Mathematics, as one of the mandatory and key school subjects worldwide, plays a vital role in equipping young people with mathematical knowledge and skills and preparing them not only for higher education but also for later private and professional life in modern society. Previous research has established that student self-concept and self-efficacy could predict and impact academic achievement (Bong & Skaalvik, 2003; Multon et al., 1991). It has also been observed for many decades that student gender, socioeconomic status and immigration background influence academic achievement, directly and indirectly (Bondy et al., 2017; Leder, 1992; Tate, 1997; White, 1982).

Self-concept refers to an individual’s global perception of him- or herself, which is built through previous experience, interpretations of the surrounding environment, and social comparisons and judgements with frames of reference (Marsh et al., 2019; Shavelson et al., 1976). Self-concept is commonly multifaceted and hierarchical, and academic self-concept is one facet of it, which has been an object of research since the 1970s (Marsh & Shavelson, 1985; Shavelson et al., 1976). Academic self-concept is considered one’s general perception of academic abilities which can be divided into a subject matter, such as mathematics, English, chemistry, and science. Mathematics self-concept, for instance, is an individual’s perceived competence in mathematics (OECD, 2013), was found strongly related to students’ general mathematics achievement (Bong & Skaalvik, 2003; Ma & Kishor, 1997).

Self-efficacy, on the other hand, is one of the closest constructs to self-concept. Perceived self-efficacy was defined as “beliefs in one’s capabilities to organize and execute the courses of action required to produce given attainments” (Bandura, 1997, p. 3). Self-efficacy judgements were central to steering an individual’s motivation and behaviour and often mediated the influence of other predictors of behaviour on a particular performance (Bandura, 1986). 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, and student characteristics to a varying degree are related to students’ mathematics achievement. There is still uncertainty, however, whether mathematics self-concept and self-efficacy predict achievement to the same extent. Also, to what extent do student characteristics, moderates the complex relations between these factors and academic achievement.

By using data from the Programme for International Student Assessment (PISA), it is possible not only to analyse the relationships among students’ characteristics, self-related constructs and academic achievement but also review to what extent differences in these relationships are conditioned across the Swedish educational system and over time.

The main aim of the study was to investigate the relative importance of student mathematics self-concept and self-efficacy for mathematics achievement in Sweden. The study attempted to address the following research questions: How do mathematics self-concept and self-efficacy predict mathematics achievement? (a) What if taking student characteristics such as gender, socioeconomic status and immigration background into consideration? (b) Do the relationships among the variables differ in the PISA 2003 and 2012 cycles? 

This study consists of students from Sweden who participated in PISA 2003 (4624 students in 185 schools) and 2012 cycles (4736 students in 209 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 firstly investigated, giving an overview of all the variables. Secondly, confirmatory factor analyses (CFA) were performed to assess the factor structure and measurement invariance across the two PISA cycles in Sweden. Single-factor models were established for MSC, MSE and STRel by using CFA, and the three levels of measurement invariances (configural, metric and scalar) were tested by using multi-group CFA. The establishment of scalar invariance of the constructs is considered the precondition of cross-group comparisons (Vandenberg & Lance, 2000). Then, multi-group structural equation modelling (MGSEM) was applied to detect the relationships among all the variables. Concerning the cluster sampling strategy in PISA, multilevel analyses (Hox et al., 2010) would also be performed to investigate the relationships between factors at both the student and school levels. SPSS 28 were used for data management and Mplus 8 (Muthén & Muthén, 1998-2019) for analyses.

The internal consistency of mathematics self-concept and self-efficacy were good in both PISA 2003 and 2012 cycles based on the values of Cronbach’s alpha (α_MSE03=.85,α_MSC03=.89,α_MSE12=.85,α_MSC12=.89). The single factor measurement models of MSC and MSE fitted the data quite well both in the separate cycles and the joint analyses. Results from the multi-group CFA revealed that MSC and MSE held measurement invariance at a scalar level over the PISA 2003 and 2012 cycles within Sweden, indicating that the comparison between the two cycles would be valid. The MGSEM results showed that mathematics self-concept and self-efficacy contributed to mathematics achievement positively in both cycles. Student economic, social and cultural status had a slightly negative effect in 2003 but a positive effect in 2012 on mathematics achievement. Native students tend to perform better than non-native students in both cycles, while gender does not significantly matter to mathematics achievement. Some preliminary multilevel analyses showed that the variance of mathematics self-concept and self-efficacy existed at the student level but not at the school level. Students’ mathematics self-concept and self-efficacy contributed positively to mathematics achievement. Girls tended to have a lower level of mathematics self-concept and self-efficacy. Students with better economic, social and cultural status tended to have a higher level of mathematics self-concept and self-efficacy and performed better in mathematics. Schools with a higher proportion of non-immigrant students and better economic, social and cultural status tended to pursue better mathematics achievement. The analysis is still ongoing. The relationships between the factors, student characteristics and mathematics achievement at the student and school levels over the two PISA cycles are under investigation. It might be possible that other relevant factors such as students’ motivation and interest in learning mathematics, school factors such as school type, would be taken into consideration.

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