Let us leave aside the personal qualities, such as love and passion for the profession, and concentrate on professional qualities of a good math teacher for modern times. In the past learning was more often than not equated with memorizing and an effective teacher was the one who could come up with most memory devices (often involving a variety of emotional devices).
Computers and internet have diminished importance of human memory. We need people who possess enough understanding to search, process and use new information more than we need people with total recall. So, for students to achieve such understanding (deep learning) we need teachers who know their subjects and are able to engage students in discussions that reveal what is “inside their minds” so that these minds can be properly “formed” (“formation” is the word used in many languages to mean “education”). An ability to use group dynamics and emotional devices remains of utter importance. Ability to use technology is helpful but, in my view, its importance is sometimes exaggerated.