Open Access

Context factors and student achievement in the IEA studies: evidence from TIMSS

Large-scale Assessments in EducationAn IEA-ETS Research Institute Journal20164:12

https://doi.org/10.1186/s40536-016-0030-6

Received: 21 September 2015

Accepted: 9 August 2016

Published: 26 August 2016

Abstract

Background

The present study investigates what factors related to the school context influence student achievement on TIMSS mathematics tests across countries. A systematic review of the literature on PIRLS, TIMSS, and ICCS was conducted upstream to identify those school, teacher, and classroom factors shown to be useful predictors of student performance in previous IEA studies. Data of student samples representative of grade 8 students from 28 countries who participated in TIMSS 2011 were analysed. The main aim of the present study is to verify what school and teacher characteristics are positively associated with students’ mathematics achievement, mainly focusing on disadvantaged schools. Furthermore, it aims at identifying how school context variables contribute to explaining the performance of students in disadvantaged schools in comparison with more advantaged schools.

Methods

A separate analysis was carried out for each considered country, and the same multilevel regression model was used on the sampled schools as a whole and treating schools with high (highest tertile) and low (lowest tertile) socio-economic backgrounds as distinct groups.

Results

The results confirmed that a high socio-economic status has a significant and positive effect on student achievement: compared with students from socio-economic disadvantaged schools, students from advantaged schools performed better in mathematics achievement. This difference is more evident in countries where the gap between rich and poor people as measured by the Gini coefficient, which measures how much an economy deviates from perfect equality, is wider. However, this difference is restricted in countries with a smaller gap between rich and poor people.

Conclusions

According to the literature in the field, the results show significant differences across countries in relation to the school and teacher characteristics that have an impact on mathematics achievement of students from low and high SES schools. Different patterns were also found within countries for low and high SES schools.

Keywords

TIMSSPIRLSICCSSchool factorsContextual questionnaires

Background

A review of the literature on how school-level factors were, and still are, used to predict and interpret student performance in some of the IEA studies—i.e., PIRLS, TIMSS, and ICCS—showed that it is quite difficult to find strong associations between school-level factors and students’ results at a country level, based on data of the type collected in comparative studies, and that wide differences are found across participating countries. Such results suggest the need for more in-depth analyses. The multi-level model for an analysis of TIMSS 2011 results presented below—intended to explore whether the impact of those factors on student achievement varies in relation to the schools’ socio-economic status—originally stemmed from that review.

School-level variables in the IEA studies

From the beginning, IEA international comparative studies have included background questionnaires to collect data on contextual factors to be linked to students’ cognitive outcomes (Postlethwaite 1967; Peaker 1975; Walker 1976). Participating students, their teachers and the principals of their schools respond to background questionnaires. These questionnaires are central to the analysis of results in terms of a range of student and school characteristics—from students’ economic, social and cultural capital to context of instruction, including schools’ human and material resources, as well as school and classroom conditions and processes (IEA 1998). The school-level variables used for the development of the questionnaire address school context (e.g., urban/rural, community resources), school characteristics (e.g., school type, school size, and instructional time), school resources (e.g., teaching materials and equipment), school initiatives in the field of specific interest to each survey, school management (e.g., funding, decision-making processes, staffing practices and teacher evaluation, curricular emphasis, and parental involvement), teachers’ characteristics and activities, teaching practices, and classroom activities (Postlethwaite and Ross 1992).

Data collected through background questionnaires are central to both international reports and secondary analyses, as they allow to better contextualise student results in the cognitive tests and help identify the school and classroom factors that have a direct or indirect impact on student performance.

International reports show that the school variables associated with student achievement are mainly those related to school context, school characteristics and resources and class characteristics (Walker 1976; Postlethwaite and Ross 1992; Schulz et al. 2010; Mullis et al. 2012a, b). CIVED and ICCS 2009 found that an open classroom climate for discussion was a positive predictor of student civic knowledge in several countries, although data about that particular school characteristic were collected through the student questionnaire and not the school questionnaire (Schulz et al. 2010; Torney-Purta et al. 2001).

However, it is exceedingly difficult to draw causal inferences, such as concluding that a particular process-related school variable is directly associated with student achievement, and wide differences across and within countries are usually reported.

Several studies indicated that teacher-related factors have effects of various magnitudes on student achievement in mathematics (e.g., Rivkin et al. 2005; Akiba et al. 2007; Akyüz and Berberoglu 2010; Tsai and Yang 2015; Winnaar et al. 2015). For example, De Witte and Van Klaveren (2014), using data from Dutch students participating in TIMSS 2003, found that high test scores are associated with teaching styles that emphasize problem solving and homework.

Furthermore, several studies used the TIMSS data for secondary analyses at individual country level.

Lee and Huh (2014) investigated the impact of teachers’ instructional strategies on student learning in mathematics and what instructional strategies are positively associated with student learning outcome in the United States. Eighth grade students’ mathematics data from TIMSS 2007 were used. Teachers’ instructional strategies were found to explain approximately 17 % at the teacher level of the learning outcome.

Nilsen and Gustafsson (2014) showed that school emphasis on academic success contributed to explaining the increased science performance in Norway between TIMSS 2007 and 2011.

However, other studies found limited evidence of this impact on student achievement in both mathematics (Luschei and Chudgar 2011; Sturman and Lin 2011; Dodeen and Hilal 2012) and reading literacy (e.g., Van Daal et al. 2006; Schagen and Twist 2008). Recently, Gao (2014) investigated whether inquiry-based instruction is more effective in influencing student science achievement than traditional teaching methods. Using the TIMSS 2011 8th grade dataset from Singapore, Chinese Taipei and the US, the author did not find a clear and positive relation between the type of instruction and student achievement.

Moreover, research has still not been able to clearly identify a pool of teacher characteristics and classroom practices that consistently improve student learning across countries (Goe 2007). In a recent review of TIMSS research literature, Drent et al. (2013) outlined the existence of wide differences across countries. Phan (2008) found that different variables are associated with mathematics achievement in different countries. In her studies, she tested three different models: (1) the instructional practices model, (2) the teacher background model and (3) a full model, including all of the variables considered in the previous models. The author found that the first model was the best for the United States; the second model served as the most efficient for predicting math achievement in Egypt, and the third model performed the best in Canada and South Africa.

Martin et al. (2000) conducted an analysis on school effectiveness using TIMSS 1995 data in countries with a large between-school variance. The authors identified several characteristics that distinguished low- from high-achieving schools and then examined school factors using hierarchical linear modelling. After controlling for student socio-economic status, the factors considered did not show a strong relationship with mathematics achievement across all countries. Only a few school characteristics, such as school climate, instructional activities and teacher characteristics were found to be associated with school achievement in some countries.

Recently, a multilevel model related to TIMSS and PIRLS 2011 was developed by Martin et al. (2013) to verify what characteristics of effective schools and of specific home backgrounds are associated with higher student achievement in reading, mathematics, and science at grade 4. The results showed that the ‘Home Resources for Learning’ variable was the strongest predictor of student achievement, with significant effects on both between and within school variance in almost every country. After controlling for the ‘Home Background’ variable, the strength of the relationship between school environment and instruction and student achievement was considerably reduced across countries. The variable ‘Schools Are Safe and Orderly’ maintained a significant effect in at least one subject after controlling for ‘Home Resources’ in 15 countries, while ‘Schools Support Academic Success’ had a positive impact on student achievement in at least one subject in 10 countries. In general, this study found considerable differences across countries in the ways school variables are related to student achievement, with similar results for reading, mathematics and science.

Analyses conducted on ICCS 2009 data have shown a limited impact of school factors on student civic knowledge, except for the open classroom climate (Fraillon et al. 2011). Attempts have also been made to explore the relationships between school factors and non-cognitive students’ outcomes for ICCS 2009. Controlling for student and school SES, the impact of school variables was shown to be negligible (Caponera and Losito 2011; Caponera et al. 2012).

Apparently, these results confirm that SES is the most important contextual factor affecting student learning outcomes (Coleman et al. 1966; Coleman 1975; OECD 2005).

The literature review carried out for this study showed a relevant impact of SES at the school level: the analysis of the influence of student socio-economic status on student achievement seemed to confirm that variables such as parent educational level and the amount of resources available at home are strongly associated with student achievement (Chiu and Xihua 2008; Ismail and Awang 2008). In some studies, an index of the overall socio-economic status for each individual school was calculated as an average of student socio-economic background, and different studies showed the relevance of this variable in explaining student achievement (e.g., McConney and Perry 2010). Furthermore, in several studies, only few variables were found to have a significant effect on mathematics achievement once the socioeconomic level of schools and students was taken into account (Wiberg et al. 2013; Wiberg and Rolfsman 2013). Recently, some studies tried to better understand whether and the extent to which school variables contribute to improving student achievement in disadvantaged schools (Baird 2008; Shepherd 2013).

Sandoval-Hernández et al. (2014) used data from TIMMS 2011 (fourth grade) to compute an HLM analysis using school factors for two sub-samples: disadvantaged students and non-disadvantaged students. They compared the results across ten European countries and found that the school factors considered in the analysis have a stronger relation with non-disadvantaged student achievement in most countries.

Based on the review of the existing literature on IEA studies’ results and with particular attention to secondary analyses derived from the TIMSS Survey, the present study aims at investigating whether and the extent to which those results may help to clarify what factors related to the school context influence student achievement on the TIMSS mathematics tests across countries. On the basis of the evidence discussed so far, the aim of the present study is to verify what school and teacher characteristics are positively associated with students’ mathematics achievement, mainly focusing on disadvantaged schools. Furthermore, it aims at identifying how school context variables contribute to explaining the performance of students in disadvantaged schools in comparison with more advantaged schools.

