thesis on mathematical knowledge of street children

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Selasa, 17 Mei 2016

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Chapter I

INTRODUCTION

Background of the Study

            Mathematics is the knowledge of numerical and calculating part of the human life. When we born then with us mathematical knowledge also grows up similar to our body growth. So, mathematical knowledge is rising to everyone through the initial phase not only to the children with parents at home but also to the street children who lives in the street. Thus everybody possesses the mathematical knowledge through the process of learning.

            Learning means it makes people to do smoothing and enriches our capacity to create something for ourselves. Learning is considered as a process of gaining skill to perceive the world where we live. Learning takes place from birth to death. Each and every child learns from the society through social contact with home family, learns to adapt with temperature provided by the environment and learns to keep mutual understanding with matter while in breasting feeding or in the form of eye contact to fulfill his/her needs. But are these actions learning or not? Is learner actually in the position of learning? Does she/he wants to learn or it occurred automatically? Is there any intention of the learner towards learning? There may be arriving several questions about learning. Sometimes that happens automatically cannot be counted as learning unless learner has any intention to do. If learner tries his/her actions towards the new goal then it is counted as learning.

            Before we go further, let us clear about the term, “street children”. Street children are those children who spend their daily bases life on the street i.e working, eating, sitting, and sleeping without the care from their parents. The knowledge of various branches of mathematics outcomes to street children’s according to their feels and needs. Man introduces great range of its application as well as street children too. Street children are also the part of our society, so they also need mathematics in their daily life. According to the Human Rights Watch (1999), clear about the term, “street children” as

“Children for whom the street, more than their family has become real home. It includes children who might not necessary be homeless or without families, but who live in situation, where, there is no protection, supervision or direction from responsible adults”.

 Similarly, according to UNICEF (2001),

“Street living children are children who may have lost their families through war or illness, or have been abandoned because they had become too much of a burden, or else ran away from their abusive, dysfunctional, poverty, stricken families and now live in the street. Moreover children from street families are children who live on the street with their local families”.

            The focus of this thesis is how street children manage their daily life by using mathematical knowledge? What kinds of knowledge do they have? How did they acquire this knowledge? Mostly, Street children are from the urban phenomenon. Street children do not have a family who is fully capable to caring for them. Hence, the social structures of the city have fully or partly replaced the families function. Nothing is greater than their family for the children.

            Society is the place where different families live in a portion of area. Street children are also the part of the society where they spent their daily bases life with their own members and gangs. It is reasonable to presume that there is a special relationship between street children and their place. Street children learn the knowledge in the society by coping through the elders as well as with their own ides over the mathematics.

            Situation becomes different when we refuse prevailing belief that knowledge is gained through formal education. Knowledge is transmitted not only through formal education but also through informal and non-formal education. Men first wanted to answer the questions how much? How many? How big?  The answers of these questions are obtained from some people after the invention of four binary operations. Mathematics is a language and basic tools of communication. Daily communication involves the frequent use of the mathematical concept and skills.

            Capital city Kathmandu has a large number of street children and young people that are street living, street working or having street family, where the street children communicate with the large number of people in Kathmandu simply to spend their daily life. Estimates put the number well over 1000 with 500 new street children arriving every year (CWIN) through figure have been hard to estimate because of frequent movement between cities. The reason behind the street children in Kathmandu are complex but includes witness to and victims of abuse home, exploitation and trafficking, the introducing of step families leading to a breakdown of relationship, single parents etc. Moreover it is no longer a secret that street children statistics.

            The report of the street children national convention held in October 1993, uses the term like “homeless”, “khate”(scavenger), “ uncared for”, “under privileged”, “sadak chhap”( street dwellers), “sadak balbalika” and kawadi ( scrappickers) to the street children. Above terms can be shown in the figure 1.1 clearly.

Source: CWIN website.

            On the other hand, the Government of the Nepal and international donors has made a commitment to children’s right to education through the framework of the education for all campaign. In particular steps have been made to promote universal access to free primary education to children. It is also recognized that many children are left behind. It was estimated that the net enrolment of children into primary education in 2011was 72 %(  CBS).

            With regard to children coming to the street, it is important to understand if this is influenced because they have never been enrolled in school or whether they have dropped out of education. It is important to understand why they have dropped out from formal education- is this a financial issue, an issue of school retention, or driven by others factors? In addition it is important to understand how much children are receiving education before coming to the street, have they received basic education, are they literate?

            Mathematics help us to solve the daily basis problem by birth to till death that’s why they have knowledge of mathematics either to share equally to each of them or to mix drugs to catch more relax by the ratio method of arithmetic mathematics. Many of the under privileged and abandoned street children come from several remote parts of the country and they ran away from their home due to domestics violence and poverty however their remains so many causes that brings children in the street. Rising of street children is burning problem in Nepal. Street children represent a phenomenon which appear to peoples feeling and awake their sympathy.

            In the question of why did they land on the road? CWIN has identified some of the reason that led a child to the street. According to this, most of the children left their house because they wanted to get rid to schooling instead of grazing cattle, assisting their parents in farm work, looking after sibling, collecting firewood and fodder. They dream of getting better ways of living in the cities on the contrary. They did not get any opportunities as they had expected prior to be in the street and these situations ultimately have made them to live in the street. Given picture speaks clearly.

 Learning mathematics makes to do smooth things and enriches our capacity to create something for ourselves. Learning is considered as a process of gaining skill to perceive the world where we live. Learning takes place from birth to death. Every child learns from their society through social contact with family. Learning is the social process. Vygotsky emphasis to reflect on their own thing about process, as a result they shift to be a higher level of cognitive activities in which children think about new symbolized, ideas and controlling the symbolic system of their culture. Street children are one example about this.

            The fact of this research thesis is related to how the street children manage their daily life. Nowadays re- habilitation center is increasing rapidly to care and establish new life style of street children. One of the most powerful knowledge with mathematics makes their life successful. This research chasten those dangerous shortcuts and enable their children to find the people back in their society which they deserved, obtain endowed with remarkable intelligent and a potential which only asked to be developed. In this thesis the researcher is in the periphery over the mathematical knowledge acquiring process of street children.

            The rationale behind focusing those children who live in the street , sleep in the street, eat in the street, wander in to the street and have special relation with street in many respect, have neither contact with their families nor have adequate information about their families. Their entire lived depend on the street and they have been able to survive with their own ideas, struggle their special job to survive on the street, is to collect scarp, selling water, selling chocolates, working as vehicle helper, selling news papers, begging on the street, pick pocketing etc. In order to buy foods, with their own calculation and own mathematical knowledge without any support of public and private institution is really interesting. Thus the study of learning mathematical knowledge about such children has inspired to researcher a lot.

Statement of the Problem

            Children are the formative stage of human development. We can hope all the children are the vital role player for tomorrow. If the children are treated properly at least under the provision of fundamental rights of the child, children are the future of the nation, twinkle star for the nation, builder of the nation, so, exploitation of the children is an affront to every standard of decency professed by civilized society.

