The Study Of Strategies In Solving Mathematical Ill-structured Problem In The Higher Grade Of Primary School

The ability of students to solve problems has always been the focus of mathematics education.In recent years,the requirements for mathematical problems have gradually become life-oriented and contextualized,emphasizing learning in context,and cultivating students' ability to solve practical problems.The ill-structured problem was first raised by the American scholar Reitman.It originally referred to practical problems in life,such as repairing computers and designing travel plans.Problems in real life situations usually do not have clear information for solution,and the solver needs to create conditions or methods to solve the problem.Compared with the traditionally well-structured problems,the ill-structured problems problems in mathematics are more closely related to real life problems.The solution of such problems can better train students' ability to solve practical problems,form advanced knowledge,and promote the development of mathematical thinking and innovative consciousness.However,in the practice teaching of mathematics,it is found that the students' performance in solving the ill-structured problems of mathematical structure is poor,so they explore the students' thinking obstacles and strategies to solve such problems,so as to carry out targeted problem-solving teaching and truly promote the improvement of problem solving ability.This article is based on the study of ill-structured problems.It mainly uses the methods of literature,text analysis,and vocal thinking to study the ill-structured problems of mathematics in primary school.Firstly,through literature review,analyze the research status of ill-structured problems,and look for insufficient research and theoretical support.Secondly,based on previous research results,according to the types of structural problems of structurally ill problems in elementary school mathematics,ill-structured problems can be classified into four types: conditional open,strategic open,conclusion open,and situation open.Through text analysis of primary school mathematics textbooks and exercise books,the meaning and solving characteristics of the four types of poorly structured problems are analyzed,and the educational value of solving the ill-structured problems is sorted out.Then,based on the SOLO classification theory,comb and construct the thinking obstacles and solving strategies for seniorstudents in elementary school to solve the structural problems in mathematics.Based on this,using vocal thinking to investigate and analyze the current situation of senior students in primary schools solving mathematical ill-structured problems,it is found that the top students in primary school mainly face situation-related obstacles,while the middle school students are overall inductive obstacles.There are significant differences in the use of cognitive strategies such as "recapitalizing points","equivalent transformations",and "orderly thinking".There are significant differences in "self-directed" and "self-monitoring" metacognitive strategies.In addition,when students solve different types of ill-structured problems,their thinking barriers and solving strategies are obviously different.Finally,combined with the theoretical basis and survey results,the teaching strategies for solving different types of ill-structured problems are proposed for the three types of thinking obstacles that students show during the solution process.In order to overcome the obstacles of clue association,overall induction and situational association in the process of solving ill-structured problems,to help students successfully solve ill-structured problems in mathematics.Use multi-representation,reverse thinking,and "hypothesis-validation-comprehensive" teaching mode teaching strategies to solve the ill-structured problems of conditional open;use auxiliary representation strategy,analysis and comparison strategy,and review and summarize teaching strategies to solve the ill-structured problems of strategic open;use the problem determination strategy,identify the problem strategy,classify and summarize the teaching strategy to solve the ill-structured problems of conclusion open;use the multiple presentation problem situation,constructive classroom,multidimensional evaluation teaching strategy to solve the ill-structured problems of situation open.