countries: Multiple regression analysis of the cohort effects

The purpose of this study was to simultaneously examine relationships between teacher quality and instructional time and mathematics and science achievement of 8 th grade cohorts in 18 advanced and developing economies. In addition, the study examined changes in mathematics and science performance across the two groups of economies over time using data from the TIMSS 1995-2007 assessments. While economy did not account for variation in mathematics and science achievement, findings from regression analyses indicated significant relationships between school inputs and achievement in both groups of countries across the years. Teaching experience was a strong indicator of mathematics performance in developing countries, while instructional time was mildly related to achievement in both subjects in advanced economies.


Introduction
As greater emphasis is placed on mathematics and science in national education systems as a means of generating a high rate of return to the economy (Schofer, Ramirez, & Meyer, 2000), there has been an increasing focus on cross-national comparisons of student performance in the two subject areas.The aim of these comparisons is to assess the quality and educational efficiency of such programs in relation to the financial reforms driven by the national economy.International donor agencies such as the World Bank and International Monetary Fund (IMF) have offered prescriptions for improving efficiency and quality of education systems, while international organizations such as the Organisation for Economic Co-operation and Development (OECD) and the International Evaluation of Educational Achievement (IEA) have emphasized measurement and comparison of school outcomes, with better education outcomes considered integral to economic and social productivity (Arnove, 2007).
The purpose of this study is to explore the relationship between levels of economic performance and mathematics and science achievement in international education systems.This is important as one influences the other in meaningful ways.On the one hand, research that examined the impact of mathematics and science on development have concluded that better education outcomes, particularly in mathematics and science, are considered integral to economic and social productivity (Schofer, Ramirez, & Meyer, 2000).This is especially salient in the globalized era in which the world economy is becoming increasingly integrated, and proficiency in the two subject areas is deemed necessary to respond to technological and scientific changes.
On the other hand, and more importantly, national school systems can also focus on extending the school inputs necessary to develop the essential sets of mathematics and science skills to produce an optimal achievement outcome that corresponds to economic growth.In addition to assessing the relationship between national economy and mathematics and science achievement, other within-school factors that enhance achievement in these subject areas are explored.One role of international studies such as the IEA is to provide individual countries with the impetus to improve students' academic achievement in different subject areas through information derived from cross-national scales of comparison.Studies that have examined mathematics and science achievement have reported that differences in national curricula -in the extent to which the intended, potentially implemented and implemented curricula reflect the culture of a countryexplained much of the variation in achievement outcomes (Cogan & Schmidt, 2002;Papanastasiou, 2000).Other studies have shown that school resources contribute to variations in student achievement in developing countries, and are better predictors of mathematics than other achievement measures (Marks, Cresswell, & Ainley, 2006;Reddy, 2005).
In this study, the relationship between Gross Domestic Product (GDP) per capita and achievement in mathematics and science is examined.GDP per capita is often used as an indicator of national economy, especially in cross-national achievement studies, based on the assumption that advanced economies also tend to be high performers in mathematics and science (Baker, Goesling, & LeTendre, 2002;Chudgar & Luschei, 2009;Ramirez et al., 2006).Two research questions are raised.First, is there an increase in mathematics and science achievement over time across the different countries, and if so, does the increase in achievement correlate with GDP per capita across the years?Second, how do school level factors -such as instructional time spent in school, teacher's formal education, and teaching experience -affect mathematics and science achievement across the two groups of economies?Additionally, do these effects vary over time?