A separate analysis was carried out for each considered country, and the same multi-level regression model was used on the sampled schools as a whole and on schools with high (highest tertile) and low (lowest tertile) socio-economic backgrounds as distinct groups. To verify whether the impact of specific school and teacher characteristics may be different in relation to the schools’ socio-economic characteristics (average student SES at school level), a hierarchical multilevel analysis of TIMSS 2011 data was conducted. The multilevel approach adopted allows for data analysis with a hierarchical structure—where the individual units (students) are “nested” within the aggregated school level. Thus, this technique makes it possible to investigate simultaneously variables measured at student level (the first level of the multilevel analysis) and the impact of some relevant school characteristics on student achievement (second level of the multilevel analysis).

Methods

Participants

The analyses presented in this paper were conducted on the TIMSS 2011 data for Grade 8 students. TIMSS used a two-stage sampling design (for a detailed description, see Martin and Mullis 2012). The overall sample consisted of 149,788 students from all participating countries, from 5177 schools.

Countries with poor reliability1 on the achievement scale were excluded from our analyses, as well as cases with missing values in one or more explanatory variables.

Measures

For the sake of brevity, only the measures that are directly relevant to the study’s aims and hypotheses will be described (for a detailed description see Martin and Mullis 2012).

Mathematics achievement scale. The scale was developed by the research group of the TIMSS project (for a detailed description of the scale, see Martin and Mullis 2012) and consisted of multiple-choice and constructed-response items. The eighth grade mathematics content domains included number, algebra, geometry, and data and chance. The cognitive domains measured were knowing, applying and reasoning. The whole item pool consisted of 217 questions. In TIMSS 2011, various combinations of the assessment items were compiled into 14 booklets while maintaining the distribution of items across content and cognitive domains. Using IRT estimates, a score of mathematics achievement was calculated for each student. The scale used to measure mathematics achievement has high internal consistency (Cronbach’s alpha international median 0.87). To take into account measurement errors, a range of five plausible values of scores in mathematics test was provided for each student (for a detailed description, see Martin and Mullis 2012). In the present study, the proficiency score for overall mathematics achievement drawn from the five plausible values obtained through the IRT methodology was used in the analyses.

The following variables derived from student, teacher and school questionnaires were used in the analyses; they are found in the literature to be good indicators of student performance in mathematics. All of the scales were constructed using IRT scaling methods, specifically the Rasch partial credit model. Using IRT partial credit scaling, student responses were placed on a scale constructed so that the mean scale score across all countries was 10, and the standard deviation was 2 (for detailed description, see Martin and Mullis 2012).

At the student level, we used the following variables derived from the Student Questionnaire and included in the TIMSS database.

Socio-economic status (SES; indicated in the International report as Home educational resources). Based on the answers in the Student Questionnaire (for a detailed description of these scales, see Martin and Mullis 2012), a general index of each student’s socio-economic status was created. The Student Questionnaire collected information about (1) student home environments, including the parents’ educational level, (2) the number of resources for study available at home, and 3) how many books there are in the home.

Mathematics self-concept (St_SCM). Students were asked to answer nine questions related to their perceived ability to study and learn mathematics, such as “I learn things quickly in mathematics”.

Students like learning mathematics (St_SLM). The scale consisted of five questions concerning the student’s interest and positive attitude towards mathematics, such as “I enjoy learning mathematics”.

Students value mathematics (St_SVM). Students were asked to answer to six questions concerning the importance of studying mathematics to their lives, e.g., “I need to do well in mathematics to get the job I want”.

Students engaged in mathematics lessons (St_EML). The scale was created based on students’ level of agreement with five statements, such as “My teacher gives me interesting things to do”.

Weekly time spent on math homework (St_HMW). The TIMSS 2011 teacher questionnaire collected information about the teachers of the students participating in the assessment. For the schools where more than one teacher per class or per school were selected, we computed the mean of the different scores. The following variables derived from the teacher questionnaire were used for the school level.

Safe and orderly school (Teach_SOS). The scale was created based on teachers’ degree of agreement with five statements regarding a disciplined climate in their schools.

Teacher working conditions (Teach_WCN). The scale was created based on teachers’ responses to five questions, such as “In your current school, how severe is each problem? Teachers do not have adequate workspace (e.g., for preparation, collaboration, or meeting with students)”.

School emphasis on academic success (Teach_EAS).

Confidence in teaching mathematics (Teach_CTM). The scale was created based on teachers’ responses to five questions, such as “In teaching mathematics to this class, how confident do you feel to adapt teaching to engage students’ interest?”

Teacher career satisfaction (Teach_CST). The scale was created based on teachers’ degree of agreement with six statements, such as “I am satisfied with being a teacher at this school”.

Collaborate to improve teaching (Teach_CIT). The scale was created based on teachers’ responses to five questions concerning the types of interactions with other teachers, such as “Collaborate in planning and preparing instructional materials”.

Instruction to engage students in learning (Teach_IES). The scale was created based on teachers’ responses to how often they used each of four instructional practices, such us “Use questioning to elicit reasons and explanations”.

The variables derived from the school questionnaire and used for the school level are the following.

Instruction affected by mathematics resource shortages (Princ_MRS). The scale was created based on principals’ responses concerning the availability of resources both at school and classroom levels, such as “How much is your school’s capacity to provide instruction affected by a shortage or inadequacy of calculators for mathematics instruction?”

School emphasis on academic successprincipal reports (Princ_EAS). The scale was created based on principals’ responses (e.g., “How would you characterize each of the following within your school?” Teachers’ degree of success in implementing the school’s curriculum).

School discipline and safety (Princ_DAS). Principals were asked to answer 11 questions regarding different discipline problems among eighth grade students at school, such as “Physical injury to other students”.

All of the variables described above, derived from both teacher and school questionnaires, are included in the TIMSS database.

In addition, the following scales were constructed ad hoc.

SES_school. The index was calculated at the school level and corresponds to the students’ SES average in each school. This index was used at the school level to select students attending schools with low socio-economic status and students attending schools with high socio-economic status.

Sum of topic taught (Teach_STT). The scale was constructed to measure how much teachers taught 19 different topics related to mathematics during the year of the test.

Teacher preparedness (Teach_PRP). A second-order factor analysis was conducted on four indices measuring teacher beliefs regarding their preparation to teach number, algebra, geometry and data. The new index explains 69 % of the variance and has good internal consistency (0.76 median Cronbach alpha across countries).

Parental involvement (Princ_PIN). A factor analysis was conducted on 10 items derived from the school questionnaire, such as “Inform parents about the behaviour and well-being of their child at school”. The index explains 69 % of the variance and has good internal consistency (0.76 median Cronbach alpha across countries).

Data analysis

The country-specific descriptive analyses were conducted using the software IEA IDB2 Analyzer—a software developed by the IEA Data Processing and Research Center for analysing data from all IEA surveys—by means of adapted macros provided by IEA TIMSS (Foy et al. 2013).

A two level hierarchical linear model was conducted by means of the software HLM 6.0 (Raudenbush et al. 2004a, b) to investigate the relationship between the school variables and student mathematics achievement, accounting for the socio-economic index. In HLM, the analysis of plausible values is done by multiple imputations.

At level 1—student level—we used the scales described earlier and derived from the student questionnaire; at level 2—school level—we used variables from both the teacher and school questionnaires described above.

In the multilevel analyses, the house weight (HOUSWGT) was used. The variable total student weight was normalized so that the sum of the weights was equal to the student sample size in the data. A proficiency score for overall mathematics achievement drawn from all five plausible values was used as dependent variable. The independent student-level variables were entered as group-mean centred student-level (level 1) variables; the independent school-level averages were entered as grand-mean centred school-level (level 2) variables.

Results and discussion

Descriptive statistics

Table 1 shows the description of participants3 in TMSS 2011 divided by class and by school.
Table 1

Descriptive statistics: number of participants

(Source TIMSS 2011 database—eight grade)

 

Number of students

Number of classes

Number of schools

Armenia

5527

236

147

Australia

5492

368

230

Chile

5521

185

184

Chinese Taipei

4951

149

147

England

3406

159

110

Finland

4127

250

142

Georgia

4358

190

164

Hong Kong, SAR

3908

118

115

Hungary

5043

244

145

Israel

4230

166

149

Italy

3677

189

184

Japan

4362

137

137

Republic of Korea

4883

145

145

Lebanon

3763

177

141

Lithuania

4747

258

141

Malaysia

5628

177

177

New Zealand

4999

231

155

Norway

3746

165

133

Romania

5296

239

146

Singapore

5874

327

165

Slovenia

4144

220

181

Sweden

4683

240

145

Thailand

5831

164

164

United Arab Emirates

12,679

564

423

Tunisia

4772

193

193

Turkey

6674

232

231

Ukraine

3316

159

148

United States

8295

439

404

Depending on the average class size in the country, one class from each sampled school may be sufficient to achieve the desired student sample size. Some countries choose to sample more than one class per school, either to increase the size of the student sample or to provide a better estimate of school-level effects (for a more detailed description see Martin and Mullis 2012). As shown in Table 1, in most countries, only one class per school was selected.

