Mathematical Cognitive Structure, Theory And Practice Of "three." Teaching Mode

This article aims at analyzing all factors which hinder students from establishing good mathematical recognition structure (MRS), based on a penetrating study on the theory of recognition structure, mathematics study, and teaching approach, compared with the concept, characteristics, main elements and procedure of development. Considering existing problems in the teaching process of mathematics course, combining my personal teaching practice with the theory above-mentioned, the author put forward "Three-Stage" and "Three-Pattern" teaching approach ("Three-Three" model), and made an empirical study on the comparison with the traditional teaching methods.It is asserted in this article that the objective of mathematics course is to establish a good MRS for the students. MRS is a system composed of mathematical knowledge, ability and quality systematically, and the three factors are inter-connected, mutually influenced and coordinated. There are three approaches to develop MRS, i.e. mathematics evolution, mathematics experiments and mathematics practice. And the aims of MRS are to make themselves usable, distinguishable and stable.It is also stated in this article that student-centered, knowledge-objected and teachers and technology-aided elements play an important role in establishing and developing MRS .In the course, central elements is internal and decisive while objective and aided elements work through influencing the central elements and are external.According to the theory of MRS, mathematical teaching activities should be value-oriented and goal-directed by making use of and developing good MRS of the students, and should reflect student-centered and self-dominated assertion. At the same time, the teachers and modern technology should be brought into full play, and the teaching contents should be developed to be well-organized, structuralized and integrated. Hence, the "Three-Three" teaching model is put forward to comply with these teaching principles.According to the three elements forming MRS, and their inter-connection and mutual progression, mathematics learning and MRS formation are divided into the phase, i.e. knowledge acquisition, ability improvement and quality development. In correspondence to the functions of the three phase, mathematics teaching is classified into three teaching patterns as theoretical teaching, empirical teaching and practical teaching, so that purposefulness. gradualism and systematism characterize mathematics teaching and are conductive to the full development of students mathematics knowledge, ability and quality.This article analyzes and sums up the experiment results of the "Three-Three" teaching model in comparison with traditional methods. The teaching content of the experiment is Unit One "Permutations and Combinations" of Chapter Nine in Book Two from Algebra and Primary Geometry for intermediate normal schools. The experiment was conducted in two classes with their mathematics at the same level through adopting two different teaching models separately. After the teaching, the two classes took the same test. In this way, a conclusion is drawn that the "Three-Three" model takes precedence over the traditional methods in teaching.