**4.1 Context**

Six primary schools in the Eastern Cape of South Africa were visited during playtime. Two of them were rural schools and four were township schools. All six schools provide education to black students from low socio-economic backgrounds; in the South African language, they are quintile 1 schools, fully funded by the government. Grade R/Reception year students' informal play during playtime was observed and documented and some pictures taken. The researcher engaged with students sometimes playing with them to get clear understanding of the games and the rules and procedures of the games.

In addition, the researcher made visits to one of the townships where the schools are situated during weekends to observe children play and document their games with the aim of triangulating with games observed from schools following similar procedures to collect the data.

#### **4.2 Consent**

Parental consent in the township was negotiated differently through engaging with parents and asking for voluntary participation of their children. This forced the researcher to only observe children from one street as in the possible second street, some parents were unavailable for consent. The children were made aware that the researcher is interested to learn their games and negotiated with them and got their ascent. The agreement was that children should play games they wish to play and be free. It was emphasized that when they lose interest in playing, they should feel free to stop playing anytime.

### **4.3 Rapport**

Before the researcher could be able to collect data, she first needed to develop trust with the parents of the children by visiting the homes of 5- to 6-year-old children in the streets and talk to the parents about what she plans to learn from the children. The engagement with the parents who were mostly mothers made them to revisit their childhood games and compare them with what they see as children play. Issues of safety were also discussed. In a way the time the researcher was going to spend observing their children became the safest time. This made their children's cousins to join during the researcher's visits. The advantage for the researcher is that some of the parents knew her as she grew in the same township. Some parents trusted her when she introduced herself; as they always listen to a radio programme, the researcher leads in discussing about

**157**

**5. Findings**

**5.1 Upuca**

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

educational challenges in the South African Broadcasting Corporation (SABC)

This data was collected over a period of 6 weeks, each school visited three times a week during the 30 minutes break time. This consisted of 9 hours spent on schools and 6 hours spent on the street in the townships on weekends. In total 15 hours was

The data from schools and the township consisted of field notes, pictures and audio of students' discussions. The field notes were typed, while the audio was transcribed and typed; the pictures were saved for reference and presentation. For each setting the data was organized in the separate file for analysis. The researcher analysed each data teasing out the game, rules and procedures. Once the structure was there, the researcher teased out the mathematical activities that were observed from each game and listed them with observed skills. This data was analysed continuously after each observation to make sure that if there are challenges, the researcher is able to address them during the next visit. A structured analytical memo was developed for each game observed. All analytical memos were developed for each game from the school setting and also to the township setting. The data was then triangulated making confirmations and checking for differences if they were any. The differences were then discussed with the students during the visits for

confirmation and identifying if the setting influenced the differences.

mathematical contribution embedded in them.

After data collection, the structured analytical memos from school data were triangulated with the structured analytical memos from the township. This data was then shared with teachers to try the games and elicit all skills they observed and knowledge from the games. Their notes were then triangulated with the researcher's notes to write the final report. Students were frequently interviewed for clarity and consensus during triangulation time. It is important to share that due to the excitement of being observed, students went overboard to play many games; some were not experts at playing. This required the researcher to only focus on the games that students mastered in their age group and focus on analysing those; hence, only nine games were documented properly and analysed properly during this study. Also the purpose of this paper was to highlight the games that develop their mathematical knowledge and skills during early years. The other observed games had a lot of potential, but young children have to master them first before they could make the

The findings had nine games that were discovered when they were grouped according to skills and concepts they developed. In avoiding repetition only one game per group is presented especially the games that cover most skills in a group. Each game is presented with knowledge gains and skills it develops (**Figures 1**–**4**).

Upuca, the name of the game, is a traditional game among Xhosas as well other Africans in the Southern African countries with different names per culture. The

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

"Umhlobo Wenene" radio station.

**4.4 Duration**

**4.5 Analysis**

spent collecting data.

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

educational challenges in the South African Broadcasting Corporation (SABC) "Umhlobo Wenene" radio station.