Table 2 shows the descriptive statistics for mathematics across countries. The results are presented by country in alphabetic order.
Table 2

Descriptive statistics: mean and s.e. for mathematics achievement

(Source TIMSS 2011 database—eight grade)

 

All students

Students from schools with low SES

Students from schools with high SES

Armenia

467 (2.8)

442 (5.1)

491 (5.9)

Australia

507 (5.5)

455 (6.7)

561 (11.6)

Chile

418 (2.7)

381 (4.7)

483 (6.3)

Chinese Taipei

610 (3.2)

566 (4.9)

656 (6.5)

England

506 (5.8)

441 (6.6)

564 (8.3)

Finland

514 (2.5)

502 (3.6)

531 (2.8)

Georgia

432 (4.0)

403 (5.0)

491 (5.7)

Hong Kong, SAR

585 (3.8)

529 (9.2)

637 (6.4)

Hungary

504 (3.5)

462 (5.2)

552 (4.3)

Israel

520 (4.1)

460 (7.2)

569 (5.4)

Italy

499 (2.5)

476 (4.3)

526 (3.9)

Japan

570 (2.6)

545 (3.8)

592 (5.0)

Republic of Korea

613 (2.9)

590 (3.6)

641 (4.3)

Lebanon

450 (3.7)

407 (4.0)

506 (5.8)

Lithuania

502 (2.5)

475 (3.7)

542 (4.1)

Malaysia

440 (5.4)

373 (6.4)

512 (5.9)

New Zealand

488 (5.5)

434 (5.3)

526 (7.2)

Norway

475 (2.4)

459 (3.3)

493 (3.4)

Romania

458 (4.1)

425 (7.7)

526 (6.1)

Singapore

611 (3.8)

567 (8.0)

660 (4.1)

Slovenia

505 (2.1)

491 (3.3)

517 (2.9)

Sweden

485 (2.2)

467 (3.4)

506 (3.2)

Thailand

429 (4.4)

397 (5.0)

493 (8.7)

Tunisia

425 (3.0)

394 (3.5)

457 (5.9)

Turkey

453 (4.2)

401 (5.3)

508 (8.0)

Ukraine

479 (3.9)

449 (5.2)

523 (6.5)

United Arab Emirates

455 (2.2)

418 (3.1)

497 (4.6)

United States

512 (3.2)

467 (3.7)

561 (5.1)

() standard errors appear in parentheses

Concerning mathematics achievement, the difference between students from schools with high and low socio-economic backgrounds varies across countries, from 26 in Slovenia to 138 in Malaysia.

Slovenia, Sweden, Norway and Finland showed less variation, whereas Malaysia, Australia, Chile, England, Honk Kong, SAR, Israel, Romania and Turkey showed a marked difference of more than one standard deviation.

Multilevel analyses

The TIMSS 2011 data were best described in two levels: student level (level-1), and school and teacher level (level-2). Level-1 was represented by student background and home resource variables that were unique across students and also by student characteristics such as self-efficacy and interest in mathematics. Level-2 was represented by instructional practices, teacher background and school background variables because each school had one mathematics class sampled. The analysis took place in three steps:
  1. 1.

    First, the variance between and within schools in relation to mathematics achievement was estimated (model 0, with no explanatory variables). This model provides estimates of the variance at each level (within and between schools) and is the reference point to determine how much variance is explained by subsequent models.

     
  2. 2.

    Second, the model was modified by introducing student-level variables (model 1, where the effects on student level were treated as fixed, assuming no variation across schools).

     
  3. 3.

    The following steps consisted of introducing school-level and class-level variables into the model (model 2). The model was then completed by adding the school’s average index of socio-economic background (model 3).

     
Table 3 shows the total variance, the between variance and the percentage of variance explained by the full model divided by all students, students from schools with low SES and students from schools with high SES. In Table 4, the full model is presented.
Table 3

Total variance and explained variance in mathematics achievement across countries

(Source TIMSS 2011 database—eight grade)

 

All students

Students from schools with low SES level

Students from schools with high SES level

Variance without controls

% of variance explained by model

Variance without controls

% of variance explained by model

Variance without controls

% of variance explained by model

Total variance

% of variance between schools

Within schools

Between schools

Total variance

% of variance between schools

Within schools

Between schools

Total variance

% of variance between schools

Within schools

Between schools

Armenia

7867

23

22

13

8490

25

22

0

7460

23

20

18

Australia

7602

62

31

63

5799

43

30

38

7374

65

34

63

Chile

6536

44

34

73

4741

23

26

12

6572

45

42

68

Chinese Taipei

10,690

21

36

68

10,491

10

37

43

8458

16

36

44

England

7509

68

19

64

4773

32

24

50

4773

32

35

0

Finland

4131

13

43

20

4097

16

40

31

3711

5

44

0

Georgia

9701

27

32

47

8904

20

30

20

9414

29

37

52

Hong Kong, SAR

7620

64

25

61

6584

47

23

8

3850

38

27

50

Hungary

8925

42

43

74

9154

37

38

77

4912

10

48

0

Israel

8991

42

31

65

8991

42

31

65

5799

20

33

3

Italy

5461

26

38

32

5322

25

32

9

4678

15

36

0

Japan

6781

11

31

53

6602

5

30

18

6647

15

28

56

Republic of Korea

7865

9

43

73

7572

2

42

51

7385

10

43

48

Lebanon

5545

43

18

66

3790

17

17

28

3953

24

22

39

Lithuania

5988

23

39

68

6024

13

43

54

4952

15

37

41

Malaysia

8652

67

10

65

4947

42

10

21

4415

43

20

13

New Zealand

7519

37

36

65

5850

24

32

45

5343

13

39

72

Norway

3988

12

48

48

3949

8

43

15

3673

8

50

27

Romania

9659

32

33

46

8504

28

24

6

8367

21

39

74

Singapore

6697

44

20

66

6279

25

24

35

4172

44

20

50

Slovenia

4990

11

44

20

5064

15

42

45

4685

7

42

1

Sweden

4465

13

42

62

4753

10

41

62

4022

7

46

0

Thailand

6960

51

10

36

5813

34

6

0

6927

55

16

59

Tunisia

5816

30

20

61

4261

11

16

12

6343

36

32

54

Turkey

12,824

35

31

70

10,154

21

22

33

12,854

35

41

65

Ukraine

7373

23

28

36

6806

15

21

0

6393

18

32

40

United Arab Emirates

7705

39

100

100

6263

23

20

31

7470

36

34

46

United States

5568

58

21

51

4241

41

21

19

4673

57

25

28

() standard errors appear in parentheses

Because results are rounded to the nearest whole number, some total may appear inconsistent

Table 4

Multilevel regression results: estimated effects on TIMSS mathematics achievement—school level

  

Intercept

SES_school

Princ_MRS

Princ_EAS

Princ_DAS

Princ_PIN

Teach_gender (female = 0)

Armenia

All schools

477 (4.0)

9 (7.9)

−2 (3.0)

7 (3.3)

−3 (3.0)

5 (6.3)

2 (20.3)

Low SES

452 (6.6)

−44 (26.2)

−1 (9.5)

5 (8.6)

9 (4.3)

18 (9.0)

−1 (28.6)

High SES

490 (5.1)

46 (22.4)

−3 (4.1)

2 (4.5)

0 (4.0)

1 (8.9)

56 (20.3)

Australia

All schools

508 (0.0)

64 (0.0)

−4 (0.0)

4 (0.0)

−5 (0.0)

−11 (0.0)

−1 (0.0)

Low SES

454 (6.0)

40 (15.5)

4 (3.3)

9 (4.3)

1 (7.2)

−11 (10.1)

18 (11.8)

High SES

559 (5.5)

98 (8.8)

9 (3.1)

1 (3.2)

−2 (4.1)

−12 (7.8)

−14 (10.3)

Chile

All schools

431 (2.5)

33 (3.4)

2 (1.2)

7 (1.3)

1 (2.2)

1 (2.4)

8 (5.7)

Low SES

375 (4.0)

4 (13.0)

−1 (3.2)

7 (2.3)

−1 (3.4)

4 (5.9)

2 (13.3)

High SES

487 (3.8)

49 (6.9)

−2 (2.5)

5 (2.5)

8 (4.9)

−4 (3.6)

0 (8.3)

Chinese Taipei

All schools

611 (2.5)

52 (4.1)

−1 (1.5)

1 (2.0)

−2 (1.6)

−4 (2.9)

11 (4.7)

Low SES

572 (3.3)

90 (15.0)

2 (2.3)

−3 (3.0)

0 (2.3)

1 (4.5)

24 (8.1)

High ES

653 (3.6)

52 (7.9)

−2 (1.3)

0 (3.3)

−4 (2.4)

−4 (4.8)

−7 (6.7)

England

All schools

502 (4.7)

51 (6.5)

7 (2.6)

−1 (3.4)

9.6 (4.8)

−7.9 (5.1)

6 (9.4)

Low SES

439 (4.6)

34 (17.2)

6 (4.6)

−0.1 (4.1)

7 (5.4)

13 (7.5)

−19 (12.5)

High SES

565 (6.7)

47 (17.0)

−3 (5.5)

0.5 (5.7)

5 (5.0)

34 (9.5)

28 (16.8)

Finland

All schools

512 (2.2)

21 (4.4)

2 (1.7)

4 (1.6)

1 (2.0)

−2 (2.5)

2 (4.5)

Low SES

500 (0.0)

76 (0.0)

3 (0.0)

8 (0.0)

2 (0.0)

−9 (0.0)

−3 (0.0)

High SES

528 (2.3)

12 (11.6)

3 (2.3)

7 (3.6)

0 (2.4)

6 (5.1)

−4 (5.7)

Georgia

All schools

450 (3.7)

19 (4.4)

−4 (2.9)

12 (3.0)

−2 (2.2)

9 (4.6)

20 (13.7)