            Mathematics is an essential for the human beings but the learning process of mathematics may be different. All children do not get formal education in the same way from different reasons. Street children who have similar characteristics of other children. Street children gain mathematical knowledge naturally according to their practice. The statement, children who have not been school, do not have mathematical knowledge is not true.

            This is the reason why the researcher took up a research project with the following research questions.

·         What mathematical knowledge do the street children possess?

·         How do they use four fundamental operations in their life?

·         How do they learn these four fundamental operations?

Significance of the Study               

            Children are an integral part of every family and community. In the absence of children, the existence of a complex society is unimaginable. So children are, “backbone of the state”, “pillar of the nation” and “rising of the sun”. Mathematics is used to solve daily life problems as well as in the field of advanced science and industry. Most of the street children refer to survive them after the short period counseling of re-habilitation center in the post of labour. So it will be better to use their mathematical knowledge in advanced industry with appropriate job, in spite of this knowledge they are neglected and abused in every step of their life. This study may helpful to decrease their oppression, discrimination and to be avoided from their family society.

            This study would be fruitful to a policy maker for the street children for the following aspects.

·         To provide a database relating to street children about their present knowledge of mathematics.

·         To make appropriate application of mathematical knowledge for the street children.

·         To make a curriculum for the non formal education.

            In the present situation, great agenda is, “rising street children”. This research mare applicable for NGO, INGO as well as UNICEF for the following points.

·         To reduce the number of street children all over the Nepal.

·         To give a suitable work according to their mathematical skills.

·         To increase their confidence level towards the mathematical knowledge.

            Also, “education for all” is the rising slogan of the today’s world and the International Commission for Mathematical Education has emerged the agenda, “mathematics for all” with education for all. So the present study would help in the achievement goal of, “Mathematical for all” as proposed by ICME.

Objectives of the Study

            The main objective of this study is to find how and with whom street children learn mathematics. Major focus of this study is to find out how street children use mathematical knowledge in daily bases life, how do street children learn mathematics with which source. For this intention this study is intended to accomplish the following objectives.

·         To identify the basic mathematical concepts of street children.

·         To investigate the process and sources of construction of these basic mathematical concepts by street children.

Delimitation of the Study

            In our country Nepal, there are nearly 30,000 street children (media). It has been in the increasing phase per day. Kathmandu is the capital city where 40% of total street children can be found. The nature and working style of street children are different in different places. Out of valley, the street children are really survived difficulty rather than the street children of valley. Among all the street children the researcher had used as below.

1.      Only seven street children had been selected over the Kalanki and New buspark.

2.      Researcher met personally six street children from the Kalanki camping which is located in Lubhu in Latitpur district, 18k.m far from the Ratnapark of Kathmandu. Only one guys had taken from new bus park who works as kulli there.

3.      Among the seven street children researcher had chosen them according to their working categories as well as their ages.

4.      Researcher had on the periphery of basic mathematical knowledge of selected street children. 

            Since this study is confined to mathematical knowledge of street children of Kalanki camping. So, result may not be generalized for all street children of Nepal, due to nature of street children. Researcher selected only seven street children, for this case study. Thus result may not cover all street children.

Operational Definition

Street children: In this research the researcher has used street children which mean those children who are not getting care from their parent and stay at the road, eat in the road as well as sleep in the road. They haven’t any more homes to stay and have the gang and family of similar children.

Rehabilitation centre: The researcher has used the term rehabilitation center to indicate the place where the street children are keeping changing their modality. In this research the name of rehabilitation center is the voice of children which is in Lubhu.

Knowledge: Information or awareness gained through experience or elders.

Children: The researcher has taken baby less than 16 years to represent the children either male or female.

Four fundamental operations: In this research the researcher used the term four fundamental operation to represent the simple mathematics operation like addition, subtraction, multiplication, and division.

Basic mathematics: The researcher has used the term basic mathematics to represent the general knowledge of which we usually do in our daily bases life i.e add, subtract, multiply, divide.

Chapter II

REVIEW OF THE RELATED LITERATURE

            The review of related literature deals with the theories of research studies which have been conducted earlier. It helps to conduct the new research in systematic manner by providing the outline of the research study and avoid the unnecessary duplication.

            In this chapter different item of literature relevant to the street children reviewed in order to know about their learning, sources of mathematics as well as other learning strategies.

Empirical literature

            CWIN (1990) did a survey research on street children of Kathmandu which is based on a survey of street children of Kathmandu, whose number is estimated at about 500. In 1990, one fifth of these children were personally interviewed and asked about their personal history, current status, income, origin etc. It was found that the children were three types, runaway children, squatter children and orphan children. Most of those children were engaged in rag picking, pottering, and begging. They suffered from different illness. They did not have access to school because they were in different about their future; they were not including in any gambling, smoking and pick pocketing but were also sometimes addicted to drinking and drugs. The study concludes that if love and care is given to these children could help them to bring back to the normal life. Although, the report aimed to describes the current problems faced by street children of Kathmandu, and it proposed same recommendations for the protection, prevention of street children and rehabilitation of those children, any objective of this study does not match with the objective of my research.

            Child Welfare Society (CWS 1996) did a country wide situational analysis of street children with the support from UNICEF, Nepal. The research report has been undertaken by taking samples from different five developmental regions mainly from 13 cities. The finding showed that it has covered the whole areas related to street children such as their gender, age group, ethnicity, reasons to leave their home, their business for the living their networks with adults and peers for support and access for their education based on interviews. The study was conducted to find out the magnitude of the problem and the location of the street children to understand how street children cope with the street life. Similarly, the study was undertaken with the view point of employing how certain factors affect by the local organization, INGOs studying the relation between wider socio-cultural, political and economic contexts both rural and urban the phenomenon of street living.

            The research has applied many methods such as questionnaires, interviews, case study, group discussion, particularly observation and visits to children home for the data collection.

            The research terms also have used some theoretical perspective to discuss the issues. The theoretical aspects they have related in their research are transformation on childhood and how children have been increasingly differentiation from adults. Among the important finding of this research the street children in Pokhara were working and going to school. This research intended to find socio- culture context of street children with is quite different than this research.

CWIN (1998) explored the current situation of street children’s in Nepal. It explains about the factors that contribute to the presence of children in street. It also mentions some sorts of general survival tricks such as begging, pottering and collecting recyclable helps from dumpsters of the street corner. The study has made some attempt to explain the psycho social aspect of street lives. In the aspect, it tries to find the sentiments of street children in terms of dealing.

