High School Mathematics Thought Disorder, A Preliminary Study

The study of mathematical thinking obstacles of the senior middle school students is of great significance to enhance actual effect of mathematical teaching.Thought is a general and indirect reaction which brain has on objective things. Furthermore, it is also a reflection of the essence and law of objective things. There are many statements on the boundary of mathematical thought. In the view of the article, mathematical thought is aimed at mathematical activity. It is a process of cognition to acquire the essence and law of mathematical objects (space form, quantity relation, structure mode) by rising analyzing, solving, applying and popularizing mathematical problems. In this process, the consciousness of brain can receive, analyze, and choose. Process and conform the information of mathematical objects. In the problem solving, if students have not fine thought quality, they will hardly solve problems smoothly. Then thought will discontinue or dislocate. This phenomenon is thinking obstacles.Traditional education puts center on teachers and books. This results in the authoritative tendency and the book tendency in thought. The condition limits the thoughts of the students and causes thinking obstacles to a degree. Quality education puts forward a new requisition that not only lets students master knowledge, but also puts attention to mental development and improving ability, especially thinking ability. However, the key of deepening students thought and conquering thought obstacles lies in the guidance of teachers. Under teachers' guidance, students can explore effective methods and ways of overcoming thinking obstacles.The article has mathematical learning ideas, theory of knowledge and psychology of constructivism as theoretical basis in studying mathematical thinking obstacles. Mathematical constructive activity is a mathematics abstract process and a process if developing and deepening uninterruptedly. Only students "construct and self -examine" and "self-examine and construct" continuously, can they construct knowledge accurately and master knowledge completely. Or they will form thinking obstacles. According to Bmner's knowledge development theory, learning itself is a process of cognition. When students understand knowledge insufficiency and partially, they will produce thinking obstacles in solving problems. The effect, which a kind of study has, another is called transference, in psychology. According to the nature and effect of transference, psychologists generally divide it into positive transference and negative transference. To make full use of transference may help students overcome thinking obstacles and improve thinking ability.The article probes into the formal factor of mathematical thinking obstacles from three aspects: meta-cognition, thinking tendency, and process knowledge of mathematical activity.Meta-cognition is cognition and control to thought and learning. It is an understanding of self-cognitive process, cognitive product or all kinds of things about cognition. In a word, meta-cognition is the cognition to cognition and the thought to thought. It is very important to cultivate students' thinking ability. In the process of meta-cognition participating regulate and control of thinking, there are three basicprinciples, that is, agent principle, aesthetic principle and reflective principle. The fundamental form by which meta-cognition gives full scope to mathematical thought is self-examination. The weakness of meta-cognition will form the deficiency of mathematical thought and lead to its obstacles.The other reason of forming thought obstacles is negative effect of thought tendency. Being affected by their former mathematical knowledge and successful experiences, students lack right cognition to the nature attribute of new conception and knowledge. Besides that, they will be affected by some factors. For example, habit, the function fixity of things, visual sense interference, non-intelligence factors and so on. All these will produce thinking obstacles.The art...