Sense of belonging is a critical universal need, as it provides people with the ability to satisfy other needs, such as self-actualisation (Maslow 1943). Bouchard and Berg (2017) define a sense of belonging as a relationally derived psychosocial design that is used to portray the ‘sense of fit’ or ‘feelings of acceptance’ that an individual feels about his or her society. The Organisation for Economic Co-operation and Development (OECD) argues that people generally and adolescents specifically yearn for stable societal associations and place significant importance on recognition, appreciation, care and support from their communities (OECD 2017). Jethwani-Keyser (2008) argues that, within the school setting, a sense of belonging provides students with a sense of safety, individuality and community, which has a positive effect on their academic, mental and socio-emotional development (OECD 2017). Belonging in school refers to the sense of association students’ experience within their peer groups, being accepted as equals in the classroom context, experiencing shared power, engaging in critical citizenship and experiencing a sense of safety and inclusion (Parekh 2014). A sense of belonging is associated with the need for structure, order, security, predictability and the absence of uncertainty. If these needs are not met, the student may experience feelings of isolation and unhappiness.

Bouchard and Berg (2017) observed that during the last 2 decades, academics have become gradually attentive to the consequences of primary school students’ sense of belonging, primarily within the school locale. Numerous research studies (Chhuon & Wallace 2014; Nichols 2008; Sakiz, Pape & Hoy 2012) have maintained that students within the school environment require a sense of belonging to support constructive development within school. They contend that less focus was given to clarifying the aspects contributing to the development of school belonging. For noteworthy exceptions, the study conducted by Bouchard and Berg (2017) explored factors that contribute to an amplified sense of belonging experienced by late primary school students. The study revealed that students foster a sense of belonging through reciprocal caring relationships with teachers, through peer friendships and through participation in extra-curricular and school-based activities. It provides a clear understanding of the students’ sense of belonging experiences in a particular context from both the perspective of teachers and students. However, the study is small in scope and thus not generalisable, and the authors do not explicitly focus on the SES of students, which is extremely important when taking into account the South African education context.

Research shows that juveniles who experience a sense of belonging in terms of their school community will probably be more inspired and perform better academically (Battistich et al. 1997; Goodenow 1993). Additional evidence shows that children and adolescents who experience a connection with their school are unlikely to exhibit dangerous and rebellious conduct (Catalano et al. 2004). Lee and Burkam (2003) argued that students with stable and gratifying social associations at school are unlikely to exit school prematurely or indulge in drug use or non-attendance behaviour. In addition, research evidence also suggests that adolescents who do not experience a sense of association or bonding with their school might be at risk of developing depression (OECD 2017; Shochet et al. 2006). These results were confirmed by similar studies (Chapman et al. 2013; Goodenow & Grady 1993; Johnson 2009; Osterman 2000; Uslu & Gizir 2016; Waters, Cross & Shaw 2010) that comprehended the impact of the existence or lack of a sense of belonging, and researchers have investigated some of the factors that may influence student behaviour and achievement in different student clusters.

Maslow’s motivational hierarchy described the theoretical construct of belonging (Maslow 1943). He contended that human beings have a basic need for belonging and that once the physiological and safety needs are sufficiently satisfied, the need to belonging (love) assumes vital importance (Schunk 2012). According to Schunk (2012), this includes intimate relationships with others, belonging to groups and having close friends and acquaintances. A person’s sense of belonging can be so influential that it creates not only a sense of worth but also the capacity to acquire healthy coping skills when undergoing intensive and painful emotions. Bouchard and Berg (2017) cite Baumeister and Leary (1995), who suggested that belonging has two characteristics. Firstly, human beings require regular personal associations where serious disagreement and adverse emotions are largely absent; secondly, is imperative for people to understand that interpersonal relationships that are solid, empathetic and enduring do exist (Baumeister & Leary 1995). This is relevant to the present study, as it delineates the hierarchy of human needs, such as sense of belonging, which needs to be satisfied, as it is unrealistic to expect students to perform well in school if they are suffering from physical or security deficiencies.

Etuk, Afangedih and Uya (2013) acknowledge the prominence of teacher qualities in realising learning objectives and intentions in a learning system. The authors define these qualities as the instructional behaviours demonstrated by the teacher towards goal attainment. Van De Grift (2007) argues that the variables associated with effective teaching are effective classroom supervision and administration, a secure and inspiring instructional climate, teacher clarity and adapting teaching and instructional approaches. Empirical researchers have associated successful teachers’ characteristics to improved student achievement in the intellectual, emotional or psychomotor outcomes of education (Etuk et al. 2013; Offorma 1994; Van De Grift 2007).

