For challenging students: The teacher is required to go back and see the root cause of the problem In most cases, you will find the student lacking the fundamentals. It is exactly here that the student is to be given lot of practice.
FOR AVERAGE STUDENTS: The teacher is required to develop logical thinking and confidence. Build up speed by giving more practice. You must gather more problems to give to students.
FOR BRILLIANT STUDENTS . Recast the problems and place it before the students. Allow them to think. Do not give the solution immediately. More focus on self thinking and self analyzing. The teacher must have enough gunpowder in his armoury so as to satisfy the hunger of outstanding students.
Mathematics is the mother of all sciences. A teacher of mathematics is a seller of mathematics. He is supposed to communicate well to his students. Students who are good in Math are generally good in other sciences as well. It is like blood flowing in all the veins of the body. No scientist/ economist has done his research with out mathematics.
The foundation of it is laid in elementary/middle level classes. Parents who wish their children to be at the top must build up the base at this level. After this level, the children nourish mathematics themselves. It is like planting the sapling now and eating the fruit later on.
As a student of mathematics, I have always been the top achiever right from grade four to my master's in mathematics. At my graduation level, I took the challenge of studying double mathematics. I took up mathematics at the top university of India---Delhi University----a university which is known for its excellence in mathematics. I also had the privilege of taking some Refresher Courses meant for Senior teachers.
I have nearly 40+ years of teaching mathematics at Senior level (grades 11 and 12) to students from India, Pakistan, Kuwait and the U.S.A. Besides this I have been preparing students for Engineering Entrance Examinations (just like ACT in U.S.) My students have done exceedingly well at the national level, some of them getting top position in mathematics Olympiad. This subject is my darling.
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