UAM
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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. |