The Study Of Instruction Design To Facilitate Primary Pupils Problems Solving Of Math

Our society is developing rapidly, economy based knowledge and society of information is coming. Under the challenges of new era, all countries in the world make out the criteria of a person of ability and the ability to solve problems as one important part of the criteria is valued more and more. And at the same time, all countries are making rapid reforms of the curricula and instruction among the basic education, strengthening the value of knowledge to the life, reconstructing the system of the curricula of basic education, strengthening the connection and integration among knowledge, and encouraging pupils' taking active part and enquiry. Under the backgrounds, people being engaged in math education commonly strength the value of problem solving. Under the background, Ministry of Education of our country has promulgated "Schema on basic education curricula reforms (trial)" and "Criterion of mathematical curricula about pan-day compulsory education (experimented)". In them, cultivation to pupils' ability to solve problems has been emphasized. To get the goal, the module of Practice and Application of Synthesis is designed in the Criterion. It has been proved that the consciousness and ability of problems solving in our primary students is not optimism. The article mainly consists four parts. Firstly, the article analyzes some things about problems solving, including what is mathematical problems, how to sort them, what is good problem of math, what's math problem solving, what's it characteristics and something about developing of the research on math problems solving in education. In part two, the article gains the general procedure of problems solving about math by analyzing the typical models about problems solving and problems solving of math. Then the article regards it as the clue and analyses the process and important factors over problems solving of math. In part three, the article is about how to design to facilitate mathematical problems solving of primary students including how to upgrade the problems consciousness of students, how to optimize the mathematical problems representation, how to train the primary students with strategies to solve problems, how to advance pupils' ability of regulating and rethinking in problem solving. The article thinks that we should create problem situations to make pupils have problems, should create human culture surroundings of democracy and equality to make pupils presume to ask something, and should teach them to how to question. To optimize the mathematical problems representation, the article thinks we can improve the quality of mathematical knowledge of them with Concept Maps. And the article tells us to how to break down the ill-attitudes of representation and grasp how to utilize all kinds of models of representation properly. And the article thinks that we can teach pupils the conditional knowledge, use the strategy of sonic-thinking, and arrange the variant exercises properly. And then the article gives something about how to cultivate the consciousness and habit of rethinking, make pupils grasp the strategies of rethinking and how to settle the activities of rethinking. In part four, the article analyzes two cases on mathematical problem solving to tell us how to have a lesson of mathematical problem solving. At last the article draws a conclusion that the core of mathematical problem solving is pupils' active participation and advanced cognition participation that is one of hot spots in education reforms and should be centre things when we make systematic design about problem solving.