Changes in affect: patterns in Grade 4 and Grade 8 students’ expressed emotional directions

Abstract

This paper targets patterns of expressed emotional directions towards mathematics. By using TIMSS data and recoding two of the instruments, we compared responses from the same student cohort in Grade 4 (11 years old) and Grade 8 (15 years old) in Sweden. Two hypotheses were tested: negative emotions including negative motivations increase with age, and there will be gender differences. By using statistical analyses, including Cramer’s V, the two hypotheses were confirmed. The results also illuminated patterns within the responses, such that boys and girls in Grade 4 differ in expressed intrinsic motivation but not extrinsic motivation. There are also indications that girls might be more likely to form negative emotional directions between grades 4 and 8 than boys, and some implications of this is discussed.

KEYWORDS:

• Affect
• emotions
• gender
• mathematics
• motivation

MSC:

• 97 mathematics education

1. Introduction

A body of research has over decades emphasized the importance of various affective constructs in mathematics education, including studies looking at the role of motivation (e.g. Dogan, 2012; Gerholm, 2016; Nyman, 2020; Nyman & Sumpter, 2019; Schukajlow et al., 2017), emotions (e.g. Hannula, 2006; Koskinen et al., 2023; Radford, 2018; Ryan & Deci, 2000; Schukajlow et al., 2017), beliefs (Jäder et al., 2017; Sumpter, 2013), and attitudes (Skouras, 2014). For a long time, research on cognition has been central, for instance, as an important tool for reflection on mistakes (e.g. Epstude & Roese, 2008), or as part of meta-cognition (Flavell, 1979; Garofalo & Lester, 1985; Schneider & Artelt, 2010; Schoenfeld, 1987). However, during the last two decades, there has been an increased focus on emotion, given its pivotal role in coping with failure, mistakes, and achievement (e.g. Blair, 2002; Fredrickson & Joiner, 2002; 2018; Raver, 2002). And recent research signals that emotions play a bigger role in learning than previously thought, both on a general level and in specific situations, such as during problem solving (e.g. Lake, 2017; Lewis, 2013; Nelson et al., 2018; Radford, 2018; Valiente et al., 2012; Young, 2020).

The differences in expressed emotions can be significant: taking Sweden and the results from TIMSS 2019 as an example, the difference in achievement between those who express they are very confident in Grade 4 compared to those who say they are not so confident is 72 points, and in Grade 8 the difference is as significant as 118 points (Mullis et al., 2020). As a comparison, several east-Asian countries, such as Japan, have a lower level of students replying that they are very confident, but the differences in achievement between the most and least confident students are still measurable (Grade 4: 54 points; Grade 8: 89 points). There are a few exceptions: a recent secondary analysis of TIMSS data looks at Korea as a cohort, where students show a strong relationship between emotional disposition and mathematics achievement (Hwang & Choi, 2020). This indicates that although affective constructs can be seen as dependent on the culture (e.g. Arievitch, 2017; Nyman, 2020), their impact within a context appears to be distinct. Hence, to understand progression or changes, we need to understand patterns within a specific context (Wiberg, 2019).

One of the patterns identified in previous research is that students’ interest in, motivation for, and engagement with mathematics is inversely proportional to years of schooling (e.g. Blomqvist et al., 2012; Hannula, 2006). However, these studies are often qualitative, with few respondents, and the larger studies on affective factors like emotion primarily cover teenagers or adults (Dowker et al., 2019) without explaining whether and how these phenomena develop over time (Batchelor et al., 2019). Another issue is that most studies tend to focus on anxiety (e.g. Batchelor et al., 2019; Lewis, 2013; Valiente et al., 2012), meaning little is known about other emotions and their nuances (Nyman, 2020). There are also indications that gender plays a part (Nagy et al., 2010; Sumpter et al., 2022). This study will address emotions and gender, and before presenting the aim and hypotheses, will situate the study within a theoretical and empirical frame.

2. Background

The background section is divided into three sections: emotions, emotions and motivation, and emotions and gender. For each section, there is an overview of relevant research, including the theoretical underpinnings of the study.

