Achievement gaps in mathematics can be found among education systems all over the world in international large-scale assessment studies (ILSAs). In almost all education systems, students’ socioeconomic status (SES) has been documented as one of the most important factors associated with achievement, known as the “socioeconomic achievement gap” (Chmielewski, 2019), while in other education systems, achievement gaps can be accounted for by gender, immigration background, ethnicity and/or urban-rural locations of schools and students (e.g., Bondy et al., 2017; Brozo et al., 2014; Song et al., 2014). In Sweden, remarkable differences can be observed between public and independent schools and the differences might be explained by a larger share of students with well-educated parents in independent schools than in public schools (Klapp Lekholm, 2008). Taking mathematics as an example, students in independent schools perform better than students from public schools in Programme for International Student Assessment (PISA), even after controlling the background variables, and the crucial difference in achievement holds consistent from PISA 2003 to PISA 2012 regardless of the sharp decline, and the advantage of independent schools has emerged over time (OECD, 2019).

The types of schools (private or public as categorised in PISA) are generally differentiated by the ownership of schools. Private schools refer to schools managed directly or indirectly by a non-government organisation (such as a church, trade union, business or other private institution), while public schools are managed by a public education authority, government agency, or governing board appointed by the government or elected by a public franchise (OECD, 2020). In the Swedish context, instead of private schools, it would be more accurate to use the term independent schools, which can be run by private organisations to operate educational activities through a publicly funded voucher system (Yang Hansen & Gustafsson, 2016) and could be running for profit (Wiborg, 2015).

Research also indicates that students’ motivational beliefs seem to be important for academic achievement in the Swedish education system (Klapp, 2018). Previous research has established that student self-beliefs could predict and impact academic achievement, among which self-concept and self-efficacy are the most identified ones (Bong & Skaalvik, 2003; Multon et al., 1991). Mathematics self-concept is an individual’s perceived competence in mathematics (OECD, 2013), and was found strongly related to students’ general mathematics achievement (Bong & Skaalvik, 2003; Ma & Kishor, 1997). Mathematics self-efficacy measures students’ expectations and conviction of what can be accomplished when they need to solve pure and/or applied mathematics tasks. Students’ mathematics self-efficacy had a strong direct effect on mathematics problem-solving despite their general mental ability (Pajares & Kranzler, 1995).

It is well established that mathematics self-concept and self-efficacy to a varying degree are associated with students’ mathematics achievement. It has also been observed for many decades that student gender, socioeconomic status and immigration background influence academic achievement, directly and indirectly (e.g., Bondy et al., 2017; Schleicher, 2006). There is still uncertainty, however, regarding how the relations among mathematics self-concept, self-efficacy, student characteristics (SES, gender, immigrationbackground) and mathematics achievement may vary for students in different types of schools (public or independent) in the Swedish education system and over the years.  

The main aim of the study was to investigate the relative importance of student mathematics self-concept and self-efficacy for mathematics achievement across Swedish public and independent schools over time, concerning student characteristics such as SES, gender and immigration background. 

This study consists of students from Sweden who participated in PISA 2003 (N=4624, n=186 from independent schools) and PISA 2012 (N=4736, n=787 from independent schools). Mathematics self-concept (MSC) was measured by five items, where the students were asked how they feel when studying mathematics. They were supposed to report whether they strongly agree, agree, disagree or strongly disagree with the statements, such as “I get good marks in mathematics” and “I learn mathematics quickly”. Mathematics self-efficacy (MSE) was measured by eight items, indicating the perceived mathematical abilities. The students were asked to report whether they feel very confident, confident, not very confident or not at all confident in facing pure and applied mathematical tasks, such as “calculating TV discount” and “understanding a train timetable”. Mathematics achievement, as defined as mathematical literacy in PISA, captures student capability in formulating, employing and interpreting mathematics in diverse contexts (OECD, 2013). Five plausible values were generated to represent student mathematics achievement. Students were categorised into males and females in PISA. In this study, students were grouped into natives (students born in Sweden and whose at least one parent was also born in Sweden) and non-natives (students born in Sweden with non-Sweden-born parents, and students born outside Sweden as well as their parents). Student economic, social and cultural status (ESCS) is an index in PISA reflecting student family educational, occupational and cultural status. Descriptive statistics were first investigated, giving an overview of all the variables. Secondly, multi-group confirmatory factor analyses (MGCFA) were performed to examine the factor structure and measurement invariance across the two PISA cycles and across the school types (the independent and public schools) in Sweden. Then, concerning the cluster sampling strategy in PISA and the intention of making comparisons in this study, multi-group multi-level structural equation modelling (MGSEM) was applied to study the relations between mathematics self-concept, self-efficacy and mathematics achievement, concerning students’ gender and immigration background. SPSS 28 were used for data management and Mplus 8 for analyses.

As mentioned earlier, Swedish students in independent schools achieve higher than those in public schools despite the extraordinary decline from PISA 2003 to PISA 2012. The overall results suggest that students with high levels of mathematics self-concept and self-efficacy tend to have better performance in mathematics. Students with better economic, social and cultural status are possibly to have stronger mathematics self-concept and self-efficacy and perform better in mathematics. Immigrant students perform considerably worse than non-immigrant students in mathematics and yet they perceive themselves as having higher mathematics self-concept and self-efficacy. Girls who, although performed equally well or even better than boys, hold nevertheless weaker mathematics self-concept and self-efficacy. At the school level, mathematics achievement is positively associated with economic, social and cultural status. Schools with larger portions of immigrant students seem to have lower economic, social and cultural status and mathematics achievement. Compared to independent schools, the influence of mathematics self-efficacy is stronger than mathematics self-concept in both PISA 2003 and 2012 in public schools. Economic, social and cultural status plays a relatively less important role in mathematics self-concept, self-efficacy and achievement in public schools. Conversely, the effect of immigration background seems to be stronger in independent schools. Girls are found to have even lower levels of mathematics self-concept and self-efficacy in independent schools. The study has significant implications for researchers and practitioners in the educational and psychological fields. Positive self-beliefs are significant representative constructs in educational psychology (Marsh et al., 2019). The results and findings from this study highlighted the important role of mathematics self-concept and self-efficacy in mathematics achievement across Swedish public and independent schools. It is important to raise teachers’ awareness of promoting students’ self-concept and self-efficacy in mathematics learning, for girls, immigrant students and students with lower SES in particular.

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