Do we require books for teaching mathematics at the primary level?
As I go back to recall the methods employed by our teachers while teaching basic operations of mathematics, no image of any book comes to my mind. We studied this subject in a very relaxed manner. It was as adventurous as learning how to ride a bi-cycle! No discussions! Just corrections. Encouragement was the guiding principle. I am convinced that introducing math books at a time, when the students start learning languages is not proper. A math book contains a perfect sentence which in turn contains an idea. The little students can’t synchronise their juvenile intellects with a matured narratives. It is simply not possible. The more math gossip is avoided the better it is for the health of teaching and learning this subject.
What should replace books at primary levels?
A very recent UNSECO report says that India is half a century late in achieving her education commitments. Now this is not good news! Less progress is not a case of frugal investment/outlay in education sector being made by the central and state governments as is alleged by Amartya Sen, ad nauseam. It is a case of both adhocism and approach casual. From the trenches of tradition to the altitudes of possibilities a whole range of fields are available for exploitation. Money! That is the goal. If someone gets educated it is his luck. A good education is an asset. A bad education destroys the world!
Till the time applied math is not introduced in school curriculum, nationally approved tutorial sheets should be introduced throughout the length and breadth of the country. It will be the first step in the long process of taking control of a drift situation. One idea can make a situation gloomy. Another can ignite a torch of hope in conditions dark! The tutorial sheets will not only bring about uniformity in the teaching of concepts but also introduce the ‘do it yourself model’. It means that the students no doubt will be burdened by the teacher in schools but will also be asked to suggest for himself/herself questions and solve them at his/her home. Once the target, say five questions of addition, is fixed the student will naturally, for self-assessment, draft questions with least degree of difficulty. In this way the first condition of involvement is created. This brings about the identification of examiner and examinee, which in turn fosters not only the habit of planning but also a degree of responsibility.
Now what are the advantages of replacing books with tutorial sheets? Obviously there will be a saving in terms of money by the parents. The school bag will lose some weight! Importantly it will have a salutary effect on the environment because fewer books mean less damage to forests. This is plain on the surface! But the greatest advantage that is available to us is that once self- assessment process starts, no two questions will match. It means that no two answers will match and here is the opportunity.
When I was beset with cultivating confidence in my ward I would offer a set of five questions to her to be completed in a given time. When the time would elapse, I would call her and check the answers. At the start she would make mistakes but I would usually ignore four of the five mistakes. In this way I planted the seed of confidence in her mind. And lo and behold! After a very short time she overcame her infirmity and would usually come up with correct answers. It proves that when we plant a feeling of progress, however false that may be, in the mind of a student, he/she is burdened with a responsibility! Earlier she had to lose nothing. Now she had to save her frugal asset which in turn planted seriousness in her mind.
Likewise, a teacher can utilise this input to cultivate confidence in the minds of the students. The teacher can overlook some mistakes to fill the students with a sense of progress. Sense of progress gives them hope. Hope makes them happy. Happiness is a state everybody wants to be in. Napoleon once said, “Give me medals and I shall win you wars!” Rewards are given to even animals to cultivate in them reflex responses which lead to improving intelligence in them.
Introduction of Geometry
It will be advantageous in case geometry is introduced at class one in all schools. The idea is that it is an activity. But no free hand use of pencil should be allowed. The use of pencil and scale at an early stage brings about the coordination of eye, hand, concentration of mind and places responsibility on the students to avoid making mistakes. Since nothing is to be crammed it will command more respect from the little students. Learning holding a pencil at an appropriate angle and moving the hand by using optimum force ultimately teaches the students how to hold a pencil while writing. Learning skills is a rigours task. Never compromise on bad hand writing.
And what could be the first lesson in geometry?The introduction of geometry shall start with the introduction of the concept of a point in the plane. And what is a plane? That needs to be drilled early on so that the students apart from thinking numerically will start thinking geometrically. And what is a point? Let us postpone it for the next time.