Flipping the classroom.

This is a model of education , possibly the future education model of Education System of the United States . It is currently best practiced with the help of websites like -Khan Academy . A photo by Knewton , shows what is is exactly.

 Thus this method provides the students two most important benefits-

1) The student can play , pause , fast forward and  rewind their teachers.
2)Each student is individually taken care of and there is a plenty of time at school for practical learning.

What is Mathematics?

Somebody once said that philosophy is the misuse of a terminology which was invented just for this purpose.  In the same vein, I would say that mathematics is the science of skillful operations with concepts and rules invented just for this purpose. The principal emphasis is on the invention of concepts. Mathematics would soon run out of interesting theorems if these had to be formulated in terms of the concepts which already appear in the axioms. Furthermore, whereas it is unquestionably true that the concepts of elementary mathematics and particularly elementary geometry were formulated to describe entities which are directly suggested by the actual world, the same does not seem to be true of the more advanced concepts, in particular the concepts which play such an important role in physics. Thus, the rules for operations with pairs of numbers are obviously designed to give the same results as the operations with fractions which we first learned without reference to "pairs of numbers." The rules for the operations with sequences, that is, with irrational numbers, still belong to the category of rules which were determined so as to reproduce rules for the operations with quantities which were already known to us. Most more advanced mathematical concepts, such as complex numbers, algebras, linear operators,  this list could be continued almost indefiniteness so devised that they are apt subjects on which the mathematician can demonstrate his ingenuity and sense of formal beauty. In fact, the definition of these concepts, with a realization that interesting and ingenious considerations could be applied to them, is the first demonstration of the ingeniousness of the mathematician who defines them. The depth of thought which goes into the formulation of the mathematical concepts is later justified by the skill with which these concepts are used. The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess. However, this is not our present subject. The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.

The complex numbers provide a particularly striking example for the foregoing. Certainly, nothing in our experience suggests the introduction of these quantities. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius. 

Maths and Marks

Genius!!!! Hmmm you got 50/50 and you dumb boy just 30. These are the frequent sentences spoken by a maths teacher.In India mathematics is measured in marks . A brilliant student is who , who brings high marks in maths and rest -dumbs!!!You might say Oh! that's quite right , you know the subject you get marks and if you don't know then you don't .

 But here is the problem- The people who are labeled "To know the subject" are the people who mug it up. They just memorize digits in the solved examples, the memorize important questions, they memorize the textbooks , they memorize the MCQs etc etc etc.....If you look at this they really don't know mathematics but they know how to mug mathematics up.

 A good mark scorer is a person who claims , feels to know everything in the subject BUT of inside the textbooks. We are not trained to use our brains to solve difficult problems but we have trained our brains to mug up difficult problems . We know how to learn concepts up but forget when the exams are over. You can take any boy of a class and give him/her a difficult problem of a concept he/she studied 2 years before .....Then there is a problem.

This not only does not let the student learn the subject well but does not teach us to enjoy its beauty .And as Bernard Russel rightly said-
Mathematics, rightly viewed, possesses not only truth, but supreme  beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.