The Theory Practice Research On How To Develop Student's Reflective Abilities In Middle Schools Mathematics Teaching

Reflection is meta-cognition, which consists of three parts: knowledge, skill and perseverance. Reflective knowledge includes declarative knowledge, procedural knowledge and conditional knowledge, while reflective skill includes experience, theory, analysis, evaluation, strategy, practice and so on.Reflection is the core and motive force of mathematical thinking activities, the basic form of mathematical thinking in which metalognition plays its role. Therefore, we can say that mathematical reflective ability is self-conscious and self-controlling ability that the students apply for their own mathematical cognition process in mathematical thinking activities, such as in mathematical learning or mathematical problem solving. It's reflection that makes real world to be mathematical.Generally speaking, to be possessed of mathematical reflective ability, one must experience four stages: unconscious reflection, passive reflection, positive reflection, and conscious reflection. However, influenced by the teacher's teaching idea, teaching methods, ways of teaching material presentation, teaching evaluation, students' maturity and their ways of cognition, almost all the students are short of reflective skill and method, which directly leads to low level of reflective ability and consciousness. The development of students' reflective ability is quite different from each other. Most of them are on the first or second stage, only a few, on the third or fourth. This greatly limited initiative and creativeness. Therefore, it is necessary and feasible to develop students' reflective ability in senior mathematical teaching.The developing of students' reflective ability is a circulation process, in which there are four steps: query arousing, demonstration, practice and reflection. Demonstration and practice is the crucial link of this process, while correct cognition of the students is the key for the positive reflection. Therefore, in order to promote students to reflect positively, and get into the habit and conscious of reflection, the teacher should take great consideration of students' thinking and attitude, and give proper evaluation to their learning process.The developing of reflective ability achieved from two ways, teaching in class and practice out of class. The concrete methods are: 1.To expose the process ofthinking, and demonstrate reflection. 2. To evaluate the authenticity to promote reflection. 3, To assign reflective task, and carry out reflection. In general, students should begin with the following three aspects in reflective mathematical learning:1. To reflect validity of knowledge, skill and technology employed in the process of mathematical problem solving.2. To reflect learning strategy and its rationality used in the process of mathematical problem solving.3. To reflect objective of mathematical activity, motivation and other non-intelligence factors.As a result, reflection changed students' cognition towards mathematical learning. They became interested in mathematical and have confidence in studying it well. Meanwhile, it enhanced their initiative and creativeness in mathematical learning. They mastered the methods and skill of thinking, got tactical knowledge, evaluated themselves properly. Some students even applied this strategy to other subjects learning. We can say that reflection is quite efficient in improving qualities of the students as a whole.However, it's a pity that reflection makes some students lose their hearts in mathematical learning, and it is not obvious in improving their scores.