2.1. Emotions

Emotions have been an object of research for a long time (Hannula, 2019), and has been described to ‘simultaneously emerge from, and shape experience’ (Liljedahl, 2014, p. 27), and Damasio (1994), arguing that we are not thinking machines that feel, but instead feeling machines that think, concluded that, ‘what comes first constitutes a frame of reference for what comes after, feelings have a say on how the rest of brain and cognition go about their business. Their influence is immense’ (Damasio, 1994, p. 160). The quotes illustrate not just the connection between cognition and affect, but also the centrality of emotions in all human activity. In general emotion research, one speaks about two concepts, feelings and emotions (Goldie, 2002; Prinz, 2005; Whiting, 2011). This division can be traced back to James’s (1884) assumption that emotions are an awareness of patterned changes in the body, a division that allows a separation between different bodily reactions (a feeling) and how an individual reports their experiences of such reactions. Emotions, as a theoretical concept, are defined as self-reported conscious experience (Prinz, 2005). The epistemological premise is that an emotion is associated with a cause or situation (here, mathematics) and the association is made in such a way that it motivates present or future behaviour towards this particular or similar cause/situation (Damasio, 1994). This is where emotional directions differ, for instance, from emotional dispositions (e.g. Hwang & Choi, 2020) which place less weight on future behaviour. Emotions can be reduced to three general emotional directions: positive, negative, and neutral (Prinz, 2005), and as a theoretical concept, are part of many other affective constructs, such as self-evaluation and motivation (Sumpter, 2020).

Previous studies on students’ emotional directions towards mathematics and mathematics education show the complexity of different emotions and other affective constructs. For instance, Nyman’s (2020) results show that boredom can disguise other negative emotions, including intra-relationships within the set of emotions. Several, mainly small-scale studies, show that younger students are more positive about mathematics than older students (e.g. Blomqvist et al., 2012; Hannula, 2006; Nyman, 2020), but large-scale assessments such as TIMSS also demonstrate such patterns: fourth-grade students, in general, were positive about learning mathematics, where 45% on average answered they liked it ‘very much’, whereas by Grade 8, this number had dropped to 20% (Mullis et al., 2020). However, these are only general results. At the same time, a recent study by Koskinen and colleagues (2023) using a new research design, in which children playing a mathematical learning game where they got emotional scaffolding, showed no significant results with respect to learning outcome. Instead, the emotional scaffolding was correlated with an increase in their expressed motivation and situational self-efficacy. Results like these call for more research of this kind since they add to the complex picture of different affective constructs and achievement.

Mullis and colleagues’ (2020) findings are nonetheless of interest since it seems that positive affect not only prevents negative affect, but also has an impact over time, thereby functioning as a tool for mediating negative affect (Moneta et al., 2012), including motivation (Damasio, 1994). It is therefore relevant to analyse beyond ‘positive’ and ‘negative’, the main emotional directions.

2.2. Emotions and motivation

Studies have shown that emotions are intertwined with other affective constructs (e.g. Hannula, 2006; Nyman & Sumpter, 2019; Sumpter, 2013). Here, we follow Damasio (1994) and motivation as a secondary construct. The two constructs combined are strongly connected to students’ achievement (Valiente et al., 2012): for instance, emotions derived from a failure can stall motivation (Bandura, 1994). The study by Koskinen and colleagues (2023) is an interesting contribution, since they conclude that, despite the limitations of the study, emotional design can improve motivation, thereby highlighting emotions, not motivation.

Motivation is defined in many ways, but common to many definitions is the relation to some type of goal (Nyman & Sumpter, 2019). Here, we see it as ‘the process whereby goal-directed activity is instigated and sustained’ (Schunk et al., 2010, p. 4). According to Damasio (1994), goals are derived from emotions, both from a state and trait perspective. Motivation is often divided into extrinsic and intrinsic motivation (Ryan & Deci, 2000), but several subscales have been identified as well. When talking about extrinsic motivation, one can separate between outward and compensation (Amabile et al., 1994). Outward covers social gains while compensation describes motives that encompass personal gains. The subscales related to intrinsic motivation are cognitive and emotional (Nyman & Sumpter, 2019; Sumpter, 2013). In this way, motivation as a theoretical construct is intertwined with emotions such that each of the first three categories can be connected to an emotion, and the fourth category – the goal – is an emotion in itself (e.g. I am doing this because it is fun or I am doing this because it makes me happy).

