Scared, Bored or Happy? Latent Profile Analyses of Primary School Students’ Academic Emotions about Math

Abstract

Emotions and motivation are central to learning. Control–value theory (CVT) and expectancy–value theory (EVT) explain how emotions and expectations of success affect students’ task engagement. Supported by these two frameworks, this study investigates the emotion profiles for maths among fourth- and fifth-grade students (N = 6778) from three European countries and their links to motivation and achievement. Methods: Using latent profile analysis (LPA), we analysed the emotional profiles in students, as well as their associations with gender, country, grade, motivation and maths achievement. Results: Five profiles emerged in the grade 4 data (Bored, Bored and Anxious, Moderate, Happy and Anxious). All five profiles were visible in the grade 5 data, coupled with an additional sixth profile, which appeared only in grade 5 (i.e., Apprehensive–Happy). Girls were found more commonly in the Anxious profile and were less likely to appear in the Happy profile. Norwegian students were more prominent in the Bored and Moderate profiles. Conversely, Portuguese students stood out more in the Anxious profile and were less present in the Bored and Moderate profiles. The Serbian dataset did not stand out, with a particular pattern observed in grade 4. Nevertheless, Serbian fifth graders were overly visible in the Bored and Anxious profile and less present in the Happy and Apprehensive–Happy groups. The Happy profile had higher scores for all task values except for cost and was, along with the Moderate profile, associated with higher achievement; the Bored and Anxious profile was associated with higher scores of cost value and lower achievement. Conclusions: A person-centred approach allowed for a more diverse view of how students experience emotions. These findings highlight the complex interplay between emotions, motivation and achievement, which is affected by cultural and educational contexts.

1. Introduction

During their schooling journey, students navigate a diverse spectrum of emotions, both uplifting and challenging, which significantly affect their academic progress, accomplishments and motivation, among other factors [1]. Traditionally, the research in this field has primarily focused on negative emotions, such as anxiety. However, contemporary research, propelled by Pekrun’s control–value theory (CVT), has progressively broadened its scope to encompass a more comprehensive range of emotions [1,2]. Additionally, emotions and motivation are intertwined because both share particular antecedents that impact the emotional and motivational states experienced across learning environments [3,4].

The results from large-scale assessments have shown a decrease in mathematics performance in the past decade [5,6], putting mathematics in the spotlight in an attempt to understand how this declining trend can be reversed. Furthermore, it has been observed that students tend to show a decline in motivation throughout adolescence [7], which usually occurs in the final years of elementary school [8]. Typically, the research in this field has employed a variable-centred approach to explore the relationships between emotions, motivation and achievement. However, such an approach does not allow for investigating nuanced individual differences. With this in mind and using a person-centred approach [9,10], the present study focused on primary school students in grades 4 and 5, with the aim of better understanding the adaptive and less adaptive emotional profiles of students and their relationships with motivation and achievement here.

1.1. Control–Value Theory of Emotions

In recent years, CVT has emerged as the main theoretical framework for explaining the role of emotions in learning contexts, particularly in academic contexts. CVT describes how specific emotional experiences are triggered in educational settings and the associations between achievement emotions and learning outcomes [3,4,11]. Specifically, achievement emotions can be defined as emotional responses that are triggered by events and actions in an academic context. In essence, achievement emotions are those emotions tied to activities such as studying and their outcomes of success or failure. These emotions can be understood as momentary state emotions experienced in a particular situation (state achievement emotions) or as enduring emotional tendencies towards achievement situations (trait achievement emotions) [11].

According to CVT, achievement emotions experienced in school contexts can be triggered by control appraisals related to accomplishing activities and the values assigned to these activities and outcomes [12,13,14,15]. Control appraisals involve individuals’ perceptions of their competence and ability to successfully carry out actions (e.g., self-efficacy, self-concept or perceived competence) and achieve results (outcome expectations). The subjective value assigned to a task or activity is linked to the perceived importance of the activity and results and can be categorised as intrinsic, extrinsic or achievement values [2]. Control and value appraisals serve as proximal determinants of achievement emotions. However, CVT also considers more distal antecedents of achievement emotions, such as social and cultural factors (e.g., quality of instruction, interactions, feedback and expectations of significant others).

CVT proposes a taxonomy for classifying emotions based on valence, activation and object focus. Here, valence refers to the positive or negative value associated with an emotion. Positive emotions, such as joy, hope and pride, have been shown to enhance students’ motivation for mastery and academic success. In contrast, negative emotions, such as anger, anxiety and boredom, are linked to avoidance motivation and lower academic performance [13,16,17]. In this case, activation entails the physiological impact of emotions by measuring the level of arousal they induce. Thus, emotions can be categorised as activating, such as hope, or deactivating, such as relief [14,18]. From the perspective of object focus, achievement emotions can be classified as pertaining to either achievement activities or outcomes. Activity emotions involve those feelings associated with engagement in achievement-related tasks (e.g., pleasure in learning and boredom in the classroom). In contrast, outcome emotions are linked to the results of these activities (e.g., relief after taking a test). Outcome emotions encompass prospective and anticipatory emotions (e.g., hope for success, anxiety about failure), as well as retrospective emotions (e.g., pride or shame following feedback on achievement).

CVT emphasises the importance of considering all three taxonomy dimensions and proposes a classification of academic emotions based on valence, activation and object focus (positive vs. negative, activating vs. deactivating and activity vs. outcome) [14]. This classification yields eight categories of emotions: (a) activity positive activating emotions (e.g., enjoyment); (b) activity positive deactivating emotions (e.g., relaxation); (c) activity negative activating emotions (e.g., anger); (d) activity negative deactivating emotions (e.g., boredom); (e) outcome positive activating emotions (e.g., hope, pride); (f) outcome positive deactivating emotions (e.g., relief); (g) outcome negative activating emotions (e.g., anxiety, shame); and (h) outcome negative deactivating emotions (e.g., hopelessness) [14].

