The Probing Pedagogical Design Of Mathematical Problems Construction And Solution

Mathematics is composed of problems which are the base for probe or exploration. The mathematics learning capacity of students is in fact a kind of probing and creative ability to solve mathematic problems. Conforming to this kind of educative rule, this project is devoted to the pedagogical operation of solving effective problems and solving them effectively, and to the three critical aims of being active to study, being good at study and being capable of solving practical problems. In view of this proceeding from the disciplinary features of the mathematics of senior high school which are high generality, strict logic and high abstract and from the thinking characteristics of senior high students which are dominant abstraction and developing dialectical logical thinking, this project strives todesign the effective problems in the course of teaching which are challenging problems, extended problems, practical problems, purposive problems and thematic problems, and carry out the effective ways in solving problems on the basis of the miniature pedagogical experiment which are dialogue. Cooperation, research, evaluation and rectification. After that, this project tries to perfectivize the human developing system (the product system) through the interactive conformity between teachers' pedagogical development system (the operative system) and students' learning development system (the aim system), which are brought about by problem-oriented teaching and problem-oriented learning.This experiment gives the following tentative conclusion: The probing teaching which involves construction and solution of mathematic problems can to different degrees activate the learning interest of students (being active to learn), cultivate their ability of probing and exploring problems (being good at study) and henceforth increase their mathematical score (being capable of solving problems). This fully corresponds and testifies the basic idea of new criteria mathematics, that is, to make students study the courses by themselves and study their own courses.