The United Nations Educational, Scientific and Cultural Organization (UNESCO 2017) provides the most recent global overview of the nature, extent and impact of school violence and bullying on the academic achievement and mental health of children. It broadly defines school violence as encompassing ‘physical violence, including corporal punishment, psychological violence, including verbal abuse; sexual violence, including rape and harassment; and bullying, including cyberbullying’ (UNESCO 2017:8). In this definition, UNESCO (2017) highlights bullying, which is the focus of this particular study, as a type of school-based violence which, in essence, would warrant the need for a definition in its own right because it has its own contentious issues (Gladden et al. 2014; Thornberg 2015). In 1993, Dan Olweus coined the first meaningful definition of bullying as ‘when someone repeatedly and on purpose says or does mean or hurtful things to another person who has a hard time defending himself or herself’ (Olweus et al. 2007:1). Since 1993, several writers (Vreeman & Carroll 2007) have expanded on Olweus’s definition of bullying, but kept his original description as a point of departure. Olweus (2016) also emphasised three key criteria for the definition of bullying, namely bullies intentionally harm others, there is repetition, and power issues are at play. Furthermore, he identified relationships and abuse as critical aspects of bullying. The relationship component implies that the bullying occurs over time for individuals, whilst the power part usually indicates that the perpetrators generally have more power than the individuals they bully. In their definition Volk, Veenstra and Espelage (2017) emphasise the point that bullying is goal-directed and that it is a specific form of aggression which is differentiated from other forms of aggression because of issues of power imbalances. According to Volk et al. (2017), such a definition is theoretically grounded and transdisciplinary. The author adopts the definition of Volk et al. (2017) because it locates bullying as an important component of aggression – both of which are critical aspects of mental health. Furthermore, the author endorses the different definitions of bullying which can be summarised as malicious intent, power imbalances, repeated behavioural transgressions, infliction of emotional distress, and unnecessary provocation. Learners are more likely to define bullying as physical and verbal abuse whilst teachers include social exclusion, power imbalances, and threats to hurt others (Naylor et al. 2006).

Over the last two decades numerous studies have shown bullying to be a global social problem (Bennett-Johnson 2004; Dahlberg 2002; Hymel & Swearer 2015; Nansel et al. 2004; Owusu et al. 2011). A global study by Richardson and Fen Hiu (2018) found that bullying ranged from 26.6% in Central and Eastern Europe and the Commonwealth of Independent States to a high of 53.1% in West and Central African region. South Africa is no exception as several studies have found an escalation in school-based bullying over the last decade (Bennett-Johnson 2004; Fitzpatrick 2006; Pillay & Ragpot 2010; Smith & Smith 2006). An analysis of bullying prevalence in South Africa by Juan et. al. (2018) noted an escalation of school bullying ranging from 12% to 61% depending on the location, Socio-economic status (SES), and culture of the school.

Besides the escalation in school bullying incidents, UNESCO (2017) points out some general global trends observed from research conducted with 100 000 young people in 18 countries. Firstly, UNESCO (2017) observed that children experienced bullying largely as a result of their physical appearance, gender or sexual orientation, ethnicity or national origin, or other reasons. Some children are bullied because they are in vulnerable situations and those who live with disabilities, are economically and socially disadvantaged, and those who are asylum-seeking and refugees. Secondly, it appears that boys are more inclined to report physical violence than girls (Walters 2020). Girls reported higher rates of indirect and relational bullying. Thirdly, the highest rates of bullying were observed in primary schools and the incidents of bullying seem to decline between the ages of 11 and 15 years. Lastly, but not least, the prevalence of bullying appears to be higher in developing countries.