#### **4.4 Duration**

*Early Childhood Education*

**4. Research design**

**4.1 Context**

**4.2 Consent**

**4.3 Rapport**

use these games in their interventions.

lected and analysed qualitatively.

the rules and procedures of the games.

should feel free to stop playing anytime.

procedures to collect the data.

to be assessed and evaluated. Some games allow for developmental levels and that needs to be integrated in the games played in the classroom. Games develop interest

This paper is a qualitative inquiry paper with a purpose to observe and gain insight on students' games inside and outside schools. Therefore, the data was col-

Six primary schools in the Eastern Cape of South Africa were visited during playtime. Two of them were rural schools and four were township schools. All six schools provide education to black students from low socio-economic backgrounds; in the South African language, they are quintile 1 schools, fully funded by the government. Grade R/Reception year students' informal play during playtime was observed and documented and some pictures taken. The researcher engaged with students sometimes playing with them to get clear understanding of the games and

In addition, the researcher made visits to one of the townships where the schools are situated during weekends to observe children play and document their games with the aim of triangulating with games observed from schools following similar

Parental consent in the township was negotiated differently through engaging with parents and asking for voluntary participation of their children. This forced the researcher to only observe children from one street as in the possible second street, some parents were unavailable for consent. The children were made aware that the researcher is interested to learn their games and negotiated with them and got their ascent. The agreement was that children should play games they wish to play and be free. It was emphasized that when they lose interest in playing, they

Before the researcher could be able to collect data, she first needed to develop trust with the parents of the children by visiting the homes of 5- to 6-year-old children in the streets and talk to the parents about what she plans to learn from the children. The engagement with the parents who were mostly mothers made them to revisit their childhood games and compare them with what they see as children play. Issues of safety were also discussed. In a way the time the researcher was going to spend observing their children became the safest time. This made their children's cousins to join during the researcher's visits. The advantage for the researcher is that some of the parents knew her as she grew in the same township. Some parents trusted her when she introduced herself; as they always listen to a radio programme, the researcher leads in discussing about

This chapter contributes in bringing fourth cultural games into the learning and teaching of mathematical concepts in the classroom and proposes that researchers

and pleasure to students something that lacks in current classrooms.

**156**

This data was collected over a period of 6 weeks, each school visited three times a week during the 30 minutes break time. This consisted of 9 hours spent on schools and 6 hours spent on the street in the townships on weekends. In total 15 hours was spent collecting data.

#### **4.5 Analysis**

The data from schools and the township consisted of field notes, pictures and audio of students' discussions. The field notes were typed, while the audio was transcribed and typed; the pictures were saved for reference and presentation. For each setting the data was organized in the separate file for analysis. The researcher analysed each data teasing out the game, rules and procedures. Once the structure was there, the researcher teased out the mathematical activities that were observed from each game and listed them with observed skills. This data was analysed continuously after each observation to make sure that if there are challenges, the researcher is able to address them during the next visit. A structured analytical memo was developed for each game observed. All analytical memos were developed for each game from the school setting and also to the township setting. The data was then triangulated making confirmations and checking for differences if they were any. The differences were then discussed with the students during the visits for confirmation and identifying if the setting influenced the differences.

After data collection, the structured analytical memos from school data were triangulated with the structured analytical memos from the township. This data was then shared with teachers to try the games and elicit all skills they observed and knowledge from the games. Their notes were then triangulated with the researcher's notes to write the final report. Students were frequently interviewed for clarity and consensus during triangulation time. It is important to share that due to the excitement of being observed, students went overboard to play many games; some were not experts at playing. This required the researcher to only focus on the games that students mastered in their age group and focus on analysing those; hence, only nine games were documented properly and analysed properly during this study. Also the purpose of this paper was to highlight the games that develop their mathematical knowledge and skills during early years. The other observed games had a lot of potential, but young children have to master them first before they could make the mathematical contribution embedded in them.

#### **5. Findings**

The findings had nine games that were discovered when they were grouped according to skills and concepts they developed. In avoiding repetition only one game per group is presented especially the games that cover most skills in a group. Each game is presented with knowledge gains and skills it develops (**Figures 1**–**4**).

#### **5.1 Upuca**

Upuca, the name of the game, is a traditional game among Xhosas as well other Africans in the Southern African countries with different names per culture. The

**Figure 1.** *Young children playing with stones and circles drawn on the floor.*

#### **Figure 2.** *Young children planing with tins and a ball.*

game uses small stones and can be played by a number of children taking turns; the smaller the group, the better. A circle is drawn on the ground where these stones are put in. The surface has to be smooth on the ground to be able to play. A player has to have one bigger stone, a spherical stone called "ingqanda" in his/her hand.
