Construction Of The Theory Under The Guidance Of High School Math Problem Solving Instruction

Problems are the core of mathematics. Solving problems is the key link and the fundamental way. The teaching of solving problems not only teaches students how to solve problems, but also throw light on the important mathematics thoughts and methods. It makes students strengthen the understanding of all kinds of concepts, formulas and theorems. So it is an individual part in the process of mathematics teaching. But under the pattern of examining education, the teaching of mathematics problems solving in high schools has many abuses. Reform is necessary.Constructivism is the further development of Cognitive learning theory, which is quite popular in the western countries nowadays. The core of this theory is that the learning process of students is not a passive acceptance of knowledge but an active construction of knowledge based on their former knowledge and experience and this activity must be carried out in a certain social environment, thus it possesses sociality. The main contents of this theory are as follows:(1) Knowledge is not absolute. The understanding to knowledge results from the influence of the experience of learners.(2)Learning is a process that students develop construction of knowledge by oneself, and it should not be passive.(3)There are already some knowledge and experience in the minds of students. Students are the persons who can participate the instruction process in a positive way. And students pursue their studies by collaboration andcommunication.(4)Teachers are the helpful, collaborative and progressive persons in the learning process. So teachers should provide real conditions and organize collaborative learning.According to the theories mentioned above, the paper tries to elicite a set of teaching principles and tactics which are much practicable in the class teaching of high school meathematics, and instruction favorable to the teaching practice.The Constructive teaching principles described in this essay are as follows:(l)Teachers should support students to have self-regulation on all problems, and encourage students to make an all-out effort to participate learning process.(2)All actions done by teachers serve the construction of students, and help students solve problems all by themselves.(3)Teachers should design learning situation which are properly difficult, make students not to accomplish mission without efforts. This way, the best learning intention in students can be stimulated.(4)Teachers should guide students in raising questions and solving questions constantly. So students will be promoted in the development of ability and quality.(5)Teachers should create a democratic atmosphere, promote the social interaction between teacher-pupil and pupil-pupil.Tactics of instruction are as follows:(l)The good cognition structure should be built. And students should grasp the stable genetic methods relevant to specific knowledge.(2)The properly difficult problem situation should be provided to the students, and it can arouse students the passion of discussion, exploration and research.(3)Teachers should instruct students in exploring and experiencing actions, and try to make students solve problems all by themselves.(4)0ne question with several answers. Students should be encouraged to achieve different answers with different methods.(5)Change question into a difficult form, make knowledge of a single example leading to understanding of the entire category. Teachers should guide students to deal with the same questions in different ways. Thus, not only the cognition structure in students will be deepened and developed, but also the ability to solve problems will be improved greatly.(6)The consciousness should be strengthened to mull over past solving process, and the thinking character should be optimized. In this way, through debating, exploring, evaluating, and the guiding of teachers, students can sum up thinking methods and accumulate experience in good time.Under the direction of this theory, I carried out a wide range of teaching practice and reached the following conclusion: It, the teaching of how to solve mathematics problems in high school under the direction of Constructivism Theory, is beneficial to the improvement of students' interestin mathematics and the transformation of their attitudes, as well as the progress in their learning.