Previous studies have reported that positive emotional directions are more likely to enhance academic behaviour and thereby interests (e.g. Fredrickson & Joiner, 2002; 2018; Nelson et al., 2018). However, some studies highlight that one can obtain different results depending on when students are asked – students’ expressed motivation and emotions towards mathematics differ depending on whether they are asked in general or before a lesson or while doing mathematics (Nyman, 2020; Takeuchi et al., 2016). The most common reply is that mathematics is considered something important for the future. However, in a state perspective, expressed motivation could be negative. Motivation also differs in character over the years, where younger students express positive intrinsic motivation and older students tend to more often stress different types of extrinsic motivation and negative intrinsic motivation (e.g. Blomqvist et al., 2012; Hannula, 2006; Nyman, 2020). The result could point to serious consequences, since when students think mathematics is hard, boring, and useless, they tend to not continue with the subject as soon they have a chance to opt out (Brown et al., 2008).

2.3. Emotions and gender

In this study, gender is treated as a social construct rather than biological sex (Connell, 2006). Gender is regarded as a system of relationships, with the constructs ‘man’ and ‘woman’ constantly negotiated and one way of understanding it is to divide it into four distinct aspects (Bjerrum Nielsen, 2003). We follow this distinction, where gender is seen as structural, symbolic, personal, and interactional. Structural gender refers to social structures such as ethnicity and social class structures. Here we find studies that model the ratio of men and women doing a PhD in mathematics compared to other subjects (Sumpter & Sumpter, 2021). Sweden is an interesting context since the ratio boy/girl is within the target of a balanced group (between 40% and 60%) for two of the three most popular upper secondary school programmes that prepare students for university; one (the most mathematically intense) being the Natural Science programme (Skolverket, 2020). The conclusion is that an equal number of boys and girls are studying the most advanced mathematics courses at upper secondary school level, meaning this is not the stage where girls opt out (e.g. Brown et al., 2008).

Symbolic gender focuses on symbols in discourses and conceptions that are attributed to gender (Bjerrum Nielsen, 2003). This attribution is bi-directional – either an object or abstract entity is considered to be male/female/neutral, or it could be how men and women are perceived in a certain context. One example of the first is the idea of mathematics as a male domain (e.g. Brandell & Staberg, 2008), and examples of the second, attributing success to ‘the hard-working woman’ or ‘the male genius’ (Leslie et al., 2015). The third aspect, and the context of this study, personal gender, speaks to how individuals experience the structure with its symbols (Bjerrum Nielsen, 2003). It includes aspects such as self-evaluations and patterns like the idea of ‘gender gap’, where girls report lower self-evaluations than boys despite having higher or similar grades (Sumpter, 2012; Sumpter et al., 2022; Zander et al., 2020; Brandell & Staberg, 2008). The last is interactional gender, which focuses on the interactions of individuals within a context comprised of the structure and its symbols. Previous studies looking at how children create gender indicate that it does not take long to establish what is considered male and female (Odenbring, 2010). These could be seen as norms which then create trajectories where acting and thinking are directed by what is considered ‘male’ and ‘female’. Gender then plays a role in the constitution of mathematical self-understanding. In one study, preschool teachers attributed different things to mathematical success depending on whether they were talking about a girl or a boy (Klein et al., 2010). Studies like these stress that gender is produced (e.g. Bjerrum Nielsen, 2003; Connell, 2006) and reinforced by schooling (e.g. Brandell & Staberg, 2008), including the relationship between gender and affect (Nyman, 2020).

Previous studies looking at gender differences show that male students in mathematics express higher and more positive self-concept, intrinsic motivation, self-enhancing ego-orientation, and higher performance expectations compared to women (Skaalvik & Skaalvik, 2004). However, when the focus was on language, women expressed higher (and more positive) intrinsic motivation. Similar results have been found with Swedish upper secondary school students (Sumpter et al., 2022). Sweden has been identified as having a problematic link between participation, motivation, and mathematics known as the ‘educational-gender-equality paradox’ (Stoet & Geary, 2018). The concept was coined to describe a paradox in a set of the most gender-equal countries within the OECD community, which also had the largest gender gaps in higher education in STEM fields. The leaders in this group are, besides Sweden, Finland and Norway. These can be compared to countries like Turkey, where gender is a neutral factor, at least in TIMSS Grade 8 (Kaleli-Yılmaz & Hanci, 2016).

