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Since well-being is an important indicator for various educational outcomes (Tuominen-Soini et al., 2012; Fiorilli et al., 2017) and, given the centrality of school in the lives of adolescents (Eccles and Roeser, 2009), it is reasonable to define well-being in relation to the educational context (i.e., academic well-being). There is no consensus on the definition of students’ academic well-being, but it is often described as a multidimensional construct, comprising several sub-dimensions. In prior studies, academic well-being has been conceptualized as being comprised of, for example, academic self-concept, perceived learning difficulties, and school burnout (Korhonen et al., 2014), school burnout, schoolwork engagement, school value, and satisfaction with educational choice (Tuominen-Soini et al., 2012), and school burnout and engagement (Fiorilli et al., 2017). Therefore, in line with previous research and as recommended by Huppert and So (2013), we conceptualized well-being as a multidimensional construct covering both negative (e.g., burnout) and positive (e.g., engagement) aspects of academic well-being in our investigation. In addition, since specifically students’ math-related self-beliefs about their competencies have been found to predict educational and occupational aspirations and choices (Parker et al., 2013), we also defined and assessed well-being within a specific domain, in this case, mathematics. Consequently, school burnout, schoolwork engagement, and mathematics self-concept were chosen as indicators of academic well-being in the present study.

School burnout mirrors that of professional burnout (Maslach et al., 2001) and can be described as a psychological syndrome caused by long-term exposure to school-related stress and pressure to achieve (Schaufeli et al., 2002; Di Chiacchio et al., 2016). Salmela-Aro et al. (2009a) designed and validated the School Burnout Inventory (SBI-9), which measures three dimensions of school burnout; exhaustion due to school demands, cynical and detached attitudes toward one’s school, and feelings of inadequacy as a student. This instrument has been applied to several academic populations, with the same three-factor structure being confirmed in Finland (Salmela-Aro et al., 2009a), Spain (Boada-Grau et al., 2015), France (Faye-Dumanget et al., 2017), and Italy (Fiorilli et al., 2014). These three dimensions are closely related (Toppinen-Tanner et al., 2005), but differently associated with various school-related outcomes (e.g., achievement: Salmela-Aro and Upadyaya, 2014; motivation: Tuominen-Soini et al., 2008, 2012) and are therefore examined as distinct constructs in the present study.

Schoolwork engagement, also suggested to be a central indicator for well-being in school (Tuominen-Soini et al., 2012; Fiorilli et al., 2017), is defined as a positive, fulfilling, study-related feeling composed by three dimensions: vigor, dedication, and absorption (Salmela-Aro and Upadyaya, 2012). Vigor is characterized by high levels of energy while studying, interest and willingness to invest in schoolwork as well as having effective strategies for coping with difficulties. Being dedicated indicates being enthusiastic and having positive attitudes toward the learning processes and outcomes, while absorption refers to being fully concentrated and involved in one’s studies, finding it difficult to detach oneself from schoolwork.

Lastly, since students’ self-beliefs are commonly used indicators of adolescent well-being (e.g., self-esteem and competence, Huppert and So, 2013; self-esteem, Tuominen-Soini et al., 2008; Parhiala et al., 2018; academic self-concept, Korhonen et al., 2014), mathematics self-concept was chosen as an indicator of academic well-being as well. Academically related self-concept is described as the mental representation of one’s competencies in academic domains (Marsh and Craven, 1997).

The dimensions of school engagement and school burnout have been found to be negatively associated (Schaufeli et al., 2002; Salmela-Aro et al., 2009b; Cadime et al., 2016). They are, however, not two opposite ends of the spectrum, but rather, independent constructs (Schaufeli and Bakker, 2004). Despite the negative correlation, studies investigating engagement and burnout among adolescents using person-centered approaches have found students with high engagement and low burnout, students with low engagement and high burnout, and students who are simultaneously highly engaged in school and exhausted due to school demands (Tuominen-Soini and Salmela-Aro, 2014; Salmela-Aro et al., 2016). Similarly, Parhiala et al. (2018) recently investigated profiles of motivation and well-being among adolescent students by using a person-centered approach, and found a group of students with rather negative well-being (i.e., school burnout, internalizing and externalizing problems, low self-esteem), who were still highly motivated in school. These findings also resemble those found by Daniels et al. (2008) and Tuominen-Soini et al. (2008, 2012), indicating that high-achieving, committed, and motivated students who value schoolwork might, at the same time, be receptive to emotional distress and exhaustion. Regarding academic self-concept, it has been found to be positively related to engagement (Guo et al., 2016), lower school burnout (Korhonen et al., 2014) and, also, attitudes toward school (Green et al., 2012).

