Teaching Math in the classroom II

This article is the sequel of the first article with the same title in which we will talk about the other facts we need to take in consideration for teaching math in classroom in the good way.
4. Common sense.
The questions and recommendations from our list are general and also natural, simple, obvious and come from the common sense. Let's take the recommendation: "Let's check the unknown! And let's think of a known problem having the same unknown or a similar one." This recommendation will make you do what would you have done anyway, without any advice from nobody, if you are seriously concerned about the problem. Are you hungry? You want to find food and you are thinking at the common ways to get it. Do you have a problem with a geometric construction? You want to make a triangle and you are thinking at the common ways to build a triangle. Do you have a problem of any other kind? You want to find a certain unknown and you are thinking at the common ways to find such unknown or a similar one. The one who proceeds this way, follows the recommendation cited in our list. And he is on the right track, it advises him to adopt a process which, frequently, proves very successful.
All
the questions and recommendations from our list are normal, simple, obvious and come from the common sense;
but they enunciate in general terms this common sense. They suggest a conduct which comes in a natural way to the mind of anyone who is seriously concerned about his problem and which is possessing a certain amount of common sense. But the one who takes the right track doesn't usually care about explaining his behavior in a flowing form and maybe he is not able to do so; our list tries to give such an expression.
5. Teacher and student. Imitation and experience. Asking a question or making a recommendation from the list, the
professor may consider two objectives: the first one is to help the student to solve the problem he is currently working and the second one is to develop his abilities so that he will be capable in the future to solve the problems on his own. Our experience shows that the questions and recommendations from our list, if they are used properly, are very often useful to the student. They have two common features: common sense and generality. Given that they come from the common sense, they come easily and natural in the mind; the student could also find them by himself. Given that they are general, they help the student in a discrete way; they are just showing a general direction and leaves him all the possibilities to take action by himself.
But these two objectives mentioned above are closely related; if the student succeeds to solve the problem which he is currently working, he adds a little on his abilities to solve problems. And also we need to not forget that our questions are general, applicable in numerous situations. If the same questions gets useful repeatedly, it's less probable that the student to not realize this which will determine him to put himself the same question in a similar situation. Putting himself the same question repeatedly he will finally manage to get the right idea.
By this success, he discovers the good road for using the question and then he assimilated it for real. We will continue. Thank you