Wentzel (1999) suggests that adolescents first develop an attachment with their teacher, prior to them developing a sense of belonging in the greater school community. A number of studies have revealed that support and encouragement provided by the teacher may have a more direct influence on adolescent engagement than that of their peers and parents (Connell & Wellborn 1991; Murray & Greenberg 2000; Newmann 1992; Uslu & Gizir 2017; Wentzel 1998). A positive adolescent–teacher relationship is considered a predictor of change in a student’s sense of belonging, motivation, outcomes, school attentiveness, performance anticipation, morals, commitment, determination and achievement (Giani & O’Guin 2010; Goh & Fraser 1998; Goodenow 1993; Murdock 1999; Sullivan, Riceio & Reynolds 2008; Uslu & Gizir 2017; Wentzel 1998).

The value of student–teacher relationships can have an effect on students’ social and emotional development and engagement at school (Anderman 2003; Battistich et al. 1995; Chiu et al. 2016; Ma 2003; Noble et al. 2008). Teachers can encourage healthy socio-emotional development in students by constructing a nurturing and deferential instructional setting (Battistich et al. 1997; Noble et al. 2008). Studies conducted by Battistich et al. (1997) and the OECD (2017) have indicated that constructive associations relating to teachers and students are significant for the socio-emotional welfare of disadvantaged students. Etuk et al. (2013) argue that students frequently evaluate their teachers in areas such as the teachers’ subject content knowledge, skill of communication, selection of suitable instructional techniques and their overall classroom supervision and administrative abilities. They further argue that teachers rated highly on these indicators (based on students’ opinions) are very likely to appreciate the assurance, gratitude and esteem of their students (Etuk et al. 2013).

A healthy student–teacher relationship and a sense of belonging are especially important in the primary and intermediate school phases. A study conducted in the United States found that students’ sense of belonging decreases from years 7 to 11 (Wang & Eccles 2011). Findings from a study in Finland showed that students’ sense of belonging significantly weakened, especially at the end of year 8. The reason for this tendency might be the fact that secondary schools offer more social networks and employ a larger number of teachers to which students need to adapt to (Ulmanen et al. 2016).

Following the work of Baumeister and Leary (1995), Goodenow (1993) and Maslow (1943), we take into account students’ perceptions of teacher engagement, students’ home SES, gender, absenteeism (as a proxy for participation) and incidences of bullying as factors that influence students’ sense of belonging and mathematics achievement.

Home SES plays a major role in a student’s sense of school belonging. International schools where students experience a higher sense of belonging are characterised by a higher SES (Taylor & Yu 2009).

Even though gender differences might exist, it is important for students to outwardly express a desire to have meaningful relationships considering that a sense of belonging is important to the mental health of boys and girls. Students who believe that they belong to the school will have confidence in their ability and are engaged in the classroom. The TIMSS 2015 uses absenteeism as a broad measure of participation, which, we would argue, is probably the most important aspect of participation. Schools that invest in extra-curricular activities, positive social relations and positive mental health can promote a higher sense of belonging and reduce absenteeism rates. South African students who scored the lowest in the mathematics assessment are likely to come from disadvantaged households, have lower levels of numeracy skills and attend less resourced schools where there is a higher level of bullying, safety and discipline problems and a lower sense of school belonging (Isdale et al. 2017).

Figure 1 displays the relationship among SES, student–teacher relationship, absenteeism (proxy for participation), sense of belonging and mathematics achievement.

This is a descriptive, exploratory and cross-sectional study that made use of secondary data on grade 5 South African students collected through the TIMSS in 2015. In 2015, the International Association for the Evaluation of Educational Achievement (IEA) offered as part of their suite of products, a TIMSS-Numeracy study, a study specifically designed for lower performing countries. South African grade 5 students were assessed on mathematics in the TIMSS-Numeracy study. Apart from the assessment of students, the study also collected contextual background information on the students themselves, their mathematics teachers and their schools. Data were also collected from parents regarding the students’ early learning experiences and development through an early learning survey. From a total of 15 783 South African schools that offered grade 5 classes in 2013, the IEA selected a stratified random sample of 300 schools. The sample of schools was stratified by province, type of school (public or independent) and language of learning and teaching (Afrikaans, English or dual [Afrikaans and English] medium). A random selection process of intact classes (as opposed to the selection of individual students) was applied for each sampled school. For South Africa, a total of 297 schools, 10 932 students, 10 376 parents or caregivers and 295 mathematics teachers participated in the study. The data were weighted to the population of South African grade 5 students. The TIMSS-Numeracy study for South Africa was reviewed by the Human Sciences Research Council (HSRC) Research Ethics Committee and received ethical clearance and approval on 14 July 2014.