As for the relation between well-being and academic performance, it has been found that the dimensions of school burnout are associated with academic performance in various ways. Salmela-Aro et al. (2009b) found that the lower the academic achievement and the lower the school engagement, the more cynicism toward the meaning of school and sense of inadequacy at school the adolescents experienced. Then again, exhaustion has been found to occur among high-achieving and motivated students as well (Tuominen-Soini et al., 2008, 2012). Schoolwork engagement has been found to have a direct, positive effect on academic achievement and can be seen as a key resource for students as they face different school-related demands. If there is an imbalance between resources and demands, where the perceived demands exceed the personal resources, it may lead to an increase in student burnout (Salmela-Aro and Upadyaya, 2014). Further, the positive link between academic self-concept and academic achievement is also well documented (Valentine et al., 2004; Möller et al., 2011), especially concerning domain-specific self-concept and achievement (Denissen et al., 2007; Guo et al., 2015b).

Researchers generally regard adolescence as a period characterized by considerable biological, social, psychological, and developmental change. However, studies that have investigated school burnout throughout adolescence have found that the overall mean level of school burnout is quite stable over time, although some students seem to experience an increase in burnout during educational transitions (Salmela-Aro and Upadyaya, 2014). Also, as students grow older, they seem to become progressively more at risk of burnout (Lee et al., 2013; Fiorilli et al., 2017), possibly due to increased school demands. Engagement, on the other hand, has been found to decrease, possibly because of changes in the school environment when students transition from elementary to secondary school (Wang and Eccles, 2012). These declines could reflect an increasing misfit between students’ state of development related to adolescence and the opportunities provided in the secondary school environments (Eccles et al., 1993). Similarly, although academic self-concept has been found to become increasingly stable during adolescence, educational transitions seem to have a detrimental effect on students academic self-concept as well (Cole et al., 2001).

Regarding well-being and gender differences, the overall trend seems to be that girls are more likely to report higher levels of school burnout than boys (Salmela-Aro et al., 2008; Salmela-Aro and Tynkkynen, 2012). However, although girls seem to be more receptive to school burnout, they are, at the same time, typically more engaged in schoolwork than boys (Salmela-Aro and Upadyaya, 2012) and attribute greater importance to academic achievement (Murberg and Bru, 2004). These results also concur with the findings by Parhiala et al. (2018), as they found that girls were overrepresented in groups characterized by rather high motivation but negative well-being.

When investigating gender differences in the domain of mathematics, a fairly consistent finding is that boys perform a little better in mathematics and have higher mathematics self-concept than girls (Nagy et al., 2006; Watt et al., 2012). The gender difference in mathematics in favor of boys seems to be the largest among the higher performing students and absent among the lower performing students (Stoet and Geary, 2013). Interestingly, gender differences in mathematics self-concept have also been found when there is no difference in the students’ mathematics performance (Pajares, 2005; Watt, 2006). These differences have often been explained in terms of gender stereotypes, that is, mathematics is commonly considered a “male” field. For example, Song et al. (2016) found that stereotypes about mathematics had both a direct and an indirect negative effect on girls’ mathematics performance.

Educational aspirations influence adolescents’ overall well-being later in life (Ashby and Schoon, 2012) and have previously mostly been predicted by socioeconomic background (Garg et al., 2007), performance-related indicators (e.g., grades), and different motivational beliefs (e.g., self-concept and interest; Nagy et al., 2006; Korhonen et al., 2016). However, investigations using students’ psychological well-being as a predictor of educational aspirations are scarce (for an exception, see Korhonen et al., 2016), even though well-being has been linked with several other important educational outcomes (e.g., achievement: Kiuru et al., 2008; motivational tendencies: Tuominen-Soini et al., 2012). Korhonen et al. (2014) investigated students’ academic performance and well-being profiles by using a person-centered approach, and found that students with low performance (in mathematics and reading) as well as students with poor academic well-being were more prone to school dropout than students with high or average performance. Therefore, one could expect academic well-being to have an effect on educational aspirations as well.

