**1. Introduction**

Distancing mathematical knowledge to a certain group of children and human beings has history. Mathematics in the past was only learnt by monks and noblemen. With time, traders participated due to discoveries they observed in different cultures and because of status they obtained through trading [1]. Even then, some cultures' mathematics were recognized and documented, while others were labelled as applied mathematics giving them a lower status than pure mathematics. This discriminatory behaviour still exists in the field and continues to exclude. South African black children like all children in the world experience mathematics from their mother's womb, where they explore and navigate such space to a level where they know and feel safe in it. The loud cry they make during birth is caused by the realization that the new space is cold as they feel the temperature, they also feel that it is big as they are unable to touch, and then as soon as they are picked up and

wrapped, they feel safe again. This indicates the exploratory nature of the human being and their spatial abilities. However, the society enters this life and starts undermining and discriminating what is already there by grouping children according to their geographical existence, race and socio-economic status.

It is difficult not to align these discriminatory behaviours with entitlement, privilege and property ownership [2]. These mathematical intuitions develop naturally for children; they start engaging in games that use mathematical abilities. Ref. [2] uses critical race theory to analyse these experiences of exclusion adjourning from land rights and ownership of land. Landson-Billing proposes using US law that ownership of land goes a long way in developing one's identity in the society. Land ownership seems to be physical; however, it contributes heavily on the psychological being and esteem of human beings. Hence, black children's games are excluded in the society because this group of human beings has no privilege, no property ownership nor esteem. Since, they are already excluded these games are never brought into class because whose games are they, matters in the discriminatory society. This is a global issue because cultural games that are recognized are those from the West such as chess because of white privilege, while on the other hand, there are African games like "umrabaraba," a logical game that was used during trade in Africa. There are other logic games such as stick fighting of the Xhosa boys and girls in South Africa. Their character is similar to those that are globally recognized but carry no property right with them and therefore excluded. This exclusion translates to classrooms where children enter classrooms labelled by default that they have no mathematical skills and knowledge from their communities and therefore learning provided to them is not connected with their mathematical knowledge they bring to school.

Hence, only if they are resilient will they succeed in mathematical learning; otherwise their self-esteem and identities are not integrated with mathematical creation [3]. This paper aims to bring forth the cultural games played by Xhosa children with their mathematical skills and the knowledge they develop.

#### **2. Mathematical exclusion**

Ref. [4] gives detail account on mathematics exclusion of young black children in South Africa. In her paper she revealed that classrooms are not resourced for mathematics stimulation for young children rather they are boring formal classrooms for adults. In addition, her paper highlights that teacher qualifications are informal and vary in terms of quality with high learner-teacher ratio. These findings are supported by [5] revealing that learners from low socio-economic backgrounds attend schooling in low socio-economic schools with no resources and teachers with inadequate qualifications for mathematics teaching. Ref. [3] list a number of "vulnerabilities" South African black and coloured students possess that hinders success in learning mathematics such as homes with no resources, schools with no resources, peers with similar challenges and language of instruction not the same as home language (p. 355). These studies show how exclusion in mathematics learning is systemic.

A commissioned review of early childhood provision in South Africa revealed that the history of segregation played a significant role in excluding young children in quality mathematics instruction [6]. In addressing this injustice post 1994, the South African government through social development opened preschools for black children with a focus of care and social development. This provision did not provide for mathematics stimulation but focused more on welfare addressing poverty. The positive outcome from this review were the universality of the reception class which assured that all 5- to 6-year-old students receive stimulation to date. The current

**153**

*Black Students' Rich Mathematical Experiences: Mathematics Concepts and Xhosa Cultural…*

challenge though is that teachers who teach these students are informally trained with varied quality of training by non-governmental organisations; hence, their classroom practices lack quality and purpose [4, 7, 8]. This indicates that education system drags itself in addressing issues of inequities in the education. This slow movement is resulting to graduates of poor quality that are also unemployable. This issue is an emergency as it is an economic factor that will scar the system for a long time and lead to more poverty experiences; currently the job losses per day are