Low SES

425 (5.5)

0 (12.5)

16 (6.5)

24 (6.0)

5 (2.4)

27 (9.1)

42 (24.8)

High SES

487 (5.3)

48 (16.0)

7 (4.4)

3 (4.3)

0 (4.7)

−6 (5.6)

5 (20.5)

Hong Kong, SAR

All schools

576 (4.0)

45 (7.0)

2 (2.2)

−2 (3.4)

14 (3.6)

−3 (5.7)

−8 (9.7)

Low SES

519 (6.7)

96 (36.3)

0 (2.6)

−13 (7.3)

13 (10.9)

−8 (7.4)

64 (18.7)

High SES

635 (3.2)

34 (7.9)

3 (2.6)

5 (2.3)

10 (4.1)

1 (4.9)

−3 (7.5)

Hungary

All schools

500 (3.1)

46 (5.4)

4 (2.4)

1 (2.6)

2 (2.5)

−3 (5.2)

1 (9.0)

Low SES

454 (4.0)

52 (9.3)

8 (3.7)

10 (3.1)

0 (4.3)

4 (6.0)

11 (12.0)

High SES

550 (3.2)

21 (7.5)

−1 (1.9)

8 (3.0)

3 (2.4)

11 (5.0)

17 (8.5)

Israel

All schools

526 (3.4)

38 (4.5)

3 (1.9)

1 (3.2)

3 (2.1)

8 (3.8)

−10 (8.5)

Low SES

526 (3.4)

38 (4.5)

3 (1.9)

1 (3.2)

3 (2.1)

8 (3.8)

−10 (8.5)

High SES

574 (4.3)

24 (10.5)

5 (3.6)

−1 (4.2)

−4 (5.2)

1 (4.3)

−10 (14.7)

Italy

All schools

498 (2.8)

27 (4.4)

2 (3.1)

0 (2.1)

2 (1.6)

0 (3.6)

−7 (7.6)

 

Low SES

471 (4.8)

12 (12.2)

−4 (5.9)

7 (3.7)

−2 (2.9)

−7 (6.4)

−6 (11.5)

 

High SES

525 (3.7)

20 (10.7)

1 (3.1)

−1 (3.8)

2 (2.2)

−7 (5.7)

−10 (9.3)

Japan

All schools

569 (1.8)

26 (4.7)

2 (1.4)

2 (1.5)

1 (0.8)

2 (2.2)

1 (5.3)

 

Low SES

550 (2.3)

24 (11.2)

2 (2.3)

1 (1.6)

−2 (1.0)

3 (3.8)

−7 (7.5)

 

High SES

589 (2.9)

39 (10.8)

−1 (2.9)

−2 (2.0)

8 (2.8)

9 (5.9)

8 (11.7)

Republic of Korea

All schools

616 (2.1)

35 (3.6)

−1 (0.7)

1 (1.0)

1 (0.8)

0 (1.9)

0 (3.9)

 

Low SES

592 (1.8)

2 (10.8)

2 (0.9)

3 (1.2)

1 (1.2)

−4 (3.1)

2 (5.8)

 

High SES

640 (2.6)

4 (7.5)

0 (2.1)

3 (2.2)

−1 (1.7)

−1 (4.2)

5 (9.3)

Lebanon

All schools

455 (2.9)

29 (3.1)

4 (1.4)

4 (1.9)

2 (1.5)

−3 (3.3)

−2 (6.6)

 

Low SES

406 (3.3)

25 (6.3)

3 (2.6)

9 (2.0)

1 (2.0)

10 (4.0)

0 (12.2)

 

High SES

500 (3.3)

18 (8.3)

5 (1.8)

3 (3.4)

4 (1.3)

−1 (5.4)

−6 (10.3)

Lithuania

All schools

503 (2.2)

42 (3.9)

−1 (2.1)

5 (2.5)

2 (2.3)

−1 (3.3)

−14 (17.0)

 

Low SES

470 (2.8)

53 (14.4)

−1 (3.2)

12 (4.7)

1 (2.2)

−8 (5.1)

−26 (24.9)

 

High SES

540 (3.0)

43 (6.9)

3 (3.7)

−1 (3.1)

−4 (4.6)

6 (5.2)

−2 (15.1)

Malaysia

All schools

437 (3.5)

64 (4.5)

0 (1.9)

−3 (2.5)

7 (3.1)

0 (4.8)

−5 (10.0)

 

Low SES

372 (4.6)

39 (14.8)

1 (3.7)

−3 (4.1)

3 (5.2)

9 (8.9)

−5 (11.8)

 

High SES

512 (4.7)

23 (8.5)

5 (3.0)

0 (4.0)

−3 (4.3)

−1 (6.9)

−9 (17.0)

New Zealand

All schools

481 (3.0)

52 (4.9)

−2 (1.7)

6 (2.2)

8 (3.6)

3 (4.1)

13 (6.5)

 

Low SES

432 (3.9)

59 (7.8)

−3 (2.6)

7 (2.9)

4 (4.7)

−3 (5.5)

10 (7.8)

 

High SES

527 (2.0)

−2 (10.7)

5 (1.7)

9 (2.2)

−5 (2.4)

18 (5.7)

−7 (4.5)

Norway

All schools

478 (1.7)

25 (3.8)

−1 (1.4)

1 (1.4)

5 (1.5)

−5 (2.6)

8 (3.9)

 

Low SES

462 (2.3)

45 (11.3)

1 (4.4)

1 (2.4)

4 (2.3)

6 (4.5)

4 (6.2)

 

High SES

495 (2.1)

33 (11.9)

0 (1.7)

1 (2.6)

6 (1.7)

−5 (3.9)

4 (6.8)

Romania

All schools

467 (3.9)

28 (3.9)

5 (3.8)

7 (3.1)

1 (2.8)

−2 (6.0)

−4 (10.9)

 

Low SES

422 (6.3)

12 (18.1)

10 (8.1)

11 (5.5)

3 (4.9)

−5 (9.3)

−12 (19.6)

 

High SES

512 (2.8)

60 (5.6)

0 (3.3)

−5 (2.5)

1 (2.3)

4 (3.7)

21 (6.2)

Singapore

All schools

612 (2.7)

55 (4.5)

0 (0.9)

2 (1.3)

4 (2.2)

11 (4.1)

2 (5.5)

 

Low SES

574 (3.8)

88 (14.9)

−1 (2.1)

4 (2.7)

0 (4.3)

−7 (6.5)

14 (10.0)

 

High SES

661 (3.9)

39 (10.7)

0 (1.3)

0 (2.9)

6 (3.3)

2 (4.3)

−19 (9.5)

Slovenia

All schools

503 (2.0)

24 (5.4)

−1 (1.2)

3 (1.3)

−1 (1.2)

−2 (2.7)

4 (5.1)

 

Low SES

489 (2.9)

79 (18.6)

−4 (2.3)

4 (2.2)

5 (2.3)

−1 (4.4)

21 (6.1)

 

High SES

517 (2.5)

35 (8.7)

−3 (2.3)

4 (2.8)

4 (2.2)

6 (4.1)

16 (6.7)

Sweden

All schools

487 (1.8)

28 (4.2)

0 (1.3)

0 (1.2)

4 (2.0)

4 (2.0)

3 (3.8)

 

Low SES

467 (2.4)

30 (7.9)

−4 (2.1)

−3 (2.4)

7 (2.3)

0 (3.2)

4 (6.3)

 

High SES

511 (2.9)

8 (10.8)

1 (3.4)

7 (3.0)

7 (3.4)

−5 (3.6)

−8 (5.5)

Thailand

All schools

438 (4.5)

36 (5.4)

3 (2.6)

0 (3.1)

−4 (4.2)

−5 (7.7)

5 (10.6)

 

Low SES

398 (6.4)

−25 (26.3)

−7 (4.7)

1 (5.3)

−8 (5.3)

17 (9.4)

2 (15.8)

 

High SES

502 (6.2)

57 (6.1)

6 (4.5)

−1 (6.9)

−11 (7.0)

27 (10.6)

8 (15.2)

Tunisia

All schools

424 (2.5)

28 (2.5)

−3 (2.3)

1 (1.3)

−1(1.4)

0 (3.3)

9 (5.2)

 

Low SES

399 (3.2)

32 (6.6)

7 (2.5)

−2 (1.5)

2 (3.1)

1 (3.2)

−7 (7.2)

 

High SES

459 (4.6)

46 (7.5)

−3 (4.5)

4 (3.0)

−5 (3.0)

3 (5.0)

3 (8.2)

Turkey

All schools

453 (2.8)

31 (2.7)

1 (2.6)

6 (1.8)

2 (1.5)

−1 (3.2)

2 (5.8)

 

Low SES

409 (4.5)

17 (7.4)

1 (3.8)

6 (3.1)

0 (3.2)

4 (6.8)

3 (10.0)

 

High SES

507 (4.6)

47 (8.7)

2 (3.5)

7 (3.2)

1 (2.4)

0 (7.0)

−1 (11.2)

Ukraine

All schools

486 (3.1)

28 (5.0)

−1 (3.7)

1 (3.8)

4 (2.1)

−1 (5.5)

9 (9.4)

 

Low SES

461 (4.8)

40 (14.9)

8 (7.7)

−5 (6.1)

−3 (3.6)

25 (14.2)

−3 (19.4)

 

High SES

518 (4.3)

51 (13.5)

1 (4.8)

7 (6.3)

7 (3.8)

3 (7.0)

69 (34.4)

United Arab Emirates

All schools

497 (3.9)

45 (8.7)

3 (1.9)

