I think I go with the first suggestion is the fact that I am open to surprises. I am a kind of teacher that tells the pupils to always open their minds to learning at any given opportunity not just from their teachers but from their parents and every other person available to offer them knowledge. I later discovered that David's mother is a Mathematician and she had finished the topic with the boy after introducing it in class.

Regarding to the question about alternatives to reward and punishment in dealing with the pupils, there are many other ways of making the pupils willing to do necessary tasks and improve their learning experiences. I encourage them that they can achieve a given task. I make them see value in doing it and let them know that the cost of doing it is within their reach. I make sure I motivate them intrinsically so that they are eager to do the task without any kind of force.