Wednesday, December 23, 2009

Mathematics and I

The following is a write up by a much loved member of Vikramshila....it is a sharing of Sutapa Di's love-hate relationship with Mathematics! Sutapa Mookerjee, is one of the senior most members of Vikramshila, a part of the Training team of Vikramshila. She has a vast experience of training behind her, has interacted with diverse groups of people all over India as a training coordinaor, can deliver lessons and sessions in no time, and yet, she has the outstanding quality that enables her to continue to look wonder eyed at the world around her.
Suatapa Di is terrfied of maths and terrified of writing...yet her Digantar course and a couple of documentation workshops, made her overcome to a large extent her fears and mental blocks! The end product is this write up that comes straight from herheart ....enjoy this piece...
Mathematics and I

At the very onset it has to be said that union of the two words, “Maths” and “I” is a very tough and unlikely one! Mathematics and I run like two parallel lines – always alongside each other, but always maintaining a certain distance and with little probability of ever converging! That the relationship between the two principle protagonists in this essay is very weak was a known fact to me; however it got further established after my attending the Foundations of Education course…!However, since I am assigned this topic, I am attempting to share some of my experiences and feelings in this regard. It may be possible that this sharing would become a catharsis for me to understand my incapability in this domain and justify it to myself.

When a living being first takes birth, she gets directly or indirectly inextricably woven with mathematics, though she may or may not realize this. Normally, one first gets formally associated or introduced to mathematics at school in class 1. And from that moment on, the person in question begins to feel that that her relation to Maths starts and remains in the classroom and the formal school sphere- i.e. it gets institutionalized.

I too am not beyond this conviction. From the very beginning of my formal introduction to maths, my fear towards the subject began and the foreboding consistently remained and cumulatively increased. However, why this fear emerged, grew and sustained itself remains hidden and forgotten today, though I will admit that there was a consciousness somewhere inside me that was aware of the development of this apprehension in my mind.

Given that the foreboding remained in my conscious mind somewhere, as a school girl, the maths classes seemed to me very long and unending. However, on the very few exceptional occasions, when I was able to solve the sums or understand what was being taught I actually did like the classes.
My Mathematics teacher was far from being a fearful creature- quite the opposite in fact, she was a small built and quite a sweet and polite person, although very very grave. She was so grave, that if by chance a smile escaped her serious demeanor, she appeared visibly uncomfortable at being caught! When this small structured lady would ask in the class “Has everyone completed?” my heart would turn cold and I would get a sinking feeling. Again, on the rare gem occasions when I did manage to complete my task I would eagerly run to teacher to show her my work and couldn’t wait to stand in line! Nonetheless, the fact remained, that these occasions were few and far between.

While writing this piece when I started thinking about my predicament ‘today’, one thought keeps recurring…that being, why this fear got built in the first place, where and when did it happen and settle in my mind and how came no one tried to find out the reason behind it? And when the reason itself was not sought, trying to solve it didn’t arise at all!

Straining my mind, the little that I remember, was that as my fear kept growing gradually, my mind automatically began acting as a machine, sorting and selecting units that it thought “I could do” and those that “I couldn’t do”. In accordance to the selection process a kind of a template was created in my mind based on which , one look at a problem would determine whether ‘I could’ and whether ‘I Couldn’t’ do it! Gradually, as algebra and geometry joined the bandwagon, my principles or sorting and selection were applied with equal force to the new entrants.

However, what was happening as a corollary was that in as much as I was going by my fixed rules of choosing and eliminating problems and sums that I could and couldn’t do, I was also ending up narrowing my sphere of knowledge and understanding. And although this narrowing down was taking place; in my mind I was unable to trace the real zone of my discomfort and the reason behind it.
Today, after many years of being associated with an organization in the education sector, I have progressed a little in my search for my zone of discomfort with mathematics. Armed with the role of a trainer in the world of education, and gradually understanding the nature of this subject, I can say that the strictly established parallel lines have somewhere dissolved and I can see a light at the end of the tunnel where Mathematics and I are progressing towards the direction of convergence.

Looking back today, I can recall how I had fervently wished and looked forward to the day when I would get my release order from the maze of mathematics. When I was a student, the release order opportunity came as early as class 8. It was only an opportunity, meaning that I had a choice of taking it, but I of course jumped at it and finally breathed free and easy.