            How do street children learn in relation to their survival? K.C (2001) did a research in the street children of Kathmandu valley focusing on learning for their survival. His main objective was to investigation how the street children learned. The study was conducted on the five street children living in the street of Kathmandu valley. He applied case study method to investigate their learning strategies. The finding of the investigation suggests that the street children have learned many things to live in the street which we learn mostly from experience, situation and some incident, since they landed in the street. Their actual methods of learning included trial and error, observation, advice from adults and imitation.

            Through this investigation is related to the general learning, it is very helpful for my research, it helps me in learning mathematical strategies.

            Pradhan (2003) did a study for her M.phil entitled “construction of knowledge in the early year Nepalese children’s learning”. Her main target was to explore the fact that how the Nepali children construct their knowledge about the world and learn from their construction? What is their construction about their world? In other word her purpose was to investigate the child construction of knowledge in social context and their learning process.

            She had taken three children including a girl to understand their construction of knowledge. These respondents belonged to the semi-urban area. The study found that children construction of knowledge mostly depends upon their communication with parents and their own qualities and the socio- cultural environment. A single construction theory was not found able to describe children construction of knowledge; in fact, it was a combination of different theories that could best describe early childhood development children construction of knowledge.

            Learning strategies of mathematical concept of out of school children
(Poudel 2005), did a research on mathematical concept of out of school children by asking how do out of school children learn? And what type of mathematical concept do the out of school children learn? This study was conducted in Tanahu district by using case study method. His finding was they learn with their work and the help of the non formal education through adults.

            The street children of Kathmandu valley approaches and comments on the daily life of street based children of the Nepalese capital ( CPCS April 2007). This book is based on daily life of the street based children in Nepalese capital. The main objectives of this book are clarifying the life situation of street children. This book is helpful for new elements suggestion this will prove useful not only NGO but also the public to understand the current situation of street children.

Theoretical literature

            This chapter deals the theoretical discussion which is needed for the interaction of the finding of the study. Many theories have been developed about the children learning and development, some are cognitive, some are behaviorist, and some are humanist while the next is social learning theory and so on. In my research I have used Vygotsky theory.

            Vygotsky has developed “socio-culture theory” and believe that children are active seekers of knowledge. In this theory knowledge is being constructed in social situation of negotiation, rather than being the reflection of the object reality. This theory stresses the interaction between developing people and the culture in which they live.

            Socio culture theory grew from the work of seminal psychologist Lev. Vygotsky who believes that parents, caregivers, peers, and the culture at large were responsible for the development of higher order functions.

            According to the Vygotsky “Every function in the child’s cultural development appears twice; first, on the social level and later on the individual level; first between the people ( inter psychological) and then inside the child (intra psychological). Vygotsky’s socio cultural theory of human learning describes learning as a social process and the origination of human intelligence in society and culture. Vygotsky believed everything is learned on two levels. First, through interaction with others, and then integrated in to the individuals mental structure (Vygotsky 1978).

            The implications of Vygotsky theory are that learners should be provided with socially rich environment in which to explore knowledge domains with their fellow students, teacher and outside experts. Vygotsky argues that the child’s development cannot be understood by studying, it needs to examine in the external world. Children are socially associated which is present right from the beginning arriving in to the complex world of the social relationship and culture. The culture itself has historical development. In my research the socio-culture theory is fitted to observe the how the street children gain the knowledge. Street children could not get the formal class to gain the knowledge; they get the knowledge through social interaction and environment of their street family as scaffolding. Vygotsky has focused of scaffolding to gain knowledge,         Scaffolding refers to the particular kind of help, assistance and support that enables a child to do a task which brings them closer to a state of competence that will enable them to carry out other similar tasks independently in the future ( Maybin, Mercer, Stierer, 1992). Children can catch the knowledge through the elders, culture especially from the game which they used to play.

            True to saying that everything new is the “well-forgotten old”, the answer to today’s challenges comes from the past-from theories of play developed in the last century by Vygotsky. These theories along with the work done by students of Vygotsky are the foundation of the approach to scaffolding play. In Vygotsky’s view (1977) make belief play reaches its highest level of development in the preschool and the kindergarten years. However, this fully developed or mature from of play does not emerge overnight.

            Children gain knowledge, where they born, which culture they follow and which society and environment they get, peer group, adults to make believe to lead development forward so this theory is fit my research according to socio-culture theory of Vygotsky.

            Also, Vygotsky defines it as private speech, which is self directed speech that children used to guide their thinking and behavior. It is as the foundation of all higher cognitive processes including controlled attention deliberate memorization and recall, categorization, planning, problem solving, abstract reasoning and self reflection. Through joint activities with more mature members of society, children come to master activities and think in ways that have meaning in their culture.

            Inter subjectivity creates a common ground for communication as each partner adjust to the perspective of the other. Adults try to promote it when they translate their own insights in ways that are within the child’s grasp. Vygotskian’s theory a range of tasks about the child cannot at handle alone but can do with the help of more skilled partners. It is as the difference between the child’s capacities to solve problems on his own capacity to love them with assistance.

            The above theoretical discussion reveals the psychological perspective and describes about the inside of the individual. This theory gives account about to learn from society, peer groups, and adults and to make belief to lead development forward. And, in the similar manner other concepts/ theories from Vygotsky’s social culture and scaffolding are useful to generalize the human behavior about their mathematical concepts. The researcher has drawn the idea from Vygotsky’s social cultural theory and scaffolding to support his understanding to how the street children learn mathematical concepts and what they learnt.

Conceptual Understanding of the Study

The conceptual understanding is established on the basis of research topics. Possible areas to fulfill the objective and theoretical framework. The main target of the study to identify the mathematical situation on camping of street children and analyze how they learn to solve their daily life problem related to mathematics with four binary operation.

Knowledge is the information or awareness gained through experience or education. When the researcher was on the field of camping, where street children are kept, the researcher generalized the knowledge gain by street children through daily works, calling passenger into micro van, they learnt some knowledge through passenger as well. Some of the street children sold mineral water in the street previously. They learnt 5,15,20 from the shopkeeper. Most important thing is that they obey the elders of their gang, and follow by well known person of their gang which is known as scaffolding and socio culture environment.

            These above mentioned a framework was drawn with the help of previous literature review, which is mentioned earlier as empirical literature. When the researcher read empirical literature then the finding becomes as daily work, helping from the shopkeeper, non formal education and scaffolding for knowledge gaining process of street children. When the researcher went to the real field he got these are the most powerful points to learn mathematics for the street children, in details it is described in chapter IV.

Chapter III

RESEARCH METHOD AND PROCEDUR

            This chapter comprises design of study, selection of case respondent, sampling process, data collection tools, data collection procedure and data analysis interpretation process. This is a case study so the researcher followed qualitative method. Qualitative research is a form of inquiry that explores phenomena in their natural setting and uses multi methods to interpret understand explain and bring meaning to them.

            Qualitative research involves the studies and collection of a variety of empirical materials- case study, personal experience, life history, interview, observation, historical interactional and visual texts- that describe routine and problematic moment and meaning in individual’s lives are its tools for data collection.

