Over the years, research in the psychology of education has increasingly been marked by investigating constructs from the socioemotional domain, that is, motivation, achievement emotions and their interaction (e.g. Eccles & Wigfield, 2020; Pekrun, 2006); the field has recognised their impact on students’ achievement, engagement in school activities, educational choices and later professional orientation (Wan et al., 2021). Recently, the concept of domain identity related to students’ self-belief about their competence at a skill-based task or activity in a particular domain has been receiving more attention (Darragh, 2016; Eccles, 2009; Malanchuk et al., 2010; Radović et al., 2018; Wegemer & Eccles, 2019). Because we situate our study in the mathematics domain, we focus on mathematics identity (MI), defining it as an individual’s sense of self in mathematics (Darragh, 2013). Math identity is argued to be among the critical factors related to student attainment, involvement, pursuit and mathematics-related affect (Cribbs et al., 2015; John et al., 2020; Miller & Wang, 2019). In mathematics education, identity is also crucial because it provides a new perspective in explaining why some students underachieve or disengage from mathematics without indicating their prior abilities (Cribbs et al., 2015; Graven & Heyd-Metzuyanim, 2019; John et al., 2020; Miller & Wang, 2019). Relevant research is scarce when involving primary education students or diverse cultural contexts.

Building on the expectancy-value perspective on identity and identity formation (Eccles, 2009), the present study explores the relationship between math identity and motivation dimensions and math achievement in primary school. Considering the social nature of mathematics identity and its dependence on the cultural context, the additional aim of our research was to explore these relationships across six European countries. Finally, we investigated potential gender and grade differences concerning mathematics identity.

Mathematics identity

In the past two decades, research on mathematics identity has intensified (Darragh, 2016; Eccles, 2009; Malanchuk et al., 2010; Radović et al., 2018; Wegemer & Eccles, 2019). The concept gained attention because it provides an alternative to cognitive deficit explanations of disengagement and underachievement in mathematics by assuming the failure to belong within the mathematics classroom instead of the failure of one’s ability (Darragh, 2013). Various authors have used MI to examine the relationship between a student and their mathematics learning context (e.g. Sfard & Prusak, 2005) and in looking for the obstacles of social origin (Grootenboer & Zevenbergen, 2008), such as a choice of pedagogical practices (Simpson & Bouhafa, 2020). Also, findings based on MI have often been used to bring up issues of access and equity in mathematics education (Radović et al., 2018). Therefore, most MI studies investigate student groups that have a history of being labelled as unlikely to succeed in mathematics, such as women (Fernandez et al., 2022) or minorities (e.g. Miller-Cotto & Lewis, 2020). However, the concept is equally essential for the mainstream student population, considering that lingering traditional approaches to teaching mathematics and accompanying rigid and strict rules deny many students an opportunity to identify with the subject (Boaler, 2002; Grootenboer & Jorgensen, 2009), leading to a large number of underachievers and mathematically low proficient students (OECD, 2019).

Grounded in the expectancy-value perspective on identity and identity formation (Eccles, 2009), coupled with symbolic interactionism and the socio-cultural paradigm, we define MI as a student’s sense of self in the domain of mathematics that encompasses a student’s self-understanding and perception of how significant others see them in the context of doing mathematics (Anderson, 2007; Martin, 2009). So far, researchers have examined identification with different school subjects from the STEM field (Simpson & Bouhafa, 2020), linking identity besides mathematics to fields such as physics (Hazari et al., 2010) and science (e.g. Trujillo & Tanner, 2014). Such subject-domain identifications are considered to be role identities (Burke & Stets, 2009)—aspects of identity that are shaped by assumptions and expectations related to a given situation or area. Therefore, MI presents only a part of a person’s identity and is in a constant and tangled interplay with other identity parts—personal identity (or Me self), which encompasses unique characteristics and experiences of a person (e.g. being smart, analytical, shy), and collective identity (or We self), which includes shared features and experiences of the social groups a person belongs to (e.g. gender or ethnicity; Burke & Stets, 2009; Eccles, 2009). Thus, the development of MI depends on whether this identification is consistent or conflicts with other aspects of a person’s identity. MI development is influenced by mathematics-related experiences such as interactions and inputs from significant others, social comparison (i.e. comparing one’s mathematics performances with those of other people), intraindividual dimensional comparison (i.e. comparing one’s own mathematics performance to performance in other domains) and so forth, along with the interpretations of these experiences that are shaped by subjective beliefs, such as mindset and values (Eccles, 2009; Simpson & Bouhafa, 2020; Wan et al., 2021).