Today however at a certain age and stage of maturity, when I look back at my life, I feel there are many things to which I have not done justice to. In this list, mathematics has added its name. Perhaps I have not done justice to it.
I however have a question, that while mathematics is inextricably woven into our lives from birth, if in later life one doesn’t participate in the formal mathematics learning process, does it act as an obstacle in one’s life?

To answer my own question, drawing from my own life I can say perhaps, at the institutional level it does. Not knowing maths has indeed affected some of my dreams and aspirations, for instance I had wished to pursue my higher studies in psychology, for which mathematics was a requisite. Needless to add, my dream remained unfulfilled.

But my life didn’t stop there. In life itself, mathematics is inextricably wound with me and will remain so. My life went on proceeding in its own rhythm, and included the rhythm of mathematics of life within it.

Sutapa Mookerjee 24/11/09
Vikramshila Education Resource Society
256 B Prince Anwar Shah Road
Kolkata 700045

Curriculum as a means to overcome Social Exclusion- Our Experiences...

The following is a piece that was evolved through Vikramshila's participation in Save the Children's national consultation on "Equal Opportunities and Inclusion in Education". Vikramshila's core activities and its action research by way of pilots has seen curriculum as an effective means of addressing the issue of social exclusion, particularly in urban slums and rural villages, where the classrooms fail to deliver to students needs and more often than not, result in high cases of drop outs. The write up tried to highlight ways in which the curriculum can act as an effective means of making education relevent and meaningful to children...
Equal Opportunity and Inclusion in Education

Vikramshila’s genesis in 1989 was as an education resource organization with the twin aims of addressing the issues of equity and quality in education. Inclusive education that would address the issue of alienation was seen as critical for achieving quality both in education and in life. This philosophy has found echo in Save the Children’s belief that education is important in breaking the cycle of exclusion and marginalization.
Vikramshila’s definition of quality education finds its foundations in this philosophy which links life and learning. The organization believes that most gaps in educational quality can be filled through
a. Curriculum design (relevance of curriculum)
b. Implementation (teacher’s capacity and teacher’s ability to exercise agency).
The formal school system is often inflexible and applies a common approach towards all students, not recognizing the needs and vulnerabilities of the deprived groups. Instead, they expected the children to adjust to the system which is distant and unrealistic to their lives. As a result of this mismatch, education remains inaccessible particular groups, in spite of physical presence of schools in a locality. This is true both for the urban slum dwellers as well as the rural villagers. In the Indian educational system, very frequently, the curriculum has very little to do with life in the rural village or the urban slum. A clear case of social exclusion and marginalization, it results in many children dropping out prior to completion of school.
2 core activities of Vikramshila attempt to attend to this issue of social exclusion by addressing the curriculum. That is by making the curriculum more relevant to the lives of the children by customizing the existing state curriculum around the child’s own histories, practices and lives.
Shikshasatra is Vikramshila’s rural experimental school that is located in village Bigha at Burdwan, West Bengal. The children come from agricultural families mostly and are provided education in a unique way that links the school learning with their life. These children too are taught in a way that ensures school readiness after which they get mainstreamed into formal government schools.
Naba Disha is an intervention for the urban deprived communities- for those living in slums, squatter colonies and streets. The programme attempts to provide quality education into the lives of those children who have either dropped out of schools or have never been to school and to then mainstream them into formal government schools after they have acquired the readiness for it. The population density of slums being extremely high, there are just not enough schools in some areas and the existing schools are unable to accommodate all children. Language mismatch often acts as a further barrier as a large number of children came from Urdu or Hindi speaking families and were unable to adjust to Bengali medium schools. In each of these centers, the curriculum attempts to address these challenges.
Both the schools have been operative for 10 years (12 years in Bigha) and have delivered a number of high school graduates and self confident young people who are aware and active. In both the cases the curriculum is the key area of intervention. It is the curriculum that addresses the issue of isolation, alienation and marginalization, providing an integrated learning not divorced from their lives and environment. It is in this way that education here acts to bring about equity and social inclusiveness.
How does curriculum act as a medium to break the cycle of marginalization and exclusion?