A method applied by the World Bank (World Bank Group 2016) and other researchers, including Gwatkin et al. (2007), Taylor and Yu (2009), and Vyas and Kumaranayake (2006), was used to develop and calculate the indices.

Each of the indices was constructed from students’ responses to sub-scales in batteries of items in the student questionnaire. The method entails using PCA to generate a weight for each item (statement) within the different batteries of items. According to this technique, the item most unequally distributed will receive the most weight. In other words, PCA gives more weight to variables with higher standard deviations (Vyas & Kumaranayake 2006). Student responses to the sub-scales were weighted according to the coefficients of the first principal component, instead of, for instance, summing responses to the sub-scales, which makes this a suitable method for analysis. Furthermore, this method uses all of the variables in reducing the dimensionality of the data.

A score was calculated for each index-variable and for each student, by weighting the responses with respect to each item pertaining to that student by the coefficient of the first Principal Component (PC1) of the concept, and then summing the outcomes. The coefficients of PC1 were used as weights because PC1 explains most of the variance in the data. The weights derived from the PCA were applied to the following equation, to calculate the scale score for each student (Ai) per index: Ai=w11*ai1−a1S1+w12*ai2−a2S2+⋯+w1n*ain−anSn[Eqn 1] where w₁₁ is the weight given to the first item within the first principal component for the specific concept, a_i1 is the value that student i gave for item 1, a₁ is the mean value of item 1 for all students and s₁ is the standard deviation for item 1 over all students (refer to Appendix 1 for an example of how the indices were calculated).

The indices were developed from students’ responses to three sets of questions in the student questionnaire (IEA TIMSS 2015). For two of the sets of items, students had to indicate how much they agreed with the given statements by selecting one of the following options: agree a lot (recoded to a value of 3); agree a little (recoded to a value of 2); disagree a little (recoded to a value of 1) and disagree a lot (recoded to a value of 0). The third index, the home socio-economic status index, was based on a set of dichotomous variables (0 indicates ‘no’ and 1 indicates ‘yes’).

The attitudes towards mathematics teachers index was developed based on responses to the following statements in question G11: ‘I know what my teacher expects me to do’; ‘My teacher is easy to understand’; ‘I am interested in what my teacher says’; ‘My teacher gives me interesting things to do’; ‘My teacher has clear answers to my questions’; ‘My teacher is good at explaining mathematics’; ‘My teacher lets me show what I have learned’; ‘My teacher does a variety of things to help us learn’; ‘My teacher tells me how to do better when I make a mistake’; and ‘My teacher listens to what I have to say’ (IEA TIMSS 2015:9).

The sense of school belonging index was developed based on the level of agreement of students with the following statements in question MS2: ‘I like being in school’; ‘I feel safe when I am at school’; ‘I feel like I belong at this school’; ‘I like to see my classmates at school’; ‘Teachers at my school are fair to me’; ‘I am proud to go to this school’; and ‘I learn a lot in school’ (IEA TIMSS 2015:12).

The home socio-economic status index was based on the availability of 15 assets in students’ homes. The information was elicited through question G5 of the student questionnaire. The items included a student’s own computer or tablet, computer to share, study desk, own room, Internet connection, own mobile phone, gaming system, dictionary, electricity, running tap water, television, water flush toilets, motor car, landline telephone and fridge (IEA TIMSS 2015:8).

Question G8 of the student questionnaire was used to obtain data from students on how often, on average, they were absent from school (IEA TIMSS 2015:9). Responses were recoded to reflect the following codes: ‘once a week or more’ or ‘once every two weeks’ were recoded as 1; ‘once a month’ or ‘never or almost never’ as 0. In other words, a code of ‘1’ was given if a student was frequently absent and a code of ‘0’ otherwise.

The IEA developed an index based on question G12 in the student questionnaire, which elicited data on the frequency at which students experienced hurtful acts committed by other people. The items included the following statements: ‘Made fun of me or called me names’; ‘Left me out of their games or activities’; ‘Spread lies about me’; ‘Stole something from me’; ‘Hit or hurt me (e.g. shoving, hitting, kicking)’; ‘Made me do things I did not want to do’; ‘Shared embarrassing information about me’; and ‘Threatened me’ (IEA TIMSS 2015:11). A higher score on the scale is more favourable; in other words, a higher value on the scale indicates that less bullying was experienced.