The consistent escalation of school bullying in certain parts of the world, as noted in the preceding discussion, has resulted in a plethora of studies focusing on various impacts of bullying on those who are bullied, such as their psychological and mental health (Bradshaw, Waasdorp & Johnson 2015; Fullchange & Furlong 2016; Jack & Egan 2018; Takizawa, Maughan & Arseneault 2014; Ttofi, Farrington & Losel 2012); school dropout (Cornell et al. 2013); socialising skills (Nansel et al. 2001); physical health (Bogart et al. 2014; McDougall & Vaillancourt 2015); and academic achievement (Ladd, Ettekal & Kochenderfer-Ladd 2017; Nakamoto & Schwartz 2010; Totura, Karver & Gesten 2014). Whilst several studies have alluded to a significant relationship between school bullying and academic success (Buhs, Ladd & Herald 2006; Ladd et al. 2017; Thijs & Verkuyten 2008), not many have focused on the association between school bullying experiences and numeracy achievement, especially in the South African context. Hence, this study sought to extend the findings of previous research (Pillay 2017) on in-school bullying by examining the association between self-reported bullying experienced by primary school children and their numeracy development. The first research question was as follows: What is the prevalence of bullying in Johannesburg schools across age, grade, gender, home language and regions? The second question was this: Is there a significant statistical association between the frequency of being bullied and the numeracy percentage across the variables mentioned in the first question? In this study, numeracy performance is considered by using the numeracy percentage obtained as the dependent variable and the bullying items as independent variables. An investigation on the prevalence of bullying in schools is likely to have social value because it can address strategies on how children could have improved the social interaction and relationships which is a key aspect of Bronfenbrenner’s (2005) bioecological systems theory.

The definition of numeracy has been a contentious issue, especially in its relationship to mathematics (De Abreu 2000; Baker, Street & Tomlin 2003; Brooks et al. 2008; Karaali, Hernandez & Taylor 2016) However, for the context of this article the definition by Geiger, Goos and Forgasz (2015) is adopted for its comprehensiveness, that is:

A global search for literature and research studies on the association between bullying experiences and numeracy achievement in children proved these to be scant. One can, however, draw from the United Nations Children’s Fund (UNICEF) Innocenti Report Card 15 (UNICEF 2018) which clearly shows that inequalities exist – even in the world’s richest countries – and have a detrimental effect on children’s academic outcomes. The report highlights the importance of peer influence on children’s academic performance and one could postulate that peer bullying is one of these influences. In fact, most studies, as pointed out earlier, show an association between bullying and academic achievement in general. Three studies in particular, however, show bullying as having a negative impact on numeracy achievement in children (Kibriya, Xu & Zhang 2015; Mundy et al. 2017; Oliveira et al. 2018).

Aligned to the research questions the results are presented across gender, age, language and school quintile in terms of frequencies, prevalence of bullying, and the association between numeracy and school bullying.

This study resulted in some important findings. Firstly, it found a high prevalence of school bullying (46.9%) which was self-reported by the participants in Johannesburg, Gauteng province. However, this finding needs to be interpreted with caution because the sample was representative of 10% of the population involved in this study. Other South African studies have noted school bullying to range within the 30% to 45% range which is more or less similar to Johannesburg as found in this study. For example, Liang, Flisher and Lombard (2007) reported 41% prevalence in Cape Town and 33% in Durban in their large-scale study; and Cluver, Bowes and Gardner (2010) confirmed that 34% of the children in their study reported being bullied in urban parts of Cape Town. Even though it is difficult to identify specific reasons for this escalation, studies have shown that all forms of abuse (Dawes, Bray & Van der Merwe 2007; Dussich & Maekoya 2007) and violence (Kahn et al. 2000) generally contribute to school bullying and there is the possibility that abuse and violence may be more prevalent in Johannesburg and surrounding areas.

Secondly, it was found that bullying was more common in higher SES children in terms of school quintiles and region locations. Most studies seem to indicate that bullying is more common amongst children from low SES groups (Noble, Wright & Cluver 2006; Tippett & Wolke 2014). Bullying may be more common amongst children from high SES because they may believe that they have more power and popularity by virtue of the resources they have (Shetgiri, Lin & Flores 2012). As such, one would expect cyberbullying to be high but it did not emerge as such in this study. This could probably be because of the fact that in most public schools, cell phones are not allowed to be used during teaching time. This could reduce the possibility of cyberbullying during school time.

Thirdly, the findings indicate that there is an association between bullying experiences and numeracy achievement, that is, children who are bullied tend to perform poorly in numeracy tests in comparison to their peers who did not report being bullied. This finding should be noted with caution because the focus of this study was on associational rather than causal relationships between bullying experiences and numeracy performance. Also, it is important to note that there is no certainty on whether bullying contributes to poor numeracy performance or vice versa. Children with bullying experiences may avoid school or not engage in classroom activities and this could account for poor numeracy performance. This point is aligned to social referencing theory that would postulate that children gather information about bullying experiences in their environment and interpret this information to determine how they will act (Feinman et al. 1992). Or children could be more vulnerable to bullying because of their poor performance. In this regard Huber et al. (2018) show how social acceptance of children in the classroom by both teachers and other learners can have a positive or negative impact on them. Bullying usually provides negative feedback to children resulting in social withdrawal.