            Since the qualitative research is about person’s life, stories and behavior, it is a non mathematical analytical procedure. The basis meanings of gathering data are observation and interviews including the field notes, documents, books, tape records, diaries and so on.

            The researcher is intended to study and explore the learning mathematical concepts of street children, so observation and interview were used to search process of learning mathematics.

Research Design

            The design of this research is case study among street children in Kalanki camping. This research is qualitative research as well as descriptive in nature.

Selection of the Case Respondents

            This research is qualitative research so the researcher had taken 7 street children for the case study. Without help of any NGOs, INGOs, researcher visited many places lonely to get contact of the street children but researcher had to entangle with many difficulties to get touch of them. They thought researcher as a rich man. As the time passed they become familiar with me. Luckily researcher got contact with camping – the voice of children – located in Kalanki but yet in  Lubhu. Researcher got such children doing many activities. Everything was available there – eating, living and studying if they desired. Researcher did not have any problem to find these children after getting contact and information about the camping where he could get different categories of the children.

            These 7 street children were the case respondent for the research because the researcher want to observe the mathematical knowledge and leaning process, for this purpose the researcher took 7 street children. Mostly street children behaved similar to the others peers, so the researcher decide to check the background of their which is found in the case study report in the rehabilitation centre. Thus the researcher took them by observing their economic condition, parents love toward them, factor to compel street child, work, age and education they obtained.

            Thus , the researcher chosen 7 street children from the rehabilitation centre of Kalanki camping simply to select them, researcher collected total children of Kalanki camping and then the researcher list out by identifying each member of Kalanki camping, then again selected them by lottery method, when the researcher categorized them according to their work, age group, economic condition, parents love, factor to compel street children and education background the researcher selected 7 street children with the help of lottery method.

Data Collection Tools

            To collect the data for the case study the researcher used the following tools.

Observation note

            The data from observation consists of detailed description of the people activities, behavior, action and personal experience. K.C (2001) wrote the direct observation has the advantages of putting researcher into first hand contact with reality it is usually possible to observe only a small individuals of groups. Researcher observed their individual experience and behavior during the working time, Playing with peers, interacting with elders and each moment where the possibility to know their mathematical behavior. Thus in this research researcher has studied the secret facts of street children about their ways of learning mathematical procedures. For this researcher had followed participatory observation

Interview schedule

            The interview consists of question to the children about their experiences, opinion, feeling and knowledge. It also helps to understand participation perception or relation, views and ideas towards certain subject matters situation, context and phenomena by her/ his facial expression. So, at first researcher had taken informal conversation interview them used a set of open ended question to the street children of kalanki camping.

Ethical Consideration

            Ethical issues are present in any kind of research. The research process creates tension between aims of research to make generalization for the goods of others, and the rights of participants to maintain privacy. Ethical consideration makes the respondents privacy, in any harm, psychological, financial, social, where the researcher interviewed and observed personally but announce the result by nick name. Here the researcher also indicated  respondents through nick name as A,B,C,D,E,F, and G to the street children of Kalanki camping.

Data Collection Procedure

            For the data collection procedure the researcher collected data by visited first, the selected area. Then researcher contacted director of camping to help the researcher. In this research the researcher observed the daily bases activities of street children which were selected. In the phase of observation the researcher observed the selected street children activities, actions, behavior, interpersonal interaction and human experience. Then, noted in the notebook for the future use. Again the researcher took interview by asking open ended question towards street children with direct question about their experience, opinion, feeling and knowledge of mathematics.

Data Analysis Procedure

            This is qualitative research, hence the major part of data analysis based on descriptive analysis. Qualitative research about personal life lives, experiences, behavior emotions, feelings, social movement as well as cultural phenomena and interaction between the nations. In this research data, information was collected with the help of interview schedule and observation form. Then categorized according to the category of the respondents responses, coding them with mutual response, meaning making, and attaching with theory  and cross match over all views and adapts to the credibility, transferability, dependability and conformability of the result of this study.

Chapter IV

ANALYSIS AND INTERPRETATION OF DATA

            This is a case study related to street children who used to live in the street. The objectives of this study are; to identify the basic mathematical concepts of street children, and to investigate the process and sources of construction of these mathematical concepts by street children.

            Over all there are a lots of street children in Nepal, among them the researcher selected only seven street children of Kanlaki, with different prospective. This research is limited into the city’s environment which cannot generalize all over the Nepal, due to their life style and sources of gaining knowledge of the city. The researcher collected the name of total street children of Kalanki camping and list out by identifying each member of camping then selected them on the basis of their work, caste, and occupation. For this research the researcher used the observation note and interview schedule to collect the data. For the data collection the researcher visited the street children of Kalanki camping regularly 30 days, to adapt their opinion and behavior, learning sources towards the mathematical knowledge. For the data analysis the researcher categorized the respondence response, coding them with mutual response, meaning making, and attaching with theory to interpret the data. The data were analyzed and interpreted for the following issues under different headings.

·         Basic mathematical concepts of street children which refers to the concept of addition, subtraction, multiplication, and division operation used by them in their daily life.

·         Process of construction of basic mathematical concepts by street children which is defined as the learning process of such mathematical concepts of them without formal school education system of Nepal.

            So far, the researcher has not explained the case respondent’s background in details. Thus, in the following paragraph, they are introduced in terms of their socio economic and cultural background in the society and how they join in the Kalanki campaign. Some street children whom the researcher observed and interviewed are associated with a shelter and thus they were from different cultural background that were leading their lives, and learning mathematics in different ways according to the context. In this regard, the researcher had tried to discuss their individual’s stories obtained. After the observation and discussion with them, the researcher found that they have learnt mathematics by different things and their ways of learning have both similarities and dissimilarities in many respects. The researcher briefly tried to discuss their individual stories by using the information that was provided to researcher by these children as below.

            Respondent A of this research was a Chamar. The caste Chamar has considered a so-called untouchable caste in our society. This is not really true in recent days, a disadvantaged caste of Nepal, and living all over the country. No written document was found where they are originated from but they are doing the same profession as “Lohar” who used to sharper the knife and other cutting metallic equipments. From the ancient period and some of them are engaged in farming. Chamar is dominated by other so-called higher caste in the society but they are trying to uplift themselves from the various suppressions of the society. They are living in close contact with Brahmans and Chhetri and, following the similar traditions and customs. They were more alcoholic previously now changing their habit. As their main occupation is – Lohar, their child also learn the skill from the very young age. Their parents teach them by giving smaller job like making different shapes as half circle, circle of this iron. When children get free time to play with hot iron then they made such circle simply to play the games by knowing that the circle moves in the road with the help of sticks. Children learn these skill by observing the players of this moving games and with the help of parents.