Theoretical Framework
This study subscribes to the education production function model in establishing the possible relationship between national economy and achievement in mathematics and science.The production function framework of economics explains the production of education as a function of different inputs that are important for a given context or country (Chudgar & Luschei, 2009).Most production function studies measure educational outcomes in terms of student achievement, although some studies have used alternative quantitative measures to assess outcomes, such as attendance rates and attitudinal scales.Among them, student performance is considered the most direct and measurable indicator of school outcomes.Measured achievement has been employed as a reasonable predictor of success in the labor market, as well as a plausible indicator of economically relevant skills.Educational inputs range from economic to sociological inputs such as investment into school resources, student's family background, and curricular contents.Although Hanushek and Kimko (2000) disputed the impact of direct spending on student achievement, Heyneman and Loxley (1983) found that both school and teacher qualities are key factors that influence student learning in numerous advanced and developing countries.This study examines school factors as educational inputs in relation to mathematics and science achievement.
Criticisms of the education production function model have pointed to the limitations of identifying reliable production functions in education based on three grounds.The first highlights the conceptual limitation of the underlying productivity model as it fails to capture the complex and dynamic nature of education production processes (Monk, 1992).The second criticism is directed at the outcomes-as-standards strategy used to identify the properties of the relevant production functions.Again, the issues focus on the conceptualization of the standards as well as their measurement, which obscure the implications for policy-making by the central authority as knowledge about the precise factors contributing to improved school effects are lacking.The third factor critiques the deficiency of the model that bases productivity on tangible and nonsimultaneous possession of material goods, without factoring non-material resources into the production function model (Hodas, 1993).
Modernization and human capital theories, on the other hand, focus on the role of education in advancing economic growth.They specifically examine the effect of human capital on economic growth, which this study does not intend to cover.The premise of their arguments also acknowledges the importance of mathematics and science as core subjects that contribute to the expansion of industrial production (Kamens, Meyer, & Benavot, 1996), and to the improvement of individual and national productivity (Schofer, Ramirez, & Meyer, 2000).A more recent study (Ramirez et. al., 2006), however, empirically supports that the established confidence of the positive effects of educational attainment on economic growth is unwarranted.Nonetheless, the study demonstrates that there is a positive relationship between national economy and mathematics and science achievement in the four Asian Tigers (South Korea, Taiwan, Hong Kong, and Singapore) that have achieved remarkable economic growth between the 1960s and 1990s.It is not surprising, therefore, that mathematics and science have been the most prevalent school subjects in reform efforts, especially in the lower secondary levels, to educate a more technically and scientifically literate population.Since the 1960s, developing nations have also adopted policy reforms incorporating mathematics and science into their primary school curricula as a means to achieve economic prosperity (Benavot, 2004).
School factors.School resources explain a larger proportion of variance in achievement for developing than for advanced economies.Heyneman and Loxley (H-L) (1983) proposed that variations in school resource quality can matter more than variations in family SES in affecting overall student achievement in less-developed nations, while the reverse holds true for developed nations.While the H-L findings have specifically been disputed in replicated studies on school effects (Baker, Goesling, & LeTendre, 2002;Hanushek & Luque, 2003), the literature on production function studies generally indicate that school resources are important and significant for student achievement in developing countries (Hanushek, 1995;Buchmann & Hannum, 2001).
Raising teacher quality was found to be critical to improving student learning outcomes (Rockoff, 2005), as student achievement is affected more by the teacher than by other factors such as class size or composition (Darling-Hammond & Sykes, 2003).This has been affirmed early on by the Coleman Report that highlighted teacher characteristics to account for more variance in student achievement than any other school resources (Coleman et al., 1966).Evidence from the U.S. showed that indicators of teacher quality, such as teacher certification and degree in the field to be taught, were the strongest predictors of student outcomes; while uncertified teachers were a weak predictor of student achievement (Darling-Hammond, 2000).Beginning teachers also performed significantly worse than more experienced teachers, which implied important gains in teaching quality for novice teachers in their first years of teaching (Rivkin, Hanushek, & Kain, 2005).Teacher qualifications and teaching experience were also positively associated with student achievement, especially in the lower grades (Hanushek & Luque, 2003).Teacher certification in science, that trained teachers to present scientific concepts and acquire mastery of content knowledge, was also highly correlated to student achievement in TIMSS (Vlaardingerbroek & Taylor, 2003).
In developing countries, teachers in general lack adequate academic qualifications, training and mastery of content compared to teachers in advanced economies (UNESCO, 2004).Research has shown mixed evidence on the relationship between teacher quality and student achievement in developing contexts.Students performed better in mathematics and English when taught by qualified teachers than otherwise in rural Kenya (Oneri & Goll, 2008), while students tended to score lower in science if the teachers majored in the subject in Romanian schools (Istrate et al., 2006).However, teacher education in developing countries was found to be effective in enhancing student performance as evidenced in 35 out of 63 studies conducted in the 1980s and early 1990s (Hanushek, 1995).This also supports the argument that achievement in developing nations is less affected by socioeconomic differences than by within-school factors.Furthermore, there was a notable difference in the way trained teachers taught more advanced grades and more difficult subjects, mainly in mathematics and science (Heyneman & Loxley, 1983).
When school systems allocated a greater amount of time on any given subject, Inkeles (1979) reported that it yielded national differences in academic performance.Subsequent studies have affirmed the positive effects of instructional time on student achievement, especially time spent on subject-specific instructions (Frederick & Walberg, 1980;Benavot & Gad, 2004).Instructional time is often discussed in conjunction with instructional quality and content, and is an essential component of school resources (Baker et al., 2004a).According to the economic analysis of time spent on school learning (Millot & Lane, 2002), instructional time is optimal as an educational input when it produces classroom learning as output, as measured by achievement tests.A comprehensive review of school effectiveness studies cited length of instructional time to be an important factor in influencing student achievement (Lewin, 1993).The actual amount of instructional time the students receive, as opposed to the intended instructional time that is often reported in large data surveys, matters more for learning outcomes, given the discrepancy between the intended and enacted curriculum in both developed and developing countries (Benavot & Gad, 2004).
In earlier studies, the length of time spent on subject content in developing countries was a consistent predictor of student achievement, with instructional time being comparable in magnitude to other school factors (Fuller, 1987).Subsequent studies (Baker, Goesling, & LeTendre, 2002;Baker et al., 2004a) have critiqued this on two grounds: the findings pertain to a period when the discrepancies in educational resources were greater than they are at present among developing economies, with the overall association between instructional time and achievement across countries being relatively small.Nonetheless, instructional time did account for more variances in science than in mathematics achievement (Baker et al., 2004a).In addition, developing nations allocated an extensive amount of instructional time to both subjects for their relevance to economic development (Kamens, Meyer, & Benavot, 1996).Cross-national research conducted between 1925 and 1985 showed that expanded time was given to mathematics in developing countries (Kamens & Benavot, 1991), but this trend was ambiguous between 1985 and 2000 with mathematics emphasized only in selected parts of the world, such as Latin America and the Caribbean (Benavot, 2004).