These MI influencing factors and processes occur at different ages and have various developmental paces (Simpson & Bouhafa, 2020), while the mathematics curriculum becomes disengaging (Wang & Eccles, 2012) and more complex as students progress from grade to grade. Therefore, tracking age differences in MI from the early education years may contribute to explaining developmental trends in the outcomes of mathematics education. However, recent meta-analyses (Radović et al., 2018; Simpson & Bouhafa, 2020) show that researchers tend to focus on post-elementary education because of methodological restrictions in assessing mathematics identity in younger students. Our search for similar studies has revealed only two MI studies focusing on students before middle school. For example, Gulemetova et al. (2022) indicate that the MI of elementary school students in grades 4 and 5 remained constant over the 2 years of the study. Bohrnstedt et al. (2020) investigate the MI of high school students, finding that MI scores decreased significantly from grades 9 to 11. The findings from these two studies suggest that negative changes in MI occur only after elementary education. However, studies have revealed gender differences in MI trajectories.

Studying MI may illuminate gender differences in the mathematics education process and outcomes (i.e. differences in performance, mathematics-related career choices and motivational and emotional elements of mathematics education). As noted, as a social identity, gender identity usually assumes expectations and values that may interfere with identification with mathematics for females. Parents’ and teachers’ beliefs about girls’ and boys’ mathematics abilities shape gender-biased expectations (Gunderson et al., 2012). Cvencek et al. (2011) show that elementary school boys (i.e. ages 6 to 10) identify more strongly with mathematics than their female peers and that even second-grade students demonstrate the “math is for boys” stereotype. These results suggest that, developmentally, the acquisition of the math-gender stereotype and its influence on mathematics self-concept emerged even before the gender differences in mathematics performance. However, another study in the USA with fourth and fifth graders found no gender differences in either the levels of MI or MI growth trajectories of girls and boys of this age (Gulemetova et al., 2022). Studies on the MI of high school students have had more unequivocal results showing that high school female students, on average, score lower on MI scales than their male peers (Alzahrani & Stojanovski, 2020; Bohrnstedt et al., 2020; Marsh & Sharpe, 2020). In addition, Marsh (2020) finds that this gender gap further widens in college; he tracks the MI trajectories of STEM students after high school, finding that male students’ initial level of MI was higher than that of girls and increased by the fourth year of college while females’ MI decreased. Cass et al. (2011), studying different aspects of MI, find that perceived recognition by others of being a good mathematics student was a more significant predictor of seeking a STEM-related career in the subsample of females than in the subsample of males.

Most of the published studies on MI are conducted in the USA, while only about 10% are European-based (Darragh, 2016; Graven & Heyd-Metzuyanim, 2019). Our literature search has revealed only one cross-country study dealing with teachers’ MI and that uses a qualitative method (Lutovac & Kaasila, 2014). However, considering the social nature of MI and its dependence on the cultural context, the high regional diversity of the sampled participants and cross-country comparisons are highly warranted.

Motivation through expectancy-value lens

Eccles’ expectancy-value theory (EVT) is one of the most prominent perspectives in motivation when it comes to the theoretical elaboration of the phenomena and its empirical validation (e.g. Arens et al., 2019; Else-Quest et al., 2010; Hong & Bernacki, 2022; Jacobs et al., 2002; Robinson et al., 2019). Based on EVT, students’ achievement, persistence and task choice depend on their expectancy for success and the value of the task.