Emotions are believed to impact the key aspects of learning, including motivation, approaches to learning methods [11,19] and academic achievement [20]. Research has shown that positive emotions (e.g., enjoyment, hope) are mostly positively related to academic achievement [11,13,17,20], as are the use of flexible learning strategies, self-regulation [14] and motivation [19]. Nevertheless, some studies have shown that positive emotions can sometimes be negatively related to academic achievement [20]. Conversely, in most cases, negative emotions are negatively associated with using more adaptive learning strategies, motivation and academic achievement [11,13,14,17,19,20]. Furthermore, according to CVT, emotions are domain-specific, meaning that control–value emotions may vary depending on the learning domain (e.g., mathematics, science, etc.) [4].

Among younger students (i.e., those in grades 4–7), achievement emotions have been investigated by employing both cross-sectional [21,22] and longitudinal [23,24,25] study designs; the results highlight a prevalence of positive emotions among younger students (e.g., enjoyment, pride) and higher levels of negative emotions among older students (e.g., anger, boredom), either about school in general or specific topics such as maths or language. Conversely, anxiety does not always show the same pattern as other negative emotions. With both younger and older students, mixed results have emerged, showing that anxiety can increase, decrease or remain relatively stable [23,24,26,27].

1.2. Expectancy–Value Theory

Expectancy–value theory (EVT) suggests that commitment and persistence in a particular task or activity arise from the interactions between the expectations of success and the importance attributed to a task [28,29,30]. This framework closely aligns with the one proposed by CVT, which suggests that those emotions linked to a specific task depend on evaluations of control and value. In both theoretical models, similarities exist between the constructs of control appraisals and expectancies because both address the perception of competence in handling a task.

Regarding value, EVT is more specific, differentiating between three subjective task values—intrinsic value, attainment value and utility value—with the additional component of named costs. Intrinsic value represents the enjoyment derived from task engagement, while attainment value reflects the significance attached to task performance intertwined with one’s identity [29,30]. Utility value stems from a task’s relevance right now in the present and to obtaining future goals and can be viewed as a form of extrinsic motivation [31]. Costs represent the perceived drawbacks or obstacles that may diminish motivation to perform a particular task, including considerations about effort, opportunity costs and the emotional or financial resources required to complete the activity [30].

Expectancies and values are positively associated with academic achievement, except for cost, which is negatively related to achievement. A meta-analysis by Pinquart and Ebeling [32] reveals a moderate correlation between expectations of success and academic achievement. Concerning subjective task values, the relationships with academic achievement are typically weaker than those with expectancies and achievement [33,34,35].

1.3. A Person-Centred Approach in the Study of Achievement Emotions

The research on the role of achievement emotions in the learning process has primarily employed a variable-centred approach [36,37]; this approach examines the relationships between variables through correlation, regression analysis or structural equation modelling to identify the general patterns in these associations. An alternative approach is the person-centred approach, which seeks to identify the subgroups or clusters within a population based on similarities or patterns in their characteristics. This methodology involves techniques such as more traditional approaches to cluster analysis and latent class and latent profile analysis (LPA), hence allowing researchers to identify distinct groups of individuals with similar profiles of variable scores [38,39]. The outcome is homogeneous yet mutually exclusive latent groups within a diverse population.

Research using a variable-centred approach can hinder the identification of particular groups or subgroups characterised by specific sets of variables [38]. This approach depicts how one variable is related to another, as if the relationships among such variables are the same for everyone. However, it is expected that the associations between variables might vary among different types of individuals because these variables also interact with one another [38]. In the case of academic emotions, a person-centred approach is even more relevant considering that emotions can co-occur in academic contexts here. The literature on emotions has often treated emotions in isolation because of multicollinearity issues [15]. In this sense, using a person-centred approach is advantageous because it allows us to identify profiles based on a range of emotions. Additionally, it enables us to relate these profiles to different academic outcomes [40].

Much of the research on emotions using a person-centred approach has focused on university students [41,42,43,44,45,46], though some studies have also been conducted with middle and high school students [36,47,48] and primary school students [24,37,49,50,51]. The instruments used to assess emotions have varied, with the Achievement Emotion Questionnaire (AEQ) being the most prevalent. Additionally, the number of emotions assessed to calculate profiles has also varied considerably. The literature has suggested a number of clusters, ranging from two [48] to seven [45], even though finding three or four clusters is the most common solution among studies.

In a North American study of fourth and fifth graders, Karamarkovich and Rutherford [37] use a person-centred approach to analyse the relationships among emotions experienced in maths, motivation and achievement. Emotions were assessed with a questionnaire in which students could select one to three emotions out of seven options (bored, challenged, excited, frustrated, happy, hopeful or nervous) related to the maths task in which they were involved. Four clusters were identified, including two positive, one negative and one mixed emotion profile. The two positive clusters exhibited the highest values for maths value, maths expectancy and maths achievement compared with the other clusters. Mata et al. [24] used a person-centred approach with third- and fourth-grade students in Portugal to identify different emotional profiles related to maths and how these profiles were associated with achievement. Because this was a longitudinal study, the authors also examined the stability or variability of the identified emotional profiles over two years. The results show three different profiles (negative, positive and moderate), revealing that profile membership was moderately stable across all four time points. This highlights that some of these young students already had firm emotional constellations for maths. The students in the positive profile showed the highest levels of academic achievement. Raccanello et al. [51] conducted interviews with fourth, seventh and eleventh graders to assess their emotions felt about literacy and mathematics, identifying six achievement emotions (enjoyment, relief, relaxation, anxiety, boredom and sadness) that served as the basis for the cluster analysis; they found three identified clusters: happy (prevalence of enjoyment), relaxed (prevalence of relaxation) and depressed (prevalence of sadness). Lv et al. [50] use the PANAS to assess Chinese students’ positive and negative affect in grades 4 to 6. A cluster analysis using positive and negative affect and academic achievement reveals three clusters: high achievers with positive emotions, low achievers with moderate emotions and average achievers with negative emotions. Hanin and Van Nieuwenhoven [49] use one item per emotion to assess three positive activating emotions (enjoyment, pride or hope), four negative activating emotions (shame, fear, worry or nervousness) and three negative deactivating emotions (sadness, hopelessness or boredom) in upper elementary school students. Using cluster analysis, they find four clusters: bored (high levels of boredom and low levels of other emotions), resigned (high levels of negative emotions and low levels of positive emotions), positive (high levels of positive emotions and low levels of negative emotions) and anxious (high levels of nervousness, worry and fear and low levels of positive emotions). The positive profile showed the highest levels of maths performance and perceived competence. In contrast, the anxious and resigned profiles had the worst results on the maths test and for perceived competence.