Methodology Data
For the TIMSS data collection, 42, 38, 48 and 59 countries participated in the eighth grade test-taking in 1995test-taking in , 1999test-taking in , 2003test-taking in and 2007test-taking in , respectively (Beaton et al., 1996;;Olsen et al., 2008; see Table 1).In addition to the mathematics and science tests, TIMSS also collected extensive information about home and school factors that influenced students' learning in these subjects.The database contains student achievement scores in mathematics and science, as well as large-scale responses to background questionnaires from students, mathematics and science teachers, and school principals in the participating countries (Gonzalez & Miles, 2001;Olsen et al., 2008).Table 1 shows the number of items in eighth grade mathematics and science assessment across the four years.To ensure reliable measurement of trends over time, items that had been used in 1995 and 1999 were also included in the 2003and 2007assessments (Olsen et al., 2008)).The data used in this study was aggregated by country as the measurement unit in the analyses.The sampling population included all the data available for the 18 countries for the four variables examined (student achievement, teaching experience, academic qualification, instructional days; see Tables 2a and 2b).In the 8 th grade sampling population for Korea in TIMSS 1995 (Table 2a), for example, 5827 students participated in the mathematics assessments (variable a); 288 mathematics teachers indicated the number of years they had taught (variable b) and 290 mathematics teachers had academic qualifications (variable c).There was an average of 143 full instructional days in the school year (variable d).

Hypotheses
There are two hypotheses in this study.The first hypothesis assumes there is a relationship between GDP per capita and mathematics and science achievement, with corresponding changes in the relationship between the two variables across time.
The second hypothesis posits that school factors -teaching experience, teachers' academic qualification, and time spent on instruction -are predictors of student achievement in the two subject areas.