Expectancy for success represents students’ belief that they can complete a task. When evaluating expectancy for success, students can ask themselves, “Can I do this task?” (Wigfield et al., 2006). Empirically and theoretically, the concept often overlaps with the constructs of self-efficacy and self-concept.Footnote 1 Researchers have often used these terms as synonymous constructs (Andreman, 2020). Likewise, although very similar to expectancy for success, we have utilised perceived competence, which can be more clearly set apart from self-efficacy and self-concept. Here, perceived competence is a student’s perception of competence over achievement-related tasks (Pekrun, 2006). Perceived competence should also be distinguished from expectancy for success, despite the strong connection between the two constructs. For the latter to be present, one should also hold positive perceptions of competence. Yet despite this conceptual differentiation, research has shown a strong overlap in empirical data between the two (Eccles & Wigfield, 2020).

The second aspect of EVT—task value—can be best described through a question that a student poses to themself when confronted with a task: “Why do I want to do this task?” (Wigfield et al., 2006). Task values comprise four subdomains: intrinsic, attainment, utility and cost. Intrinsic value can be defined as a person’s enjoyment of participating in a task. Attainment value represents the personally based importance that students attach to engaging in certain activities. Although both intrinsic value and attainment can be associated with interest, according to the person-object theory of interest (Krapp, 2002), intrinsic value is closer to feeling-related valence, while attainment is more associated with a value-related valence or personal importance of a task (Gaspard et al., 2015). In addition, attainment value is derived from the anticipated fit of perceived task characteristics with the individual’s core self-schema and social and personal identities and may be considered the closest to MI. Unfortunately, empirical work on the relationship between attainment value and MI is mainly missing because of a lack of empirical measures tying the two concepts (Eccles & Wigfield, 2020). The utility value can be defined as the usefulness a student attaches to a particular task or activity for short- and long-term goals. Unlike intrinsic value and attainment, utility is instrumental and more associated with extrinsic motivation (Ryan & Deci, 2020). Like attainment value, utility also connects to personal goals and a sense of self. Meanwhile, the distinctions between intrinsic, attainment and utility values are subtle, contributing to their high correlation, yet each targets goals relevant to one’s sense of identity or core values in different ways. The last aspect of task values is cost, which can be defined as the subjective evaluation of how much effort, opportunity and emotion one will invest to accomplish the task. Cost works in a way that tends to be lower when other task values and perceived competence are higher, leading to lower academic achievement and persistence (Perez et al., 2019). In connection with MI, it can be seen as the value component that is the least tied to MI.

Perceived competence and task values are important for academic achievement, engagement and career choices (Eccles & Wigfield, 2002, 2020; Wigfield & Eccles, 2000; Wigfield et al., 2006). Some studies even show that EVT constructs may overshadow achievement when observing career choices and engagement. Andersen and Chen (2016) find that expectancies and values mattered more for occupational plans than math achievement. Still, Jansen et al. (2021) show that high achievement in several domains could affect student choices only if comparing these domains engages their self-concept and values. The importance of domain specificity related to EVT constructs is a well-researched aspect of the theory (Arens et al., 2019; Benden & Lauermann, 2022; Schukajlow et al., 2023). Gaspard et al. (2018) conclude that academic domains could be ordered on a verbal-math continuum regarding perceived competence and values (Gaspard et al., 2018). For the present study, our primary focus is on perceived competence and task values in the mathematics domain.

Development of perceived competence and task values

Differences in the perceived meaning of competence and task values among children of different ages have been observed. The phenomenon also includes age variations concerning which value will be the most dominant (Eccles, 2009; Eccles & Wigfield, 2020; Wigfield & Eccles, 1992; Wigfield et al., 2015).

Young children’s perceived competence and task values are assumed to be relatively independent. Intrinsic value will be especially salient from an early age, when the perception of competence is yet to be fully developed. Over time, utility and attainment values become more prominent (Wigfield & Eccles, 1992). By late elementary school, intrinsic value, attainment and utility value continue to develop as distinct but highly related factors (Eccles & Wigfield, 1995). During development, from relatively independent task values and competence, children attach more value to tasks or activities in which they perform well, meaning that perceived competence and values become more interrelated. The implication is that changes in perceived competence are followed by changes in values (Jacobs et al., 2002). Generally, children’s competence beliefs and math values tend to decline from middle childhood to early adolescence (Jacobs et al., 2002; Koller & Baumert, 2001; Watt, 2004; Wigfield et al., 2015). By early adolescence, perceived competence is usually stabilised, which points to the importance of exploring earlier developmental stages when EVT constructs are highly malleable (Wigfield et al., 2015).