Other gender differences can be found in expressed attitudes and self-beliefs in relation to mathematics (and science) which increase with age (McGeown & Warhurst, 2020), including a gender confidence gap (Zander et al., 2020). This is particularly interesting since studies show that boys/men tend to overestimate their ability in relation to their grades and achievements (e.g. Sumpter, 2012; Sumpter et al., 2022). There are also gender differences in the connection between grades and career choices (e.g. Dekhtyar et al., 2018). Such results could be part of an explanation for gender segregation, for instance, in postgraduate education (Sumpter & Sumpter, 2021). These studies have in common that they focus mainly on older students or adults, while studies looking at younger children are few and use qualitative methods.

3. Aim and hypotheses

Given this background, the aim is to study Grade 4 and Grade 8 students’ expressed emotions about mathematics, including motivational aspects with respect to age/grade and gender. Two hypotheses are tested: (1) Grade 8 students express more negative emotions, including negative motivation towards mathematics compared to Grade 4 students; and (2) there are gender differences.

4. Methods

The methods section is divided into data collection, including how instrument items were selected and coded, and methods of analysis.

4.1. Data collection

The data came from TIMSS 2015 and TIMSS 2019 with Sweden as a cohort. By using representative samples from the year 4 cohort from TIMSS 2015 and the year 8 cohort from TIMSS 2019, allows us to make comparisons. TIMSS is the only large-scale international assessment where the same survey data are used for two different grades, allowing studies over time. Sweden is, besides being in the group of ‘educational-gender-equality paradox’ countries (Stoet & Geary, 2018), a country with a strong link between TIMSS results and grades, both for year 6 and year 9, meaning that the achievement results are representative for the nation (Wiberg, 2019). Also, like Korea (Hwang & Choi, 2020), this is a country with a strong relationship between emotional disposition and mathematics achievement. Instead of looking at the pre-set indices, a qualitative analysis was made of the different instruments where each item was compared to a selected definition of emotion (e.g. Prinz, 2005; Sumpter, 2020) and motivation (e.g. Schunk et al., 2010) including the different subscales (e.g. Amabile et al., 1994; Nyman & Sumpter, 2019; Sumpter, 2013). Such recoding allows us to look at nuances within emotional directions (positive/neutral/negative), here described as motivation and will allow us to see if girls and boys differ in all different types of motivation.

To compare replies from Grade 4 (11 years old) and Grade 8 (15 years old), we used only items that were posed to both age groups, which resulted in two instruments: (1) ‘Students Like Learning Mathematics’ (nine items), a scale with a strong relationship to achievement in mathematics on a general level (Mullis et al., 2020); and (2) ‘Students Confident in Mathematics’ (nine items). An example of how ‘Students Like Learning Mathematics’ items were recoded is the first, ‘I enjoy learning mathematics’, which is coded both as an emotional direction, positive (e.g. Sumpter, 2020), and a positive intrinsic motivation as a subcategory emotion (e.g. Nyman & Sumpter, 2019; Sumpter, 2013). This could be compared to the third item, ‘Mathematics is boring’, which has the same subscale but different emotional direction, negative. An overview of the first nine items and how they were coded is presented in Table 1.

Table 1. Students like learning mathematics.

Item	Emotional direction	Motivation	Motivation subscale
I enjoy learning mathematics	Positive	Intrinsic	Cognitive Emotional
I wish I did not have to study mathematics^R	Negative	Extrinsic	Outward
Mathematics is boring^R	Negative	Intrinsic	Emotional
I learn many interesting things in mathematics	Positive	Intrinsic	Cognitive
I like mathematics	Positive	Intrinsic	Emotional
I like any schoolwork that involves numbers	Positive	Intrinsic	Cognitive
I like to solve mathematics problems	Positive	Intrinsic	Cognitive Emotional
I look forward to mathematics lessons	Positive	Intrinsic	Emotional
Mathematics is one of my favourite subjects	Positive	Intrinsic	Emotional

Note: R stands for reverse coding.

As we can see in Table 1, most items would fall into intrinsic motivation as defined by Ryan and Deci (2000), and only one item is coded to cover mainly extrinsic factors. Several items are within the subscale Emotional (e.g. Nyman & Sumpter, 2019) since the focus on emotions as a goal (‘Mathematics is boring’) or connected to a goal (‘I look forward to mathematics lessons’). Two items are coded to span both Cognitive and Emotional aspects – the first since it has both enjoyment (an emotion) and learning (a cognitive goal) as two factors in the statement, and the second talks about liking problem solving, which is different from solving routine tasks and applying procedures, and is therefore expected to require some cognitive challenge (e.g. Jäder et al., 2017).

The scale Students Confident in Mathematics was coded in a similar manner (Table 2).

