 — 3.7 1.2 4.82 3.99Canada 186 5.1 3.7 1.1 4.15 2.94Colombia 183 30.1 2.4 1.2 5.36 5.39Cyprus 172 15.3 3.3 1.2 2.75 2.11Czech Republic 198 17.1 3.9 0.9 4.36 2.28Denmark 2001 — 3.8 1.1 4.11 3.35England 190 5.9 3.6 1.2 5.85 4.35France 174 14.0 3.3 1.1 3.84 3.51Germany 195 17.1 3.6 1.3 4.23 4.06Greece —2 — 3.1 1.0 3.26 2.26Hong Kong 173 25.8 2.6 1.2 2.72 3.81Hungary 183 7.9 3.9 1.2 4.27 2.74Iceland 162 9.0 4.0 1.0 5.01 6.50Iran 205 29.3 2.5 0.8 2.75 4.31Ireland 168 4.0 3.3 1.2 4.72 3.19Israel 206 20.0 3.6 1.1 5.22 2.85Japan 231 5.4 3.32 — 2.00 1.19Korea (South) 208 24.1 3.3 1.2 0.95 3.19Kuwait —2 — 2.6 1.3 4.38 5.36Latvia 176 10.7 4.3 1.0 6.42 4.44Lithuania 185 22.6 3.5 1.1 5.24 3.68Netherlands 196 12.2 3.3 1.2 3.04 2.49New Zealand 189 7.3 3.9 1.1 4.45 3.04Norway 1851 — 4.0 1.1 3.01 1.69Portugal 180 19.8 3.0 1.2 4.41 4.37Romania 174 12.2 2.9 1.5 4.03 5.14Russia Federation 190 24.3 3.6 1.1 4.56 3.42Scotland 191 5.8 3.3 1.3 8.36 4.39Singapore 2001 — 2.9 1.1 1.82 1.50Slovak Republic 195 17.4 3.5 1.0 3.68 4.02Slovenia 179 14.0 3.5 1.1 4.02 3.19Spain 180 18.8 3.5 1.2 3.36 4.33Sweden 181 17.4 3.9 1.1 4.27 2.52Switzerland —2 — 3.4 1.2 2.07 1.47Thailand 198 9.9 2.5 0.7 2.79 2.43United States 178 4.1 3.5 1.3 3.30 2.53

1 Data from the education ministry of the country.2 International mean substitution.Note: For number of books at home: 1 5 0–10; 2 5 11–25; 3 5 26–100; 4 5 101–200;5 5 more than 200. Index of poor attendance measures percentage of absenteeism,arriving late at school and skipping classes.Source: IEA TIMSS (Third International Mathematics and Science Study, 1996).

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TABLE A-III. (ii) Descriptive statistics for predictor variables in TIMSS data (grade 8,n 5 39)

Education Perceived dif� culty Perceived dif� cultyaspiration level of math level of science

