Conference Agenda

One of the basic skills for success in the knowledge society is the ability to learn. The Finnish national learning to learn (L2L) assessment program was launched in the mid-1990s as a result of a worldwide interest in the measurement of cross-curricular competences (Hautamäki et al., 2013).

The Learning to learn longitudinal assessment brings significant value and gathers sufficient information about learning outcomes and monitor changes in students’ competence during the basic education (Hoskins & Deakin Crick, 2010).

In Finland, L2L is assessed by administering cognitive tasks measuring general reasoning and thinking skills, and self-evaluation scales measuring beliefs and attitudes towards learning (Hautamäki & al., 2002). The concept of mathematical thinking is a traditional part of Learning to learn assessment.

Children’s learning-related beliefs, self-concept and interest in a particular subject play an important role in their school performance, particularly in mathematics. In educational research, academic self-concept has been defined as students' perception of themselves within the academic environment (Marsh, 1990, Marsh and Scalas, 2010).

In this regard, it is of interest how the development of mathematical thinking occurs in schoolchildren during schooling and what other factors can influence the development and improvement of mathematical thinking.

Of particular interest in presented study was the development of mathematical thinking skills and mathematical self-concept (Marsh et al.,1988), as part of learning-related beliefs from the third grade to the ninth grade during the completion of basic education.

The main purpose of this study is to answer the following questions:

1. How do pupils` mathematical thinking skills and mathematical self-concept develop during the comprehensive school years from the third to the ninth grade?

1. Do mathematical self-concept on the third and the sixth grade predict the level of mathematical thinking skills on the sixth and the ninth grade?
2. How do gender and mother’s education explain the level differences and change of mathematical self-concept?

The study's overall purpose is to explore the formation of student academic self-concept (ASC) in the subjects of English and mathematics. ASC is commonly defined as self-perceived academic ability and is related to cognitive and non-cognitive outcomes such as academic engagement, goal-setting, task choice, persistence and effort, intrinsic motivation, strategy use, academic achievement, and future career selection (Bong & Skaalvik, 2003; Marsh et al., 2019). When students perceive their previous experiences of academic activities to be positive and when they perceive that they are capable of managing future academic activities, it is thus an advantage that goes beyond immediate academic success. Rather, ASC has been shown to have prolonged effects (Marsh et al., 2001).

Because ASC frequently has been shown to be important for student success, much research has been dedicated to explaining how it is formed. The main explanation is the big-fish-little-pond effect (BFLPE), which posits that equally abled students perceive their abilities differently depending on their context (Marsh et al., 2008). A student in a high-achieving context would rate their ability to be lower than a student in a lower-achieving context, even if both students have the same abilities.

In 1962, tracking was introduced in the subjects of English and mathematics in all secondary schools in Sweden (Grades 7-9). With recommendations from teachers, students were to choose between advanced and general courses in the two subjects (Marklund, 1985). The general courses were easier and given at a slower pace than the advanced courses and tended to have lower class-average achievement. Tracking is no longer a formal practice in Swedish compulsory education, but it commonly occurs when teachers organise education in Sweden and internationally (Trautwein et al., 2006).

ASC is a well-researched area, but so far, only a few studies have conducted longitudinal analyses to investigate effects over time. There is also a need for studies that look at how ASC is affected by school systems with some form of tracking (i.e., ability stratification, ability grouping etc.). The specific purpose of the study is to explore the effects of non-tracking and tracking in secondary school on ASC in upper secondary schools. With longitudinal data from the 1980s and 90s, ASC will be measured in Grade 6 (pre-tracking) and Grade 10 (post-tracking).

Previous Research

In a longitudinal study, Marsh et al. (2001) compared students from former East and West Germany (N = 2 778). They found that when East and West Germany reunited and the schools merged, the students who had attended the selective and ability-stratified schools in West Germany were more strongly affected by the negative BFLPE when compared to the East German students. Before the reunification, East German students had not experienced an ability-stratified school system. The difference between the merged students decreased with time when the former East German students became integrated with the more selective school system. Overall, the findings of Marsh et al. (2001) indicate that school policies and systems may have an impact on the formation of student ASC.

Similarly, Liem et al. (2013) found that compulsory school students in low-ability streams in English and mathematics had higher self-concepts than students in high-ability streams when student achievement was controlled for. However, Herrmann et al. (2016) investigated the German within-school track system (N = 1 330) and found that the negative BFLPE for students in the advanced mathematics track disappeared when they controlled for positive assimilation effects. The positive assimilation effect is similar to the basking-in-reflected-glory (BIRG) effect, which both refer to the notion that attending a high-achieving class or school positively affects ASC.

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.