Table 2. Students confident in mathematics.

Item	Emotional direction	Motivation	Motivation subscale
I usually do well in mathematics	Positive	Intrinsic Extrinsic	Cognitive Compensation
Mathematics is more difficult for me than for many of my classmates^R	Negative	Extrinsic	Outward
Mathematics is not one of my strengths^R	Negative	Intrinsic	Emotional
I learn things quickly in mathematics	Positive	Intrinsic	Cognitive
Mathematics makes me nervous^R	Negative	Intrinsic	Emotional
I am good at working out difficult mathematics problems	Positive	Intrinsic	Cognitive
My teacher tells me I am good at mathematics	Positive	Extrinsic	Outward
Mathematics is harder for me than any other subject^R	Negative	Intrinsic	Cognitive
Mathematics makes me confused^R	Negative	Intrinsic	Emotional

Note: R stands for reverse coding.

Table 2 shows how one statement is interpreted to cover both intrinsic and extrinsic motivation since it is not clear what the phrase ‘do well’ is referring to – if it is a personal reflection on problem-solving skills, it can be cognitive intrinsic motivation with a positive emotional direction, whereas if it is referring to achievements such as passing a test or grades given by a teacher, it can be extrinsic motivation (i.e. some sort of compensation). This instrument also has emotions and cognition as different goals, such as ‘I learn things quickly in mathematics’ and ‘Mathematics makes me confused’. Two items are also coded as motivation as an outward goal since the items relate to the surrounding environment, the teacher, and the classmates (e.g. Amabile et al., 1994). This means the number of items in each category is: Intrinsic total (n = 15) which comprises Cognitive (n = 8) and Emotional (n = 9); and Extrinsic total (n = 4) which comprises Outward (n = 3) and Compensation (n = 1).

The instruments were completed by 4132 students in Grade 4 (boys: n = 2054; girls n = 2078) from the cohort of TIMSS 2015; and 4090 students in Grade 4 and 3922 students in Grade 8 (boys: n = 2003; girls n = 1919) from the cohort of TIMSS 2019. A sampling method was used to achieve a nationally representative sample of schools and students, allowing us to compare results over time. In Sweden, the strata for drawing a national sample of schools are: accountable authority (public/independent), the school’s average merit rating, and the measure of size. In total, 144 schools participated in TIMSS 2019 Grade 4 and 159 schools in TIMSS 2019 Grade 8.

4.2. Methods of analysis

Given the theoretical underpinning and the aim to study emotional direction (e.g. Prinz, 2005; Sumpter, 2020), the choice here was to interpret the two response categories ‘Agree a lot’ and ‘Agree a little’ as positive emotional direction, and ‘Disagree a little’ and ‘Disagree a lot’ as negative emotional direction. As presented earlier, two hypotheses were tested: (1) Grade 8 students express more negative emotions, including negative motivation and confidence towards mathematics compared to Grade 4 students; and (2) there are gender differences. Indices were created on the construct level for categorical variables (extrinsic and intrinsic) and sub-categorical variables (cognitive, emotional, outward, and compensation). We calculated the strength of association between different groups of students (grade, gender, and grade/gender) based on the categorical and sub-categorical variables by using a modified chi-square test with Cramer’s V. Cramér’s V is an effect-size measurement for the chi-square test of independence, and it measures how strongly two categorical fields are associated. When applying Cramer’s V, the following interpretation was made (Akoglu, 2018): > 0 No or very weak; > 0.05 Weak; > 0.10 Moderate; > 0.15 Strong; > 0.25 Very strong. Given that TIMSS is a large-scale assessment incorporating 62 countries (Mullis et al., 2020), it is presented without explicit theoretical underpinnings, which means that if researchers want to understand the results, a theoretical framing needs to be added. One example of a recent study is Yıldırım (2022) who uses a sociocognitive perspective to understand the results in algebra. The results are here interpreted using Bjerrum Nielsen’s (2003) theoretical framework for gender and Damasio (1994) and Prinz’s (2005) theoretical framing for emotional direction and motivation.

5. Results

The results are divided into two sections. First, we present the results from the comparisons between Grade 4 and Grade 8, and then the gender differences. An overview of the responses with respect to the positive provides an introduction to the results (see Tables 3 and 4).

Table 3. Students like learning mathematics: Grade 4 (n = 4090) and Grade 8 (n = 3922).

