Research On Triangle Problem Strategy What Solved Based On Ill-structured Problem In Senior High School Mathematics

It is a necessary knowledge in the college entrance examination,which triangle what solved is the content of the section “Plane vector and its application” in the module of “Geometry and Algebra” in high school mathematics.In 2020,the ill structural problems of triangle are appeared in the Shandong and Hainan volumes of the college entrance examination.Although the emergence of these problems improves the difficulty of solving problems,but we find that the thinking ability increased,the essence of mathematics comprehended,achievement experience enhanced,and the cultivation of core literacy promoted for students in the process of analyzing and solving problems.Three problems are solved via literature research method,statistical analysis method and case analysis method as follows:(1)We make a statistical analysis about the knowledge points,mathematical thinking methods,key abilities and questions examined in solving the problem of ill structure problem of triangle in the new round of college entrance examination reform;(2)We analyze the current situation of solving the ill structure problems of triangle to senior three students by using Gagne information processing mode and Polya problem-solving theory;(3)Through the analysis,the influencing factors are obtained,and the corresponding teaching countermeasures and solutions are put forward.The results are as follows:Firstly,the problem of the ill triangle structure solved is taken as an example in the college entrance examination questions after the new round of college entrance examination reform,there is a research object that takes the senior graduating students of S district middle school in Huizhou,based on the characteristics of making of college entrance test about the ill triangle structure problems that solved,missing conditions and open conclusion of the ill problems,the form of test investigated for students,we make a statistical analysis of the students’ answers,the conclusions what obtained are as follows:(1)Knowledge: simple application of sine theorem and cosine theorem,problems in triangular trilateral relations and trigonometric function values of special angles;(2)Ability: It is weak that students’ the ability of reasoning and demonstration,calculation and solving and problem analysis,and their corresponding mathematical operation literacy and logical reasoning literacy have not been reached the requirements of level 2;(3)Mathematical thoughts: the problem of unsuccessful transformation due to intellectual errors;(4)Strategy: the choice of alternative conditions is not based on the substance implied in the determined conditions,resulting in strategic errors.Secondly,for the existing problems of students,four teaching countermeasures and nine problem-solutions are given.With regard to teaching:(1)reveal the essence of mathematics and return to the origin of knowledge and thoughts;(2)Using mind mapping to develop students’ relevant thinking;(3)Making good use of problem variants to cultivate students’ critical thinking;(4)The teaching method is to cultivate students’ ability of reverse thinking and flexibility.Problem solving strategies:(1)Analyzing common information from the angle;(2)Schema representation;(3)Starting from the two theorems or using comparative analysis to find alternative options;(4)Defining the transformation direction of alternative options according to the determined conditions or the problems;(5)Using special case method to transform problem representation;(6)Using "priority strategy method" to select triangle;(7)Subdividing the problem-solution process;(8)Demonstration and solution steps;(9)Transposition reasoning verification method.Lastly,according to the proposed teaching strategies and problem-solution strategies,the classroom implementation is carried out,and the overall effects of the control class and the experimental class before and after the implementation are compared.