1 (2.6)

3 (2.5)

8 (5.6)

−1 (9.2)

 

Low SES

420 (3.5)

31 (9.1)

1 (2.0)

2 (1.8)

1 (1.4)

0 (3.8)

38 (9.1)

 

High SES

497 (3.9)

45 (8.7)

3 (1.9)

1 (2.6)

3 (2.5)

8 (5.6)

−1 (9.2)

United States

All schools

507 (2.4)

40 (3.3)

2 (1.2)

1 (1.6)

−3 (2.0)

2 (2.6)

−6 (5.2)

 

Low SES

473 (3.7)

30 (8.6)

−1 (2.1)

2 (2.6)

−4 (4.1)

4 (3.7)

−11 (8.1)

 

High SES

558 (4.5)

46 (13.4)

2 (2.1)

0 (2.9)

−4 (4.0)

6 (5.1)

4 (9.8)

  

Teach_WCN

Teach_EAS

Teac h_SOS

Teach_CTM

Teach_CST

Teach_CIT

Teach_IES

Teach_PRP

Teach_STT

Armenia

All schools

3 (2.8)

3 (3.1)

2 (2.6)

5 (3.1)

−1 (2.7)

0 (2.5)

0 (2.1)

−20 (12.7)

0 (1.8)

 

Low SES

6 (7.9)

4 (5.3)

−2 (5.1)

−2 (4.6)

−2 (4.7)

−7 (8.1)

3 (4.8)

−9 (20.0)

−1 (4.4)

 

High SES

3 (3.4)

1 (4.0)

−5 (3.9)

7 (4.8)

0 (3.7)

3 (2.1)

1 (3.2)

−8 (16.2)

2 (2.5)

Australia

All schools

−1 (0.0)

4 (0.0)

−1 (0.0)

3 (0.0)

−2 (0.0)

3 (0.0)

−1 (0.0)

−6 (0.0)

−1 (0.0)

 

Low SES

1 (3.7)

3 (3.8)

−2 (3.7)

1 (3.9)

1 (3.8)

4 (2.8)

3 (4.1)

−3 (7.3)

2 (1.7)

 

High SES

−4 (3.8)

8 (4.4)

−5 (5.9)

9 (2.8)

−3 (2.7)

0 (3.9)

−4 (4.3)

−7 (18.7)

4 (1.9)

Chile

All schools

0 (1.4)

0 (1.6)

2 (1.2)

−1 (1.8)

4 (1.6)

1 (1.2)

−2 (1.6)

2 (2.9)

1 (1.0)

 

Low SES

−1 (2.6)

−6 (2.8)

0 (2.4)

0 (5.2)

9 (2.8)

3 (3.6)

3 (4.1)

1 (6.8)

2 (1.9)

 

High SES

3 (2.5)

0 (2.2)

1 (3.1)

−4 (3.9)

−1 (3.1)

0 (1.6)

−1 (2.0)

−2 (18.9)

1 (1.3)

Chinese Taipei

All schools

0 (1.8)

1(1.7)

1 (1.4)

−1(1.3)

−3 (1.9)

−1 (1.2)

1 (1.0)

2 (2.7)

−2 (1.2)

 

Low SES

0 (2.4)

0 (3.1)

0 (3.2)

2 (2.2)

−6 (3.3)

0 (2.0)

2 (1.8)

4 (5.6)

2 (1.5)

 

High SES

3 (2.9)

1 (2.5)

0 (2.4)

2 (2.0)

−1 (3.3)

6 (2.3)

0 (1.7)

2 (3.3)

−4 (2.4)

England

All schools

−5 (3.2)

1 (3.2)

4 (3.3)

0 (3.7)

3 (2.5)

−2 (2.4)

−1 (2.2)

−6 (7.6)

1 (6.0)

 

Low SES

0 (4.6)

1 (3.5)

9 (3.9)

13 (6.0)

7 (3.6)

−6 (3.0)

−3 (3.1)

18 (12.6)

5 (19.0)

 

High SES

−2 (3.4)

−2 (6.2)

3 (5.6)

0 (5.0)

2 (2.4)

4 (4.5)

3 (4.6)

−5 (12.0)

−5 (28.0)

Finland

All schools

−2 (2.0)

−1 (1.7)

2 (1.8)

0 (1.3)

−1 (1.5)

−2 (1.4)

1 (1.1)

4 (4.5)

0 (1.2)

 

Low SES

−2 (0.0)

−3 (0.0)

5 (0.0)

−2 (0.0)

6 (0.0)

−5 (0.0)

0 (0.0)

−11 (0.0)

4 (0.0)

 

High SES

−2 (2.6)

0 (3.1)

−3 (2.3)

−2 (2.2)

3 (2.2)

2 (1.8)

−1 (1.7)

−2 (7.6)

4 (2.7)

Georgia

All schools

0 (2.0)

10 (2.7)

2 (3.0)

−1 (2.1)

−2 (2.3)

4 (2.2)

1 (2.2)

6 (6.2)

3 (2.0)

 

Low SES

6 (4.8)

3 (6.0)

−4 (5.1)

1 (3.7)

−9 (5.6)

11 (2.6)

3 (4.0)

−6 (7.9)

4 (2.8)

 

High SES

−2 (3.5)

7 (3.3)

3 (4.3)

−4 (5.0)

−1 (2.9)

−4 (7.1)

5 (3.8)

35 (21.1)

−4 (4.2)

Hong Kong, SAR

All schools

−3 (3.5)

2 (3.7)

3 (3.1)

−1 (2.7)

2 (2.6)

0 (2.6)

0 (2.3)

8 (6.4)

4 (1.8)

 

Low SES

17 (7.4)

2 (6.5)

2 (6.4)

−2 (4.4)

19 (6.8)

3 (3.9)

1 (4.2)

25 (7.5)

−6 (3.4)

 

High SES

0 (2.7)

−6 (4.7)

8 (2.7)

3 (2.9)

−2 (2.5)

−5 (2.3)

8 (1.7)

16 (3.7)

−3 (4.6)

Hungary

All schools

−1 (1.7)

0 (2.8)

1 (2.1)

−4 (3.0)

−4 (1.9)

−2 (2.6)

3 (2.3)

7 (3.9)

−8 (2.8)

 

Low SES

1 (2.0)

0 (4.0)

2 (3.1)

20 (5.7)

−1 (2.4)

−6 (3.8)

10 (4.0)

14 (5.0)

8 (3.3)

 

High SES

−4 (2.2)

4 (2.4)

−1 (2.6)

2 (2.1)

−3 (2.8)

1 (4.2)

0 (2.2)

−1 (2.4)

−3 (2.4)

Israel

All schools

7 (2.3)

3 (2.0)

5 (2.2)

0 (1.8)

2 (2.1)

−1 (2.0)

1 (2.2)

4 (4.2)

0 (1.6)

 

Low SES

7 (2.3)

3 (2.0)

5 (2.2)

0 (1.8)

2 (2.1)

−1 (2.0)

1 (2.2)

4 (4.2)

0 (1.6)

 

High SES

−7 (4.7)

2 (3.2)

8 (4.4)

−2 (3.6)

2 (2.8)

0 (3.7)

−4 (4.7)

11 (7.8)

−2 (1.8)

Italy

All schools

0 (1.8)

4 (2.3)

1 (1.8)

1 (1.5)

−1 (1.8)

−2 (1.6)

3 (1.6)

0 (2.5)

−1 (1.7)

 

Low SES

1 (3.3)

5 (4.6)

4 (3.7)

4 (2.7)

−1 (2.9)

2 (3.8)

10 (2.9)

−5 (4.4)

2 (3.3)

 

High SES

0 (3.3)

3 (3.4)

−5 (2.7)

−1 (2.9)

0 (3.9)

1 (2.5)

−3 (2.7)

−5 (5.6)

3 (2.9)

Japan

All schools

1 (1.0)

3 (1.0)

0 (1.3)

0 (1.1)

1 (1.1)

0 (0.9)

0 (1.2)

1 (1.8)

2 (1.1)

 

Low SES

2 (1.5)

3 (1.5)

5 (3.2)

1 (1.4)

1 (1.4)

−5 (2.3)

0 (1.8)

−1 (2.3)

2 (2.0)

 

High SES

0 (1.7)

4 (1.8)

−3 (3.4)

5 (1.9)

7 (2.5)

2 (1.6)

−3 (2.1)

14 (4.1)

−3 (2.9)

Republic of Korea

All schools

1 (1.1)

3 (1.1)

−1 (1.5)

2 (0.7)

0 (1.2)

1 (0.8)

0 (1.0)

−2 (1.7)

0 (0.5)

 

Low SES

0 (1.2)

2 (1.6)

−1 (1.8)

−2 (1.0)

2 (1.5)

3 (1.0)

3 (1.2)

−3 (2.1)

0 (0.8)

 

High SES

0 (1.4)

2 (2.0)

−1 (2.3)

−1 (1.3)

−3 (2.0)

0 (2.4)

0 (2.4)

0 (3.9)

−1(1.1)

Lebanon

All schools

1 (1.5)

1 (1.8)

1 (1.9)

2 (1.5)

−1 (1.5)

2 (1.5)

−1 (1.9)

−1 (3.6)

1 (1.1)

 

Low SES

6 (2.9)

6 (2.8)

−3 (1.6)

7 (2.5)

6 (1.9)

1 (1.8)

−1 (2.5)

−7 (5.1)

4 (1.8)

 

High SES

1 (2.5)

0 (2.5)

2 (3.7)

−2 (2.7)

−2 (1.9)

−1 (1.8)