Knowledge about domain specificity and the situated nature of EVT (Arens et al., 2019; Benden & Lauermann, 2022; Eccles & Wigfield, 2020) has opened further questions regarding perceived competence and value trajectories and their relations for different domains. However, most of the current studies are focused on EVT components of adolescents or young adults (e.g. Arens et al., 2019; Benden & Lauermann, 2022; Hong & Bernacki, 2022; Parrisius et al., 2022; Perez et al., 2019; Robinson et al., 2019; Wang & Pomerantz, 2009; Weidinger et al., 2020), while the preadolescent period is left relatively unexplored in the light of new findings about EVT.

Gender and cultural differences

Besides studying the development of EVT, there has always been considerable interest in group differences in achievement motivation and the effect of different cultural groups on the development of perceived competence and values. Researchers have repeatedly called for more research on the situational nature of motivational theories, including their possible cultural specificity (Nolen, 2020; Schukajlow et al., 2023). Studies show that the construction of one’s gender identity is followed by the development of gender-specific interest in the span between the ages of 3 and 8 (Wigfield et al., 2015). However, despite many years of research, there are still no unequivocal findings regarding the differences between boys and girls. EVT proposes that gender differences in perceived competence and values related to specific domains emerge through the processes by which children are socialised into gender roles (Eccles & Wigfield, 2020).

One line of research shows that boys have higher academic perceived competence and self-confidence in mathematics and feel less anxious about their math abilities than girls. Boys were also more intrinsically and extrinsically motivated to learn math than girls (Else-Quest et al., 2010; Huang, 2013; Hyde et al., 1990). In one of the most cited studies, Jacobs et al. (2002) track the differences between boys and girls in several domains from 1st to 12th grade. Their study shows that the gender gap was the greatest during lower elementary school when boys had higher perceived math competence. However, over the years, the gender gap started to decrease, and by the end of high school, girls valued math more than boys.

In contrast, some studies show that, except for utility, boys value math more than girls (Chow & Salmela-Aro, 2011; Watt, 2004). Gaspard et al. (2015) propose that the inconsistency in the findings comes from inconsistent operationalisation of the EVT constructs. Therefore, they test the structure and gender differences of the four value beliefs. Although the structure of values was similar for boys and girls, gender differences tended to favour boys. Girls had less intrinsic value and perceived math as less personally essential and less useful for their general and professional futures, and also perceived higher emotional costs and effort. The authors conclude that mathematics for girls was of no personal importance or usefulness for their future goals, which may have clear implications for how girls develop MI. However, these findings were based on adolescents, and it is yet to be tested whether the same insights apply to preadolescents (i.e. the same type of differences emerge or no gender differentiation is yet observed).

Regarding the cultural differences in EVT, empirical studies are even more scarce. Generally, scholars have focused more on ethnic differences (e.g. Harris, 2006; Rodriguez et al., 2009), but some studies have also examined cultural differences and education systems within these diverse environments. For example, Wang and Pomerantz (2009) explore the differences between American and Chinese children, finding that the value of academics decreased among American children while, among Chinese students, it remained relatively stable. On the other hand, Huang (2013) does not find differences in self-efficacy between individualistic and collectivistic cultures. The newest meta-analysis on PISA data shows that, in countries with more significant gender equity, there is a greater number of female students who are in the top 5% in mathematics (Keller et al., 2022), while Else-Quest et al. (2010) point out that gender equity is essential not only for girls’ math achievement, but also for their self-confidence and valuing of mathematics. However, similar to gender differences, past research has focused more on cultural differences among adolescents and young adults than primary school students, observing the differences between very distinct cultures (e.g. America and China) compared with Europe alone.