In a recent study by Korhonen et al. (2016), school burnout was found to have a negative indirect effect on educational aspirations through interest, but also, interestingly, that higher levels of school burnout were directly related to higher educational aspirations for girls. Since girls have been found to be overrepresented in groups of students with high levels of both engagement and school burnout (Tuominen-Soini and Salmela-Aro, 2014), it is possible that ambitious and success-oriented girls, despite feeling exhausted, still hold high educational goals (Tuominen-Soini et al., 2008; Tuominen-Soini and Salmela-Aro, 2014).

Researchers have found positive relations between students’ schoolwork engagement and educational and career aspirations (Kenny et al., 2006; Wang and Eccles, 2012). Hill and Wang (2015) revealed that this relation is reciprocal. Eccles (2007) suggested that students are more likely to engage in school if they understand the importance of engagement and achievement for their future. In contrast, it might be that students’ engagement in school also has the potential to shape goals and aspirations, as observing one’s own experiences at school provides the information needed to set up and meet educational goals (Bandura, 1991). Further, studies have found that students who are engaged with their schoolwork not only aspire for higher educational goals, but also complete higher education studies (Li and Lerner, 2011; Wang and Eccles, 2013).

Academic self-concept has consistently been found to be an important predictor of educational and career choices (Nagengast and Marsh, 2012; Parker et al., 2012) and aspirations (Korhonen et al., 2016), even when controlling for achievement (Parker et al., 2013). In a study by Guo et al. (2015a), academic self-concept was not only a key predictor of educational aspirations, but also a stronger predictor of long-term occupational aspirations and educational attainment than IQ and task values. Similarly, positive associations have been found between domain-specific mathematics self-concept and educational aspirations (Parker et al., 2013).

Previous research on mathematics performance and aspirations has focused primarily on the type of aspiration (i.e., the specific kind of occupation), particularly on the connection between mathematics performance and career choices in the science, technology, engineering, and mathematics (STEM) field. Overall, mathematics performance has been regarded as a critical filter, limiting later educational and occupational aspirations, and was therefore included in the present study. Shapka et al. (2006), for example, investigated the connections between early mathematics performance, gender, and career aspirations in ninth grade students and found, that students with lower grades in math had lower career aspirations than average- and high-performing students, even when controlling for overall academic achievement. Furthermore, mathematics performance has been found to predict educational aspirations even when controlling for relevant motivational and well-being constructs like interest, academic self-concept, and school burnout (Parker et al., 2014; Guo et al., 2015a,b; Korhonen et al., 2016).

The students’ mathematical skills were assessed with a standardized online assessment test (KTLT; Räsänen et al., 2013). The test development consisted of two steps. First, the candidate items with known difficulty level were selected from mathematical tasks originally used in the national assessments. Second, the item bank of 130 items were selected to be used in the test based on a sample of Finnish speaking students (N = 1157). All subjects solved subsamples of 40 items (with 10 anchor items in each test). The Cronbach alpha reliability was 0.89 (Räsänen and Leino, 2005). In this study the Finnish-Swedish translation of the battery was used. In this version the norms (IRT-values) were calculated from a sample of Finnish-Swedish speaking students (N = 1140) from grade levels 7–9 representing a national sample at that age.

The online assessment has three steps. First the student is asked to evaluate a difficulty of a single calculation task (easy, average, difficult). Based on the student’s answer, the system randomly selects the first item from a pool of items from easy, average, or hard items defined by their IRT delta value (difficulty parameter). In the second step, the system gives additional four items randomly from the pool of the items. In the third step, the system starts to recalculate a theta value (the estimated level of skill in the logit scale) after each given solution and selects the most informative item to be presented based on the delta and beta values (difficulty and discrimination parameters) from the remaining pool of items. The termination rule of the third step is that the theta value changes less than 2% from the current skill estimate after presenting a new item or that the subject has reached the maximum number of items (20) to be presented. To help the interpretation of the results the system transforms the student’s theta value automatically into a more familiar scale for educational practitioners using the test with a mean of 100 points (SD = 15). Likewise, the results in this study are presented using these transformed values.