7 (2.8)

−8 (4.8)

3 (1.4)

Lithuania

All schools

−1 (1.4)

0 (1.5)

0 (2.0)

2 (2.0)

0 (1.6)

−1 (1.7)

−3 (1.9)

−3 (7.6)

−1 (1.6)

 

Low SES

0 (1.8)

3 (2.6)

0 (3.1)

9 (2.5)

−2 (2.5)

−1 (2.7)

6 (2.6)

−11 (10.7)

0 (2.2)

 

High SES

0 (2.4)

2 (2.7)

0 (2.4)

6 (2.4)

1 (1.7)

−3 (2.2)

4 (2.8)

2 (11.2)

4 (2.5)

Malaysia

All schools

−5 (2.5)

2 (2.0)

−1 (2.4)

−1 (1.9)

1 (2.5)

−3 (2.7)

2 (1.9)

9 (4.0)

−1 (1.2)

 

Low SES

−1 (3.0)

−1 (3.2)

−8 (3.6)

−1 (2.5)

10 (4.9)

−3 (3.7)

1 (2.6)

12 (5.2)

−1 (1.5)

 

High SES

−1 (6.1)

5 (2.6)

0 (4.2)

2 (3.1)

−2 (3.3)

−1 (4.9)

3 (2.4)

2 (9.4)

0 (1.9)

New Zealand

All schools

−2 (1.4)

0 (2.3)

4 (2.0)

−4 (1.7)

0 (1.6)

0 (1.9)

2 (2.1)

7 (3.6)

−1 (1.2)

 

Low SES

−4 (2.4)

−3 (3.1)

4 (3.7)

−4 (2.3)

4 (2.4)

1 (2.2)

5 (2.3)

10 (4.3)

4 (1.7)

 

High SES

0 (2.3)

4 (2.1)

5 (2.3)

−2 (2.2)

−4 (2.4)

0 (2.1)

0 (1.9)

13 (2.6)

2 (1.4)

Norway

All schools

−1 (1.3)

3 (1.8)

0 (1.4)

1 (1.2)

0 (1.1)

3 (1.0)

0 (1.3)

6 (2.4)

1 (0.7)

 

Low SES

1 (1.8)

−1 (3.8)

−1 (3.1)

4 (2.0)

−1 (1.8)

4 (2.0)

1 (2.2)

−6 (4.1)

−1 (1.5)

 

High SES

6 (2.6)

10 (3.2)

−2 (2.3)

1 (1.4)

2 (2.4)

1 (1.8)

2 (1.3)

6 (2.4)

−1 (1.3)

Romania

All schools

−1 (2.4)

0 (2.4)

1 (3.3)

3 (4.1)

−2 (1.8)

0 (3.5)

4 (2.7)

8 (8.2)

−3 (2.1)

 

Low SES

1 (4.2)

−1 (4.6)

1 (4.7)

4 (6.8)

−3 (3.9)

−3 (5.1)

7 (5.4)

11 (12.6)

−3 (4.1)

 

High SES

−2 (2.4)

7 (2.2)

−2 (2.2)

−5 (3.9)

−2 (1.6)

0 (2.2)

4 (3.1)

27 (17.5)

2 (1.4)

Singapore

All schools

−2 (1.6)

1 (1.5)

0 (1.9)

1 (1.8)

1 (1.6)

3 (1.3)

2 (1.9)

1 (5.0)

−1 (1.1)

 

Low SES

−3 (3.4)

−4 (2.3)

−3 (2.8)

1 (3.8)

6 (3.1)

0 (3.4)

4 (2.6)

3 (5.8)

0 (1.3)

 

High SES

−1 (2.8)

3 (3.3)

5 (3.8)

−4 (2.1)

−1 (2.9)

2 (2.8)

6 (2.9)

10 (9.2)

−3 (1.5)

Slovenia

All schools

−1 (1.1)

3 (1.5)

−2 (1.5)

1 (1.5)

−1 (1.6)

2 (1.3)

−1 (1.1)

8 (3.7)

2 (1.4)

 

Low SES

0 (2.3)

8 (3.3)

0 (2.3)

0 (2.5)

−3 (2.1)

1 (1.5)

−3 (2.2)

12 (3.6)

3 (2.2)

 

High SES

1 (1.3)

0 (2.6)

−7 (2.8)

6 (2.6)

2 (1.9)

3 (2.0)

−2 (1.4)

16 (4.3)

0 (1.6)

Sweden

All schools

2 (1.2)

3 (1.4)

−1 (1.5)

−1 (1.4)

1 (1.0)

1 (0.9)

−1 (1.1)

1 (3.0)

0 (0.5)

 

Low SES

0 (1.4)

3 (3.3)

4 (2.7)

−5 (2.8)

3 (2.4)

1 (1.8)

0 (1.3)

12 (6.6)

1 (1.0)

 

High SES

5 (3.2)

1 (2.2)

2 (1.8)

−1 (2.4)

0 (1.3)

4 (1.2)

−3 (2.9)

5 (4.8)

−1 (1.0)

Thailand

All schools

−1 (3.7)

1 (2.8)

−2 (2.7)

2 (2.2)

0 (5.0)

−2 (2.2)

2 (2.8)

−5 (4.3)

1 (1.2)

 

Low SES

1 (4.8)

4 (5.2)

0 (3.2)

4 (3.8)

−17 (15.7)

1 (3.9)

−5 (4.5)

−7 (6.2)

−1 (1.8)

 

High SES

4 (8.1)

5 (3.9)

6 (5.1)

7 (3.6)

−2 (4.9)

5 (2.2)

3 (4.5)

2 (5.9)

−3 (2.2)

Tunisia

All schools

4 (1.7)

3 (1.5)

2 (1.4)

−3 (1.6)

0 (1.3)

0 (1.0)

2 (1.3)

−3 (3.2)

1 (0.8)

 

Low SES

−3 (3.2)

0 (2.0)

5 (2.1)

−3 (2.2)

−2 (1.9)

0 (1.8)

3 (1.7)

5 (3.3)

0 (1.5)

 

High SES

−3 (4.1)

1 (3.2)

−4 (3.4)

−2 (3.0)

1 (3.3)

−1 (2.5)

7 (3.0)

−11 (7.0)

3 (1.4)

Turkey

All schools

5 (1.7)

−2 (1.7)

8 (1.9)

2 (1.5)

0 (1.3)

−2 (1.6)

2 (1.6)

6 (3.1)

2 (1.5)

 

Low SES

4 (2.1)

−4 (2.8)

8 (2.9)

3 (2.6)

1 (1.7)

5 (2.4)

5 (2.6)

14 (6.3)

3 (2.0)

 

High SES

−5 (2.7)

−3 (3.1)

8 (3.8)

0 (2.9)

−3 (2.7)

0 (2.9)

2 (3.1)

10 (5.2)

1 (2.0)

Ukraine

All schools

0 (2.7)

1 (3.3)

0 (2.9)

−1 (4.1)

1 (2.8)

0 (3.6)

1 (2.6)

−3 (3.7)

6 (2.6)

 

Low SES

−2 (4.6)

11 (4.5)

−7 (4.5)

−9 (7.8)

6 (5.1)

−4 (6.9)

−2 (3.8)

−3 (6.2)

4 (6.7)

 

High SES

−2 (4.1)

−4 (6.4)

−3 (4.3)

15 (8.5)

3 (4.0)

1 (4.5)

1 (3.9)

0 (6.9)

4 (3.2)

United Arab Emirates

All schools

−2 (1.8)

6 (2.7)

2 (3.8)

−2 (2.8)

6 (2.7)

−4 (2.2)

−1 (3.2)

10 (5.4)

3 (1.7)

 

Low SES

0 (2.2)

3 (2.5)

5 (2.6)

−1 (2.0)

0 (2.2)

−6 (3.1)

1 (2.5)

−5 (5.1)

1 (1.1)

 

High SES

−2 (1.8)

6 (2.7)

2 (3.8)

−2 (2.8)

6 (2.7)

−4 (2.2)

−1 (3.2)

10 (5.4)

3 (1.7)

United States

All schools

0 (1.2)

0 (1.5)

−2 (1.6)

1 (1.7)

−2 (1.4)

0 (1.0)

0 (1.8)

2 (4.4)

3 (0.9)

 

Low SES

−1 (1.9)

1 (2.1)

0 (2.1)

2 (2.8)

−6 (2.4)

0 (1.6)

−1 (3.4)

−3 (5.8)

−2 (1.3)

 

High SES

5 (2.2)

0 (2.9)

−6 (3.7)

2 (3.3)

−3 (2.4)

1 (1.7)

−1 (3.2)

−6 (6.5)

5 (2.3)

  

Student_gender (female = 0)

SES_student

St_SLM

St_SVM

St_SCM

St_EML

St_HMW

Armenia

All schools

−9 (2.6)

5 (1.0)

5 (1.0)

−2 (0.8)

16 (1.1)

0 (0.8)

−8 (1.9)

 

Low SES

11 (5.1)

5 (1.3)

5 (1.6)

5 (1.3)

18 (1.1)

1 (1.7)

15 (4.4)

 

High SES

8 (3.7)

4 (1.6)

4 (1.5)

0 (1.0)

13 (1.6)

0 (1.3)

−5 (3.0)

Australia

All schools

−2 (3.8)

6 (1.3)

2 (1.1)

−1 (1.2)

14 (1.2)

−2 (1.1)

0 (2.4)

 

Low SES

−5 (5.1)

7 (1.3)

1 (1.6)

−1 (1.3)

14 (1.1)

−1 (1.7)

