ACTIVITY BASED LEARNING OF INTEGERS

In the edifice of Pedagogical Sciences, Mathematics Education assumed a distinct niche for its role in developing mathematical understanding in School children, and helping teachers for exploring newer models of teaching mathematics, founded on Psychological Principles as well as Scientific, logical and methodological reasoning.

In general, it is found and experienced that young children irrespective of rural and urban setting, private or public administration of schools, or belonging to families of different Socio-Cultural-economic status, feel uncomfortable, afraid of, and scared of mathematics as a curricular subject.

From pedagogical point of view, it is said that learning is facilitated when it follows the maxims of concrete to abstract, easy to difficult, known to unknown etc. In the very Primary stage, when the alphabets of a language are introduced in the mindset of the children, they are arranged in meaningful words, such as ANT (A N T), BAG (B A G), CAT (C A T) and so on, then the teacher analyses the word to focus on the letters. Most of the time, he/she uses pictures of the object like those of Ants, Bags, Cats etc. From visual perception, children hear and utter this sound, the phonetic form of the object, then they are shown the discrete alphabet A B C etc. and simultaneously they are asked to write the letters and practice them. More than one sense organs are involved in this action.

What we do in case of Mathematics, in teaching-learning of integers 1, 2, 3, …etc. we show the visual forms of the same, pronounce them, and ask the child to memorize them in association with their visuals. But here no meaningful use of the figures is introduced in the process. Because of the limitations of Teaching of Mathematics, Primary teachers are trained to teach their children to count some objects like sticks, etc. and associate the counting with the figures of integers, and their phonetic characters, sometimes with the help of ‘abacus’, thus initiating some activities leading to learning of the integers.

With the background of direct experiences of Teaching mathematics and continued action researches in actual classroom situation, Dr. Sk. Samsul Alam presented a series of experiments conducted in the classroom, scrupulously involved the children in relevant activities-meaningful and goal-oriented-and of course, based on Psycho-Pedagogical Principles. Experiments were followed by observations and inferences drawn accordingly. Gradually, step by step through cognition of integers, perceptions and conceptualization of their interrelationship in regard to four principles of computation-addition, subtraction, multiplication and division, the teacher (facilitator) could enable the children to play, work and enjoy in the ambience of elementary mathematics, inside and outside the classroom.

For better understanding, the aforesaid discussion I would request the reader of this book and of course the concerned teachers of Mathematics to go through the last chapter (conclusion) first, and then follow the writer in the subsequent characters-tables, exercises, illustrations and rules arrived at, for critical analysis of the contents therein.

1. Piaget, the noted psychologist, in his discoveries on cognitive development of children-verbal and non-verbal, put stress on two major steps of acquiring knowledge – assimilation and accommodation – truly speaking, through perception, the children explore the field they are exposed in, pickup and collect information and experiences, assimilate them, conceptualize the elements and after careful and logical classification of the contents, accommodate them in respective cubicles in the brain (chamber of consciousness). Piaget, coined the bunch of similar of homogeneous concept and SCHEMA (sing. SCHEMATA). As and when the Schema (e.g. the Schema of ‘0’, the corner stone of integer education), are distinctly built up in the mind, they are translated in every action related to numerical and computational skills.

One of the unique features of this book needs Special mention. That is, the treatment of negative integers-its introduction in elementary mathematics. This negativeness of integers as if begins from the midpoint zero (0) of the continuum, a number line and extends to the left as negative numbers (integers), is difficult to conceptualize without the help of examples/illustrations/activities. Dr. Alam invented all possible means to concretize the idea of negative integers in the cognitive map of the students at elementary level. His treatment and suggestions for the teachers are lucidly presented in the chapters concerned. These activities are easy to do, interesting to know and clear for understanding.