1.4. The Current Study

Based on the previously described theoretical background, we focus on the emotional experiences of primary school students (i.e., grades 4 and 5) across three countries (i.e., Portugal, Serbia and Norway). Given the ability of a person-centred approach to observe students’ differences across a range of characteristics, in this case, a range of emotions known to co-occur, we focus on mathematics-related anxiety, boredom and enjoyment. Keeping in mind the importance of emotional experiences to learning, motivation and academic achievement [11,15,19,20] and the fact that these experiences are formed early on, we examined them in primary school children, an age group scarcely investigated. Studying this area with a somewhat younger age group is especially useful for recognising nonadaptive profiles early in the schooling experience so that educators can intervene early in students’ academic paths. In addition, we rely on the AEQ-ES [52] and cross-country data to obtain better insights into the possible nuances between primary school students situated in different educational settings.

Concerning the cross-country comparison, the chosen national systems differ. In Norway, primary and lower secondary education comprises 10 years, and students typically start school during the year of their sixth birthday. These 10 years of education are divided into two main stages. The first seven years (years 1–7) are called the primary level (barnetrinnet), and the three subsequent years (years 8–10) are called the lower secondary level (ungdomstrinnet). In Serbia, mandatory education lasts eight years and is referred to as primary school (osnovna škola). The first four years are organised as class teaching (i.e., one teacher teaches all subjects), while grades 5 to 8 are organised as subject teaching (i.e., a different teacher teaches each subject). In Portugal, the educational structure consists of three main stages: elementary school (grades 1 to 4), middle school (grades 5 to 9) and secondary education, covering grades 10 to 12. Like Serbia, the Portuguese system transitions from class to subject teaching between grades 4 and 5. This transition does not exist in Norway, nor does any summative grading exist. Both Serbia and Portugal introduce grading earlier. In the present paper, we use the term primary while acknowledging the systemic differences across the countries involved. We formulate the following research questions:

RQ1: What are the emotional profiles of primary school students concerning mathematics? Considering the different nature of the examined emotions in connection to their valence, activation and object focus [13,14,15,16,17,18], as well as other studies using a person-centred approach [37], we postulate the existence of both optimal (with the prevalence of enjoyment) and less optimal (involving prevailing negative emotions) student profiles, including those that seem to be more ambiguous in nature (i.e., mixed profiles).

RQ2: Can we distinguish the same types of profiles between grade 4 and grade 5 students? Although both grades pertain to primary school children, we assume the possible existence of different profiles because of the children’s development. At the same time, in Portugal and Serbia, students transfer from class to subject teaching. Although students in Serbia remain with the same group of peers and their school environment does not change, students in Portugal need to adjust to new surroundings. Thus, adjusting to a new school environment can significantly trigger a new constellation of emotional responses (i.e., profiles). Similar occurrences are visible when observing motivation [53].

RQ3: Are the selected profiles equally visible across different countries? Similar to the expectations connected with the previous research question and differences in the trajectories students follow in transitioning from class to subject teaching in Serbia and Portugal but not Norway, as well as the school setting changing in Portugal, we postulate the existence of less optimal student profiles in Portugal and Serbia after transitioning to subject teaching and the school setting changing.

RQ4: How are students’ emotional profiles linked to task values and perceived competence? Considering the studies observing the relationship between task values and perceived competence and emotions [19], we postulate more optimal emotional profiles are positively linked to perceived competence and all task values, except cost. A reverse association is expected for less optimal emotional student profiles.

RQ5: How are students’ emotional profiles linked to their achievement? The literature has indicated that positive emotions, such as enjoyment, are positively related to academic achievement [11,13,17,20]. Similarly, in most cases, negative emotions (i.e., anxiety and boredom) have been negatively associated with achievement [11,13,14,17,19,20]. We postulate that less optimal profiles score lower on maths tests and that the opposite is true for more optimal emotional profiles.

2. Materials and Methods

2.1. Participants

The data originated from international longitudinal research focused on the development of mathematics motivation in primary education [names omitted for review purposes]. The current investigation uses data from the second wave of the [name omitted for review purposes] project, collected in 148 schools across three of the six participating European countries, totalling 6778 grade 4 and grade 5 students (see

Table 1. Overview of the participants.

Countries	Norway		Portugal		Serbia
Students	Grade 4	Grade 5	Grade 4	Grade 5	Grade 4	Grade 5
	1216 (50.6% girls)	1245 (46.6% girls)	866 (48.6% girls)	1275 (50.8% girls)	1145 (49.7% girls)	1031 (49.4% girls)

Note: Most schools participated with one classroom per grade.

for details).

