The last decades of research in the psychology of education are increasingly marked by an investigation into constructs from the socioemotional domain – academic emotions, motivation, and interaction. One of the concepts that are getting more research attention is related to students' self-understanding about how good they are at a skill-based task or activity in a particular domain (Darragh, 2016; Radovic et al., 2018). As part of the academic identity, these beliefs can significantly influence student achievements, engagement in school activities, as well as choices regarding the field of education, and later professional orientation (Wan et al., 2021). In mathematics education, identity is additionally important in research because it gives a new perspective in explaining why many students underachieve or disengage from mathematics, without referring to their cognitive abilities (Graven & Heyd-Metzuyanim, 2019). Starting from symbolic interactionism and socio-cultural perspective, we define mathematics identity (MI) as a student's self-conception in the domain of mathematics. The concept gathers both student's self-understanding and the perception of how significant others see them in the context of doing mathematics (Anderson, 2007; Martin, 2009). There are several sources that children can use to shape motivational beliefs about their abilities and interests in different academic domains – including social feedback from significant others, such as parents and teachers, objective achievement evaluation, social comparisons, etc. (Wan et al., 2021). On the other hand, MI could be related to students' expectancy when evaluating possible success in particular tasks or activities (Wigfield et al., 2006). Students' self-relevant beliefs about how good they are in certain domains and expectations of success in specific tasks can significantly shape student engagement, persistence, effort, and, ultimately, achievement. Based on the Expectancy-value theory (EVT) students' expectancy for success in a task and value for a task, will serve as important factors for student engagement and learning, thus influencing student's achievement, persistence, and task choice (Eccles & Wigfield, 2020; Pekrun, 2006). Both MI and motivation for learning occur and develop at different ages and have different developmental paces, interacting with mathematics curriculum, teacher's practices, school climate, family's expectations, gender stereotypes, and many more factors, as students progress from grade to grade. In this paper, we focused on motivation for learning math, and exploreed how the identity of students in primary school is related to their motivation for learning mathematics, specifically perceived competence, and task values. Further, we explored the relationship between motivation, achievement, and math identity in the early years of learning mathematics, which can significantly shape later attitudes toward mathematics. 

The main aim of this research was to explore the relationship between math identity and dimensions of motivation on one hand and math achievement on the other, in lower grades of compulsory education when students start with math learning. Considering the social nature of MI and its dependence on the cultural context, the additional aim of our research was to explore those relationships in different cultural contexts, that is, in six European countries. Finally, we investigated the potential gender and grade differences in connection to MI.

Participants were 11782 primary school students from six countries - 3rd grade (n=5700, 50,8% female, Mage= 9.06 years) and 4th grade students (n=6082, 50.5% female, Mage=10.05 years); from Estonia (n=1694), Finland (n=1772), Norway (n=2135), Portugal (n=2116), Serbia (n=2161) and Sweden (n=1904). Parents' consent forms were obtained for each student. The paper-and-pen questionnaires were administered during regular classes. Four of the five dimensions of the Expectancy-Value Scale (Peixoto et al., 2022), were used to assess students' motivation for mathematics: intrinsic value (e.g., I like doing math), utility (e.g., What I learn in math I can use in daily life), attainment (e.g., Being good in math is very important to me personally), and perceived competence (e.g., Math is easy for me). Each dimension was set on a 4-point Likert scale, from "a lot of times" to "never". The MI scale, measuring how much students believe math is important for their identity, was adapted for this study, comprising 6 items (e.g., I think I am a math person) also anchored at a 4-points scale. Math achievement was measured by a test covering major curricular topics. Math problems comprising the test (12 tasks in grade 3 and 14 tasks in grade 4) were gathered from the previous TIMSS assessment (Approval IEA-22-022). A joint scale of math competence was established across grades due to overlapping items in the grade-specific tests. For each correct answer, students received one point, which resulted in 12 points maximum score for 3rd, and 14 points for 4th grade. We applied the Rasch measurement model to estimate students' math scores, based on all items included in both tests, with 7 items that served as the linking items. Student Math scores are estimated at the scale with an average score of 500 and a standard deviation of 100. To explore the relationship between math achievement, motivation, and identity we tested regression models in MPLUS 8.8, with math identity criterium variable and motivational dimensions, math achievement score, gender, and grade as predictors. Since motivational dimensions were highly correlated, we tested four separate models for each dimension. The model introduced the country as a moderator to identify potential differences among different education systems. The research received ethical approval in each country from the relevant IRB.

Results revealed that all four models fit the data well. All predictors from EVS were significant for students' math identity in all countries (intrinsic value χ2/df = 8847, RMSEA = .06, CFI = .96, TLI = .96, SRMR = .11; attainment χ2/df = 9805, RMSEA = .07, CFI = .92, TLI = .93, SRMR = .09; utility χ2/df = 6790, RMSEA = .05, CFI = .94, TLI = .95, SRMR = .08; perceived competence χ2/df = 11342, RMSEA = .07, CFI = .92, TLI = .93, SRMR = .11). Nevertheless, in four countries (Estonia, Finland, Norway, and Portugal) boys had significantly more positive math identity compared to girls. No gender differences were captured in Sweden and Serbia. Furthermore, in all countries, Motivational dimensions had a stronger association with MI than math achievement. Generally, among motivational dimensions, interest and perceived competence had the strongest association with students' MI, but there were some specific patterns of relations between motivational dimensions and MI for each country. Regarding the students' grades, results showed that older students perceive themselves less as "math persons" than younger students in all countries, although effect sizes differ. These results contribute to a better understanding of the relationship between identity and motivation in primary school students. Specifically, these results indicate country or, more specifically, its education system is a moderator in the relationship between motivation and identity, which will be further discussed. Further, these results indicate that Grade 4 students tend to have a lower identification with math than Grade 3 students despite their progression in math curriculum and math competence. Taken all together, these results suggest that depending on experience and different educational practices in various educational systems, children have diverse opportunities for the development of math identity. MI development seems to depend on the same factors, with different effects.

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