Mathematics achievement scores were calculated on a scale with a centre point of 500 and a standard deviation of 100. The curricula of the 48 participating countries were broadly represented in the achievement tests. To ensure non-biased testing, the items were adapted according to data from curriculum analysis. The assessment instruments were also piloted. The achievement tests were administered in each school’s language of instruction, either English or Afrikaans. The IEA applied matrix-sampling assessment designs, which grouped the entire pool of items into a series of blocks to obtain estimates of students’ proficiency in mathematics that are both accurate and cost-effective. Each student completed four blocks, each containing approximately 10–14 assessment items. As far as possible, within each block, the distribution of items across content and cognitive domains matched the distribution across the item pool overall. Individual students were thus tested on a subset of the complete pool of assessment items. Five plausible scores were calculated for each student based on the performance of all students on all tested items. All quantitative analyses of mathematics achievement report on the average of the five plausible scores.

Bivariate correlation coefficients (Pearson product–moment correlation coefficient) were calculated for students’ attitudes towards teachers and students’ sense of school belonging. Students’ attitudes towards teachers and students’ sense of school belonging were strongly positively correlated, r(8839) = 0.60, p = 0.000. This suggests that there is a statistically significant, strong positive linear relationship between the two variables. Thus, if a student had a positive attitude towards his or her mathematics teacher, he or she would also have a positive sense of school belonging and vice versa.

A simple linear regression was furthermore calculated to see if attitudes towards teachers significantly contributed to predicting students’ sense of school belonging. A significant regression equation was found (F[1,8837] = 4943.31, p < 0.05), with an R² of 0.359. The measure of students’ predicted sense of school belonging is equal to 0.062 + 0.420 × (attitudes towards teachers). Thus, the attitudes towards teachers as a proxy for student–teacher relationship had a significant positive effect on students’ sense of school belonging.

Independent-samples t tests were performed for boys and girls to, firstly, compare attitudes towards teachers and, secondly, to compare sense of school belonging. A significant difference in the attitude towards teachers was observed for boys (M = 0.010, SD = 4.1) and girls (M = 0.444, SD = 4.0); t (9449) = 5.202, p = 0.000. The results also showed a significant difference in sense of school belonging for boys (M = -0.037, SD = 2.9) and girls (M = 0.310, SD = 2.7); t(9521) = 6.00, p = 0.000.

These results suggest that girls really had a more positive attitude towards primary school mathematics teachers and they also had a higher sense of belonging at school than boys.

A stepwise regression analysis was performed to evaluate the predictor value of the selected independent variables on mathematics achievement as depicted and based on the conceptual framework of the study. Thus, the regression model measured the level of association between student–teacher relationship, sense of school belonging, absenteeism, extent of bullying, home SES and gender on mathematics achievement of grade 5 students.

At step 1 of the analysis, the independent variable, home SES, was entered into the regression equation and was significantly related to mathematics achievement (F[1,8718] = 1294.99, p < 0.001). The multiple correlation coefficient was 0.40, indicating that approximately 15.8% of the variance of mathematics performance could be accounted for by home SES (adjusted R² = 0.158, p < 0.001). Table 2 shows that all variables were entered into the equation at step 6 of the analysis and were significantly related to mathematics performance (F[6,8713] = 480.72, p < 0.001). The multiple correlation coefficient was 0.52, indicating that approximately 27.0% of the variance of mathematics performance could be accounted for by the six independent variables (adjusted R² = 0.270, p < 0.001).

Thus, as depicted in Table 2, the regression equation for predicting mathematics achievement based on the conceptual model of the study was mathematics performance = 305.87 + (9.99 × home SES index) + (9.88 × bullying index) + (-35.86 × absent) + (2.75 × student–teacher relationship index) + (13.73 × gender) + (1.41 × sense of belonging index).

The results furthermore showed that girls performed on average 14 points higher than boys and students who were frequently absent performed 36 points lower than their peers. It is also evident that home SES had the strongest association (β = 0.35, p < 0.001), while the frequency of acts of bullying experienced had the second highest association (β = 0.19, p < 0.001) with mathematics performance.

It is important to note that after controlling for home SES, bullying, gender and absenteeism, students’ attitudes towards teachers (proxy for student–teacher relationship) (β = 0.11, p < 0.001) and sense of belonging (β = 0.04, p < 0.001) significantly contributed to mathematics performance.

The data used in the study were from the Trends in International Mathematics and Science Study (TIMSS). Ethical clearance for conducting the TIMSS in South Africa was obtained from the Research Ethics Clearance Committee of the Human Sciences Research Council on 14 July 2014 (Ethical clearance number: REC 1/19/03/14).