It is important to note that the poor quality of teaching students receive is not the only factor of exclusion. Their cultural experiences also are not regarded as contributing knowledge to the mathematical learning experiences. Furthermore, English continues to have power over learning in general; hence, mostly language is becoming a barrier towards excellent performance for those who learn in language different than their own. A summary of literature that discusses the language exclu-

Trends in International Mathematics and Science Study (TIMSS) 2015 results indicate clearly that students who write test in their spoken language at home perform far better than those who are tested in a foreign language. [9] revealed a significant difference of (p = .008) that was observed between a group of students whose proficiency in English was nurtured in an intervention and those who were in the control group, an indication that English holds a key towards successful access to mathematics learning for students. These findings reveal already that students with home language other than English are automatically excluded from learning; hence, an added challenge to them is to be proficient in English. This relationship between English language of instruction and students' proficiency in English has been highlighted in the US research too for students whose home language is not English [10–13]. Student participation and comprehension in mathematics learning are hindered by poor English fluency, and it impedes engagement with mathematical ideas [14, 15]. Hence, poor fluency in English excludes students from mathematics successful experiences. Ref. [16] asserts that language is a socio-cultural tool that allows students to gain access to ideas. This socio-cultural tool develops as an external tool while the child is born. Through interaction and observations with adults, the child begins to internalise vocabulary s/he hears; in doing so this, vocabulary becomes an internal tool to use to engage. Vygotsky then argues that when this vocabulary is used, it is no longer an external tool but an internal one. All children gather this language tool from their immediate environments and from their homes, and this tool becomes their cultural capital [17]; they use to make sense of the world. [18] highlights the importance of language in teaching and learning mathematics; they mention that the use of sociocultural theory in teaching mathematics is highly important as it embraces the language of the student and

South Africa is one of the countries that has tried to address the language issues of multilingualism. However, the country struggles to align its language policies with the practice for the benefit of the students. [36, 28] revealed how South African young children get exposed early to English numeracy. This creates challenges to the teaching as educators who teach these students also lack foundational mathematics language in their own home languages similar to the students [36]. These are the results of the South African apartheid system that created deeper wounds to the education of the black child. The identity of teachers that has been determined by fluency in other people's languages such as Afrikaans and English

sion in mathematics teaching and learning is discussed and shared below.

*DOI: http://dx.doi.org/10.5772/intechopen.81039*

**2.1 Language exclusion**

make connection for successful learning.

increasing, and the buying power is decreasing heavily.

#### *Black Students' Rich Mathematical Experiences: Mathematics Concepts and Xhosa Cultural… DOI: http://dx.doi.org/10.5772/intechopen.81039*

challenge though is that teachers who teach these students are informally trained with varied quality of training by non-governmental organisations; hence, their classroom practices lack quality and purpose [4, 7, 8]. This indicates that education system drags itself in addressing issues of inequities in the education. This slow movement is resulting to graduates of poor quality that are also unemployable. This issue is an emergency as it is an economic factor that will scar the system for a long time and lead to more poverty experiences; currently the job losses per day are increasing, and the buying power is decreasing heavily.

It is important to note that the poor quality of teaching students receive is not the only factor of exclusion. Their cultural experiences also are not regarded as contributing knowledge to the mathematical learning experiences. Furthermore, English continues to have power over learning in general; hence, mostly language is becoming a barrier towards excellent performance for those who learn in language different than their own. A summary of literature that discusses the language exclusion in mathematics teaching and learning is discussed and shared below.