	Positive Grade 4 TIMSS 2015	Positive Grade 8 TIMSS 2019
I enjoy learning mathematics	All: 3486 (85.6%) Boys: 1730 (85.0%) Girls: 1756 (86.2%)	All: 2411 (62.3%) Boys: 1294 (65.3%) Girls: 1117 (58.7%)
I wish I did not have to study mathematics^R	All: 3221 (79.8%) Boys: 1568 (77.7%) Girls: 1653 (82.0%)	All: 2190 (56.6%) Boys: 1130 (57.3%) Girls: 1060 (55.8%)
Mathematics is boring^R	All: 2826 (70.8%) Boys: 1392 (69.6%) Girls: 1432 (72.0%)	All: 1768 (46.5%) Boys: 925 (47.9%) Girls: 843 (45.1%)
I learn many interesting things in mathematics	All: 3396 (83.7%) Boys: 1699 (83.6%) Girls: 1697 (83.8%)	All: 2101 (54.8%) Boys: 1151 (58.5%) Girls: 950 (50.3%)
I like mathematics	All: 3081 (76.4%) Boys: 1527 (75.7%) Girls: 1554 (77.1%)	All: 1968 (51.7%) Boys: 1083 (55.3%) Girls: 885 (47.2%)
I like any schoolwork that involves numbers	All: 3025 (74.4%) Boys: 1548 (76.0%) Girls: 1477 (72.8%)	All: 1687 (44.4%) Boys: 974 (49.4%) Girls: 713 (37.6%)
I like to solve mathematics problems	All: 2789 (68.5%) Boys: 1447 (71.0%) Girls: 1342 (66.0%)	All: 1799 (46.9%) Boys: 1003 (50.7%) Girls: 796 (42.0%)
I look forward to mathematics lessons	All: 2568 (63.2%) Boys: 1293 (63.5%) Girls: 1275 (62.8%)	All: 1303 (34.0%) Boys: 727 (36.9%) Girls: 576 (30.4%)
Mathematics is one of my favourite subjects	All: 2233 (54.8%) Boys: 1157 (56.7%) Girls: 1076 (52.9%)	All: 1245 (32.6%) Boys: 711 (36.0%) Girls: 534 (28.0%)

Note: R stands for reverse coding.

Table 4. Students Confident in Mathematics: Grade 4 (n = 4090) and Grade 8 (n = 3922).

	Positive Grade 4 TIMSS 2015	Positive Grade 8 TIMSS 2019
I usually do well in mathematics	All: 3778 (92.8%) Boys: 1898 (93.1%) Girls: 1880 (92.5%)	All: 2689 (70.0%) Boys: 1460 (74.4%) Girls: 1229 (64.8%)
Mathematics is more difficult for me than for many of my classmates^R	All: 2991 (74.0%) Boys: 1496 (74.1%) Girls: 1495 (73.9%)	All: 2393 (62.4%) Boys: 1268 (64.9%) Girls: 1125 (59.6%)
Mathematics is not one of my strengths^R	All: 3250 (80.9%) Boys: 1628 (80.9%) Girls: 1622 (81.0%)	All: 1824 (47.9%) Boys: 1001 (51.5%) Girls: 823 (43.5%)
I learn things quickly in mathematics	All: 3310 (81.7%) Boys: 1695 (83.6%) Girls: 1615 (79.9%)	All: 2270 (60.0%) Boys: 1273 (65.6%) Girls: 997 (52.8%)
Mathematics makes me nervous^R	All: 3074 (76.3%) Boys: 1567 (77.7%) Girls: 1507 (74.9%)	All: 2649 (69.8%) Boys: 1451 (74.9%) Girls: 1198 (63.6%)
I am good at working out difficult mathematics problems	All: 2751 (68.0%) Boys: 1493 (73.6%) Girls: 1258 (62.3%)	All: 1763 (47.2%) Boys: 1046 (53.6%) Girls: 717 (37.8%)
My teacher tells me I am good at mathematics	All: 3477 (86.5%) Boys: 1762 (87.6%) Girls: 1715 (85.4%)	All: 2232 (59.7%) Boys: 1229 (64.4%) Girls: 1003 (53.9%)
Mathematics is harder for me than any other subject^R	All: 3266 (80.8%) Boys: 1647 (81.5%) Girls: 1619 (80.2%)	All: 2581 (67.8%) Boys: 1407 (72.7%) Girls: 1174 (61.9%)
Mathematics makes me confused^R	All: 3163 (78.0%) Boys: 1574 (77.7%) Girls: 1589 (78.3%)	All: 2133 (56.9%) Boys: 1225 (63.5%) Girls: 908 (47.9%)

Note: R stands for reverse coding.