2.2. Measures

2.2.1. Achievement Emotion Questionnaire—Elementary School (AEQ-ES)

The AEQ-ES [52] assesses three emotions (anxiety, boredom and enjoyment) in three different contexts: attending maths classes, doing homework and taking mathematics tests. The students answered each item on a 5-point Likert scale ranging from ‘not at all’ to ‘very much’ in a pictorial format. We used a gender-neutral face to display the different levels of each emotion (Figure 1).

The AEQ-ES is composed of 28 items: 12 for anxiety (4 for anxiety in class, 3 for anxiety related to homework and 5 for test anxiety), 7 for boredom (4 for boredom in class and 3 for boredom when doing homework) and 9 for enjoyment (4 for enjoyment in class, 2 for enjoyment with homework and 3 for enjoyment when taking tests). The model fit, following Lichtenfeld et al.’s [52] recommendation, was confirmed for each emotion. The model parameters in grade 4 were as follows: enjoyment (CFI = 0.998, RMSEA = 0.043, SRMR = 0.008), anxiety (CFI = 0.994, RMSEA = 0.049, SRMR = 0.018) and boredom (CFI = 0.994, RMSEA = 0.071, SRMR = 0.008). In grade 5, the following parameters were recorded: enjoyment (CFI = 0.996, RMSEA = 0.056, SRMR = 0.012), anxiety (CFI = 0.990, RMSEA = 0.059, SRMR = 0.023) and boredom (CFI = 0.998, RMSEA = 0.059, SRMR = 0.007). The reliability of each emotion subscale was adequate, with Cronbach’s alpha ranging from 0.75 for anxiety related to homework to 0.94 for boredom in class (

Table 2. Reliabilities for the AEQ measures.

	Class	Homework	Test-Taking
Anxiety	0.82	0.75	0.92
Boredom	0.94	0.91
Enjoyment	0.93	0.82	0.85

). Metric invariance information can be found in Appendix A.

2.2.2. The Expectancy–Value Scale (EVS)

The EVS [33] is a scale comprising 25 items distributed across five dimensions: perceived competence (5 items, e.g., ‘Math is easy for me’, Cronbach’s α = 0.85), intrinsic value (5 items, e.g., ‘I like doing math’, Cronbach’s α = 0.90), attainment value (5 items, e.g., ‘Being good in math is very important to me personally’, Cronbach’s α = 0.84), utility value (5 items, e.g., ‘What I learn in math, I can use in daily life’, Cronbach’s α = 0.85) and costs (5 items, e.g., ‘Learning math requires too much of my time’, Cronbach’s α = 0.75). The students answered on a 4-point Likert scale from ‘never’ to ‘a lot of times’. The model fit was confirmed for each grade—grade 4 (CFI = 0.957, RMSEA = 0.051, SRMR = 0.045) and grade 5 (CFI = 0.954, RMSEA = 0.051, SRMR = 0.043). Metric invariance information can be found in Appendix A.

2.2.3. Maths Achievement

Mathematics achievement was measured using 14 mathematics problems selected from the released items of the TIMSS 2011 grade 4 assessment (IEA Approval 22-022). There were two different versions of this test, one for fourth-grade students and one for fifth-grade students, covering topics such as numbers, geometry and data display, all of which were included in the curricula of each participating country. Educational experts and practitioners in each country served as external experts to ensure the appropriate choice of maths items. The chosen items were piloted before their use in the main study (i.e., the data used in this investigation). The test was timed, lasting 30 min, with each correct answer earning a point, leading to a maximum score of 14. The test scores for the students in both grades were estimated using the Rasch measurement model, incorporating all the items included in the tests (i.e., the grade 4 and grade 5 versions shared several items, serving as linking items and allowing the tests to function on the joint scale). The scores were anchored to a scale with a mean of 500 and a standard deviation of 100.

2.3. The Analytical Approach

The principal analyses relied on a series of LPAs in Mplus [54] conducted separately for the grade 4 and grade 5 data. LPA is a variant of the latent variable mixture modelling technique that tests the fit and significance of a set number of latent profiles among individuals within a dataset [9,10,55]. In determining whether there was a single pattern or a mixture of latent profiles, all three emotions were entered into the LPA, covering different aspects (i.e., attending maths classes, doing homework and taking maths tests). The process resulted in the following constructs to constitute the LPA analyses in both grades: boredom class (BORDCLS), boredom homework (BORDHW), anxiety class (ANXCLS), anxiety homework (ANXHW), anxiety test (ANXTEST), enjoyment class (ENJCLS), enjoyment homework (ENJHW) and enjoyment test (ENJTEST).

Models with two to nine latent classes (k = 2–9) were tested to reveal the number of profiles emerging from the data. All the models were initially estimated using 5000 random start value sets with 100 iterations, and the 200 best solutions were retained for the final optimisation stage. The number of start values and iterations increased with the complexity of the models tested. The cut-off for the entropy index [10,56] and a combination of the bootstrapped likelihood ratio test (BLRT), the Vuong–Lo–Mendell–Rubin likelihood ratio test (VL-LRT) and the Lo–Mendell–Rubin adjusted LRT test (LMR), as suggested by [57], were considered when choosing the final solution. The final model was again validated using Geiser’s [56] recommendations for using the best log likelihood value.

Upon establishing the primary latent profiles (RQ1) and observing the differences between grades (RQ2), the student distribution across countries was observed via the crosstabs option (RQ3). Differences between the examined profiles across task values and perceived competence (RQ4) and achievement (RQ5) were analysed using the BCH method for continuous correlates [58,59].

3. Results

The results are displayed in line with the research questions. First, we examine the distinguished profiles (RQ1) and observe possible differences between grades 4 and 5 (RQ2). Next, we examine cross-country differences (RQ3) and how each profile links task values to perceived competence (RQ4) and achievement (RQ5).