The Current Study

Consistently, the expectancy of success (perceived competence from now on) and task values are linked to domain achievement, career choice and engagement (e.g. Andersen & Chen, 2016; Eccles & Wigfield, 2020; Jansen et al., 2021). Studies have also shown the potential of MI to add to our understanding of why some children fail in mathematics or are disengaged, irrespective of prior ability (Darragh, 2016; Malanchuk et al., 2010; Radović et al., 2018; Wegemer & Eccles, 2019). At the same time, it has been shown that MI, task values and perceived competence appear at different ages and develop following unique developmental paths (Eccles, 2009; Eccles & Wigfield, 2020; Wigfield & Eccles, 1992; Wigfield et al., 2015). Given that EVT constructs are highly malleable at earlier developmental stages (Wigfield et al., 2015), with the majority of studies focusing on adolescents or young adults (e.g. Arens et al., 2019; Benden & Lauermann, 2022; Hong & Bernacki, 2022; Parrisius et al., 2022; Perez et al., 2019; Robinson et al., 2019; Wang & Pomerantz, 2009; Weidinger et al., 2020), the current study can shed some light on the preadolescent period. Similar contributions rest in connection to the development of MI because most studies focus on middle school students and beyond (Radović et al., 2018; Simpson & Bouhafa, 2020).

The main focus of the current investigation is to (1) explore the relationship between math identity and different aspects of task values (i.e. intrinsic, utility and attainment values) and perceived competence, on the one hand, and math achievement, on the other hand, on primary school students as they start with math learning. Although task values are assumed to be relatively independent, intrinsic value is known to be salient from the earliest period (Eccles & Wigfield, 1995; Wigfield & Eccles, 1992). Because positive relationships between the examined task values and MI are expected, we assume the strongest valence between intrinsic value and MI and will test this assumption for the preadolescent period. At the same time, because students later attach more value to tasks or activities where they perform well (Jacobs et al., 2002; Wigfield et al., 2015), MI could be more strongly related to students’ perceived competence when evaluating possible success in particular tasks or activities (Wigfield et al., 2006), as well as math competence as a whole. However, whether this can be distinguished during the preadolescent period is to be tested.

Taking into account the social nature of MI and its dependence on the cultural context (Darragh, 2016; Graven & Heyd-Metzuyanim, 2019), the second research question revolves around (2) exploring those relationships in different cultural contexts, that is, in six European countries (i.e. Norway, Sweden, Finland, Estonia, Portugal and Serbia). Although this focus is more exploratory, the few studies in this area (Else-Quest et al., 2010; Keller et al., 2022; Wang & Pomerantz, 2009) lead us to expect somewhat different patterns across the European countries we examine. For example, although Scandinavian countries are often seen as very similar, recent studies indicate distinctive patterns in teacher education, grading and testing culture and embedded values in the classroom (Frønes et al., 2020). Conversely, countries with distinct previous socialist traditions (e.g. Serbia) have maintained certain value aspects not visible in the northern part of Europe. Nevertheless, the primary purpose of the current study is to establish a joint model for the six countries by observing direct relationships alone, which will serve as a baseline for later investigations.

Finally, we investigate (3) potential gender and grade differences connected to MI. Considering earlier findings, we would expect that gender affects math identity, with boys scoring higher on MI (Cvencek et al., 2011), and that the results would be similar between grades when taking into account the stability shown in the studies of Gulemetova et al. (2022), but not later on (Bohrnstedt et al., 2020).

Methods

The data came from an international longitudinal study focused on the development of mathematics motivation in primary education—Co-constructing mathematics motivation in primary education–A longitudinal study in six European countries (MATHMot for short)—funded by the Research Council of Norway (grant number 301033). The current investigation uses data from the first wave of the MATHMot project. The participants were 11,782 primary school students from six countries: third-grade (n = 5700, 50.8% female, M = 9.06 years) and fourth-grade students (n = 6082, 50.5% female, M = 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. All survey instruments were administered in paper-and-pencil format during regular hours of mathematics instruction.

Variables

The Expectancy-Value Scale (EVS; Peixoto et al., 2023) was used to assess the diverse aspects of students’ motivation for mathematics. EVS comprises five dimensions (intrinsic value, attainment, utility, cost and perceived competence), totalling 28 items anchored on a 4-point Likert scale. The fit model for the whole scale was confirmed for the current sample (CFA = 0.957, TLI = 0.953, RMSEA = 0.041, SRMR = 0.063) based on the following criteria: RMSEA < 0.08, CFI > 0.90 and TLI > 0.95 (Brown, 2015). However, because we excluded the cost dimension from the present investigation and the subscales were used independently in the model, each of the four subscales was also tested for consistency. All four dimensions show satisfying fit (please see Table 1 for details) and reliability (Cronbach’s alpha ranges from 0.7 to 0.87). The metric invariance was established for each subscale (see Appendix 1).