Mathematics self-concept was measured with three items from Marsh’s (1992) Self Description Questionnaire I (SDQ I) scale (also see Arens and Hasselhorn, 2015). The items (e.g., I learn things quickly in mathematics) were assessed by a five-point Likert-type scale ranging from 1 (completely false) to 5 (completely true). The items were back-translated from English to Swedish.

Schoolwork engagement was measured by the Schoolwork Engagement Inventory (EDA; Salmela-Aro and Upadyaya, 2012). The inventory consists of nine items measuring energy (e.g., When I study I feel that I am bursting with energy), dedication (e.g., I am enthusiastic about my studies), and absorption (e.g., Time flies when I am studying) in relation to schoolwork in general. The items were assessed through a seven-point Likert-type scale ranging from 0 (never) to 6 (every day). Both one- and three-factor solutions of schoolwork engagement are applicable when using the inventory (Salmela-Aro and Upadyaya, 2012). Accordingly, a composite score was computed from all items to indicate overall schoolwork engagement in the present study. The Swedish version of the inventory was obtained from the PISA2015 questionnaire (OECD, 2016).

School burnout was assessed by the nine-item School Burnout Inventory (SBI; Salmela-Aro et al., 2009a). The SBI scale is divided into three subscales: four items measuring emotional exhaustion (e.g., I feel overwhelmed by my schoolwork), three items measuring cynicism toward the meaning of school (e.g., I feel that I am losing interest in my schoolwork), and two items measuring the sense of inadequacy at school (e.g., I often have feelings of inadequacy in my schoolwork). This three-factor structure has been confirmed in several previous studies (see Salmela-Aro et al., 2009a; Fiorilli et al., 2014; Tuominen-Soini and Salmela-Aro, 2014). All items were assessed using a six-point Likert-type scale ranging from 1 (completely disagree) to 6 (completely agree). The Swedish version of the inventory was obtained from the PISA2015 questionnaire (OECD, 2016).

We measured students’ idealistic and realistic educational aspirations according to two statements representing overall educational aspirations: Highest academic degree I want to achieve and Highest academic degree I will probably achieve, assessed using a 4-point ordinal scale (1 = comprehensive education, 2 = vocational upper secondary education, 3 = polytechnic education, and 4 = university education). These two items were combined to a composite score representing students educational aspirations.

Reliability coefficients and correlations between all the measures are reported in Table 1.

The LCFA was performed simultaneously for seventh and ninth grade data on items representing academic well-being in Times 1 and 2. A model was specified in which all items for each scale were allowed to load on the corresponding factor only. On the basis of previous research, we expected that the items from the School Burnout Inventory (SBI; Salmela-Aro et al., 2009a) would load on three separate factors: exhaustion, cynicism, and inadequacy (Salmela-Aro et al., 2009a; Tuominen-Soini et al., 2012), that the nine items from the Schoolwork Engagement Inventory (EDA; Salmela-Aro and Upadyaya, 2012) would load on a single engagement factor, and that the three items measuring mathematics self-concept from Marsh’s (1992) Self Description Questionnaire I (SDQ I) would load on a single mathematics self-concept factor (Arens and Hasselhorn, 2015). We therefore specified a model with three school burnout factors (exhaustion, cynicism, and inadequacy), a schoolwork engagement factor, and a mathematics self-concept factor as factor indicators.

Due to slight non-normality in the items measuring burnout, we used maximum likelihood with robust standard errors as estimators in the analyses. We used chi-square (χ²), the comparative fit index (CFI), the Tucker–Lewis Index (TLI) and the root mean square error of approximation (RMSEA) as model-fit indicators. The CFI and TLI vary along a 0-to-1 continuum, and values greater than 0.90 and 0.95 reflect acceptable and excellent fit to the data, respectively. RMSEA values of less than 0.05 and 0.08 reflect a close fit and a reasonable fit to the data (Marsh et al., 2004). When comparing nested models, it is suggested that support for the more parsimonious model requires a change in the CFI of less than 0.01 and in the RMSEA of less than 0.015 (Chen, 2007). A prerequisite for meaningful comparison is that the measures are invariant across time points, that is, they measure the same underlying construct(s). LCFA allows for testing measurement invariance by specifying a series of nested models, where the endpoints are the least restrictive model with no invariance constraints, and the most restrictive model constraints all parameters to be the same across time points (Bollen, 1989). As a baseline model for testing measurement invariance, we specified a model imposing no invariance constraints on the factor loadings and indicator intercepts, assuming the same factor structure (configural invariance) at both time points. This model fitted the data very well. Next, we fitted a model where the factor loadings were constrained to equality (factorial invariance) across the time points, and this did not worsen the model fit. Finally, we compared the factorial invariance model against a fully invariant model, with both factor loadings and indicator intercepts constrained to equality (scalar invariance). The fully invariant model fitted the data well and did not worsen the model fit, indicating that the levels of the underlying items are equal at both time points. Therefore, the prerequisite for meaningful measurement invariance was achieved. The fit indices for the models tested are presented in Table 2.

