High-level Mathematical Thinking And Mathematical Self-monitoring Capacity Relations

Advanced mathematics has made a qualitative leap both in ways and in subjects compared with primary mathematics. Its abstract content and logic always put students in puzzle in learning. The survey has proved that there is close relationship between students' scores of maths and their self-monitoring ability and the mathematical thinking. So the level of thought quality and mathematical self-monitoring ability are the most important factors to affect students' scores of maths. The relationship between the thought quality and self-monitoring ability is that of cause and effect, the self-monitoring ability being the cause and the thought quality the effect. In fact, they are two sides of a same coin, constituting the important parts of the whole thought construction. The thought quality is the external form of the thought construction functions, representing a surface layer, while the self-monitoring ability is the internal form of organization, a deep layer.Nowadays in school mathematical education, teachers pay more attention to mathematical knowledge and problem-solving techniques than to knowledge-discovering process and teaching and application of mathematical thinking methods, more to the cultivation of students' ability to cope with tests than to the cultivation of their ability to think and research. This has not adapted to the current request of quality-oriented education. Therefore, it is critical to cultivate students' self-monitoring ability, increase students' mathematical thought quality and solve the problem how to teach students to study, thus developing students' intelligence and creativity and promoting the all-round development of students' whole quality.