3.1. Students’ Emotional Profiles

Table 3. Overview of the evaluated models for grade 4.

#No.	Log Likelihood	#fp	AIC	BIC	SABIC	LMR	BLRT	VL-LRT	Entropy	SCF
2	−19,915.961	25	39,881.92	40,029.35	39,949.91	/	/	/	0.902	48.23%
3	17,625.216	34	35,318.43	35,518.93	35,410.9	0	0	0	0.92	20.66%
4	−16,525.71	43	33,137.42	33,390.99	33,254.36	0.005	0	0.0047	0.906	15.76%
5	−15,513.02	52	31,130.04	31,436.68	31,271.46	0.0025	0	0.0024	0.912	11.64%
6	−14,428.004	61	28,978.01	29,337.72	29,143.91	0	0	0	0.918	8.37%
7	−13,897.027	70	27,934.06	28,346.84	28,124.43	0.0336	0	0.031	0.909	7.67%
8	−13,302.804	79	26,763.61	27,229.47	26,978.46	0.3683	0	0.3633	0.917	5.27%
9	−12,845.91	88	25,867.82	26,386.75	26,107.15	0.1199	0	0.1178	0.915	4.31%

Note. #No = number of profiles; #fp = degrees of freedom; AIC = Akaike’s information criterion; BIC = Bayesian information criterion; SABIC = sample-size-adjusted BIC; LMR = Lo–Mendell–Rubin adjusted likelihood ratio test; BLRT = parametric bootstrapped likelihood ratio test; VL-LRT = Vuong–Lo–Mendell–Rubin likelihood ratio test; SCF = smallest class frequency.

and

Table 4. Overview of the evaluated models for grade 5.

#No.	Log Likelihood	#fp	AIC	BIC	SABIC	LMR	BLRT	VL-LRT	Entropy	SCF
2	−21,294.619	25	42,639.24	42,787.35	42,707.92	/	/	/	0.888	49.35%
3	−18,982.607	34	38,033.21	38,234.64	38,126.62	0	0	0	0.914	25.56%
4	−17,997.07	43	36,080.14	36,334.89	36,198.27	0.0165	0	0.0158	0.902	13.11%
5	−17,120.925	52	34,345.85	34,653.92	34,488.7	0.2672	0	0.2636	0.892	13.61%
6	−16,221.534	61	32,565.07	32,926.46	32,732.64	0.0472	0	0.0458	0.901	11.67%
7	−15,671.844	70	31,483.69	31,898.4	31,675.99	0.0002	0	0.0002	0.899	8.22%
8	−15,129.389	79	30,416.78	30,884.81	30,633.8	0.2719	0	0.2649	0.905	7.36%
9	−14,711.741	88	29,599.48	30,120.83	29,841.23	0.4511	0	0.4477	0.903	5.86%

Note. #No = number of profiles; #fp = degrees of freedom; AIC = Akaike’s information criterion; BIC = Bayesian information criterion; SABIC = sample-size-adjusted BIC; LMR = Lo–Mendell–Rubin adjusted likelihood ratio test; BLRT = parametric bootstrapped likelihood ratio test; VL-LRT = Vuong–Lo–Mendell–Rubin likelihood ratio test; SCF = smallest class frequency.

provide an overview of the models tested using the LPA [56] with the solutions ranging from two to nine groups (k = 2–9). To determine the best solution for the number of profiles, we considered not only the statistical parameters but also the interpretability of the profiles using CVT as the overall theoretical background.

As a result, we decided to retain a solution of five profiles for grade 4 and six profiles for grade 5. In grade 4 (Table 3), solutions in the range of three to seven profiles would be statistically acceptable. However, only a solution with five profiles provided qualitatively distinct student groups that were interpretable from the point of view of CVT and previous similar studies [36,42,47,49,51]. Conversely, solutions displaying three, four, six or seven profiles either offered indistinctive profiles, differing only from a quantitative point of view, or displayed two qualitatively equivalent profiles, differing only in the average factor scores for the examined dimensions.

A similar trend was observed for the grade 5 solutions (Table 4). Although several solutions were statistically acceptable (i.e., three-, four-, six- and seven-profile solutions), only the six-profile solution yielded solutions qualitatively different for the full range of observed profiles, which were also interpretive and relevant from the CVT viewpoint and that of prior research [36,42,47,49,51].

Further observation of the five-profile solution in the grade 4 data and the six-profile solution in the grade 5 data revealed that the profiles were the same: five of the extracted profiles in the grade 4 solution were the same as those in the grade 5 solution. The only different profile was the sixth profile that emerged in the dataset for grade 5. Thus, we describe the profiles for grades 4 and 5 together, while the novel profile emerging in grade 5 data will be described last. Each profile has a unique label for easier distinction when conversing with the profiles. Labels were chosen to depict the profiles’ most distinctive features (see Figure 2 and Figure 3).

The first student profile, labelled ‘Bored’, is distinctive because it has the highest scores on BORDCLS and BORDHW and extremely low scores for the variables from the enjoyment range (ENJCLS, ENJHW and ENJTEST).

The second profile includes students who scored high in the boredom range (BORDCLS, BORDHW) and those who scored high in the anxiety range (ANXCLS, ANXHW, ANXTEST). Thus, we labelled the profiles ‘Bored and Anxious’.

The third profile, labelled ‘Moderate’, indicates students who do not seem to have distinctively negative or positive emotions about maths. They score low on the anxiety spectrum (ANXCLS, ANXHW, ANXTEST) and around the mean for boredom (BORDCLS, BORDHW) and enjoyment (ENJCLS, ENJHW, ENJTEST).

The next profile, populated by students with high scores for enjoyment (ENJCLS, ENJHW and ENJTEST) and low scores for boredom (BORDCLS and BORDHW) and anxiety (ANXCLS, ANXHW and ANXTEST), is labelled the ‘Happy’ profile.