Variables
Dependent variable.The TIMSS International Database contains achievement data for students in mathematics and science and related background data for 1995, 1999, 2003 and 2007.As dependent variables, student achievement in mathematics and science are taken from the 18 countries across the years.Each subject has five sets of plausible values based on which analyses are replicated five times per subject in this study.Plausible values are derived from five imputed values per student response to account for the error inherent in the multiple imputation process (Martin et al., 2004).
Independent variables.The TIMSS International Database includes data for school and student level variables.Teacher quality and instructional time variables are pertinent to this study at the school level.The data used to indicate teacher quality are teaching experience and teachers' academic qualification.For both subjects in 1999, teaching experience was expressed in terms of the number of years taught (open-ended numerical response) and academic qualification in terms of four categorical responses: 1 = Did not complete secondary school; 2 = Secondary school only; 3 = BA or equivalent; and 4 = MA/PhD In some cases, the variable for teacher's academic qualification expanded to six categories: 1=Did not complete ISCED 3; 2=Finished ISCED 3; 3=Finished ISCED 4; 4=Finished ISCED 5B; 5=Finished ISCED 5A, first degree; and 6=Finished ISCED 5A, second degree or higher.ISCED denotes International Standard Classification of Education and the levels indicate the following (UNESCO, 1997): ISCED 3=Upper secondary education; ISCED 4=Post-secondary non-tertiary education; ISCED 5A=Tertiary programs that are largely theoretically based and intended to provide sufficient qualifications for gaining entry into advanced research programs and professions with high skills requirements, last 3-4 years full-time (e.g. higher education); ISCED 5B=Tertiary programs that are shorter than 5A that focus on occupationally specific skills geared for entry into the labor market.For the purpose of consistency across the years, the six categories were collapsed into 1, 2-4, 5 and 6 to correspond to the four categorical responses used in 1999.
Instructional time is measured in terms of the number of full instructional days in the school year.

Analyses
Consistent with the first hypothesis, repeated measures was used to determine the relationship between GDP per capita and 8 th grade mathematics and science achievement across the years.Repeated measures analysis provides information on the time trend of the dependent variable under different conditions, with the responses to individual conditions over time an important element of analysis (Kuehl, 1994).This study used a quasi-repeated measures design since the mathematics and science tests were cross-nationally administered to a cohort group of 8 th grade students across the four years.As dependent variables, mathematics and science achievement were measured for all 18 countries that participated in TIMSS studies in 1995, 1999, 2003 and 2007.Hence, the five plausible scores for each subject were observed at each time point.The 18 countries were categorized into advanced and developing economies, with changes in both categories assessed over time.The two categories were derived from the classification of advanced and developing economies used by the IMF World Economic Outlook (IMF, October 2010): Bulgaria, Hungary, Iran, Lithuania, Romania and Russia are categorized as the six developing economies, while the remaining 12 are advanced economies.
For the second hypothesis, multiple regression was conducted to test the relationship between the school factors and student achievement.As the TIMSS 1995 data for Bulgaria was missing, a total of 17 countries were examined in the regression analysis for 1995.The regression model conveyed the level of significance of each variable on mathematics and science achievement across the two groups of countries over time.