The fourth significant finding was that bullying was most prevalent amongst children aged 10 who were mostly in Grade 4 (44.7%). These children were also found to have the lowest score on the combined numeracy test and differed statistically significantly from learners in Grade 7, the 12- and 13-years’ age groups at the 1% level of significance. Whilst this study did not determine any particular reasons to explain why the Grade 4 group had the lowest mean score in the numeracy test, the results confirm the findings of the Annual National Assessments (DoBE 2014). The finding that bullying is more prevalent in the early grades corroborated other studies which observed a decline in the incidents of school bullying in older learners (Salmivalli 2002; Seals & Young 2003; Selekman & Vessey 2004; Van der Ploeg, Steglich & Veenstra 2020). Some researchers noted that the reason for this could be because of children having to leave the safety of the home environment and venturing into a new school climate for the first time where their social difficulties could be detected (Vlachou et al. 2011).

The above findings are significant from a bio-ecological systems theoretical perspective because they implicitly highlight the importance of viewing school bullying and numeracy achievement as operating within multiple systems and levels (Divecha & Brackett 2020). At the individual level, it infers that there are traits within the children themselves that contribute to bullying behaviour and numeracy achievement. Particularly within the context of this study, grade, home language and socio-economic status were identified as important categorical variables to consider in relation to school bullying and numeracy achievement. With reference to grade, it was found that school bullying was most frequent amongst children in Grades 1 to 6 and declined in Grade 7 as they grew older. This suggests the importance of implementing anti-bullying programmes from the primary school level. Also, the support for numeracy development associated with bullying should begin in the early years of schooling. Regarding gender, girls in this study were more engaged in verbal bullying and boys in physical bullying. Fullchange and Furlong (2016) indicate that boys generally display more aggression than girls. This indicates the need for specific interventions for boys and girls and, more importantly, a focus on specific strategies to combat aggressive behaviour in boys.

Finally, all interventions directed at addressing school bullying should take socio-economic environments into consideration, as noted in the differences amongst quintile groupings and education districts in this study where the high socio-economic status schools and districts displayed increased levels of bullying. Other studies noted converse findings where bullying was more prevalent in low SES settings (Tippett & Wolke 2014). Both high and low findings show the need for SES to be considered when anti-bullying strategies are implemented in schools (Greeff & Grobler 2008; Liang et al. 2007; Noble et al. 2006; Seals & Young 2003).

The above findings imply that school management teams should be geared at ensuring that schools are safe places for teaching and learning to occur. There should be increased access to mental health services and support for victims of bullying as well as those who bully others, such as individual and group counselling programmes. Anti-bullying programmes should be infused across the school curriculum and in the early years it should be concretely directed at developing social skills as well as behaviour and emotion regulation skills (Vlachou et al. 2011). Also, it is crucial that school-based interventions should be directed at providing academic support for children who experience bullying to improve their school performance, especially in numeracy achievement, within the context of this article.

The study relied on self-report measures, which always have the possibility of inaccuracy and intentional distortion, which could be a limitation of the findings. Another limitation was that the schools which participated in the study were the ones that chose to stay until the completion of the research, so selection bias cannot be excluded. Furthermore, the sample was representative of 10% of the population and may not necessarily be a true reflection of schools and learners who participated in the study. Also, the study was dominated by female learners and learners who used English as home language. Despite these limitations, this study confirms that bullying is highly prevalent in primary schools in and around Johannesburg, and it is associated with numeracy performance. It is vital to note that the study focused on associations and in no way insinuated causal relationships between bullying prevalence and numeracy achievement. The results emphasise the need for primary school-based interventions to prevent bullying and to support children who are experiencing numeracy difficulties associated with bullying. From a bio-ecological systems perspective, one would emphasise the importance of school-based interventions operating on multiple systems levels because the battle against school bullying could only be won through strong collaborations of parents, learners, schools, government, nongovernmental, religious and community-based organisations. Such collaborations are essential for the provision of school mental health services to successfully combat the negative repercussions of school bullying and its association with poor numeracy achievement in children. The findings in this study and the implications for school-based interventions discussed are likely to have global value because bullying and numeracy are prevalent in all primary schools.