#### **2.1 Language exclusion**

*Early Childhood Education*

**2. Mathematical exclusion**

learning is systemic.

wrapped, they feel safe again. This indicates the exploratory nature of the human being and their spatial abilities. However, the society enters this life and starts undermining and discriminating what is already there by grouping children accord-

It is difficult not to align these discriminatory behaviours with entitlement, privilege and property ownership [2]. These mathematical intuitions develop naturally for children; they start engaging in games that use mathematical abilities. Ref. [2] uses critical race theory to analyse these experiences of exclusion adjourning from land rights and ownership of land. Landson-Billing proposes using US law that ownership of land goes a long way in developing one's identity in the society. Land ownership seems to be physical; however, it contributes heavily on the psychological being and esteem of human beings. Hence, black children's games are excluded in the society because this group of human beings has no privilege, no property ownership nor esteem. Since, they are already excluded these games are never brought into class because whose games are they, matters in the discriminatory society. This is a global issue because cultural games that are recognized are those from the West such as chess because of white privilege, while on the other hand, there are African games like "umrabaraba," a logical game that was used during trade in Africa. There are other logic games such as stick fighting of the Xhosa boys and girls in South Africa. Their character is similar to those that are globally recognized but carry no property right with them and therefore excluded. This exclusion translates to classrooms where children enter classrooms labelled by default that they have no mathematical skills and knowledge from their communities and therefore learning provided to them is not connected with their mathematical knowledge they bring to school. Hence, only if they are resilient will they succeed in mathematical learning; otherwise their self-esteem and identities are not integrated with mathematical creation [3]. This paper aims to bring forth the cultural games played by Xhosa children with their mathematical skills and the knowledge they develop.

Ref. [4] gives detail account on mathematics exclusion of young black children in South Africa. In her paper she revealed that classrooms are not resourced for mathematics stimulation for young children rather they are boring formal classrooms for adults. In addition, her paper highlights that teacher qualifications are informal and vary in terms of quality with high learner-teacher ratio. These findings are supported by [5] revealing that learners from low socio-economic backgrounds attend schooling in low socio-economic schools with no resources and teachers with inadequate qualifications for mathematics teaching. Ref. [3] list a number of "vulnerabilities" South African black and coloured students possess that hinders success in learning mathematics such as homes with no resources, schools with no resources, peers with similar challenges and language of instruction not the same as home language (p. 355). These studies show how exclusion in mathematics

A commissioned review of early childhood provision in South Africa revealed that the history of segregation played a significant role in excluding young children in quality mathematics instruction [6]. In addressing this injustice post 1994, the South African government through social development opened preschools for black children with a focus of care and social development. This provision did not provide for mathematics stimulation but focused more on welfare addressing poverty. The positive outcome from this review were the universality of the reception class which assured that all 5- to 6-year-old students receive stimulation to date. The current

ing to their geographical existence, race and socio-economic status.

**152**

Trends in International Mathematics and Science Study (TIMSS) 2015 results indicate clearly that students who write test in their spoken language at home perform far better than those who are tested in a foreign language. [9] revealed a significant difference of (p = .008) that was observed between a group of students whose proficiency in English was nurtured in an intervention and those who were in the control group, an indication that English holds a key towards successful access to mathematics learning for students. These findings reveal already that students with home language other than English are automatically excluded from learning; hence, an added challenge to them is to be proficient in English. This relationship between English language of instruction and students' proficiency in English has been highlighted in the US research too for students whose home language is not English [10–13]. Student participation and comprehension in mathematics learning are hindered by poor English fluency, and it impedes engagement with mathematical ideas [14, 15]. Hence, poor fluency in English excludes students from mathematics successful experiences. Ref. [16] asserts that language is a socio-cultural tool that allows students to gain access to ideas. This socio-cultural tool develops as an external tool while the child is born. Through interaction and observations with adults, the child begins to internalise vocabulary s/he hears; in doing so this, vocabulary becomes an internal tool to use to engage. Vygotsky then argues that when this vocabulary is used, it is no longer an external tool but an internal one. All children gather this language tool from their immediate environments and from their homes, and this tool becomes their cultural capital [17]; they use to make sense of the world. [18] highlights the importance of language in teaching and learning mathematics; they mention that the use of sociocultural theory in teaching mathematics is highly important as it embraces the language of the student and make connection for successful learning.