Country Mean SD Mean SD Mean SD

Australia 2.55 0.73 2.85 0.77 2.76 0.76Austria 2.15 0.47 2.93 0.90 2.44 0.80Belgium (Flemish) 2.19 0.86 2.96 0.83 2.63 0.63Belgium (French) 2.74 0.54 2.74 0.84 2.63 0.75Canada 2.74 0.63 2.52 0.87 2.60 0.82Colombia 2.04 0.97 2.36 0.88 1.99 0.80Cyprus 1.97 0.96 2.59 0.88 2.52 0.85Czech Republic 2.31 0.78 2.88 0.77 2.66 0.47Denmark 2.32 0.71 2.60 0.80 2.57 0.56England 2.571 — 2.93 0.73 2.94 0.71France 2.60 0.63 2.92 0.82 2.73 0.66Germany 1.71 0.73 2.80 1.00 2.58 0.72Greece 2.44 0.86 2.64 0.87 2.51 0.66Hong Kong 2.56 0.77 2.80 0.78 2.66 0.75Hungary 2.10 0.80 2.78 0.78 2.75 0.49Iceland 2.60 0.71 2.67 0.77 2.64 0.65Iran 2.53 0.80 2.21 0.93 1.89 0.78Ireland 2.45 0.82 2.97 0.80 2.94 0.78Israel 2.48 0.84 2.91 0.84 2.58 0.82Japan 2.75 0.45 3.11 0.66 3.01 0.61Korea (South) 2.84 0.50 2.91 0.67 2.91 0.63Kuwait 2.02 0.43 2.32 0.97 2.06 0.88Latvia 2.18 0.89 2.84 0.71 2.76 0.62Lithuania 2.37 0.79 2.98 0.71 2.56 0.50Netherlands 2.32 0.83 2.80 0.83 2.57 0.56New Zealand 2.48 0.79 2.73 0.77 2.71 0.72Norway 2.58 0.72 2.61 0.79 2.53 0.71Portugal 2.46 0.81 2.87 0.80 2.48 0.62Romania 1.87 0.91 2.65 0.94 2.41 0.67Russia Federation 2.58 0.76 2.88 0.73 2.63 0.53Scotland 2.57 0.69 2.932 — 2.81 0.73Singapore 2.97 0.22 2.76 0.78 2.61 0.71Slovak Republic 2.31 0.79 2.76 0.74 2.53 0.48Slovenia 2.47 0.74 2.94 0.80 2.79 0.52Spain 2.57 0.77 2.76 0.85 2.66 0.80Sweden 2.17 0.80 2.58 0.79 2.54 0.58Switzerland 1.99 0.66 2.78 0.84 2.55 0.76Thailand 2.54 0.72 2.73 0.69 2.56 0.67United States 2.47 0.86 2.59 0.92 2.44 0.86

Note: For education aspiration: 1 5 some secondary school; 2 5 � nish secondary school;3 5 beyond secondary school.For perceived dif� culty level of math/science (response to ‘Math/science is an easysubject’): 1 5 strongly agree; 2 5 agree; 3 5 disagree; 4 5 strongly disagree.1 Data copied from Scotland.2 Data copied from England.Source: IEA TIMSS (Third International Mathematics and Science Study, 1996).

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Cross-national Differences in Mathematics and Science Achievement 223

TABLE A-III. (iii) Descriptive statistics forpredictor variables in TIMSS data (grade 8,

n 5 39)

Number of biologicalparents at home

Country Mean SD

Australia 1.74 0.47Austria 1.78 0.45Belgium (Flemish) 1.83 0.40Belgium (French) 1.74 0.47Canada 1.67 0.52Colombia 1.50 0.66Cyprus 1.74 0.51Czech Republic 1.81 0.41Denmark 1.72 0.47England 1.73 0.46France 1.78 0.45Germany 1.76 0.47Greece 1.80 0.45Hong Kong 1.86 0.41Hungary 1.85 0.39Iceland 1.72 0.51Iran 1.89 0.37Ireland 1.88 0.34Israel 1.83 0.43Japan 1.811 —Korea (South) 1.83 0.46Kuwait 1.85 0.39Latvia 1.68 0.52Lithuania 1.77 0.47Netherlands 1.87 0.34New Zealand 1.73 0.49Norway 1.75 0.46Portugal 1.81 0.47Romania 1.61 0.60Russia Federation 1.75 0.46Scotland 1.73 0.47Singapore 1.87 0.42Slovak Republic 1.78 0.46Slovenia 1.84 0.39Spain 1.85 0.41Sweden 1.78 0.43Switzerland 1.78 0.44Thailand 1.77 0.54United States 1.62 0.54

1 Data adopted is the mean of the four Asiancountries for this variable in TIMSS (Korea,Singapore, Hong Kong and Thailand).Source: IEA TIMSS (Third International Math-ematics and Science Study, 1996).

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