Table 1 Dimensions of EVS used in the present study (entire sample)
Full size table

The MI scale comprises six items combining perceived personal mathematics identity items (e.g. I think I am a math person) and perceived recognised mathematics identity items. In the latter, students are informed if they perceive that significant others (i.e. friends, family, math teacher) see them as math persons (e.g. My family thinks of me as a math person). The scale was adapted and further advanced based on the prior work of Vincent-Ruz and Schunn (2018) and Miller and Wang (2019). All items are anchored on a 4-point Likert scale. The model fit for the scale was satisfactory (CFI = 0.997, RMSEA = 0.038, SRMR = 0.011), and scale reliability was confirmed (0.80). Measurement invariance parameters were adequate (see Appendix 1 for details).

The math test is comprised of 12 problem tasks in grade 3 and 14 problem tasks in grade 4. Seven math problems appear in both the grade 3 and grade 4 versions of the test and serve as the linking items. The problems were chosen from the list of released items administered in grade 4 of the TIMSS 2011 cycle (Mullis et al., 2012). All items selected for the mathematics test were approved for use by the IEA (Approval IEA-22–022) and depict the curriculum range of the countries involved in the study. The test was timed (i.e. 25 min in grade 3 and 30 min in grade 4). For each correct answer, the students received 1 point, which resulted in 12-point maximum scores for 3rd grade and 14 points for 4th grade. We applied the Rasch measurement model to estimate students’ math scores based on all the items included in the tests, including the seven shared (linking) items. Student math scores were calculated on the scale with an average score of 500 and a standard deviation of 100.

Students’ sex was coded as a dichotomous variable (0 for girls). The grade variable was also dichotomous, distinguishing between grades 3 and 4.

Analytical procedures

All constructs were inspected for descriptives and possible outliers before the main analyses. Measurement invariance was checked for the MI construct and the four motivation dimensions across countries and grades. To explore the relationship between math achievement, task values, perceived competence and identity, we tested the regression models in Mplus 8.8 (Muthén & Muthén, 1998–2017). Math identity was the criterion variable, and task values (i.e. intrinsic, utility and attainment values), perceived competence, math test score, sex and grade acted as the predictors. Because task values and perceived competence were highly correlated (Peixoto et al., 2023), we tested four separate multiple regression models for each dimension (see Fig. 1). The model introduced the country as a moderator variable; each country’s multiple regression model was estimated separately.

Fig. 1
figure 1

The analytical model. Note: The analytical model presents only the key predictors and criterion variables, while residuals and correlation between the predictors are omitted for simplicity. “Mot” denotes the intrinsic value, utility value, attainment value and perceived competence aligned with the model specification. In each model, one of the motivation constructs was tested, coupled with math achievement score, sex and grade as the predictors. The models were repeated for each country

Full size image

In this way, we were able to identify statistically significant differences in regression weights for each predictor among the different education systems while establishing a joint model across the countries. The model fit was evaluated based on the criteria presented above (Brown, 2015).

Results

The results section is organised around the three research questions. First, we examine the relationship between math identity and different task values (i.e. intrinsic, utility and attainment values) and perceived competence, on the one hand, and math achievement, on the other hand. Following this, we present the results exploring those relationships across different cultural contexts. Finally, we examine the gender and grade differences connected to MI.

Relationship between math identity, motivational constructs and achievement

The model fit information is presented in Table 2. The results revealed that all four models fit the data in an acceptable manner. The CFI, TLI and RMSEA values were within the desired range, while SRMR was somewhat above the desired value for the intrinsic value and perceived competence dimension models, thus indicating potential intercorrelations between the residuals (Brown, 2015). All predictors from the motivation spectrum, that is, intrinsic, utility and attainment values and perceived competence, were significant for students’ math identity across the examined countries (see Table 3 for a complete overview). Motivational dimensions had a stronger association with MI than math achievement throughout all the examined models and countries. Among the motivational dimensions, the intrinsic value indicated the strongest association with students’ MI (estimate range 0.629 to 0.758), while the weakest relationship was found for utility value (estimate range 0.481. to 0.618; see Table 3).