The fifth profile, labelled ‘Anxious’, includes students who scored the highest on the anxiety emotion range (ANXCLS, ANXHW, ANXTEST). It is worth noting that the perceived scores are not at their extremes. There are no distinctive patterns for the two other emotions, enjoyment and boredom, with the scores around the mean or slightly above/below the mean.

The final sixth profile could be captured only in grade 5 and is labelled ‘Apprehensive–Happy’. This group has the second highest score for enjoyment (ENJCLS, ENJHW and ENJTEST), and their anxiety levels (ANXCLS, ANXHW and ANXTEST) are slightly above average. In the next section, we provide information on the grade and gender differences between the profiles.

3.2. Profile Differences across Grades and Gender

The frequency of the profiles for each grade is displayed in

Table 5. Profile frequency across grades.

	Grade 4 (%)	Grade 5 (%)
Bored	13.79%	12.64%
Bored and Anxious	11.64%	11.67%
Moderate	19.63%	19.20%
Happy	23.89%	13.43%
Anxious	31.04%	25.69%
Apprehensive–Happy	/	17.36%

. Although the first three profiles—Bored, Bored and Anxious and Moderate—share similar frequencies between the grades, the Happy profile is less frequently present among students in grade 5. The Anxious profile shows a similar trend, which is present less often in the grade 5 sample.

The Apprehensive–Happy profile amounts to close to one-fifth of the sample and in absolute values corresponds to the difference in the number of decreased students in the Happy and Anxious profiles.

Observing the boy–girl prevalence across the profiles, we can see that in grade 4, differences can be observed (χ2 = 23.927, df = 4, p < 0.001), with girls being present statistically more often in the Bored and Anxious profile and less frequently in the Happy profile. For grade 5, again, we observe statistically significant differences (χ2 = 118.405, df = 6, p < 0.001). Girls are less frequently present in the Bored and Happy profiles. Conversely, girls are overrepresented in the Bored and Anxious, Anxious and Apprehensive–Happy groups (

Table 6. Gender and profile frequency.

	Grade 4 (% Girls, SR)	Grade 5 (% Girls, SR)
Bored	45.5% (−1.0)	31.9% (−4.5)
Bored and Anxious	57.6% (2.0)	57.4% (2.2)
Moderate	47.8% (−0.5)	40.4% (−2.8)
Happy	43.8% (−2.0)	39.5% (−2.6)
Anxious	53.1% (1.6)	57.7% (3.4)
Apprehensive–Happy	/	58.7% (3.1)

Note: Cells indicate within-profile frequencies. SR stands for standardised residual. An absolute value of the standardised residual above 1.96 is statistically significant.

).

3.3. Profile Differences across Countries

Analyses of the cross-country differences (χ2 = 295.130, df = 8, p < 0.001), here when observing within-profile membership, indicate grade 4 students in Norway are more present in the Bored and Moderate profiles and less visible in the Happy, Anxious and Bored-Anxious profiles (

Table 7. Countries and frequency of emotional profiles.

		Norway, % (SR)	Portugal, % (SR)	Serbia, % (SR)
Bored	Grade 4	56.50% (6.3)	10.00% (−6.7)	33.50% (−0.3)
		21.20%	4.75%	13.40%
	Grade 5	56.5% (5.7)	15.3% (−5.9)	28.1% (−0.2)
		19.0%	5.9%	12.4%
Bored and Anxious	Grade 4	26.50% (−2.9)	36.20% (2.4)	37.20% (0.8)
		8.30%	14.45%	12.40%
	Grade 5	27.9% (−2.9)	31.3% (−0.6)	40.8% (4.0)
		8.5%	10.8%	16.3%
Moderate	Grade 4	53.00% (6.2)	10.90% (−7.6)	36.10% (0.6)
		28.10%	7.35%	20.40%
	Grade 5	57.6% (7.4)	14.8% (−7.5)	27.7% (−0.5)
		29.5%	8.6%	18.6%
Happy	Grade 4	28.50% (−3.4)	32.60% (1.8)	38.90% (1.9)
		18.60%	27.00%	26.90%
	Grade 5	34.2% (−1.1)	43.1% (3.2)	22.6% (−2.2)
		12.2%	17.3%	10.6%
Anxious	Grade 4	27.80% (−4.3)	42.60% (7.5)	29.60% (−2.4)
		23.80%	46.45%	26.90%
	Grade 5	27.9% (−4.3)	40.2% (3.2)	31.8% (1.5)
		19.1%	31.2%	28.6%
Apprehensive–Happy	Grade 4	/	/	/
		/	/	/
	Grade 5	25.9% (−4.2)	51.4% (6.8)	22.7% (−2.5)
		11.7%	26.2%	13.4%

Note: White cells indicate within-profile frequencies, and shaded cells indicate within-country frequencies. SR represents the standardised residual and is a reference value for both within-country and within-cell frequency. For ease of reading, the SR value is kept in white cells. An absolute value of the standardised residual above 1.96 is statistically significant.

). The Anxious and Bored–Anxious profiles are more indicative of anxiety among Portuguese grade 4 students, while the Bored and Moderate profiles are underrepresented.

Among fourth graders in Serbia, only the Anxious profile is present at a lower rate than expected. For the grade 5 country differences (χ² = 319.433, df = 10, p < 0.001), again, when observing the within-profile membership, students in Norway are overrepresented in the Bored and Moderate profiles and appear less than expected in the Bored and Anxious, Anxious and Apprehensive–Happy profiles. Fifth graders in Portugal are less visible in the Bored and Moderate groups and are overrepresented in the Happy, Anxious and Apprehensive–Happy profiles. Serbian fifth graders are overly visible in the Bored and Anxious profile and less present in the Happy and Apprehensive–Happy groups.

