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?

2. 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?
3. How do gender and mother’s education explain the level differences and change of mathematical self-concept? 

Data (=2200) were drawn from a longitudinal Learning-To-Learn study in which a whole age cohort of third graders from the capital area of Finland were followed up until the end of the comprehensive school. Data collection consisted of three measurement points (i.e. year 2016 when pupils were at third grade, year 2018 when pupils were at sixth grade and year 2021 when pupils were at ninth grade). Measures that were used based on the framework of Finnish learning to learn test (Hautamäki et al., 2002). Mathematical thinking skills were measured with two task types. The first task type, the Hidden Arithmetical Operators task (Arithmetical Operations for short) was developed by Demetriou and his colleagues (Demetriou et al., 1991). In each item there were one to four hidden operators (e.g., [(5 a 3) b 4 = 6). In the second task sections of invented mathematical concepts (Sternberg et al., 2001), two invented mathematical concepts, lag and sev, were conditionally defined (for example, if a > b, lag means subtraction, otherwise multiplication, etc.). After this, the student was given a problem to solve (for example, how much is 4 lag 7 sev 10 lag 3), where the definitions had to be applied. Mathematical self-concept was measured with a scale based on Marsh’s work on academic self-concept (Marsh et al., 1988). The scale consisted of three items on a seven-point Likert scale ranging from one (not true at all) to seven (very true). Data were analysed with SPSS24 for descriptive statistics and Mplus 7.2 for linear growth curve models. First, we analysed the development of mathematical thinking skills and mathematical self-concept at the level of the whole data, after which differences in development depending on the gender and mother’s education level were examined.

Preliminary analyses showed that students’ mathematical thinking skills improved over time whereas self-concept in mathematics decreased statistically significantly from the third to the ninth grade. This result aligns with earlier international findings of the decline of self-beliefs by age. The linear growth curve model fitted the data well (RMSEA = .035; CFI = .992; TLI = .973). The initial level of self-concept in the third grade statistically significantly predicted the student's success in the sixth-grade mathematical thinking test. Sixth grade’s mathematical thinking skills test score correlated significantly with the slope of mathematical self-concept indicating that the development of pupils’ mathematical self-concept differed depending on their performance in mathematical thinking skill test. Students who did well in the test of mathematical thinking skills at sixth grade experienced a milder decrease in their mathematical self-concept than other students. Mathematical thinking skills test score at sixth grade, initial level of mathematical self-concept at third grade as well as the slope of mathematical self-concept predicted statistically significantly the test result in mathematical thinking skill test at ninth grade. Overall, the model explained about 38% of the variance of ninth grade mathematical thinking skills test result. Gender was a statistically significant predictor of children’s mathematical self-concept. Boys' mathematical self-concept was stronger than that of girls. In addition, girls experienced a stronger decline in their self-concept over time than boys did.

Bong, M., & Skaalvik, E. M. (2003). Academic self-concept and self-efficacy: How different are they really? Educational Psychology Review, 15(1), 1–40. Hox, J. J. Demetriou, A., Platsidou, M., Efklides, A., Metallidou, Y., & Shayer, M. (1991). The development of quantitative-relational abilities from childhood to adolescence: Structure, scaling, and individual differences. Learning and Instruction, 1, 19–43. Guay, F., Marsh, H. W., & Boivin, M. (2003). Academic self-concept and academic achievement: Developmental perspectives on their causal ordering. Journal of Educational Psychology, 95(1), 124–136. https://doi.org/10.1037/0022-0663.95.1.124 Hautamäki, J., Arinen, P., Eronen, S., Hautamäki, A., Kupiainen, S., Lindblom, B., & Scheinin, P. (2002). Assessing learning-to-learn: A framework. National Board of Education, Evaluation 4/2002. Hautamäki, J., Kupiainen, S., Marjanen, J., Vainikainen, M.-P., & Hotulainen, R. (2013). ). Oppimaan oppiminen peruskoulun päättövaiheessa: Tilanne vuonna 2012 ja muutos vuodesta 2001 [Learning to learn at the end of basic education: Situation in 2012 and change from 2001]. University of Helsinki. Department of Teacher Education Research Report 347. Unigrafia. Hoskins, B., & Deakin Crick, R. (2010). Competences for learning to learn and active citizenship: Different currencies or two sides of the same coin? European Journal of Education, 45(1), 121–137. Crossref. ISI. Marsh, H. W., Byrne, B. M., & Shavelson, R. J. (1988). A Multifaceted Academic Self-Concept: Its Hierarchical Structure and Its Relation to Academic Achievement. Journal of Educational Psychology, 82(4), 623–636. https://doi/10.1037/0022-0663.80.3.366 Marsh, H. W. (1990). The structure of academic self-concept: The Marsh/Shavelson model. Journal of Educational Psychology, 82(4), 623–636. https://doi.org/10.1037/0022-0663.82.4.623 Marsh, H. W., Scalas, L. F., & Nagengast, B. (2010). Longitudinal tests of competing factor structures for the Rosenberg Self-Esteem Scale: Traits, ephemeral artifacts, and stable response styles. Psychological Assessment, 22(2), 366–381. https://doi.org/10.1037/a0019225 Sternberg, R., Castejon, J.L., Prieto, M.D., Hautamäki, J., & Grigorenko, E. (2001). Confirmatory factor analysis of the Sternberg Triarchic Abilities Test in three international samples. European Journal of Psychological Assessment, 17, 1-16. Vainikainen , M-P & Hautamäki , J 2022 , Three Studies on Learning to Learn in Finland :Anti-Flynn Effects 2001-2017 ' , Scandinavian Journal of Educational Research , vol. 66 , no. 1 , pp. 43-58 . https://doi.org/10.1080/00313831.2020.1833240