Two interconnected principles – relevance and participation lie at the center of the working philosophy of the schools. A truly relevant curriculum is shaped by the circumstances of the students of the particular classroom, by their daily lives and experiences.
Curriculum is viewed as a dynamic process - one that goes much beyond the ‘syllabus’ and involves using life experiences of children as meaningful opportunities for learning; one in which the learner is at the heart of the learning process. It is also considered a working document and as such the teacher has the liberty to set its pace according to the child and to go back and forth in its delivery. When curriculum evolves into such a process, it automatically ensures that the alienation encountered by the majority of children in our schools no longer exists and both the children’s and parents’ expectations from the school are met.
Both the projects operate in a way to ensure holistic learning. A typical classroom will see the children divided into 4-5 learning groups according to their levels sitting together in small groups around round tables (in the case of Bigha). - Each group has a set of competencies mapped for each subject. The children study and learn at their own pace and can move up to the next level, once they have attained all the competencies. This kind of flexibility creates an enabling atmosphere in the classroom where there is encouragement and nurturing which results in children working without fear of failure.
The projects being a holistic endeavour in the sphere of equity and quality in education, education itself is seen very holistically in order to attain this end. As such learning and activity are not limited to attainment of the designed competencies alone. The projects take the “Critical Pedagogy” and ‘Multiple Intelligence’ theories at its heart. The teachers thus strive to provide children with the faculties of critical thinking, reflection and analysis and understanding of all issues pertaining to their lives. Learning “how to learn” is emphasized over “what to learn”.
Health, nutrition and sanitation are issues that are greatly emphasized in the classroom as well. For instance, a classroom experiment on water purification becomes a success as a lesson in science as well as sanitation. Children are encouraged to question each aspect of their life and their curriculum, so that they do not become passive ‘depositaries’ of irrelevant information, rather, become active creators of knowledge.
In addition, creative and artistic activities are also a part of the curriculum and pedagogy, as these activities; for instance juggling, drama, fine arts, crafts, yoga, balancing, logic puzzles etc, requires and generates concentration and cooperation- skills that are essential for going through life , even on a day to day basis. In addition, the massive rise of self esteem that the children receive upon mastery of an intricate task is beneficial for generating self confidence in them. These activities go way beyond functional literacy to develop creative and critical faculties.
Creating a relevant curriculum means that the child’s cultural background as well as prior knowledge base needs to be taken as the starting point of learning. Relevance can also mean integration of issues from the student’s homes and communities into class work.
Innovative Pedagogy- Both projects while being restricted within the walls of the state curriculum, use its special discretion to interpret the text in such a way as to make it relevant to the lives of the children. The teachers put strong emphasis on contextualizing the text and link it rationally and logically to the realities of these children. This unique pedagogy is seen to have had great success as it ends up generating interest, and creates consciousness among the children towards the text, the classroom and the larger society. For instance, in EVS one of the topics in the state curriculum may be “water”- yet this topic is not dealt with in a rote based textual way- rather the children are made to think about water in their life and surroundings- questions are asked and discussions and debates are held on issues such as- “what are the sources of water? What are the sources of water in your locality? Where does water supply in your locality come from? Is it adequate? Is there evidence of water wastage? How much water do you use in a day? How much water is used by an average family? Who uses maximum water? Who wastes a lot of water? How can this be tackled? Are there open taps in the locality? Does it add to the already existing water crisis? How can this be dealt with? Where does drinking water come from? Is it pure? How can water be purified for drinking? What measure can you take to ensure that your drinking water is safe? Can you think of ways to reduce water scarcity?, Do you know about water wars ? Etc.” In this way through dialogue and brainstorming, a regular lesson of a text is made so much more challenging, interesting and meaningful for children.

In Bigha the school’s science curriculum is perhaps the most dramatic way that life and learning have been linked, and the community is actively gaining from the scientific procedures that affect their lives- e.g. pesticide usage, pH balance, chemical fertilizers, HYVs, importance of crop rotation, soil, organic farming, experiments on bio degradable and non biodegradable items are a part of the classroom. A demo kitchen garden at the school campus also exists.