The within-country patterns (Table 7, shaded cells) show different absolute values, but the overall patterns are the same. At the same time, even if the absolute values for the Bored and Anxious groups appear to be different in grade 4 in Norway, the standardised residual value still indicates a more frequent pattern than expected for the first group and a less frequent pattern than expected for the latter.

3.4. Student Emotional Profiles, Motivational Dimensions and Achievement

Across the profiles, the Happy profile consistently scores the highest on all task values, except for cost (

Table 8. Student profiles and motivational dimensions.

		Intrinsic Value M (SE)	Utility Value M (SE)	Attain. Value M (SE)	Cost M (SE)	Perceived Compet. M (SE)	Maths Test M (SE)
Bored	Grade 4	−0.938 (0.027)	−0.695 (0.035)	−0.715 (0.031)	0.543 (0.022)	−0.420 (0.03)	529.597 (7.312)
	Grade 5	−0.872 (0.029)	−0.685 (0.039)	−0.657 (0.033)	0.454 (0.021)	−0.306 (0.040)	594.418 (8.067)
Bored and Anxious	Grade 4	−0.96 (0.036)	−0.530 (0.045)	−0.504 (0.039)	0.753 (0.026)	−0.935 (0.034)	489.014 (6.971)
	Grade 5	−1.016 (0.034)	−0.588 (0.045)	−0.521 0.038	0.721 (0.024)	−1.007 (0.035)	570.228 (7.173)
Moderate	Grade 4	−0.003 (0.024)	−0.187 (0.029)	−0.189 (0.026)	−0.106 (0.018)	0.242 (0.025)	586.025 (6.5013)
	Grade 5	0.087 (0.024)	−0.109 (0.028)	−0.149 (0.025)	−0.170 (0.017)	0.353 (0.029)	646.925 (6.713)
Happy	Grade 4	0.918 (0.021)	0.599 (0.023)	0.598 (0.021)	−0.607 (0.018)	0.703 (0.023)	585.590 (6.009)
	Grade 5	1.114 (0.027)	0.677 (0.030)	0.638 (0.027)	−0.658 0.021	0.955 (0.030)	649.370 (7.661)
Anxious	Grade 4	0.047 (0.018)	0.078 (0.021)	0.110 (0.019)	0.014 (0.014)	−0.167 (0.018)	513.257 (4.875)
	Grade 5	−0.179 (0.020)	−0.097 (0.025)	−0.037 (0.020)	0.151 (0.014)	−0.333 (0.022)	576.722 (5.468)
Apprehensive–Happy	Grade 4	/	/	/	/	/	/
	Grade 5	0.590 (0.024)	0.452 (0.027)	0.451 (0.024)	−0.339 (0.018)	0.237 (0.028)	587.202 (7.132)

Note: Each cell depicts an average factor score for the observed dimension (e.g., task value). See Appendix B for a complete overview of the differences across the profiles.

). Conversely, the highest values for cost are reported for students within the Bored and Anxious group, followed by those in the Bored profile. This pattern is consistent across grades. For perceived competence, again, the highest scores are noted in the Happy profile, with the opposite trend for the Bored and Anxious group and the Bored profile. The Moderate and Apprehensive–Happy profiles fall within the mid-range. Nevertheless, their orientation towards the task values differ, with the Apprehensive–Happy profile taking a more strongly positive stance than the Moderate group, reporting them towards the negative pole.

Concerning achievement, the Happy and Moderate profiles score the highest on maths tests in both grades. This was somewhat unexpected considering that the Moderate group show lower perceived competence values. Consistently, the students in the Anxious and Bored profiles score the lowest on the maths test in both grades, followed by those in the Anxious group.

4. Discussion

Relying on the vast amount of literature on the importance of emotional experiences to learning, motivation and academic achievement [11,15,19,20], we have focused on these experiences in a sample of primary school students (i.e., grades 4 and 5) across three countries (i.e., Portugal, Serbia and Norway). Heavily relying on the person-centred approach allowed us to simultaneously observe the students’ differences across anxiety, boredom and enjoyment, which is often not possible within variable-centred research because of the high correlations between these emotions. However, they are known to co-occur; hence, there is a need for synchronised investigations.

We postulated the existence of profiles with a prevalence of enjoyment and those where negative emotions would reign, coupled with so-called mixed profiles. All of these assumptions were confirmed. Although other studies may use different constellations of achievement emotions, we found a profile similar to that identified in earlier studies [37,49,51]—the Happy profile. In a similar vein to Karamarkovich and Rutherford [37], we also captured negative profiles (Bored, Anxious and Bored and Anxious profiles), as well as mixed profiles (the Apprehensive–Happy profile). A Moderate profile was also distinguishable, corresponding to the prior results of Earl et al. [42] and Ganotice et al. [36]. These results support the idea that students form emotional responses early on and that recognising these can aid in helping them learn, strive and succeed academically.

Our grade 4 and grade 5 samples largely share the same type of emotional response profiles. However, when observing the profiles from the perspective of their occurrence, none of the profiles in the two adjacent age groups can be observed as being truly dominant. In fact, in grade four, we observed that the Bored and Anxious profiles account for just over 10% of the students, representing the minimum percentage of students per profile. On the other hand, we observed the greatest prevalence in the Anxious profile for grade 4, being slightly less than a third of all the fourth graders (31%). It is worth remembering that grade 5 reveals a sixth profile, meaning that it is rather natural that the prevalence of profiles is lower in this grade. Moreover, across both samples, only one clearly favourable profile could be distinguished—Happy. In addition, this profile is less frequent in the grade 5 sample than in the grade 4 sample. At the same time, we clearly identify several negative profiles in both age groups—Bored, Anxious and Bored and Anxious profiles—that jointly create a decisive majority of children with an unfavourable set of emotional responses to maths as early as grade 4. Hence, we can conclude that as early as primary school, children already have a set of negative emotions associated with learning maths, and this is observed within a large portion of the student community. This finding supports the idea that negative emotional profiles do not result only from changes occurring from primary to middle and/or secondary school (e.g., transition to subject teaching) and that the research should invest in a better understanding the antecedents of such profiles to find adequate procedures and strategies to prevent them from occurring in primary school.