As Tables 3 and 4 illustrate, not all students replied to all items. The number of total responses per item in Grade 4 varies between n = 4001 and n = 4083 and in Grade 8 between n = 3768 and n = 3884. The rate of positive response is based on the number of responses in each item. The response rates for the negative replies are the remaining percentages.

5.1. Comparing Grade 4 and Grade 8

The first hypothesis is that Grade 8 students express more negative emotions, including negative motivation towards mathematics, compared to Grade 4 students. The results are presented in Table 5.

Table 5. Comparison: Grade 4 (n = 4090) and Grade 8 (n = 3922).

Motivation	χ2	p	Cramer’s V	Interpretation
Intrinsic	1000.36	<.001	0.377	Very strong
Cognitive	958.96	<.001	0.357	Very strong
Emotional	1001.12	<.001	0.371	Very strong
Extrinsic	1096.61	<.001	0.380	Very strong
Outward	991.30	<.001	0.360	Very strong
Compensation	879.27	<.001	0.333	Very strong

The differences between Grade 4 and Grade 8 are significant where the latter group are more negative (emotional direction) for all the motivational categories.

5.2. Gender differences

The following results are about gender differences, and we present the results for Grade 4 first (Table 6).

Table 6. Gender differences: Grade 4.

Motivation	χ2	p	Cramer’s V	Interpretation
Intrinsic	54.25	.162	0.122	Moderate
Cognitive	78.65	<.001	0.143	Moderate
Emotional	37.11	.093	0.100	Moderate
Extrinsic	19.27	.082	0.070	Weak
Outward	11.58	.238	0.054	Weak
Compensation	13.28	<.005	0.057	Weak

The results in Table 5 indicate differences between boys and girls regarding intrinsic motivation; however, no differences concerning expressed extrinsic motivation. It should be noted that although there are significant differences in Compensation, Cramer’s V signals only weak differences. The results for Grade 8 differ (see Table 6):

As we can see in Table 7, both intrinsic motivation and extrinsic motivation generated significant differences, in particular regarding the items coded as intrinsic motivation. Boys’ replies are different compared to Grade 4, and are now more negative (or not as positive) towards mathematics, both when looking at subscales of intrinsic motivation and subscales coded as extrinsic motivation.

Table 7. Gender differences: Grade 8.

Motivation	χ2	p	Cramer’s V	Interpretation
Intrinsic	169.65	<.001	0.223	Strong
Cognitive	132.11	<.001	0.190	Strong
Emotional	117.51	<.001	0.182	Strong
Extrinsic	53.51	<.001	0.121	Moderate
Outward	38.75	<.001	0.102	Moderate
Compensation	58.23	<.001	0.123	Moderate

The next step is to look at boys and girls separately and make a comparison with respect to age group. Table 8 presents the results from comparing girls.

Table 8. Comparing girls: Grade 4 and Grade 8.

Motivation	χ2	p	Cramer’s V	Interpretation
Intrinsic	667.08	<.001	0.434	Very strong
Cognitive	626.67	<.001	0.409	Very strong
Emotional	654.19	<.001	0.424	Very strong
Extrinsic	653.51	<.001	0.416	Very strong
Outward	591.35	<.001	0.395	Very strong
Compensation	544.13	<.001	0.372	Very strong

Both intrinsic motivation and extrinsic motivation generated significant differences, and girls in Grade 4 differ from girls in Grade 8 where the former are more positive towards mathematics and mathematics education. A similar pattern is observed looking at boys, see Table 9.

Table 9. Comparing boys: Grade 4 and Grade 8.

Motivation	χ2	p	Cramer’s V	Interpretation
Intrinsic	397.23	<.001	0.338	Very strong
Cognitive	395.62	<.001	0.325	Very strong
Emotional	395.64	<.001	0.330	Very strong
Extrinsic	457.63	<.001	0.347	Very strong
Outward	412.42	<.001	0.328	Very strong
Compensation	352.93	<.001	0.297	Very strong

Table 8 results show that both intrinsic motivation and extrinsic motivation generated significant differences. The pattern is the same for boys as for girls: boys in Grade 4 are more positive towards mathematics and mathematics education.

