Guide Mathematics in Western Culture

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  1. Item Preview
  2. Expertise. Insights. Illumination.
  3. Mathematics in Western Culture, First Edition
  4. Mathematics in Western Culture by Morris Kline - AbeBooks

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. Therefore, this racial exclusion demands more research to be conducted. By doing this it is encouraging more exploration of cultural artefacts and practices that influence mathematical growth and thinking. 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. 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.

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 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. Lack of resources for learning influences the quality of mathematics instruction negatively [ 25 , 26 , 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. 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.

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.

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.


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It develops ownership of mathematical knowledge and allows for more creation and activity. 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.

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While doing so it also presents the mathematics embedded in the cultural games explored. 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 to be assessed and evaluated. Some games allow for developmental levels and that needs to be integrated in the games played in the classroom.

Eastern Vs Western Culture Differences

Games develop interest and pleasure to students something that lacks in current classrooms. This chapter contributes in bringing fourth cultural games into the learning and teaching of mathematical concepts in the classroom and proposes that researchers use these games in their interventions. Therefore, the data was collected and analysed qualitatively. 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. 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. 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.

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. The advantage for the researcher is that some of the parents knew her as she grew in the same township. 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.

Expertise. Insights. Illumination.

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. 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 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. The game starts at the beginning in ones until stones are finished. Then the second round will be in twos led by the winner, then threes, fours, until tens. The winner is always the one with many stones during counting time when stones are finished: The player throws the spherical stone vertically while moving stones out of the circle fast and catch the stone on its way back.

The next step is to throw the stone again vertically while pushing back to the circle, the stones leaving only one outside the circle. A good player might play until all the stones are finished. Then they will move to the next round of playing in twos repeating the procedure. To move to the next round, all players should have at least managed to collect ten stones not less.

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Mathematics in Western Culture, First Edition

If less, you still stay in the previous round of collecting ones, while others move to collecting twos. The game develops the following: Object counting—one to one correspondence. Subitising is nurtured automatically as the player needs to spot groups of numbers before selecting with the hand. It is a good game for developing the following skills: Eye and hand coordination. Black Toti is a children game played in South Africa; its popularity to other African countries is not known.

Mathematics in Western Culture by Morris Kline - AbeBooks

A square is drawn with a small chord in each right angle of the square. Tins of different sizes are collected and put on top of each other so that they balance at the centre of the square to form a pyramid. There is also a ball to play with. It is important to note that the tennis ball is not a favourable one for this game as it runs too far. Most children prefer the plastic ball for this game, or they create their own with plastic bags.

In some cases, they use the tennis ball. One player must have a ball and stand along the border of the square and hit the cans with the ball. The runner has to count to 24 before the tins are balanced; if not, they lose the game; if they finish 24, the game is over, and they have a point as a team.