Middle School Mathematics Teaching Of Cognitive Ability

In teaching mathematics, according to the modern theory, it is of great significance to cultivate the cognitive skill, which not only affects the learning process and result but also directly influence the forming and development of the students' future mathematical ability. This paper is written to sketch out the research work done on cultivating the cognitive skill with the following generalizations:I. The students' cognitive structure is the material base for cognitiveII. skill. In teaching mathematics, stresses must be put on the perfection of the cognitive structure. The reflective ability in solving mathematical problems plays an important role and acts in the forming of the cognitive structure. Both experiencing and understanding the process of happening and developing of the mathematical knowledge and taking an active part in learning activity by way of experimenting and observation are very beneficial to the forming of the students' cognitive structure.III. The teaching of cognitive policy is an important method in perfecting the students' cognitive process. And the teaching of cognitive policy must be combined with the teaching of concrete mathematical material and also be combined with the students' experiencing activity and teacher's cooperative teaching. In practice, it is found that students may easily neglect the managing policy of the cognitive resources, therefore, it demands strengthening in concrete teaching practice.IV. The research on modern teaching method shows that the level of reflectively cognitive skill has a direct effect on the result of mathematical learning. In cultivating the reflectively cognitive skill, students need to know their task of learning, to understand the position and function of their mathematical knowledge and also the conception and habit of self-evaluation. In guiding the students to draw conclusions on their mathematical learning, it is also very useful to the heightening of the students' self-cognition level and to the promoting of their reflectively cognitive skill.V. Improving cognitive skill can finally be realized through the heightening of the students' self-supervision level. The self-supervision in learning may include three aspects: self-supervision before learning activity, self-supervision during learning activity and self-supervision after learning activity. The above three aspects must be carried out throughout the teaching of mathematics, so as to cultivate students' initiative in learning and mastering the way of thinking in mathematics. Reflection is the core of the ability of self-supervision. In teaching mathematics, it is essential, through many different channels, to cultivate the student's habit of reflection.VI. The students' cognitive skill in mathematical learning takes shape from vagueness to clarity, from unfamiliarity to familiarity. In teaching mathematics, the teacher ought to evaluate the student's cognitive process with appreciative views. Only through the evaluation and revision of the students' own cognitive process can the teacher make improvements in the students' cognitive process and encourage the development of the students' cognitive skill.