Table 2 Model fit information
Full size table
Table 3 Standardised regression weights across models and countries
Full size table

Shared and unique patterns among the examined countries

Despite some general patterns, unique relationships were also captured by observing the association between the motivational dimensions and MI. In Serbia and Portugal, perceived competence (PC) showed the most substantial contribution to MI (0.774 and 0.755), whereas this held for intrinsic value in the other four countries (ranging from 0.710 in Norway to 0.758 in Finland). Among the predictors and countries, utility was the “least relevant,” except in Norway, where this held for PC, which was the least relevant dimension for Norwegian students (see Table 3 for more details).

Also, although a general pattern of math achievement was outperformed by motivational constructs, the relative contribution of math achievement towards MI was not equal across all the countries, holding the strongest for Serbia and Estonia. Its contribution to MI was the lowest in Norway (see Table 3 for details). Across other countries, the estimates were relatively equally distributed.

Gender and grade differences

Boys had significantly more positive perceptions of their own math identities in four countries (i.e. Estonia, Finland, Norway and Portugal) than girls. Although significant, these differences seemed to be less pronounced in Finland. No difference between the sexes was captured in Sweden and Serbia, irrespective of the observed models (see Table 3 for details). Regarding the students’ grades, the results showed that older students (i.e. those in grade 4) perceived themselves less as “math persons” compared with their younger peers in all countries. It should be noted that the magnitude of the grade differences was the most comprehensive in Serbia (− 0.516 to − 0.521) and smallest in Norway (− 0.204 to − 0.209; see Table 3).

Similarities and differences across countries

By including the country as a moderator variable in the multiple regression model, we tested the statistical significance of the regression weights for each country pair (see Appendix 2). Based on these findings, we could conclude that the highest similarity between regression weights was observed between Estonia and Finland, Finland and Sweden and Portugal and Norway. When the regression weights for these countries were compared, only 1 out of 16 comparisons was statistically significant (i.e. showing a dissimilarity between the country pairs). Moreover, this analysis suggests that the regression model for Serbia was the most dissimilar to other countries. A comparison of regression weights between Serbia and Portugal suggested that the difference was statistically significant in 14 out of 16 regression weights. A comparison between Serbia and Norway, as well as Serbia and Finland, indicated that 10 out of 16 regression weights were different, while a comparison between Serbia, Estonia and Sweden suggested a statistically significant difference in 8 out of 16 regression weights. Students learning mathematics in Serbia seemed to have a distinctive experience in forming math identities compared with students from other countries.

Discussion

The main focus of the present paper revolved around the relationship between math identity, task values (i.e. intrinsic, attainment and utility value) and perceived competence, on the one hand, and math achievement, on the other hand. Considering the nature of the constructs (Wigfield et al., 2015) and scarce findings for the preadolescent period (Arens et al., 2019; Benden & Lauermann, 2022; Hong & Bernacki, 2022; Parrisius et al., 2022; Perez et al., 2019; Radović et al., 2018; Robinson et al., 2019; Simpson & Bouhafa, 2020; Wang & Pomerantz, 2009; Weidinger et al., 2020), we explored these links within the context of six European education systems (Darragh, 2016; Graven & Heyd-Metzuyanim, 2019; Keller et al., 2022; Wang & Pomerantz, 2009) and potential gender and grade differences concerning mathematics identity (Cvencek et al., 2011; Gulemetova et al., 2022).

The results showed that all predictors from the motivation spectrum were significant for students’ math identity across all six examined countries (Jacobs et al., 2002; Wigfield et al., 2006, 2015). At the same time, we assumed the association to be the strongest with intrinsic value because of its salient nature across the development period (Eccles & Wigfield, 1995; Wigfield & Eccles, 1992). This result was confirmed in four out of six countries. In Serbia and Portugal, however, math identity was more strongly related to perceived competence, supporting the argument for its importance when evaluating possible success in particular tasks or activities (Wigfield et al., 2006).