Results
In both subjects, advanced economies (Group 1) performed better in mathematics and science than developing economies (Group 2) in 1995, 1999, 2003 and 2007 (see Tables 3a and 3b).Developing countries also showed a consistent improvement in both mathematics and science performance across the four points in time.For the first hypothesis, repeated measures analysis indicated that there was considerable growth in achievement within the two groups of countries from 1995 to 2007 even though the variation in the mean scores was small between the two groups.As shown in Tables 4a and 4b, the interaction effect was not statistically significant between GDP per capita and 8 th grade mathematics and science achievement.However, achievement was significant across the years for all mathematics plausible scores, F(3, 88) = 3.96, 4.08, 3.93, 4.02 and 3.92, p < 0.05 (see Table 4a); and all science plausible scores, F(3, 88) = 4. 73, 5.16, 5.37, 5.27 and 5.73, p < 0.05 (see Table 4b).For the second hypothesis, three school inputs (teaching experience, academic qualifications, and number of instructional days in the school year) were used to identify educational production processes and their influences on student achievement.Multiple regression was conducted to examine the effect of these school variables on mathematics and science achievement in both groups of countries: teaching experience (in terms of the number of years taught), academic qualification, and the number of full instructional days in the school year.The regression analyses showed significant effects of school variables on mathematics achievement in developing countries, and on both subjects in advanced economies, across the years.Teaching experience and the number of full instructional days were significantly associated with mathematics performance in advanced economies from 1995 to 2007, with the two variables explaining 14 percent of the proportion of the overall mathematics achievement (see Table 5a).Teaching experience and mathematics achievement, however, were inversely related implying that more teaching experience did not necessarily correspond to improved mathematics performance in developed countries.The number of full instructional days was also significantly related to science achievement for all five plausible scores (0.34, 0.33, 0.33, 0.32, 0.33, p<0.05; see Table 5c) in developed countries across the years.Instructional days accounted for 7 percent of the variance in science achievement, with positive beta weights that were twice as strong as either of the two teacher quality variables.
Similar to the findings for mathematics achievement in developed countries, teaching experience was also a significant factor that influenced mathematics achievement in developing economies from 1995 to 2007.Moreover, teaching experience was positively related to mathematics performance, as indicated by the five plausible scores for mathematics (0.68, 0.69, 0.68, 0.69, 0.68, p<0.05; see Table 5b), explaining 47 percent of the performance variance in the six developing countries.To further examine the effects of school factors in the developing countries, eight separate multiple regression analyses were conducted by subject per year.While there were no meaningful influences of the school variables on science achievement, teaching experience was again significantly related to mathematics performance in 2007 (1.27, 1.27, 1.27, 1.27, 1.26, p<0.05; see Table 5e), a factor that solely accounted for 53 percent of the variance in mathematics achievement in developing economies.
The overall results indicate that achievement variances for the two groups have reduced and the gap in variances between the two groups have narrowed since the H-L (1983) findings.The results nevertheless support their conclusion that school resources continue to be more influential in student outcomes in developing than in developed contexts: 81-90 percent of achievement variance was explained by school factors in the former, while the figures were considerably reduced to 22-27 percent in the latter.

