Junior High School Mathematics Problem Solving Learning, Spontaneous Insight And Metacognition Empirical Research

The solving mathematics problems is one of indispensable means in studying mathematics, the mathematician all needs to come to improve self mathematics accomplishment by solving problems even disregarding being pupil, junior school student, high school student, college student, graduate student, mathematics teacher. At home and abroad, the research in solving problems, has at present mainly:the pattern of Cognition constructs, the pattern of automation technical ability forms,the pattern of model construction and the pattern of open problem, etc. in the middle(high) school solving problems are at the steps of copying simply and variant exercise (the characteristics in our mathematics teaching), many teacher and students are busy in all kings of mathematics exercises, and make some generalization in very low degree. Some mathematics teachers teach the ways and the tactics in solving mathematics problems (has extremely strong individuality difference and the generalization is in very low degree).but Luo Zeng Ru put forward a very useful way in learning solving mathematics problems:The simplicity copies, the variant practices, the consciousness understanding and the spontaneously analyses. the four step formula of Luo Zeng Ru in learning solving mathematics problems is validity and useful. and it is supported by many theories about solving mathematics problems.This paper reviews the basic theories of mathematical problem solving instruction, divided into the following three aspects:(1)the basic concepts of mathematics problem-solving focuses primarily on mathematical problem and solving mathematical problems;(2) Overview of Psychological Studies in mathematical problem solving focuses primarily on the psychology theory of problem solving and mathematical problem solving in psychology theory; (3) the pedagogy of mathematics problem solving profile, divided into study abroad and domestic research profile overview. to extend the theory in mathematics education,we begin our study in the base of the four step formula of Luo Zeng Ru in learning solving mathematics problems. And the examination in our study certificate middle school student in learning to solve problems existing the stage of understanding spontaneously,and we also want to demonstrate the validity of the analysis process of solving problems to the middle school student, further, We will bring forward the new way of training solving problems,(four steps formula). At the same time, we return back to oneself monitor the ability, CPFS structure and spontaneous relation understanding, analysing conscientiously a room's, and effect demonstrating oneself monitors to solving problems further thinking that the further exploration student mathematics solves problems. the study results are mainly:(1) student learns to solve problems process has a stage of understanding spontaneously. (2) conscientious analysis is conducive to a student in solving problems. (3) the ability of student mathematics ego monitors have a directive function in solving problems. (4) the individual factorization CPFS structure test is positive correlation with the test results of factorization problem.Student learns to solve problems process has a stage of understanding spontaneously. but there are many problems still needing study, such as why there is a stage of understanding spontaneously in learning to solve problems process, and how we can improve the ability of student mathematics ego monitors.