            Respondent A was born in Sarlahi district, And Living in Kalanki camping till now. He has two brother and two sisters. His father work in farm field near to his village and mother works as housewife. He is the elder son of his parents. Due to the poor economic condition his parents has small house with four Aana field. He had interested to study in school. However, the poor economic condition of his parents, he moved to Kathmandu to do something, that’s why he works in Boutique centre. He earns Rs 100 per day when he moved to work; one of the secret things is that; he is here due to pay Rs 18,000 loan of his parents. He has a little bit knowledge of mathematics. He calculates with his own ideas. The researcher described his calculation method in details after the short history of selected street children.

            A Second respondent named B was Pariyar. Let’s moved to the caste Pariyar- is also one of so-called untouchable and disadvantage caste of Nepal. The profession of the Pariyar is especially- tailoring- from the ancient period. They are also alcoholic earlier, now they changed their habit, slowly begun to joint their children at school, some are found in government office and teaching profession. The government and other project are lunched their programs to uplift Pariyar as well as other disadvantaged group. Pariyar are famous to play drums in the social and religious ceremonies such as marriage, naming and other religious rituals.  Pariyar, whom the researcher has taken for the research purpose, does not have idea to play such instrument and sewing skill too. He was born in 2060 BS in Haripurba, 9 chamar tol, Sunsari. His father works in Panjab. His mother also engage in house work, similar as others, who dead after the birth of four children in 2067 BS. After the death of his mother, his father got married with other woman, that’s the reason he got of step mother. Pariyar is a healthy boy. His brother is engaged to sell “ pani puri”. His parents have only two Aana field in village area. They lived in hut. Due to the domestic violence he moved to Kathmandu by truck in the mid night, and then he joined with street children in Balkhu. He told to the researcher that he did not get any food till 6 pm in Balkhu of his first day of Kathmandu, and then he was lying in the street and drunk the water near to small café, and beg maize near to maize seller and got a relief. Then he started his own business, by collecting the leaf of Gaja near to the river and then made it dry to the purpose of smoke and sold it the people with a cheapest price. With this job he collected a little bit money only for survive, and got the knowledge of calculation.

            In this research two respondents are from Magar community. Respondents C and D both are Magar, The caste Magar is one of the oldest tribe of Nepal. And Magar’s are scattering  across the length of the country and also some part of India. The habitant of these people is the Terai region, where the hills commence and the small lower hills of the Mahabharat lekh, and some places in the high altitude mountainous area. The Magar tribe has been divided into basically seven sub castes: Thapa, Aale, Rana, Budhathoki, Roka, Gharti, Puri but here some differences must be made. Magar are mainly dependent on agriculture, in addition to agriculture they are found keeping goats and sheep’s. Magar people have their own language and they live in joint families. Respondent C , whom the researcher had selected for his study, only had idea about his caste Thapa Magar.

            First, Thapa Magar is 14 years old young child. His hometown is Bhairahawa, Rupandehi district. He has one brother who lives in Butwal. But he moved to Kathmandu due to loneliness in home. His father sells woods, to earn some money by bringing from the jungle and his mother work as caregiver ( dhai aama) for the other family.

            First, Magar moved in Kathmandu by stolen 1000 rupees from his father pocket along with bicycle, and he sold this bicycle in Rs 500  in Chitwan. And then he took a truck to come in city Kathmandu. When he arrived in Kathmandu he started to work in hotel as a dish washer, after some days he moved to street to rubbish the bicycle, t- shirt, helmet etc and sold it in the cheapest price. Not only this bur also he started to collect the rag in the street, by selling the goods he learns a little bit knowledge over the mathematics.

            Respondent D was second street children of Magar community. He is 13 years old. He read in class one. His father and mother works together in Hatbazzar by selling  drum stick “Neuro saag”, which is known as vegetable in Nepali. When he was in school he learnt 1,2,3 up to 100. He can say but cannot write even a single word “one”. Previously he worked in Palpa purano Buspark as a vehicle washer by leaving his study. His parents has small house in Batase dada in Palpa. One day he planned to go Butwal simply to visit with well known bus driver. When he reached in Butwal he ran away from their near to old market (purano tarkari bazzar), in Butwal where he felt too cold. Near to him someone is taking about sunsine in Kathmandu  (Kathmandu ma gham lagechha). Then he planned to go Kathmandu and moved from there and came into Ratrapark. After finishing his money, he got an idea to sell the water bottle in street and asked some money in street and started his job by selling water in the street. He can recognize only the money not the numbers written in the money.

            The fifth respondent  named E was Khadka from Dolakha. Especially Khadka is known as a Chhetri. They could be found in all over the Nepal. Some of them are settling  in the city area. After the retirement from the military service and foreign country job, most of them depend on agriculture. In addition they are in security forces of different countries like India, Britain, and Singapore as well as in Nepal.

            Most of the Khadka family is interested in security force. So male of these family are encouraged to make their body physically fit rather than education. Girl child is taught for household activities, to make woolen clothes. They learnt such skills by observing their parent. Respondent E’s father and mother live in jadibuti in Bhaktapur. They work in street as a grocery (nanglo pasal). He is a single child of his parents, even he is single and cannot get care from parents due to economic condition.

            The Khadka, whom the researcher selected in his study, does not have idea about his culture and other ethnicity. Just he was found him in the street that’s why he is well known about the street life. He has great ides to pick pocketing, when he saw a crowded of people, he used to run there for pick pocketing. One day he was catched and got a big slap then he left this job and moved to new buspark with one of the elder to do work as kulli and started to work in new buspark as a kulli to earn money not only this but also he started to take the drug ( den gum). With his work experience he got the knowledge of weight and distance of mathematics.

            Respondent F was Lama, One of the so-called supreme castes of Gurungs. They have their own language and their physical structure is like mongoloid nature. The majority of lamas are in close contact with Brahmins and Chhetri.

            Respondent F was 16 years old, with heavy body structure. He didn’t know about his father and mother and can’t say that where he was born. When he knows himself, he was in the street in Kalanki. Due to his heavy body structure, other street children obey the rules of him He was the boss of his gang and all the children gave him money for buy drug   and collect the  money from other street children and he calculate his own way to share equally, when he did mistake to share then he learn from other street children. In this way he was well known about the money up to hundred and then he planned to work himself in vehicle helper (khalasi) in micro bus.

            Respondent G was Gautam, known as Brahmins, and they scatted all over the Nepal with highest population. Brahmins are very forward in the society. They mostly engaged in farming and government job. They are so- called worshipping class in our society. Since Brahmins are known as so-called preserver and conserver of Hindu religion, and they have followed this religion and worship Shiva, Vishnu, Ram, Krishna and thousands of other deities of the Hindu pantheon.

            Respondent G is 8 years old. He only knows about his parents, when he was 6 years old in Bhanjyan. He left his parents in crowed of fair (mela) in Bhanjyan. Then he took the way to go to his home, but that way was wrong and he became to Dharke in the evening. He thought to beg the food in hotel and said his name to the hotel owner. Due to Brahmins caste, he got food by believing hotel owner Brahmins are god and our priest and also got some coins.