Discussion and Conclusion
The results for the first hypothesis in this study do not support previous findings that national economy accounts for variation in mathematics and science achievement (Baker, Goesling & LeTendre, 2002;Heyneman & Loxley, 1983).Three plausible reasons explain this phenomenon.First, the age groups to which the achievement tests were administered differ.While this study examined results from 8 th grade mathematics and science achievement, Heyneman and Loxley's (1983) study was based on primary school academic achievement in 29 high-and low-income countries.Second, mass institutionalization of education in developing countries, supported by the state and international agencies, may explain the diminishing effect of national economy on mathematics and science achievement, as demonstrated by Baker and colleagues (2002) in their follow-up analysis of Heyneman and Loxley's (1983) study.Third, TIMSS does not cover a wide range of economies as the tests were administered to countries that had sufficient available resources to participate in TIMSS.This eliminated countries at the lowest end of the economic spectrum while largely including those from the upper-middle-and high-income economies.
The mean group differences in student achievement indicate that developed countries performed better than developing countries overall, although interesting observations can be made at the country level.Advanced economies like the U.S. and England (mean plausible scores 474, 495, 504, 506 for the U. S. and 484, 500, 507, 515 for England for 1995S. and 484, 500, 507, 515 for England for , 1999S. and 484, 500, 507, 515 for England for , 2003S. and 484, 500, 507, 515 for England for and 2007 respectively) respectively) consistently scored lower in mathematics than developing nations such as Hungary and Russia (mean plausible scores 513, 537, 532, 523 for Hungary and 506, 528, 510, 520 for Russia for 1995, 1999, 2003and 2007 respectively) across time.Although the two cases from each group are anomalous to the overall group findings, it is evident that Hungary and Russia are cross-nationally better in 8 th grade mathematics and science than the U.S. and England, with the pattern persistent across the four years.This can be attributed to the traditionally heavy emphasis placed on mathematics and science education in the former communist states.Conceptions of teaching mathematics were also substantially different in Bulgaria as compared to the conventional pedagogical beliefs and practices found in England (Andrews & Hatch, 2000).
The results for the second hypothesis examining the effects of school variables validate previous research that school factors still exert significant effects on variance in student achievement (Hanushek, 2006).In this study, teaching experience was the strongest predictor of mathematics achievement in developing countries across all years (Tables 5b).This is consistent with the H-L findings in which the impact of teaching experience on student achievement was proportionately greater for developing countries than for developed countries.Teaching experience remained the strongest predictor of mathematics achievement for developing economies in 2007 (Table 5e) explaining slightly more than the achievement variance for all years combined.One possible explanation for the predominance of teaching experience as a predictor of student performance is that at the primary and lower secondary levels, teachers gain greater competence over the years in the subject matter and teaching skills, which contribute to better teaching outcomes as evident in student achievement (Rivkin, Hanushek, & Kain, 2005).In addition, mathematics is a cumulative subject in which the effects of teacher's prior content knowledge on student performance becomes stronger at the advanced levels (Whitehurst, 2002).
The number of full instructional days in a year was significantly related to mathematics and science achievement in developed countries across the years (Tables 5a and 5c).While this concurs with studies that found quantity of instructional time to be a common indicator to assess student achievement (Millot & Lane, 2002;Benavot & Gad, 2004), the strength of the association between the two variables was low indicating that instructional time is a weak predictor of student performance.A plausible explanation may be that the quality of instruction matters more than the quantity of instructional hours, and that time on task is more effective in enhancing student outcomes.Research that studied the percentage of instructional time utilized in various countries found that the actual number of days engaged in learning was considerably lower than the number of days in the school year (Abadzi, 2007).
Teaching experience, in contrast, was negatively associated with mathematics performance in the same group of advanced economies across the four time points.Research on mathematics teaching in three developed countries -U.S., Germany and Japan -has shown the positive effects of teaching experience on student performance when a system of researchand-development has been established within the schools.For example, Japanese mathematics teachers reported that their individual lessons improved gradually as they participated in developing and sharing knowledge based on their own teaching practices (Stigler & Hiebert, 1999).
This study confirms that school resources continue to play an influential role on mathematics and science achievement in both advanced and developing economies.In view of the findings, two policy implications are made.First, teaching experience was a consistent and strong predictor of student performance in mathematics over time in developing economies, which implies that governments in these countries should not only provide teacher training in the subject -whether in the form or pre-service or on-the-job training -but also ensure that the trained teachers stay on in the school system through incentives and continuous professional development.These measures can prevent the attrition rate of teachers that commonly occurs in their first years of teaching.Second, the number of full instructional days was a positive and significant predictor of mathematics and science achievement over time in developed economies.The association, however, was weak implying that the amount of instructional time allocated in the curriculum may not necessarily be critical to achievement.Instead, and more importantly, the effective use of time spent on learning tasks may be a more accurate indicator of student performance.Educational policymakers can, therefore, consider strategies to reduce the gap between the intended and actual time spent on learning tasks in the curriculum to maximize learning outcomes.A few concrete measures may be to train teachers in effective mathematics and science instructional techniques; and to increase teacher accountability through systematic teacher evaluations and regular meetings in which teaching practices are developed and shared during the school year.
Note.Group 1 = Advanced economies; Group 2 = Developing economies.Variable labels for sampling population: a = Student achievement; b = Number of teaching years; c = Teacher's academic qualifications; d = Number of full instructional days in a year.n/a = Data has not been included in the TIMSS International Database.m = Missing data as items were omitted or not administered.
Note.Group 1 = Advanced economies; Group 2 = Developing economies.Variable labels for sampling population: a = Student achievement; b = Number of teaching years; c = Teacher's academic qualifications; d = Number of full instructional days in a year.n/a = Data has not been included in the International Database.m = Missing data as items were omitted or not administered.

Table 1
Number of Participating Countries and Items, 1999hematics and Science in Grade 8 for 1995, 1999, 2003 and

Table 2b
Distribution of Sampling Population by Country and Variables inScience for 1995Science for  , 1999Science for  , 2003Science for   and 2007

Table 4a
Repeated Measures Analyses for Mathematics Achievement: Plausible Values 1-5

Table 4b .
Repeated Measures Analyses for Science Achievement: Plausible Values 1-5 Note: Values enclosed in parentheses represent mean square errors.*p < .05.

Table 5a
Summary of Regression Analysis for Variables Predicting Mathematics Achievement for Group 1 (Developed Note.Variable labels: A = Teacher's academic qualifications; B = Number of years taught; C = Number of full instructional days.R² = .14for all Plausible Values 1 to 5. *p < .05.

Table 5d
Summary of Regression Analysis for Variables Predicting Mathematics Achievement for Group 2 (Developing