South Africa is one of the countries that has tried to address the language issues of multilingualism. However, the country struggles to align its language policies with the practice for the benefit of the students. [36, 28] revealed how South African young children get exposed early to English numeracy. This creates challenges to the teaching as educators who teach these students also lack foundational mathematics language in their own home languages similar to the students [36]. These are the results of the South African apartheid system that created deeper wounds to the education of the black child. The identity of teachers that has been determined by fluency in other people's languages such as Afrikaans and English

has created teachers who are not proficient in any language as their home languages were never used as cultural capital. Research cannot only focus on students when addressing language proficiencies; teachers also need intervention that can develop their esteem and pride of their home languages too.

## **2.2 Racial exclusion**

Ref. [19] asserts that race is overlooked when discussing challenges observed in mathematics performance. This paper supports this assertion by supporting it with empirical evidence. For example, South Africa started participating in the TIMSS study in 1999 observing the trends of reporting the challenges of poor performance that were aligned with disadvantage learners, overcrowded classrooms and lack of resources [20]. However, revisiting these findings the students who were in overcrowded classrooms, disadvantaged and in schools with no resources were all black. The next trend of reporting this participation again highlights inequities and lack of foundational knowledge due to poor early mathematics exposure [21]. Again who were the learners who were mostly affected by the inequities, who lack foundational knowledge and also are exposed to poor mathematics instruction? The response is again black students. The 2011 and 2015 TIMSS findings did not bring anything different; although again race is not mentioned, the same black students are the ones who continue to perform poorly. Ref. [22] argue that within mathematics learning and research, there is a silent privilege that needs to be exposed. Critical race theory unravels and unpacks how white privilege continues to close access and opportunities to those who are non-white. Also it unravels how this privilege prevails through entitlement and unfounded generalisations that align whiteness automatically with success.

In the context of South Africa, research is taking too slow in unravelling racial issues that are highly embedded on educational practices including methodologies used to address educational issues. South Africa has top performing students in the National Certificate that come from low social backgrounds studying in under- or unsourced schools. However, these students repeatedly demonstrate that resilience is innate to them and therefore poverty, and discrimination cannot impede their performance. Research needs to tap on these students' traits and learn from them the qualities that they possess to be able to nurture other students from similar backgrounds.

Therefore, this racial exclusion demands more research to be conducted. This paper will only contribute by exposing black children's cultural games that have potential to nurture and influence black learners' identities within mathematics learning and experiences. By doing this it is encouraging more exploration of cultural artefacts and practices that influence mathematical growth and thinking.

#### **2.3 Economic exclusion**

Students reject a school science that is disconnected from their own lives, a depersonalized science, where there is no space for themselves and their ideas (p. 13).

The UNESCO [23] shared the above quote with the aim of asserting educators and researchers that scientific knowledge that does not align with one's experiences and thought has no place in students' conceptualization of the world they want to conquer. The global community faces challenges of attrition of scientists due to the fact that only the elite and the haves receive quality stimulation, while the majority who lives under poor socio-economic situation are deprived from such experiences.

**155**

*Black Students' Rich Mathematical Experiences: Mathematics Concepts and Xhosa Cultural…*