−1 (4.4)

 

High SES

−4 (5.3)

6 (1.3)

1 (1.3)

0 (1.0)

14 (1.3)

−2 (1.2)

0 (2.8)

Chile

All schools

10 (3.4)

4 (0.7)

0 (1.0)

0 (0.8)

17 (0.8)

3 (0.9)

1 (2.2)

 

Low SES

6 (4.3)

5 (1.5)

2 (1.5)

−1 (1.2)

16 (1.4)

3 (1.1)

−3 (4.0)

 

High SES

13 (3.0)

2 (1.3)

−1 (1.0)

2 (1.0)

17 (0.8)

4 (0.8)

3 (2.8)

Chinese Taipei

All schools

15 (2.1)

12 (0.8)

5 (1.0)

2 (0.9)

17 (0.9)

−2 (0.9)

10 (2.7)

 

Low SES

12 (3.8)

12 (1.7)

7 (2.0)

2 (1.9)

16 (1.3)

−1 (1.9)

10 (4.4)

 

High SES

22 (3.5)

10 (1.2)

4 (1.8)

4 (1.3)

16 (1.5)

−1 (1.5)

10 (2.9)

England

All schools

5 (2.4)

8 (1.1)

−1 (1.2)

0 (1.0)

11 (0.9)

0 (1.0)

−2 (2.5)

 

Low SES

−5 (4.7)

10 (2.1)

−4 (2.8)

1 (2.0)

14 (1.9)

2 (1.8)

−1 (5.7)

 

High SES

−5 (3.7)

7 (1.5)

0 (1.4)

−1 (1.2)

11 (1.2)

−1 (1.4)

−3 (3.7)

Finland

All schools

−9 (2.3)

8 (0.7)

2 (1.0)

1 (0.9)

17 (1.2)

−5 (1.0)

8 (1.4)

 

Low SES

−7 (3.7)

7 (1.7)

2 (2.1)

1 (1.4)

17 (1.2)

7 (1.6)

9 (3.3)

 

High SES

14 (3.9)

6 (1.3)

1 (1.7)

1 (0.9)

16 (1.2)

−3 (2.3)

6 (6.0)

Georgia

All schools

−1 (3.9)

8 (1.3)

3 (1.3)

4 (1.1)

21 (1.7)

0 (1.3)

12 (2.1)

 

Low SES

5 (8.7)

15 (2.8)

1 (2.1)

−1 (2.4)

21 (2.8)

−2 (2.6)

10 (3.7)

 

High SES

−2 (3.8)

5 (1.8)

2 (1.4)

6 (1.3)

21 (1.5)

1 (1.2)

18 (3.5)

Hong Kong, SAR

All schools

9 (2.4)

0 (0.7)

3 (0.9)

1 (0.8)

9 (0.8)

0 (1.4)

−2 (2.6)

 

Low SES

12 (3.4)

0 (1.3)

3 (1.5)

2 (1.2)

11 (1.5)

−1 (1.3)

1 (3.2)

 

High SES

6 (2.8)

1 (1.2)

4 (1.3)

2 (0.9)

8 (0.9)

1 (1.1)

−1 (2.2)

Hungary

All schools

−3 (2.3)

12 (1.0)

−2 (1.2)

0 (0.9)

19 (0.8)

−2 (0.9)

4 (1.7)

 

Low SES

−5 (5.1)

16 (1.7)

−2 (2.7)

0 (2.3)

20 (1.7)

−1 (1.6)

1 (3.4)

 

High SES

−1 (2.5)

8 (1.2)

0 (0.9)

0 (0.8)

18 (0.9)

3 (1.2)

5 (2.2)

Israel

All schools

−4 (0.0)

9 (0.0)

−1 (0.0)

2 (0.0)

17 (0.0)

4 (0.0)

7 (0.0)

 

Low SES

−4 (3.4)

9 (0.7)

−1 (1.0)

2 (0.8)

17 (0.8)

4 (0.9)

7 (2.2)

 

High SES

3 (6.1)

9 (1.4)

1 (1.3)

0 (1.3)

15 (1.3)

4 (1.6)

−6 (4.2)

Italy

All schools

1 (0.0)

8 (0.0)

0 (0.0)

3 (0.0)

19 (0.0)

2 (0.0)

3 (0.0)

 

Low SES

1 (5.0)

9 (1.6)

2 (2.3)

−2 (1.8)

17 (1.7)

−3 (2.1)

5 (3.7)

 

High SES

1 (4.7)

8 (1.1)

−1 (1.9)

0 (1.8)

19 (1.5)

4 (1.9)

2 (3.0)

Japan

All schools

9 (0.0)

11 (0.0)

2 (0.0)

4 (0.0)

19 (0.0)

2 (0.0)

10 (0.0)

 

Low SES

13 (4.0)

12 (1.4)

2 (2.4)

3 (1.9)

20 (1.9)

−2 (2.1)

2 (5.4)

 

High SES

7 (3.0)

11 (1.6)

1 (1.4)

4 (1.6)

18 (1.9)

1 (1.2)

9 (4.3)

Republic of Korea

All schools

4 (0.0)

13 (0.0)

3 (0.0)

6 (0.0)

22 (0.0)

0 (0.0)

3 (0.0)

 

Low SES

−3 (5.1)

12 (1.5)

2 (2.0)

8 (1.5)

24 (1.6)

−1 (1.3)

3 (4.2)

 

High SES

8 (3.3)

15 (1.2)

4 (1.6)

6 (1.2)

19 (1.5)

0 (1.4)

3 (3.8)

Lebanon

All schools

4 (0.0)

2 (0.0)

2 (0.0)

0 (0.0)

11 (0.0)

−1 (0.0)

−2 (0.0)

 

Low SES

−1 (7.2)

0 (1.5)

5 (1.7)

1 (1.4)

8 (1.4)

0 (1.2)

7 (3.4)

 

High SES

3 (3.4)

2 (1.0)

0 (1.1)

−1 (0.9)

13 (1.2)

−1 (1.3)

0 (2.4)

Lithuania

All schools

12 (0.0)

11 (0.0)

1 (0.0)

−1 (0.0)

21 (0.0)

7 (0.0)

4 (0.0)

 

Low SES

16 (5.9)

14 (2.3)

1 (2.4)

1 (1.9)

25 (2.1)

10 (2.3)

1 (3.6)

 

High SES

10 (3.7)

8 (1.3)

0 (1.3)

0 (1.0)

19 (0.9)

5 (1.3)

7 (2.6)

Malaysia

All schools

−2 (0.0)

3 (0.0)

8 (0.0)

0 (0.0)

9 (0.0)

6 (0.0)

4 (0.0)

 

Low SES

−3 (3.2)

2 (0.9)

9 (1.1)

2 (0.9)

3 (1.6)

5 (1.1)

2 (2.0)

 

High SES

−5 (2.7)

1 (0.8)

5 (1.0)

1 (0.8)

10 (1.2)

7 (0.8)

5 (1.9)

New Zealand

All schools

−2 (0.0)

9 (0.0)

1 (0.0)

−1 (0.0)

19 (0.0)

5 (0.0)

−3 (0.0)

 

Low SES

8 (4.5)

10 (2.2)

−1 (1.7)

1 (1.4)

19 (1.5)

8 (1.2)

6 (4.3)

 

High SES

−6 (4.3)

10 (1.5)

1 (1.4)

−2 (1.5)

19 (1.2)

−2 (1.8)

−1 (4.8)

Norway

All schools

6 (0.0)

8 (0.0)

1 (0.0)

2 (0.0)

17 (0.0)

3 (0.0)

2 (0.0)

 

Low SES

12 (5.3)

11 (1.4)

3 (2.3)

4 (1.3)

15 (2.2)

5 (1.4)

−5 (3.4)

 

High SES

−3 (2.7)

9 (0.8)

−1 (1.3)

−2 (1.1)

17 (0.9)

0 (1.0)

4 (3.1)

Romania

All schools

−3 (0.0)

14 (0.0)

2 (0.0)

3 (0.0)

18 (0.0)

2 (0.0)

16 (0.0)

 

Low SES

3 (3.2)

12 (1.5)

4 (1.3)

−3 (1.1)

16 (1.3)

−3 (1.6)

18 (3.9)

 

High SES

7 (3.4)

13 (1.3)

1 (1.4)

−1 (1.1)

20 (1.0)

5 (1.4)

13 (2.4)

Singapore

All schools

−3 (0.0)

5 (0.0)

3 (0.0)

0 (0.0)

12 (0.0)

5 (0.0)

15 (0.0)

 

Low SES

−5 (4.7)

7 (1.3)

2 (1.6)

−1 (1.5)

14 (1.4)

7 (2.0)

25 (4.0)

 

High SES

4 (3.4)

1 (1.3)

4 (0.9)

0 (0.8)

9 (0.9)

2 (1.0)

−3 (2.0)

Slovenia

All schools

−2 (0.0)

12 (0.0)

0 (0.0)

−1 (0.0)

2 (0.0)

8 (0.0)

4 (0.0)

 

Low SES

−3 (4.0)

11 (1.7)

3 (1.3)

0 (1.3)

26 (1.2)

5 (1.9)

2 (2.9)

 

High SES

2 (4.0)

11 (1.3)

1 (1.4)

−3 (1.3)

21 (1.9)

6 (1.3)

8 (2.4)

Sweden

All schools

9 (0.0)

8 (0.0)

2 (0.0)

2 (0.0)

18 (0.0)

−2 (0.0)

6 (0.0)

 

Low SES

−8 (5.6)

9 (1.8)

3 (2.4)

