A good mathematics teacher needs to create ``infectious enthusiasm” among students.

A good mathematics teacher creates among students ``infectious enthusiasm" said Dr.K.Govindaraju, while addressing the mathematics teachers of High schools in Trichy on Saturday, 29, May 2011 in SEVAI Shanthi Matriculation Higher Secondary school. He further added ‘Every great mathematics teacher has his or her own teaching style and philosophy, good teachers respect their students, effectively engage students by treating teaching and learning as a collaborative process and by showing their students that their thoughts and opinions are valued. It can be really good motivation for students to feel that they're working with their teacher to develop their understanding of a sum in mathematics class situation. Having students ask and answer questions about the material being covered is a great way to get them really thinking about the ideas for themselves. Also, some teachers really encourage their students to talk to each other and it is a great way to show students how much they can learn from each other, independent of their teacher. Along those lines, great teachers should challenge their students. They should encourage their students to get out of the mindset of "I only know as much as my teacher tells me". In math, many students end up expecting all the problems they encounter to be similar to some example they've been shown. An invaluable skill that great teachers pass on to their students is the ability to take their knowledge and skills and apply them in unfamiliar situations. It's important to show students that they can do things on their own. Great mathematics teachers provide positive encouragement and credit where it's due. Especially in math, good teachers provide motivation and explanation for the material. It's so easy to get caught up in formulas and theorems and simply ignore where they came from but it's so important to make sure that students realise that math doesn't just come out of nowhere. Even in cases where rigorous explanations are a little beyond the students, good teachers can appeal to their students' intuition and give basic ideas about why things are true. Being able to show students that math is all about logic and reasoning and that it should make sense I think is the mark of a really incredible teacher’.

Dr.K.Govindaraju further said ‘A good mathematics teacher should motivate the math and engage the students. Take the example of solving linear equation. One can start by telling students the formal rules for how to manipulate an equation, but I think students will find this very dry, and won't understand why they are doing what they are doing. It becomes an exercise in memorization. Instead, one can start with problems that can be solved with such equation. One can first get students to solve them with other techniques (e.g. guessing and checking or using some sort of graph). After a while one realizes there should be an easier way, which turns out to be solving a linear equation. This way the students understand why the formal math was developed, understand how to apply it, and see how it is related with other ideas (like graphs). Right now teacher might ask where one can find good problems to use in this way. I think I will ask that as a separate question. A good math teacher makes their students do math. I think it is crucial that every student, in every math class, every day, solve some math problems. Some of these should be easy (i.e. just practice solving equations, once they have been introduced), and some should require more creativity. It is of course a mistake to drill students with boring problems until they hate the subject, but it is also a mistake to let them do "interesting" or "discovery based" math all the time, and not make them practice the techniques they discover. A good math teacher should convey the beauty of the subject. One of the other answers said ``infectious enthusiasm" was needed. That would be great, but in reality not all math teachers can be that charismatic. Even without a great deal of charisma, it is possible to show students the wonder of extracting a simple answer from a seemingly difficult question, and the beauties of the tools that help one do this’.-Govin