A Survey On The Current Situation Of Applying Reduction Think-Method In Senior One Students

Mathematical think-method is the essential understanding of mathematical theory and knowledge system,which is the foundation of the generation and development of mathematics.High school curriculum standards emphasize that mathematics curriculum should highlight the internal logic and thought methods of mathematics.Reduction think-method is the core of middle school mathematics thought method,and many thoughts are permeated with reduction thought."The problem is the heart of mathematics",and reduction think-method is a powerful tool to solve mathematical problems.However,the current classroom generally emphasizes the evaluation of knowledge standards,and ignores the evaluation of the formation of mathematical thoughts.The evaluation of reduction think-method lacks sufficient attention,and a mature measurement framework has not been formed yet.Starting from the connotation of the reduction think-method,combined with the concerns of the reduction think-method in journals and books and the actual teaching situation in middle school,this study tries to establish a test framework for the current situation of the application of the reduction think-method by senior-one students.The test was compiled from the four transformation dimensions of symbolic-graphic transformation,specialization,reverse transformation and variable substitution,and 102 senior-one students in a middle school in Xiamen were investigated.According to the specific situation of the test,representative students are selected for interview.Specifically,the main questions of this study are:1.What is the current situation of senior one school students applying reduction thinking method to solve mathematical problems?2.What problems do senior high school students have in applying reduction thinking method?The quantitative analysis of the data of the test leads to the conclusion of research question 1:The overall conversion ability of senior-one students is not very ideal,at the lower level of medium.The detailed analysis of each dimension shows that there are differences in the application of the four transformations among senior-one students.Among them,students use symbolic-graphic transformation best and achieve a good level;The level of specialization and variable substitution is similar,and the overall performance is lower than medium.The most underperforming dimension is the reverse dimension.From the perspective of differences among students of different academic levels,the average performance of the four dimensions is superior students>ordinary students>poor students,and there are differences in the significance of the three levels of students in different dimensions.The mean performance of boys is higher than that of girls in all dimensions,but the stability of girls’ overall performance is better than that of boys.By qualitative error analysis of the problem solving of the test and combining with the interview results,the conclusion of research question 2 is obtained.senior-one students have the following four problems in understanding and applying reduction thought method:(1)Affected by stereotypes of thinking,the driving force of transformation is not enough;(2)Lack of prior knowledge;(3)The consciousness of reverse transformation is weak,and the specialized understanding is biased;(4)Return to stay in the method of imitation,not fully grasp the essence of thought.Based on the above research conclusions,the following teaching suggestions are put forward:(1)Grasp the infiltration opportunity of new knowledge teaching,deepen students’ understanding of the thoughts and methods of reduction;(2)Give play to the key role of problem-solving teaching and help students to flexibly use the thoughts and methods of reduction;(3)To construct a concrete and rich system of reduction thoughts and methods in students’ minds through horizontal comparison and expansion.