Multi lingual centers- The issue of multilingualism is faced in many centers of Naba Disha, where children come from varying backgrounds- Bengali speaking, Hindi speaking and Urdu Speaking. In order to deal with this issue of multi lingual classrooms the teachers apply the selective method in approaching the principle of language. The four main components of Language – Listening, Speaking, reading and Writing are approached in this method by first concentrating on the Listening and Speaking skills of the children through which they have already acquired a vast vocabulary from their homes and peers. This vocabulary is then put to use by the creation of vocabulary dictionaries. Word lists and vocabulary dictionaries made by the children themselves are used by teachers to then introduce them to the idea of the same word in a different language. E.g. ‘Safed’ in Hindi, ‘Shaada’ in Bengali. In this manner more lists are generated for colours, animals, things, fruits, birds etc. This way dictionary keeps expanding and children learn more and more words.
In terms of language- the whole word approach is used in the case of dealing with older children who enter the Naba Disha Centers- the words they know already are used, in the forms of lists and from these they are broken down to letters and matras. The letter to word approach is more useful when dealing with children who enter Naba Disha at a much younger age.
The word walls, dictionaries and lists are made in all the languages operative in the center and these are then lined to the existing curriculum.
The teachers develop- a) work cards and work sheets of different languages
b) Graded material
c) Hanging Material that has one language on one side and another language on the other side.
The Morning Assemblies are conducted where children speaking different languages all sit together and share their experiences with the teacher and the class in their own language. The others all gradually learn to follow each language.

Moving beyond Functional Literacy - Creative and artistic activities together with sports, juggling ,yoga, clubs and groups are greatly emphasized and form a core part of the curriculum at Bigha as well as Naba Disha centers.
The curriculum encourages drama and fine arts as a part of the education of these children. Drama and other arts encourage reflective thinking, analysis and critical understanding of issues affecting the lives of the children and enable them to question inequalities and deprivations. They begin to express their feelings and articulate their thoughts. The issues of migration, eviction, natural disaster, relief camps, local and village histories have been set in drama by these children.

Not only have they thought sensitively on these issues, but the process of actually transforming ideas into a drama encouraged research skills, it gave way to enhancement of elocution and articulation skills, acting and expression development. All these efforts paved way to enhance their learning abilities and helped the children shed their inhibitions in the classroom.

At Naba Disha for instance, at a center where the community experience eviction of slums, the children decided to write a drama dealing with eviction- the plot revolved around friendship between a rich and a poor girl, including themes of eviction, migration and refugee relief camps. The play was performed in Naba Disha’s annual cultural fest and was a great success, both in the artistic sense of dramatization, as well as, as an avenue through which the students could understand the complex and sensitive issues around them.
On another occasion, a similar attempt to make education relevant to the lives of the children, the center decided to begin a project examining the area’s local history. They learned that the area had a famous metal box factory that had closed down 15 years ago. Intrigued, the children conducted interviews to learn what the factory produced, and when and why did it close down. With the help of the teachers, the children organized this information into a story and a dramatist put the story into a stage production which was a part of the annual cultural festival.

An Inclusive and Fearless Environment Ensures better learning- It has been noticed that many children belonging to different socio-religious backgrounds come to the Naba Disha centers because of the inclusive environment that it provides. Adequately trained teachers and personnel are able to deal with several social, personal and community issues and provide help to the children accordingly. Moreover as teaching methods and materials are appropriate, meaningful and relevant it makes learning a joyful experience.
In some cases a special curriculum is designed for the children, for instance at a particular center a girl with no prior education began to attend Naba Disha. After a few days she began to feel embarrassed that younger children had more education than she had- in this case, the teachers worked with her through a special curriculum which included vocational education and practical skills like letter writing and communicating with the police. Now in class 5, this girl is a teacher’s assistant in the center

In addition the Bigha School as well as the Naba Disha centers operate by keeping the different learning levels flexible. Children move to the next level only after acquiring the competencies set for the previous level. The children are not hurried through these learning levels and work at their own pace. This creates a very enabling and fearless atmosphere in the classroom, where effective learning takes place.

Community Participation in the Child’s Education Improves Learning- Increased awareness of the community- including mothers, fathers, community elders and local youth and their participation in the education of their children is an essential and critical aspect in ensuring effectiveness in the child’s learning. The project has provided opportunities to engage with major events of the in the childrens’ community through, for instance, cultural festivals and community mobilizations on issues of health, nutrition, sanitation etc. Initiating ‘Amar Boi’ that consists of regular diaries written by children has been a medium through which children trace their family histories and identities, migration routes, maps of the locality and so on. In this effort, the community elders are interviewed by the children and thus they begin to take interest in the children’s initiatives and education.

At Bigha, the Eco group, the Sathi Group and the Mothers Groups are all evidence of community participation. Village timelines, crop and land patterns are mapped by children after thorough research involving interviews and analysis.

Working within the perimeters of the state curriculum, the projects have invented and reinvented alternate pedagogies and learning transaction processes that ensure that education does not divorce the children from their realities as is often the case in formal schools. This is essential to address the issues of equity, quality in education, in fostering greater equality of opportunity and inclusion in education.