Finally, we observed two adjacent age groups, each captured at one point in time. Thus, we are cautious when stating that there are fewer students in the Happy group in grade 5 than in grade 4. However, the existence of a novel profile in grade 5—the Apprehensive–Happy profile—triggers our assumption that students may transition to other profiles. Similar findings have been reported by Mata et al. [24], indicating that profile membership is moderately stable across all time points. Our assumption is coupled with the additional challenges that the students in Serbia and Portugal go through (i.e., transition from class to subject teaching): students in Portugal are faced with the additional task of adjusting to a new school environment, which can significantly trigger a new constellation of emotional responses. As noted earlier, similar occurrences are visible when observing motivation [53]. Additionally, of the three countries, Portugal has the highest student frequency in the Apprehensive–Happy profile. Hence, given the obtained results, as well as our knowledge of the different school systems of each participating country, we advance the hypothesis that both a change in the school setting (as is the case for Portugal, when students change schools in the transition from grade 4 to grade 5) and changes from class to subject teaching may lead to some students fluctuating from Happy to an Apprehensive–Happy profile. It is worth noting that if such a hypothesis was to be supported by adequate evidence, students would maintain their enjoyment. However, they start to feel anxiety which they did not feel in primary school. Therefore, strategies to avoid such levels of anxiety should be employed in school systems where significant changes are made at this stage from primary to middle school.

When observing country differences, boredom alone is more prevalent among Norwegian students, coupled with a flatter emotional response, which is pertinent to the Moderate profile. The Anxious profile is more prominent in Portugal, along with the Anxiety–Enjoyment constellation, which is typical of the Apprehensive–Happy profile. In Serbia, boredom and anxiety are more visible across grade five when students transition to subject teaching. These findings highlight the importance of cultural context and educational specificities in shaping how children feel about learning. The varying levels of boredom and anxiety across the studied countries emphasise the need to study each context individually and conduct intercontextual comparisons.

Based on studies observing the relationship between task values and perceived competence and emotions [19], we postulated that better emotional profiles would be linked positively to perceived competence and all task values except cost. This assumption was confirmed, coupled with a reverse association (i.e., positively associated with cost and negatively associated with perceived competence and other task values), which is often expected for less optimal emotional student profiles [49,50]. Interestingly, mixed profiles such as Apprehensive–Happy are oriented positively towards all task values except cost, whereas orientation towards perceived competence is positive but in a lower range. The orientation of the Moderate profile leans towards the negative across the task values, which may be linked to a ‘flatter’ emotional demeanour concerning mathematics as a subject. Thus, neither intrinsic, utility nor attainment values are positively viewed when observing the average student scores within this profile.

Finally, we observed how students’ emotional profiles related to their achievement. Among them, the Happy profile scored the highest on the maths test in both grades, followed by the Moderate profile. Although situated within the variable-centred paradigm, prior research has shown that positive emotions, such as enjoyment, are positively related to academic achievement [11,13,17,20] Similarly, negative emotions, that is, anxiety and boredom, are negatively related to achievement [11,13,14,17,19,20]. The results also align with those of Lv et al. [50], who report on high achievers with a positive emotion profile, and Hanin and Van Nieuwenhoven [49], who examine a positive profile showing the highest levels of maths performance. Consistently, students in the Anxious and Bored profile scored lowest on the maths test in both grades, followed by those in either the Anxious or Bored group.

Although the results provide new insights for the research, especially at the level of differences in countries’ educational systems, the current study has several limitations that should be taken into account. First, the emotional and motivational measures were self-reported, even though achievement was measured using a test, which strengthened the reliability of the results. A second limitation was the cross-sectional nature of the study. Future investigations should benefit from longitudinal designs to study the transitions between profiles (e.g., using latent transition analysis). For example, the new cluster appearing in grade 5 (Apprehensive–Happy) seems to be formed from individuals coming from the Anxious and Happy groups, but this is a hypothesis that latent transition analysis could clarify, similar to the approach of Mata et al. [24] but taking into account a cross-country perspective and all the fine-grained changes when transitioning from grade 4 to grade 5 within different education systems.

Despite these limitations, the current research has demonstrated the potential of a person-centred approach to studying emotions, enabling the emergence of differentiated profiles that would be obscured in the classic variable-centred approach. Nevertheless, profiles such as Apprehensive–Happy or Bored and Anxious should be confirmed in future research given the distinctive differences between these two and possibly very diverse approaches to supporting students within such profiles as they grapple with mathematics. From the CVT perspective [14], the latter Bored and Anxious group may be particularly vulnerable because their emotional response combines activity and the outcome of negative emotions. At the same time, the former, the Apprehensive–Happy group, holds some personal strength because grappling with maths may still be depicted as enjoyable despite the fear of adverse outcomes. Finally, the present study contributes to the body of research highlighting the importance of emotional experiences for academic achievement and the inextricable interplay between emotions and motivation. It shows that experiencing positive emotions is related to positive expectancies of success and positive values, whereas experiencing negative emotions is detrimental to both expectancies and values (Bored and Anxious and Anxious profiles). At the same time, mixed emotional responses, such as the Apprehensive–Happy profile, show that some spark of enjoyment still contributes to fewer adverse outcomes and the perception that things may end in success. In contrast, anxiety alone seems to be more detrimental to students reaching negative outcomes and perceiving a negative success expectancy.