**3. Capital-/asset-based approach in teaching and learning of** 

Refs. [24, 32, 33] have proven that young students have demonstrated that they have high capabilities in mathematics regardless of their socio-economic background, ethnicity and geographical origins. These researchers propose the use of students' capital/assets in nurturing mathematics knowledge. Capital/asset refers to their ways of knowing and communicating and experiences that are mathematical and have been ignored. Ref. [34] indicates that there are diverse mathematical experiences from different cultures that nurture mathematics in early ages. Some cultures develop spatial reasoning first through hunting, while others develop measurement concepts through construction, and others develop diverse concepts through games, etc. If this is the case, tapping into these diverse mathematical experiences and heritage is more capacitating for students from these cultures. It develops ownership of mathematical knowledge and allows for more creation and activity. Ref. [35] argues that drawing knowledge from the students' languages and cultural-rich knowledge when teaching them creates healthy nurturing learning environments. Such environments will create spaces where mathematical creation of knowledge belongs to all, and the disadvantaged groups of students will take active participation in such creation and bring forth diverse-rich innovations in mathematics. This chapter focuses on exploring the cultural capital of Xhosa students in the Eastern Cape of South Africa. While doing so it also presents the mathematics embedded in

A lot of research has been conducted under ethnomathematics trying to find cultural experiences with mathematics. However, mathematics knowledge was not exposed, and that resulted in integration that had some flaws. The focus was the cultural practices than the mathematics embedded in them [17]. Teacher empowerment becomes very important in understanding play with a purpose. Games are fun and occupy students longer developing their concentration abilities; they need structure and reflection. Amount of skills and knowledge attained from them has

mathematics instruction. Lack of resources generally indicates economic exclusion. This economic exclusion begins from home where parents are sometimes jobless or earn below poverty levels. Ref. [24] states that this variable is a cruel unjust variable. Lack of resources for learning influences the quality of mathematics instruction negatively [25–27]. In addition, [28] reveal that quality educators highly influence mathematics learning of students from low socio-economic homes. This finding argues for quality human resources to be provided to all students for mathematical experiences that are successful. Refs. [29, 30] describe quality mathematics teachers as teachers with excellent content knowledge of mathematics, who have insight into mathematics progression and who are able to develop self-regulation in students. The best performing countries in the world make sure that they choose the best performing graduates to join teaching [31]. This also means that these teachers will earn equally with their colleagues in other fields. Countries that perform poorly do the opposite. If providing students with high-quality education has the gains, research has already been proven. Why do systems continue treating education as a "Cinderella" of the systems? Economies need engineers, scientists, innovators and inventors who will produce those high-skilled citizens if the teacher in the classroom is not a high performer him- or herself. Educational systems need to be reflective and truthful to themselves if growth is the agenda of their missions. Otherwise, the current practices look like they are planned and have a purpose that

*DOI: http://dx.doi.org/10.5772/intechopen.81039*

is negative to the societies.

the cultural games explored.

**mathematics**

Socio-economic variable has rooted itself in the centre to obstruct or allow quality mathematics experiences. Internationally, research has revealed how the socio-economic variable plays a significant role in the provision of quality

#### *Black Students' Rich Mathematical Experiences: Mathematics Concepts and Xhosa Cultural… DOI: http://dx.doi.org/10.5772/intechopen.81039*

mathematics instruction. Lack of resources generally indicates economic exclusion. This economic exclusion begins from home where parents are sometimes jobless or earn below poverty levels. Ref. [24] states that this variable is a cruel unjust variable. Lack of resources for learning influences the quality of mathematics instruction negatively [25–27]. In addition, [28] reveal that quality educators highly influence mathematics learning of students from low socio-economic homes. This finding argues for quality human resources to be provided to all students for mathematical experiences that are successful. Refs. [29, 30] describe quality mathematics teachers as teachers with excellent content knowledge of mathematics, who have insight into mathematics progression and who are able to develop self-regulation in students.

The best performing countries in the world make sure that they choose the best performing graduates to join teaching [31]. This also means that these teachers will earn equally with their colleagues in other fields. Countries that perform poorly do the opposite. If providing students with high-quality education has the gains, research has already been proven. Why do systems continue treating education as a "Cinderella" of the systems? Economies need engineers, scientists, innovators and inventors who will produce those high-skilled citizens if the teacher in the classroom is not a high performer him- or herself. Educational systems need to be reflective and truthful to themselves if growth is the agenda of their missions. Otherwise, the current practices look like they are planned and have a purpose that is negative to the societies.
