We are the teachers. We will have to take the initiative to develop the concept of the students. But unfortunately we don’t do that. For example, Calculus is completely a new branch of Mathematics. Before starting calculus the students should have the clear idea about ‘Mapping’ or ‘function’. But most of the students start Calculus from ‘Limit’. And we, the teachers don’t insist them to make the concept in ‘Mapping’. Some students read this chapter but do not form the concept on it.
We can describe the function with the shooting game. In various fare we shoot balloons with air gun.Now think that the packet of the bullet is the domain set and the balloon board is the co domain set. The air gun makes the correspondence between the two sets by obeying some rules.This rule is called mapping.

If one bullet can hit a no.s of balloons, it is an 'ONE TO MANY' mapping.

If more than one bullet is used to hit a of balloon, it is an 'MANY TO ONE' mapping.

If one bullet and one balloon correspondence, it is an 'ONE TO ONE' mapping.

Always remember that the bullets should be exhausted, otherwise the mapping will not be defined. But the some of the balloons may not be hit by the bullets.

If all the balloons are hit by the bullets, it is an 'ONTO' mapping, otherwise it is called an 'INTO' mapping.

The set of burst balloons is called ' RANGE' set.

All we know that Mathematics has mainly three branches, Arithmetic, Algebra and Geometry.In my survey I saw that the students of secondary level like Algebra.But they agree that in future Arithmetic will be helpful in various competitive exam.Al we know that Geometry is a very interesting branch of Mathematics. But unfortunately students are least interested in Geometry. What is the reason behind that ? Amazingly they answered that Geometry mainly based on logic and conception and they do not want to exerciser their brain to solve the puzzle of Geometry.They demanded more classes in Algebra.They want to cram the formulas and want to solve the problem by using the formulas blindly. This habit is very bad for future education and mainly in applied field in education.So the students give up to cram............

Sometimes the common people say that the girls are weak in Mathematics. But I do not agree with them. I made a survey in 10 eminent schools of Kolkata over 347 students and I saw that boys and girls have the same efficiency in doing Mathematics.I have given them a MCQ type achievement test questions consisting of 30 problems, 10 from Arithmetic, 10 from Algebra and 10 from Geometry.Then I evaluated the answer scripts and made a statistical calculation saw that both girls and boys are equally equipped in Mathematics. So the girls carry on, just take the taste of Mathematics more and more........

I am a teacher of Mathematics. Since last 12 years I am trying to give the Mathematical thoughts to my students. But unfortunately, sorry to say, the students of now do not want to go deep into the concepts of Mathematics. Now students want to get marks, high result, chance into a good college or university but they do not want the beauty of Mathematics. Mathematics is a subject full of marvelous logic. The life and it is better to say that the whole world is based on different kind of logic. Mathematics is a subject which has no ambiguity and hastiness. All are going on in a disciplined way to a perfect destination. If one wants to think that Mathematics is a tour, then the solutions of different types of problems may be compared with the tourist spots with full of enjoyments. The logical steps, the inner concepts, the thoughts are the natural beauties besides the way to go. Mechanical methods may solve the problems, but it is like to reach the destination by air, not through the surface into which one can enjoy the beauties of the roadsides.