We used a person-centered approach to investigate what patterns of academic well-being and mathematics performance students show, and how stable these patterns are during one school year. The goal in the person-centered approach is to group students into categories, containing students who are similar to each other (Muthén and Muthén, 2000). To identify the cluster memberships in longitudinal data, we used the I-States as Objects Analysis (ISOA) procedure (Bergman and El-Khouri, 1999, 2003; Bergman et al., 2003), as it is optimal for studying short-term development. The key assumption for the ISOA approach is that the same typical patterns occur at all time points, although the proportion of the sample that belongs to each typical pattern may vary across time, and that some individuals may change the typical pattern they belong to. ISOA is based on data with the same set of variables measured at all time points, and the I-state is defined as an individual’s pattern of variable values at a specific time point. Since the present study consists of two time points, each person is characterized by two I-states. The I-states can therefore be identified despite of the time dimension, and the classification can be used to describe individual development.

First, our longitudinal data were reorganized in a way that the data for each student for both measurement points was coded as a separate case. Second, a series of LPAs (Muthén and Muthén, 2000; Vermunt and Magidson, 2002) was carried out on the reorganized data to identify students with similar patterns of academic well-being and mathematics performance. LPA is a probabilistic or model-based variant of traditional cluster analysis (Vermunt and Magidson, 2002). Its goal is to identify the smallest number of latent classes (groups) that adequately describe the associations among the latent continuous variables. In the analyses, one class is added in each step until the model optimally fits the data. To choose the best fitting model, Bayesian information criterion (BIC) and Vuong–Lo–Mendell–Rubin (VLMR) likelihood ratio test were used as the statistical criteria. The model with a lower BIC value is considered to provide a better fit to the data, and a resulting p-value of less than 0.05 for VLMR suggests that the estimated model is preferable over the reduced model (Lo et al., 2001). Furthermore, the usefulness and interpretableness of the latent classes (e.g., the number of individuals in each class) were also considered to choose the best fitting model. The LPAs were performed separately for seventh and ninth grade students and, in the LPA models, covariances were allowed to vary across clusters. Finally, the data were reorganized in such a way that the data for each student at both measurement points were again handled as two successive measurements of the same individual.

The stability of and changes in academic well-being and mathematics performance profiles (i.e., group memberships) within a school year (from Time 1 to Time 2) were examined through configural frequency analysis (CFA; von Eye, 1990). CFA compares the observed to expected frequencies in a cross-tabulation and asks whether cell frequencies are larger or smaller than could be expected by a base model. The base model selected for frequency comparison was the first-order CFA, which assumes that all variables under study may show main effects and are independent of each other (von Eye, 1990, 1996). By means of CFA, we searched for typical and atypical patterns. A type is a pattern that is observed more frequently than expected by chance, and an antitype is a pattern that is observed less frequently than expected by chance. In the present study, we focused on finding specific classes that the students tend to stay in more frequently than would be expected by chance (i.e., individual stability) as well as whether there are changes between the classes that cannot be ascribed to chance fluctuations (i.e., individual change).

One-way ANOVAs were conducted to examine differences in academic well-being and mathematics performance between the profiles. ANOVAs were also conducted to investigate how students in the different academic well-being and mathematics performance profiles differ with respect to their educational aspirations at Time 1 and Time 2.

A chi-square test was performed to examine the association between the academic well-being and mathematics performance profiles and gender. Then, we examined the adjusted residuals in each cell to see in which specific profile gendered differences occurred. If the residual exceeded the critical value of 1.96 in a z-distribution for either boys or girls, they were overrepresented in the profile.