6. Discussion

A recent paper addresses the need for secondary analysis of TIMSS data with respect to the mathematics achievement profiles, since there are patterns not visible in the TIMSS report (Yıldırım, 2022). We argue that the same reasoning could be applied to the results from TIMSS surveys, and therefore the aim was to study patterns in changes of affect between girls and boys and between Grade 4 and Grade 8. Secondary analysis started with a recoding of the instruments (e.g. Mullis et al., 2020) using previous research (e.g. Nyman & Sumpter, 2019; Sumpter, 2013), followed by additional statistical analysis. Two hypotheses based on previous research were posed and the analyses showed that, as predicted, there was a lower level of expressed emotional direction towards mathematics in Grade 8. These results are in line with previous studies (e.g. Blomqvist et al., 2012; Hannula, 2006). Nevertheless, recoding the two instruments from TIMSS allowed us to explore whether there were any nuances that could not be detected by looking at single items or the various indices generated from these instruments. What we can add to the research field is that all motivational categories show very strong, according to Cramer’s V (e.g. Akoglu, 2018), significant differences. This is a slightly different result compared to earlier studies where older students were more likely to stress different types of extrinsic motivation and negative intrinsic motivation (e.g. Blomqvist et al., 2012; Hannula, 2006; Nyman, 2020). It should be noted that these studies are mainly qualitative, and differences could be due to how data were collected. As stated earlier, although the strength in our methodology was the opportunity it presented to study nuances, it cannot further explain nor explore why respondents opted for certain responses. The general pattern, however, is that Grade 8 students are more negative than Grade 4 students and it appears that this develops over time (e.g. Batchelor et al., 2019). Given previous research suggests that when students couple mathematics with negative affect they do not continue to study the subject once they can opt out (Brown et al., 2008), one implication is that if we want more students to continue with mathematics, it could be worth targeting affect in general and emotional in particular to effect the change. This relevance increases with the important role emotions seem to play in education (e.g. Blair, 2002; Fredrickson & Joiner, 2018; Lake, 2017; Lewis, 2013; Nelson et al., 2018; Radford, 2018; Raver, 2002; Ryan & Deci, 2000; Valiente et al., 2012; Young, 2020), and given that positive affect mediates negative affect (Moneta et al., 2012). One suggestion for further research is thus to prioritize emotions, as Koskinen and colleagues (2023) did in their study, to see if a positive change in emotional directions also leads to changes in expressed motivation.

The lower level, that is, more negative responses, was true both for girls and boys, a result that differs from other countries where gender is a neutral factor in TIMSS (e.g. Kaleli-Yılmaz & Hanci, 2016). Nonetheless, further analysis highlighted some interesting nuances regarding Grade 4, where boys expressed a more positive emotional direction regarding intrinsic motivation compared to girls, a result that was not repeated in the same way regarding extrinsic motivation. The result regarding boys and higher intrinsic motivation has been discussed before (e.g. Skaalvik & Skaalvik, 2004), but in these studies, the students were older. The results from the present study, with its focus on younger students, are therefore a contribution. When adding the results from Grade 8, the conclusion is similar to previous studies (e.g. Blomqvist et al., 2012; Hannula, 2006; McGeown & Warhurst, 2020): gender differences in emotional direction towards mathematics, including motivation, increase with age. Given the equal distribution of students in upper secondary school in Sweden, including in the Natural Science programme (Skolverket, 2020), the results from the present study (in the context of personal gender) are not aligned with structural gender (e.g. Bjerrum Nielsen, 2003). If we had treated gender as biological sex (e.g. Kaleli-Yılmaz & Hanci, 2016), the results could signal that girls are ‘born this way’ and not that mathematics is (still) a male domain (Brandell & Staberg, 2008).

One possible conclusion, if one regards emotion as the starting point of motivation (e.g. Damasio, 1994), is that although girls do study advanced mathematics at upper secondary school, they have already formed a negative emotional direction, including motivation, towards mathematics somewhere between Grade 4 and Grade 8 (e.g. Batchelor et al., 2019). If so, this could potentially explain the segregated labour market and higher education (e.g. Dekhtyar et al., 2018; Sumpter & Sumpter, 2021), or the ‘educational-gender-equality paradox’ (Stoet & Geary, 2018). Such a conclusion, however, requires additional supporting findings.

Disclosure statement

No potential conflict of interest was reported by the authors.