            Respondent G was a Brahmin, and then he got food and money from the hotel owner. when he reached in Kathmandu after the long time on foot he felt tired and slept in the street without taking food, then next day he started to collect the money by begging the people who walk in the footpath. Later on, he joined to rag collecting and so on. Children learn these things by imitating and practicing with their senior members.

            Communicating with these seven street children, the researcher was inspired a lot. Being the street children is really heart touchable things. No one wants to spend such a tragic life, but there is no any other way to survive in this challenging world. These seven street children are become in the street, not by their own interest. The similarities among these street children are; all the street children have the problem of economic, their parents are not so rich that’s the reason they can’t fulfill their children’s interest as well as care too and Parents thought themselves to survive. In this critical situation they haven’t any other way to full fill their duties towards their children. All the street children started their own job while they are in the street and all these respondents live in the street in the night.

            On the other hand, dissimilarities of these seven street children are; they are from different society and castes. And all of them are not educated from the school because when the researcher gave them some mathematical problem related to count, add, subtract they weren’t able to solve and they were even don’t know that what is school means? Only one child got chance to read in grade one. These seven street children are from places as the result their acquiring process of knowledge is also different, some of them learns from elders, some of them from school and remaining of them are from shopkeeper as well as from the society where they lives.

            The above discussion of personal stories of each respondent shows that they were from different parts of Nepal with cultural background. Moreover, they have some mathematical knowledge learned from society when interaction with elder members of society and friends of peers groups, in our so-called caste system found in our society has dominated to deprived people which compels children to be street children.

            This research is encompassed with in basic mathematical knowledge of street children and how they learnt / construct basic mathematical knowledge even in street without formal education of school. These issues are thus analyzed and interpreted under the different heading and follows:

·         Concept of addition and it’s learning process.

·          Concept of subtraction and it’s learning process.

·          Concept of multiplication and it’s learning process.

·          Concept of division and it’s learning process.

Concept of Addition and it’s Learning Process

            During the discussion and interaction with the street children and information provided by them, the researcher came here to describe the concept of addition , in short term it is known as “ add”, which is familiar word for all and most necessary concept for the human life, which gives the meaning of “ to joint so as increase”. In this research most of street children were familiar to the addition, for this, respondent A and respondent B said addition means “thetotal number”. Whereas the third respondent said “all” and the other respondent argue the meaning “the total number”. But the seventh respondent of this research said the term addition means “to joint so as to increase”. The concept toward the addition of street children gave the actual meaning which is familiar to all over the world in the subject of mathematics. These above mentioned replied were the similar to the concept of addition which we read in our classes of formal school. The total number means the all together with the sum of given calculation. In the calculation toward addition the street children were more familiar than the researcher expected. The respondents of this research said meaningful meaning of addition as to join so as increase. These concepts were more capable to share in the school children whom we teach in the real classroom teaching. Previously they were engage in any kinds of work like as dish washer, rag picking, and play to join the different parts of the poster of hero which was attached in the wall. This poster they used over the body to protect from cold in the winter, thus the mentioned concepts were learnt by their daily bases life in the street. For this concept Vygotsky said that the child cannot handle alone but to accomplish with the help of adults and more skilled peers. As children engage in co-operative dialogs with more mature partners, they take the language of these dialogue make it part of their private speech and use this speech organize their independent efforts in the same way.

            For the concept of addition they also learnt by their elders, peers when they work in their daily life. They were more familiar with the money; in the practice with the money they got the concept of addition with the co-operation dialogues with more mature parents.

            For the process of addition respondent A can add by counting orally without any doubt only for the two digits. For the describing the ways of his addition, when the researcher gave “GOTTI” to him in two different places, left and right hands 8 and 5 respectively then he started to calculating it by pairing method as below: the researcher asked to calculate it how many gotti do you have now in your both hands he replied as:

2                    2

2                    2

2                    1

2                    0

8                   5

12      +          1 =      13

When he adds he used pairing method he made 4 pair of 8 and 2 pair of 5 and remaining as 1. Then again he adds 6 pair as 12 and remains 1 and said 13. For this addition, he learnt when he was at work. To know the his process the researcher asked how did you get this idea, he replied as

“I worked in boutique centre, in the boutique centre when I  attached the “sinning metals in the saries I used to keep one pair in one place, that means two lighting metal at one place. With this process I  can add easily how many these sinning metals I  used in one row or in column”. For the addition of two digits up to 20 I used similar process. Over than 20 I cannot capable to add. Some times when I is in dilemmas then I used to add my fingers properly by counting 1,2,……13.

            The above response shows that the addition process is learnt by street children in the work, when interact with pair groups. Thus this view is also supported interaction method to learn. In this regard Vygotsky (1930-1935) believed that child behavior is always guided by culture and environment of society. The society’s environment creates child to learn.

            Thus, it is concluded that, he learns pair and became familiar with pairing method of addition. With the active participation he learns about pair with the help of his work place which creates the environment by adults.

            Similarly the third respondent add for the 8 and 5 he used his fingers and cannot solve the large amount of addition as 20+38. He was familiar to the number 5 when he adds 10+15 then he used 10+5+5+5 by saying 10,15,20,25. He added with the help of his fingers to remember how many times he used 5.when the researcher asked him how did you familiar with the number five, he replied as

“previously I work in the street as water seller at that time shopkeeper gave me a bottle of water when I give 3 fives and I sold it in 4 fives which means 20 rupees, the shop keeper showed me sold it if they give a big red note which is similar to this. With this practice I became familiar with the number 5,10,15”.

            The above response shows that the addition process learns by street children in the workplace when interact with the adults. In this regard vygotsky said reflecting upon the case, knowledge creates with the help of scaffolding, which means with the help of elders as shopkeeper he gain the knowledge of 5,10,15 With this daily work.

            Among them respondent G, said his previous story to became a faster and forward up to do add for one digit, with the help of his finger rather than other children. He said as

“I  used to play flute in my hometown so in  playing process, fingers play most important role that’s the reason I  was familiar with my finger and I can easily remember that how many finger did I  used to close the hole of flute and how many remain to close. With this process I was well-known about the finger games”.

            With the practice of playing instrument the learner’s knowledge structure is in facilitating thinking in the content field is to measure of learning. Here, Private speech indicates as with his own idea he could create the knowledge in his environment.

            Respondent B read in class one so he can add by writing in his own copy. He used lining method which we read in our formal education in class room, as 8+5 =////////+/////=13. For this case the theory of vygotsky said a child can learn by the scaffolding, in this case he used lining method which is the concept we learn in formal school with the help of teacher. This process is similar to the all of children who learns in the school. Almost of the respondent did the addition by thinking it is the total process with the help of binary and lining method. Some of the respondent A,C and G are more familiar to the term addition but not to the sign of add. They could add the number in their daily activities mostly the addition was related to the money. They could perform addition up to two digits without knowing the carries over. They had not learnt addition from the institution and did not have the wider concept of it.

