A Study On Mathematical Problem-solving Strategies Of High School Students

During my ten years’ teaching career,it has been found that many students can’t make good use of the basic knowledge that has been learned to solve mathematical problems of the senior high school.The strategy of mathematical problem solving is the specific guideline to achieve the goal of solving problems,the media of transforming ideas into concrete solutions.It lies between the concreteness of the method of problem solving and abstractness of the idea of problem solving.Therefore,the strategy of mathematical problem solving is an important factor which influences the problem solving of mathematics.Exploring mathematical problem-solving strategies can practically guide the effective and scientific teaching of the problem-solving strategies and thus improve the ability of mathematical problem-solving.Accordingly,by using paper and pencil tests,task-based interview,the comparative research,and the Ten Strategies of Problem-Solving by professor Luo Zengru,a “High school math problem-solving strategy test” was edited to do research on the choice of strategies of mathematical problem solving when students are asked to find as many ways as possible to solve a mathematical problem and the different performances of strategies of mathematical problem solving between the science students and arts students,as well as between the boys and girls.It can also show the use of strategies in different conditions.In order to reflect the scientific nature and representativeness of the tested samples,this research has selected the gifted class of arts,the gifted class of science and the middle class as samples of research,which involves134 students and then collected and sorted out the problem-solving strategies used by students in solving mathematical problems,with data analyzed through Spss.Below is the conclusion of the research:1.Strategies of mathematical problem-solving used by students(1)the strategies used by students : positive and negative interaction,integration of separation and combination,combination of numbers and shapes,effective addition,pattern recognition,differential analysis,mutual transformation,Enlightening the truth through the beauty,mapping.(2)The application of strategies of mathematical problem-solving: When solving the mathematical problems,most students can make good use of the positive and negative interaction,integration of separation and combination strategies.The second most used strategies are pattern recognition and effective addition.And then,there come combination of numbers and shapes and mapping.Mutual transformation,enlightening the truth through the beauty and differential analysis are least used.2.The different performances of the use of strategies of mathematical problem solving.(1)The differences of using strategies of mathematical problem solving between arts students and science students,and differences between boys and girls: Most arts students and science students use positive and negative interaction,integration of separation and combination strategies and there are no obvious distinctions.Differential analysis,mutual transformation and enlightening the truth through the beauty are not popular with students.There are some distinctions between another 4 strategies: Art students are obviously better at pattern recognition and mapping;science students are better at combination of numbers and shapes,and effective addition.The characteristics of using strategies by boys and girls are almost the same as those of science students and art students.(2)Different performance results of mathematical problem-solving strategies in different situations: In order to reflect the difference of students’ strategies in different situations,in this study,the relative quantity was used to compare the strategies adopted in the restricted situations and those in the open situation.:In process restricted situation,the differences of strategies of mathematical problem solving between art students and science students,and the difference between boys and girls agree with the previous analysis of the differences of using strategies of mathematical problem solving between arts students and science students,and differences between boys and girls;In the process-open situation,science students are better than arts students in the application of three strategies.Boys are also better at using the three strategies than girls.The difference between science and arts is more obvious.The three strategies used by high school students in restricted situations are better than open situations,with the pattern recognition strategies standing out.