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Learning of Mathematics

Children from slums in cities learn to speak in two to three languages at a very early age, their mother tongue, the regional language and Hindi. They count cricket scores at lightning speeds. The children working with carpenters never make mistakes while making a right angle or a plane. There are countless examples of children using mathematics and mathematical skills in their day to day life. The same children when sent to school fail in mathematics. The problem lies not in the children's capabilities, or in mathematics as a subject; but in the method and language of teaching mathematics.

Areas of difficulties in Math Learning :
1. Language of Learning Mathematics
2. Method Of Learning Mathematics
3. Classroom Culture

1. Language of Learning Mathematics
One interesting and important discovery made during our teaching activity was that the difficulty that children have with mathematics is largely linguistic and not conceptual.

Learning a new subject in an unfamiliar language is doubly difficult. For example, many brilliant students from the vernacular stream fail in college, because of their unfamiliarity with the English language. Their learning problem is not conceptual, but linguistic. Similarly, children have a double difficulty learning MATHS in the traditional way – in the alphanumeric language. i.e. through written numbers, and symbols. Writing and numbers, are two new abstract skills which the children are just beginning to learn. The alphanumeric language is a new and unfamiliar language for children. Mathematical operations like addition and subtraction are unfamiliar abstract operations. Learning addition and subtraction in the alphanumeric language involves a double level of abstraction. For children it means learning a new unfamiliar abstract skill in a new unfamiliar abstract language. This appears to be the main reason why children find mathematics difficult.

Things-Language Approach :
The learning process, therefore, must be broken into two stages.
First – teach the new abstract concept in a familiar language.
Second – translate the familiar language into the alphanumeric language
of writing and numbers.

What is this ‘familiar language' in which we should first teach the abstract operations like additions and subtractions? Our experience in teaching children mathematics has repeatedly confirmed that the language in which children most readily understand mathematical concepts is the language of ‘thing symbols’: things used in a symbolic manner. In the rest of the paper we use the word ‘thingol’ to denote ‘thing symbol’ Cuisenaire rods are excellent examples of ‘thingols’. With the help of Cuisenaire rods children readily learn to estimate and match lengths. When they can do this consistently, they have intuitively grasped the concept of addition and subtraction, though without mentioning numbers. (In our teaching experiments we have developed a cheaper, yet more effective improvement on Cuisenaire rods: ‘Jodo Cubes’.)

In our teaching experiments we have been able to develop a wide variety of thingols

to teach all aspects of primary school mathematics. We have also developed a definite sequence in which the various topics have to be taught, so that the child proceeds from understanding to understanding, developing confidence and skills along the way and most importantly, a liking for mathematics. We are thus in a position to define a comprehensive alternative pedagogy for teaching primary mathematics.

Our experiments with hundreds of children have proved that if each concept is first learnt in things-language with its real-life connections; and then sequentially in action-language, pictorial-language and alphanumeric language, children master the concepts with ease and with complete understanding. The transition from real life mathematics and things-language to alphanumeric language is a real problem for the children and if the method incorporates thingols and other tools for smooth transition, every child in each class can master mathematics.

2. Method Of Learning Mathematics
The traditional method is based on rote learning. Children learn a number of rules to be applied to various problems.

This series of rules goes on and on and finally the children find themselves in the mess of rules and do not know which rule should be applied in the given problem.

This mechanical method of teaching soon leads to a void in their understanding of the subject and eventually to confusion, fear, and finally hatred towards it.

The traditional method of teaching mathematics is designed for dropping out (Pushing Up) 90% of the students at the school and college levels and succeeds well in its objective.

Universal Active Mathematics Method (UAM Method):
This method of teaching is for universalization of mathematics education. It uses the universal language of mathematics, that is the things-language. It uses Reality based content and activity-based Do and Discover method. It is aimed at

equipping the students with a confident understanding of maths competencies.

UAM method connects the real life math with its things-language representation as well as alphanumeric expression.

This method is tried and tested in all types of schools - rural, tribal, local government schools in urban areas and even the elite schools in Mumbai. In all these schools the teacher-student ratio is 1 : 60 to 1 : 40.

3. Classroom Culture (And also the culture of entire math program)
One way teaching and competitive learning environment are the main factors affecting learning of mathematics. Changing classroom culture is critical to universalising primary school mathematics.

UAM Culture : Every math period in UAM method is conducted in groups of 5, in a mathlab or in classroom. Children learn with cooperative learning, understanding and self-confidence.

The attempt is to inculcate a liking for and even a love for mathematics in the participants ( both students and teachers). Since a taste for food cannot be inculcated by force feeding, the method, pace and general culture prevailing during this experiment is a very important part of the system. This must be understood by all the participants, especially the adult participants. The initial orientation as well as ongoing discussions with the teachers develop this relaxed and joyful approach to learning.

However, this approach is not a readymade product which can be programmed into the participants. It has to be worked out in practice. The program itself is based on a do and discover approach. Many problems are faced while implementing this method in reality. The problems are an important part of the learning process. The approach is not to hide the problems, but to identify, confront and discuss them thread-bare.

The teachers must be oriented to get rid of the ‘wrong answer’, ‘right answer’
approach. They must learn to recognise that the mistakes that the children make in tackling problems are as important as the ‘right answers’, as a clue to the learning process. They have to try to control the impulse to take short cut and give the right answer. Instead they have to learn to pose simpler problems which the children can solve and discover for themselves.

Three basic principles are adopted while teaching the students.
1. Teach only through understanding and not by rote.
2. Go to the next level only when the child is completely confident with the earlier level.
3. Use only those learning materials, which are easily available in the local environment. Avoid sophisticated, expensive teaching aids. i.e use only low cost or no cost materials which can be easily replicated.

Low Cost Effort :
The emphasis on low –cost and no-cost materials from the outset means that the teaching kit can be immediately universalised - it can be used by low-income schools, and rural schools. Some additional innovation may be necessary for the Rural Maths kit, since some materials available in urban areas may not be available in villages. But we do not anticipate much fundamental difficulty in identifying these alternative materials.

Navnirmiti is working on Universal Active Math Method with active participation of teachers from 106 schools.
We invite you to join this effort to universalise alternative mathematics learning.


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