            Similarly the others respondent learn the addition as the above mentioned ways, by using the fingers and help of the peers, with the help of elders and shopkeepers, passenger as well.

            From the description and analysis the researcher knows that learning occurs through the active participation of the learner with the help of adults, peers and other society.

Concept of Subtraction and it’s Learning Process

            The street children were not familiar with the term “subtraction”. When the researcher moved to the concept, over all he got the result as subtraction indicates as reduce from big to small from the selected respondents.

Subtraction is the process to make it less from the large value by reducing from big to small or from small value, reach up to large value by adding necessary value, these added values is said to be the subtraction.                                                                (Street children)

            Actually subtraction is the process where we define as the difference between the two numbers; where street children also gave the similar sense as reduce from big to small.

             To investigate the process about the subtraction the researcher gave 20 marbles to each and took 8 from each then he asked how many marbles do you have now? As a result four respondent gave the right answer other were getting confused still to the last time. To analysis the process, the researcher divide in to two groups as x and y. in the group x there were respondent B,D,F  and G who gave the right answer and in the group y there were respondent A,C and E. The researcher made two group because in the group x have the similar process where as in the group y they cannot well performed.

            Then the entire member in x group said 12. For the process, all of them, of group x have similar way to do it. When the researcher asked one member of group x he replied as

“ at first I took all twenty marbles and removed eight from these twenty marbles then I start to count from  9,10,11,12,13,14,15,,16,17,18,19 and 20 with the help of fingers. As a result I  took 9,10,11 as the nominally and count 9 as 1, 10 as 2 similarly 20 as 12.

            The above response shows that the subtraction process is learnt by street children by copying adults and also with the previous knowledge of addition.

For the group x  , they only know that to do subtract at first we have to take small number than add some more to reach the large number that is a little bit difference than we learnt in the school. In the formal school the teacher taught as 20-8=////////////////////=12 means keep the large number at first then reduce the small number from the large number. Where as in the street children are familiar as to take small at first and reach up to large number. Street children also used similar method when they go to buy the things to the shopkeeper, when they buy chocolates of 3 rupees with the note of 5 rupees they subtract as at first took small number as 3 and reach up to 5 by counting 4,5 with their fingers. These 4,5 are the just the number to reach the note 5 rupees. These 4,5 are the nominal when they count 4, 5 then they used their finger 4 as 1 and 5 as 2 and found the result as they took back 2 rupees from the shopkeepers. As a result they can do subtract with the result correspondence to their hands finger. Over the finger they were confused.

            These all of group x had done similar manner, for the sources of this process they used their previous knowledge of addition 20-8=? They used to reach 20, add some number as 8+1+1+1+1+1+1+1+1+1+1+1+1= 12, when they played with the betting something they subtract as above system as additionally, which is different from the formal school.

            In this regard vygotsky believed that looking the matter from the opposite perspective , could one suppose that a child behavior is always guided by meaning that a preschooler behavior’s is so arid that he  never behaves spontaneously simple because he think he should behave otherwise? This strict subordination to rules is quite impossible in life, but in play it does and it is always possible. Thus play creates a knowledge vygotsky further writes “in play” a child is always above his average age, above in his daily behavior. In this case of group x they were in the simple counting process for the concept of subtraction. Vygotsky also said that child sees one thing and act differently in relation what they saw. Group x mastered learning through playing by emerging rules and more rigid they demand greater in his application, it can be regarded as a means of developing abstract mathematical thought.

            From the above analysis it is concluded that learning mathematical skills developing through games and previous knowledge of addition, superficially play bears little resemble to the complex mediated from of thought and volition it leads to change in the behavior.

Concept of Multiplication and it’s Learning Process

            Multiplication is known in short term as multiply. Multiply means to increase in number or quantity and to add (a number) to itself a stated number of times. When the researcher asked to the selected children in the concept of multiply most of them are unknown , in fact street children are unable to solve the problem of multiply directly because they don’t have chance to learn from formal education but street children had the creative mind which creates lots of knowledge. In the case of multiply even they don’t know the table but it has been found that  they had the knowledge because when the researcher gave to add 8+5 in that case the respondents used to make it 4 pair of 8 which shows 2*4=8 which is known as multiply in mathematics. Thus the street children learn by their own way without knowing this is multiply. In another case , the respondent used 5+5+5 and said 5,10,15 which also refer that table of 5, which is the part of multiply, thus it can be conclude that street children know the multiply in their own ways not similar to school. Whereas in the case of multiply respondent F has a little bit idea about it, he was the vehicle helper, the researcher asked to the respondent when you asked the vehicle fair to the passenger, if they give three persons at once with fifty rupees then how did you do this? He replied as

“When the passenger gave vehicle fair of three person by one of them then I used addition method to multiply. That means when the passenger gave 50 rupees for 3 persons with actual 10 rupee fair to each of them I calculate as 3*10=10+10+10=30 in this way I calculate 30rupee and return back them 20 rupee. In this way I calculate a little bit knowledge over the multiply”.

            From the learning process of subtraction he learnt during the time, when he worked in vehicle. The above response shows that the multiplication process is learnt by street children in the work place in vehicle as well as by previous knowledge of addition interacting with previous knowledge.

            In this regard Vygotsky said that private speech, which is self directed speech that children used to guide their thinking and behavior. It is as the foundation of memorization and recall, categorization and self reflection. In this case respondent F also learnt this multiply with the help of addition which is his own self directed speech.

            From the above analysis it is found that they are unknown about the multiplication operation and its sign. From the discussion and interaction with them it had found that they used this multiply concept on the basis of addition. They took it as long addition. They learned multiplication from their own practice during the long experience in money calculation. They internalized it by their individual practice, self guided and self reflection. This concept is drawn from the games which they play.

