1. Let's help the student. One of the most important tasks for a teacher is to help his students in the right way. This task is not so easy as it seems; it requires time, experience, dedication and healthy principles. The student must gain a larger independently work experience. If he is let alone with his problem, hot helped or helped partially and insufficient, he might not progress at all. If the teacher helps too much, the student has nothing left to do. The teacher must help, but not too much and not too less, so that the student to have a rational part of work for himself also. Mo matter if the concerned student is not able to do a big deal, the teacher must give him the illusion that he works independently. To realize this, the teacher must help his student in a discrete, not annoying way. The best is that the student to be helped in a natural way. The teacher must place himself in the student position, to see his learning difficulties, to try to understand what happens in his mind and to put him a question or to show him one step that he could also had in mind.
2. Questions, recommendations, intellectual operations. Seeking to help the student in an efficient way, but in a natural and discrete way, the teacher is headed to put always the same question and to show the same steps. This way, in countless problems, we need to ask: "Which is the unknown in our problem?". We can change the words and ask the same thing in a different way than before: What is required? What do we want to find? What do we need to search? The goal of these questions is to concentrate the attention of the student over the unknown. Sometimes we get the same effect in a more natural way by a recommendation like: "Let's check the unknown!" The question and the recommendation follow the same result; they tend to trigger the same mental operation. It is useful to gather and group the questions and recommendations typical worthy for the student when a problem is discussed with him. The list we need to study contains questions and recommendations of this kind, chosen and ordered carefully; they are just as useful for someone who solve problems working individually. The list enumerate, not in a direct way, intellectual operations typical helpful in solving problems. These operations are passed in the list according in the order they occur most frequently.
3. The generality it's an important characteristic of the questions and recommendations which are in our list. Let's take the following questions: "Which is the unknown in our problem we need to find? What are the data we know in our problem that we can use? Which is the condition in our problem we need to respect? " . These questions have a general application, we can formulate them with good results in any kind of problems. Their benefit is not limited by the subject of the problem. We can have an algebra or geometry problem, mathematical or not, theoretical or practical, a serious problem or just simply a game; no matter its state, these questions keep their sense and can help us solve the problem. It's true that there is a restriction or limitation, but it has nothing to do with the subject of the problem. Some questions and recommendations from the list are applicable only for the problems in which we need to find something and not for the problems in which we need to prove something. If we have a problem of the last kind, we must take in consideration other questions. We will continue. Thank you
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