There are mathematics achievement differences between mainstream students and immigrant students across European countries in large-scale surveys (Andon, Thompson, & Becker, 2014). Academic success could be one of the key components for immigrant students to become productive members of the modern society. However, educational opportunities and educational resources provided at schools and home are not equal for mainstream and immigrant students (OECD, 2010, 2012). There is a strong association between mathematics achievement and educational opportunities and educational resources provided at schools and home (Marks, Cresswell, & Ainley, 2006; Schmidt & Maier, 2009; Shin, Slater, & Backhoff, 2013). Furthermore, immigrants often score lower on these background variables. Therefore, controlling for these background variables might decrease mean mathematics achievement differences among mainstream and immigrant students. In PISA 2012 mathematics results a decrease in mathematics performance difference among Turkish immigrants and European mainstreamers was found after background variables were controlled (Arikan, van de Vijver, & Yagmur, 2017). Immigrants’ mathematics achievement could show differential results whether immigrants are first or second generation. In some European countries, first generation immigrants were more successful whereas in other countries second generation immigrants were more successful. Controlling background variables might produce different results for also immigrant group comparisons in different direction for each European country.

Identifying student and country level predictors of mathematics achievement for immigrant students could provide relational information how to increase immigrant achievement in the long run. At student level, student aptitude variables are relevant such as liking to learn mathematics, being confident in mathematics; as background variables, home resources for learning, bullying, and sense of school belonging might be related to achievement (Walberg, 1981). At country level, the migrant integration policy index (MIPEX) score of education (education domain score), the human development index and general government expenditure on education might predict the achievement (Arikan et al., 2017; Fossati, 2011).

With these perspectives in mind, the research questions of this study are:

1. Does the magnitude of mathematics achievement gap between immigrant and mainstream 4^th grade students differ across European countries in TIMSS 2015?   
2. Does the magnitude of achievement gap between first generation and second generation 4^th grade immigrant students differ across European countries in TIMSS 2015?
3. What would be the mathematics achievement gap between immigrant and mainstream 4^th grade students when home resources were controlled in TIMSS 2015?
4. What would be the mathematics achievement gap between first generation and second generation 4^th grade immigrant students when home resources were controlled in TIMSS 2015?

Which student and country level variables predict mathematics achievement of immigrant students in various European countries?

Participants The data of the study was obtained from TIMSS 2015 database. This study used all 4th grade students that were identified as immigrant or mainstreamer who had participated TIMSS 2015 from Belgium, Denmark, England, Finland, France, Germany, Ireland, Italy, Netherlands, Norway, Spain and Sweden. Mainstream students were students who were born in that country, and their parents were born in that country. First generation immigrant students were students who were born out of that country and their parents were born out of that country. Second generation immigrant students were students who were born in that country and their parents were born out of that country. Measures TIMSS gathered data about students’ mathematics achievement via mathematics test and about student characteristics via student questionnaire. The plausible mathematics values reported in TIMSS were used as achievement indicators. The index of home resources for learning was used to identify remaining achievement differences among student groups. The index of home resources is a combination of number of books in the home, number of home study supports, highest level of occupation of either parent and highest level of education of either parent. As student level predictors, we used liking to learn mathematics, being confident in mathematics; home resources for learning, bullying, and sense of school belonging were used as background variables to predict mathematics achievement. These indices were reported by TIMSS using related questionnaire items. At country level, the migrant integration policy index (MIPEX) scores of education, the human development index and general government expenditure on education were used as predictors. Data Analysis In order to answer the first and the second research questions, for each European country, mathematics achievement differences among related groups were tested by t-test and effect sizes were reported. As TIMSS has special sampling and test design, IEA IDB Analyzer program that takes into account the sampling weights and the plausible values was used to identify the mathematics achievement differences (IEA, 2017; Rutkowski, Gonzalez, Joncas, & von Davier, 2010). For the third and the fourth research questions, propensity score matching method was used to create similar mainstream and immigrant groups in terms of home resources. The MatchIt R package (Ho, Imai, King, & Stuart, 2011) was used to do the matching and to estimate propensity scores. Then remaining achievement differences among the groups were tested. For the last research question, a multilevel regression analysis was conducted.

Achievement differences mainstream and immigrant students before controlling home resources The preliminary analysis showed that for all countries, immigrant 4th grade students performed significantly lower than mainstreamers, except in England. These differences in terms of effect size ranged from 0.11 (Ireland) to 0.78 (Sweden). For England, immigrant students got higher mathematics scores than mainstream students, although the score difference was not significant. When average mathematics score of first and second generation immigrant students was compared, for England, Italy, and Sweden, second generation immigrant students performed better than first generation immigrant students ranged from 0.21 (Sweden) to 0.62 (Italy). Only in Spain, first generation immigrant students got higher mathematics scores than second generation immigrant students (d = 0.22). For other countries the differences were not significant. Achievement differences mainstream and immigrant students when controlling home resources Matching students according to home resources is expected to decrease achievement difference among mainstream and immigrant students. However, the decrease could be different for each European country. The final results related to remaining achievement differences among mainstream and immigrant students will be presented in this section. Additionally, mathematics achievement differences between first and second generation immigrants after matching according to home resources will be presented. Factors predicting 4th grade immigrant student’s achievement In this part, student and country level predictors of mathematics achievement of immigrant students will be identified. In student level, student aptitude variables such as liking to learn mathematics, being confident in mathematics; environmental variables such as home resources for learning, bullying, and sense of school; in country level, the MIPEX education domain score, the human development index and general government expenditure on education will be used.

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