Concept of Division and it’s Learning Process

            The street children whom the researcher selected were unknown about the concept of division and its sign. But they could perform it only for the small number with the help of their fingers but not clearly and easily. That’s why the researcher applied the games to get the concept and process about the division. One day the researcher decided to bring the “SELROTI” for their Tiffin. And he took 60 roti from the bakery café and asked to the selected respondent to divide it equally then the respondent started to talk with each other to share it equally but no one came at first to share then the researcher immediately takeout 20 coins from his pocket had asked to share equally. Then the respondent A started to give each of them by one- to-one method and gave one rupee coin to each. Then respondent came and asked to the researcher some coin to divide to some children then the researcher gave 10 coins to share only for the five children , who were in the last row of the class he also share similar method as above. Then the researcher asked who can share equally rather than this method then found that no one can share except this ways. So lastly the respondent G came and took 20 dish for the Tiffin and started to share them by keeping one-to-one methods to each dish, and repeated 3 times and said 3 roti to each of us, which is the division of 60/20=3. This is the same way of above mentioned. Even street children hadn’t ides about divide but they can share equally in the small portion of everything. In the formal education, student used to divide by using table, but the street children had not idea about the table so they used one-to-one method which gives the result as divide. In this regard Vygotsky’s socio culture theory said children are the active seekers of knowledge. In this theory also said that knowledge is being constructed in social situation of negotiation, rather than being the reflection of the object reality. Vygotsky argues that the child’s development cannot understand by studying that it needs to examine the external world. Children are socially associated which is present from the beginning arriving into the complex world of the social relationship and the culture. The culture itself has historical development .socio-culture theory. Thus this method of sharing also related to the cultural phenomena, for example when mother came from the market she took chocolates to the her children and she share one to one to the children in the home town that the reason that they acquire the knowledge from the cultural phenomena, which method is differ than the formal education system. From the above analysis, it can easily said that learning mathematics occur from socio-culturally as well. A street child who is working as a lobour on the street, is also learn the mathematics not only through memorization of formulas, practicing long time from given examples only. It occurs and develops through active participation in the culture and help from the mature parents as well as private speech.

            From the above, it is observed that street children have mathematical knowledge which they need in their daily life. Even they had the knowledge of either to add or multiply but they cannot do as properly. No one encourage them to solve the problem related to the basic mathematics but they used to solve by their own way which gives real output but in process it is different. Their mathematical skills developed during the staying period on the road, with the help of scaffolding and socio-cultural system of Vygotsky theory. 

Chapter V

SUMMARY, FINDING, CONCULSION AND RECOMMENDATION

            This last and concluding chapter concern with summary, finding, conclusion and recommendation. The first section reveals the summary, the next section list the major findings and conclusion derived on the basis of research analysis and final section present recommendation for future study.

Summary of the Study

            Most of us, from the distance, might visualize that the street children have no idea, feeling, learning, intelligence and they do not possess potentialities. Before being attached with them, the researcher had the same kind of feeling and understanding because their activities and nature showed that they are worthy and only problem creatures. All of them live on the pavement of road, living their lives by stealing, begging and collecting rags from the dumping sites. After this research the researcher found that they are not like as researcher thought. Most of them are engaged in different activities, earning money, saving for tomorrow and living their life.

            This is the case study of street children. The purpose of the study was to dig out the basic mathematical knowledge of street children and the learning sources of mathematical concept. For this purpose the other specific objectives of the study were to describe the different variables related to street children possess. We have to learn from some essential elements, from their lives and behaviors. After arriving in the road either knowingly or unknowingly, they have learned many mathematical skills from their dwelling on the street and doing different jobs around the cities. Without formal education, they have learnt many mathematical skills and performing their tasks easily. In many aspects they have learned such mathematical skills from the environment they got by themselves. In some extents, they are learning such skills by observing from others where they live. Their peers, parents and other elders with whom they are working are also helping them to learn those skills naturally.

            After analysis and interpretation of different data the researcher found that street children have basic mathematical knowledge i.e addition, subtraction, multiplication and divide, which they need to survive in the society as well as buy and sell the daily bases things of their lives. Even they have a little bit different process to do basic mathematics, but the result was similar to the formal education system where as street children learnt these process with the help of peers, elders, society and environment they lived. In the formal education teacher teaches theoretically but the power of practical knowledge is stronger in our daily life, which the street children have.

Finding of the Study

            Street children had mathematical knowledge which is in the hidden phase, but they easily used when they need. They have their own way to calculate the things and learnt this by private speech, peers groups and environment where they lived.

The findings of the study were mentioned as below.

·         Street children advanced the basic mathematical skills by their own efforts to run their daily bases life.

·         Street children learn addition by their active participation with the money and fingers interacting with adults, peers and other society.

·         Street children learn subtraction through games and previous knowledge of addition.

·         They learn multiplication from their own practice during the long experience with the money calculation as well as took a longer addition process for the multiply which is directed by peers and elders.

·         They learn division from the one-to-one corresponding method by sharing different things of their life, which is related to the cultural phenomena.

·         They are learning mathematics practically not theoretically.

·         In some cases games and play were very important tools to learn mathematical skills. Mostly their culture, environment and their peers helped them to learn mathematics.

Conclusion

Most of street children do not even see the gate of school; they have learnt some mathematical skills by engaging in some sorts of activities on the pavement of the road. No one guides them to learn but they learnt much of mathematical skills knowingly or unknowingly. They did not have any theoretical understanding about the mathematical skills but had wider practical concept. Especially street children learn addition by active participation with the money and finger, in the work place where as in the case of subtraction; they used previous knowledge of addition. They subtract not from big to small number but reach to big number from small one, which is differ from the formal education system. Street children learn multiply by longer addition process which they acquire in the working field, and for divide they use one to one corresponding method to share any object to each of them.

            From this research the researcher concluded that they learned such skills by their own practice rather than instruction from any institution. Basic mathematical concept learned and mastered by them are in the social context. Street children had basic mathematical skills to run their daily activities, these skills they learn from the society/culture where they live and work with the help of peers, elders as well as cultural phenomena which is also supported by socio- cultural theory of Vygotsky.

Recommendation

            This is a case study of street children of their basic mathematical knowledge and learning sources. This research is on the basis of Kalanki camping where the street children kept. This research itself isn’t complete research. Thus the researcher suggested for the following further study.

·         The application of mathematics on the street by literate children.

·         Hawkers and their mathematical construction.

·         Varieties of mathematical knowledge of street children.

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INTERVIEW GUIDE LINES

Serial number…                                                                 Place of working…..

Name of Respondent…..                                                    Age ………

Sex……..                                                                            Caste/Ethnicity….

Literacy status………..                    

·         COUNTING PROCESS

- Can you count these all coins?

- How many coins are there?

- How many fingers do you have? Show me one by one and tell me each number by showing my finger.

- How many friends are there in this camping? Who are they?

- How did you learn to say 1,2,3,4…?

·         KNOWLEDGE OF ADDITION

-How many children are here?

-Can you tell me how many friends do you have now?

-Take these 8 gotti in left hands and 5 in left then tell me how many  

 do You have? Show me the process?

-can you add 10+15? How?

- How do you add 20+38?

·         KNOWLEDGE OF SUBTRACTION

-Take this 20 marbles and give me 8 than how many do you have? Show me the process?

-can you make it equal by giving me some marbles?

 

·         KNOWLEDGE OF MULTIPLICATION

-can you play marbles? how many needs to play 3 persons having 5 to each?

-if I give 5 rupee to each than how much should I have to give 7 of you? Show me the process?

·         KNOWLEDGE OF DIVISION

-          If I give 80 sweets for you can you share it equally?

-          Can you divide 15 coins to me , you and your best friend? How?