Aside from the knowledge, a mathematics teacher should be a person

1. with excellent communication skills to express concepts and ideas to his students and colleagues

2. good, personable, that encourages and values students' participation in their learning from asking to answering questions correctly or otherwise. Some one that knows no question is trivial for a student learning mathematics, as misunderstanding a symbol, concept, relation may be a huge obstacle to the smooth continuity of abstract learning for students.

3. of good character in work place and an honest promoter of mathematics and mathematics teaching and of truth, as the virtue of mathematics is truth.

4. who promotes professionally ( related to social dimensions ) the only cardinal way of learning mathematics is DOING MATHEMATICS

5. that knows mathematics is also an excellent antidepressant more than any other social activities.

Математика это:

-  часть культуры;

- мировоззрение;

- инструмент в повседневной жизни

Методика обучения математике должна включать в себя дедуктивные и индуктивные подходы к изложению материала.

A very high, and very rapid capacity for abstraction.

—g

A key point would be the ability to link abstract concepts to everyday situations.

The neuroscientist David Eagleman, in his book 'Incognito', demonstrates how abstract mathematical concepts are taken on board much better and faster when related to everyday situations - because of the way our brain works.

Keith Devlin, coming from a totally different angle, had made the very same point in 'The Math Gene' 

The mathematics teacher must know how the brain learns and keep your students alert and relaxed at the same time. For this you need to develop their social skills, so that creates a pleasant atmosphere in the classroom.

The question asks social skills, not professional and mathematical skills as abstraction and cognitive activities of the subject are mathematical.

Besides I want to reduce the superlative I used " excellent  communication skills"  skills to just a moderate skill of communication in human languages as mathematics by it self is a language which has its rules, syntax and semantics. The reason I said this is because if some one wants to teach a foreign language he/she should not be expert in his/her language but expert in that foreign language. 

The priority has to do with getting students to feel comfortable and not threatened.

Often on the very natural difficulty of the language of mathematics, another difficulty arises. I mean a hostile, fearful or defensive physiological response to learning mathematics.

In this context, the teacher should be able to reverse the situation?

Dear Guillemo,

Have you encountered such a mathematics teacher while you were a student? I did not have one when I was a mathematics students and I am not that kind of mathematics professor now. I always welcomes any type of question my students have and explain to them until they get the concept and understand it. 

I share your opinion. My vision is related to the unwillingness of students to learn mathematics despite the traditional view of mathematics teachers. I mean that mathematics teachers should thoroughly understand how the human brain learns.

Indeed it is necessary to know how the human brain works, but I am afraid that is not the job of a mathematics teacher/professor. When I was a student, there wasn't any special treatment or incentive from teachers but I just liked mathematics for its abstraction, its extraordinary use in other fields of science and for society. Perhaps it is  the field of study that enables humans to condition how to think right and become a just person. Regarding students'  unwillingness to learn mathematics, there is a very outstanding reason  we see.  

Contemporary society is changed to a society of celebrity, wealth and luxury and because of that people are influenced by those who live in their neighborhoods or afar in different and luxurious life styles than others. Those differences are purely differences of material wealth  and for that reason young people want to be like those celebrities of wealth not of knowledge in which non of them studied mathematics. That is the kernel of the matter, not a dislike per se  for mathematics but finding it unhelpful to become what they want to become in the world of celebrities of wealth and luxury.

Dear Dejenie, 

I'm not sure if I agree with you here. All of the students I know - and for that matter all of the young folks I know - could not possibly care less about ostentatious wealth, being famous, bling bling, luxury, fashion trends, and other braindead pursuits. Not a single person I know happens to harbor the slightest interest in celebrities. They could not possibly care less about who Lady BlaBla is or what she does, etc. 

I would think that those uninterested in, or ill-equipped to study, math or the hard scences from the word go - i.e. people who might perhaps want to become involved in fashion or whatever - might indeed be interested in bling bling, but that is not the cause of their lack of interest in science , it is a side effect of their personality type. Maybe you happen to have come across that type, but you may not generalize

Dear Chris,

I  concur with you on the most common reason perhaps we assume we know , ill preparedness and therefore dislike to the subject, because of over population of abstractions and symbols used (as their argument) and therefore a sense of detachment. If personalities do matter, then that probably is what I meant, because personalities and social cultures of almost all young students becoming similar globally due to globalization. But as you said, I am not completely putting the blame on bling bling culture but on well living cultures.  Perhaps I am suggesting  causes different from being ill preparedness and phobia to the subject so that we have some reasons as to why students do not want to study mathematics. I know students who say they want to study other disciplines than mathematics for the mere reason that studying mathematics will not offer good life after graduation, which is not by any standard, a generalized observation and statement.