−3 (1.7)

19 (2.7)

0 (1.6)

11 (4.1)

 

High SES

13 (4.4)

8 (1.2)

2 (1.9)

−2 (1.5)

18 (1.3)

−3 (2.1)

4 (4.0)

Thailand

All schools

−4 (0.0)

2 (0.0)

9 (0.0)

3 (0.0)

7 (0.0)

6 (0.0)

−2 (0.0)

 

Low SES

−8 (4.3)

−1 (1.7)

8 (1.8)

6 (2.0)

3 (3.2)

5 (2.3)

0 (2.8)

 

High SES

0 (2.9)

1 (1.0)

10 (1.2)

1 (1.0)

8 (1.5)

6 (1.1)

−2 (2.7)

Tunisia

All schools

12 (0.0)

3 (0.0)

2 (0.0)

0 (0.0)

14 (0.0)

3 (0.0)

3 (0.0)

 

Low SES

14 (2.8)

2 (1.1)

1 (1.2)

−1 (1.2)

13 (1.3)

3 (1.2)

1 (2.1)

 

High SES

9 (3.6)

6 (1.5)

0 (1.5)

1 (0.9)

15 (1.7)

−2 (1.1)

3 (2.4)

Turkey

All schools

9 (0.0)

9 (0.0)

−1 (0.0)

1 (0.0)

22 (0.0)

−1 (0.0)

4 (0.0)

 

Low SES

−9 (5.5)

5 (1.4)

1 (1.6)

2 (1.4)

19 (1.5)

2 (1.5)

1 (3.6)

 

High SES

11 (3.3)

9 (1.3)

−1 (1.5)

0 (1.3)

23 (1.1)

4 (1.3)

9 (3.4)

Ukraine

All schools

2 (0.0)

10 (0.0)

−1 (0.0)

0 (0.0)

28 (0.0)

3 (0.0)

1 (0.0)

 

Low SES

−3 (8.0)

18 (3.1)

2 (2.8)

1 (2.3)

26 (4.4)

−3 (2.6)

0 (3.6)

 

High SES

10 (3.5)

7 (1.3)

1 (1.5)

−2 (1.2)

28 (1.5)

4 (1.4)

6 (2.7)

United Arab Emirates

All schools

−5 (0.0)

5 (0.0)

3 (0.0)

−1 (0.0)

18 (0.0)

5 (0.0)

2 (0.0)

 

Low SES

−16 (10.3)

5 (0.9)

2 (1.4)

2 (0.9)

18 (1.2)

3 (1.0)

1 (2.7)

 

High SES

−5 (4.4)

5 (1.2)

3 (1.1)

−1 (0.8)

18 (0.8)

5 (1.1)

2 (2.7)

United States

All schools

4 (0.0)

4 (0.0)

0 (0.0)

0 (0.0)

11 (0.0)

3 (0.0)

−1 (0.0)

 

Low SES

4 (2.7)

2 (0.8)

1 (0.9)

−1 (0.8)

11 (0.7)

4 (0.8)

−2 (1.8)

 

High SES

1 (2.2)

3 (0.7)

2 (0.9)

0 (0.6)

9 (0.7)

3 (0.7)

1 (2.1)

() standard errors appear in parentheses; statistically significant (p < 0.05) coefficient in italics

As expected, after removing the influence of SES at school level, the between-school variance appeared reduced, except for Slovenia (as far as low SES schools were concerned) and Chile, Georgia, Japan, Republic of Korea, Thailand, Tunisia, Turkey, United Arab Emirates and the United States (as far as high SES schools were concerned).

School emphasis on academic successprincipal reports is positively related to student achievement in 7 out of 28 countries (Georgia, Hungary, Australia, Finland, Lebanon, Lithuania, Republic of Korea).

Parental involvement is negatively related to student achievement in low SES schools in 4 out of 28 countries: Georgia, Hungary, New Zealand, and Malaysia.

Teacher preparedness was found to be positively associated with achievement in low SES schools in 5 countries (Turkey, Hong Kong, Hungary, New Zealand, Malaysia). Instruction to engage students in learning was found to be positively associated with achievement in low SES schools in 4 countries (Hungary, Republic of Korea, New Zealand, Tunisia) and negatively associated with it in 2 countries (Italy and Lithuania). Confidence in teaching mathematics was found to be positively associated with achievement in disadvantaged schools in 4 countries (England, Lebanon, Lithuania, Norway) and negatively in one country (Hungary).

The results exhibited a different impact of the considered variables on the analyses of different countries. For example, in New Zealand, Thailand and Ukraine, the full model of high SES schools explained a higher proportion of between-school variance, while parental involvement, school emphasis on academic success (principal reports) and safe and orderly school (teacher report) had a significant impact on mathematics achievement compared with low SES schools.

Conclusion

The main aim of the present study was to evaluate the impact of context factors on mathematics achievement, focusing on students attending socio-economic disadvantaged schools across countries participating in TIMSS 2011. Context factors reflecting the availability/non-availability of economic and cultural resources within the family context play a relevant role in determining student performance. As expected and according to previous studies (see, e.g., Sirin 2005; Chiu and Xihua 2008; Ismail and Awang 2008; Levpušček et al. 2013), our analyses showed that a high socio-economic status has a significant and positive effect on student achievement: compared with students from socio-economically disadvantaged schools, students from advantaged schools performed better in mathematics achievement. This difference is more evident in countries where the gap between rich and poor people as measured by the Gini coefficient, which measures how much an economy deviates from perfect equality, is wider.4 Those countries are Chile, England, Turkey, Malaysia and Israel. However, this difference is restricted in countries with the smallest gap between rich and poor people, namely in northern European countries, such as Finland, Norway and Sweden, and in Slovenia. Two exceptions are represented by Japan and Australia. In Japan, although it has a large gap between rich and poor, the difference in mathematics achievement is about half of a standard deviation. In Australia, the gap between rich and poor people is not so high, but the difference in mathematics achievement is around one standard deviation.

Moreover, according to the literature (Martin and Mullis 2013; Drent et al. 2013; Phan 2008), the results show significant differences across countries in relation to the school and teacher characteristics that have an impact on mathematics achievement of students from low and high SES schools. Different patterns were also found within countries for low and high SES schools.

As for other variables considered in this study, such as parental involvement, other studies showed discordant results (e.g., McNeal 1999). It is possible that this difference is due to schools’ attempts to have more direct and stronger relationships with the parents of students with learning problems. Furthermore, in advantaged schools, parental involvement and emphasis on academic success have an impact in a small group of countries, although this association has different directions in different countries.

Some limitations to this study should be noted. First, to gain a deeper understanding of the present findings, it is necessary to consider the large differences in teaching mathematics across countries (Mullis et al. 2012). A second limitation is that the data used in this study are related to only one school year. As a consequence, generalizations about the influence of context factors on student mathematics achievement should be taken with some degree of caution. Analyses on more than one dataset are needed for a clearer picture of what school factors are associated with mathematics achievement.

Additionally, a more general methodological issue should be investigated. The type of constructs and variables used in the questionnaire development, the way these constructs and variables are operationally defined, the self-reported nature of the collected data, and the type of data analyses carried out all may contribute to explaining the difficulty of finding strong associations between students’ performance and process-related school variables. Additionally, the construction of indicators of teaching processes may require a different approach, namely a systematic observation of classroom practices (Postlethwaite and Ross 1992). Furthermore, the results suggest that even more advanced and “complex” analytical methods and designs of analysis should be tried to address some of the issues outlined here, in an effort to extricate the effect of SES from that of other variables.

Despite these limitations, the present study investigated the relationship between context factors and student achievement across countries on a large and representative sample of students, assessed by a well-established international standardized test. It should be noted that such standardized tests have been used increasingly in recent years by educational and political decision makers to improve teaching and learning in mathematics and the quality of education systems. The results of the present study suggest the opportuneness of using school-level factors not only for cross-country comparisons but also for an in-depth investigation into the differences existing within individual countries. Moreover, as already shown by other studies (Sandoval-Hernández et al. 2014), the results of the international comparative studies could be used to study the impact of school factors in disparate school contexts. Different school factors seem to play a different role in different school contexts within each individual country.

Footnotes
1

In TIMSS 2011 International Results in Mathematics, students were considered to have an achievement too low for estimation if their performance on the assessment was no better than that they could achieve by simply guessing on the multiple choice assessment items. However, such students were assigned scale scores (plausible values) by the achievement scaling procedure, despite concerns about their reliability. We excluded countries with reservations about reliability of average achievement because the percentage of students with achievement too low for estimation exceeds 15 % (Mullis et al. 2012a, p 456).

 
2

The IDB Analyzer allows handling complex sample designs, using plausible value methodology and calculating correct standard errors when conducting analysis with large-scale surveys. The IDB Analyzer creates an SPSS code that can be used to conduct statistical analysis considering the complex sample and assessment structures of these databases. The software allows combining data from different countries for cross-country analysis and selecting specific subsets of variables. In addition, it provides several different procedures for analysis, such as the computation of means or percentages of any background variable of interest for a whole country or subgroup within a population (IEA 2012).

 
3

In this study, we only included the countries that had an adequate reliability concerning average achievement in mathematics and where all of the items used in the analyses were administered.

 

Declarations

Authors’ contributions

EC and BL are the authors of this research paper and have directly participated in the planning, execution, and analysis of this study. Both authors read and approved the final manuscript.

Competing interests

Both authors declare that they have no competing interests.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)
Department of Education, Roma Tre University
(2)
National Institute for the Educational Evaluation of Instruction and Training (INVALSI)

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