Conversely, across all the countries, the overall relationship between motivational constructs and identity was stronger than that between math identity and achievement. Earlier, it was shown that EVT constructs might surpass achievement when observing career choices and engagement (Andersen & Chen, 2016; Jansen et al., 2021), and such a pattern was also confirmed in our results. At the same time, the contribution of math achievement to math identity, although surpassed by the EVT constructs, was the strongest in Serbia, which enforces academic grading at all stages of primary education. Although these evaluations were descriptive in grade 1, starting in grade 2, they became numerical, ranging from 1 to 5 as the highest mark (Official Gazette of RS, 34/2019, 59/2020 and 81/2020). Across all other countries, summative evaluation was either absent (e.g. from grade 8 in Norway) or only introduced as students transitioned to subject teaching (e.g. from grade 5 in Portugal).

Concerning cultural differences, these were found and aligned with some earlier findings (e.g. Wang & Pomerantz, 2009). Although general patterns held for all countries, for example, a stronger relationship between motivational constructs and math identity compared with identity and achievement, the contribution of particular task value (e.g. utility value in Norway compared with Sweden and Finland and contribution of perceived competence in Serbia and Portugal) or achievement (e.g. Serbia) to math identity varied. This shows that the culture or organisation of the education system was an important moderator of how certain relationships unfold, even if the constellation of examined factors was the same (Frønes et al., 2020).

Boys had significantly more positive math identities in four countries (i.e. Estonia, Finland, Norway and Portugal) than girls. Although this aligns with the results of Cvencek et al. (2011), it also corresponds to the findings of Gulemetova et al. (2022), who do not find such differences similar to our results for Serbia and Sweden. Previous studies more consistently favour boys when observing older students (Alzahrani & Stojanovski, 2020; Bohrnstedt et al., 2020; Marsh & Sharpe, 2020). Cass et al. (2011) also show that perceived recognition by others had a stronger effect on MI in girls. However, perceived personal and perceived recognition were still very much intertwined for the age group we observed now, which may mask some underlying differences and similarities between these groups. Similarly, EVT proposes that gender differences in domain-specific perceived competence and task values surface through socialising into gender roles (Eccles & Wigfield, 2020). A similar process could be expected for MI, knowing that parents’ and teachers’ beliefs about girls’ and boys’ mathematics abilities shape gender-biased expectations (Gunderson et al., 2012).

The results showed that older students (i.e. those in grade 4) perceived themselves less as “math persons” than their younger peers in all countries. This contradicts the results of Gulemetova et al. (2022), who observe similar age groups, and aligns with Bohrnstedt et al. (2020), who focus on high school students. However, an important difference between this study and that of Gulemetova et al. (2022) is that the latter is longitudinal. Thus, differences in applied methodologies could explain the differences in the current results. Further studies, which will be possible for the examined sample, should also investigate the “grade slump” longitudinally. In this way, recent results may receive a stronger foothold if confirmed and contribute to further understanding of what happens in the transition from class to subject teaching concerning MI and task values and perceived competence (Eccles & Wigfield, 2020).

Limitations and further research

Although the present study had the opportunity to use a large cross-country sample, the current data cover only one time point, meaning that no direct causal observations can be claimed. In addition, we relied on self-reported measures (except in the case of the math test). Nonetheless, the results have confirmed some of our assumptions or prior research, thus shedding light on the particular relationships in the preadolescent period and whether these could be seen across similar systems or are distinct from only one of the six systems observed. Further observation will consider a longitudinal perspective, following the same students across two time points. This will also allow us to capture the transitional period between class and subject teaching in some of the observed countries, which could enable a more nuanced understanding of the patterns we observe now and the established model, which purposively followed only the direct relationships.

Conclusion

The current results have contributed to a better understanding of the relationship between MI and motivation in primary school students. Specifically, they indicated that the country or, more specifically, its education system was a moderator in the relationship between motivation, math achievement and MI. Further, the results have also shown that grade 4 students tended to have a lower identification with math than their grade 3 peers, despite math curriculum and competence progression. Combined, all the results lead us to conclude that, depending on the experience and different educational practices in various educational systems, children have diverse opportunities to develop math identity. MI development depends on the same factors, but diverse surroundings produce varied effects.