Investigation On The Current Situation And Research On The Cultivation Strategy Of Mathematics Generalization Ability Of Senior One Student

With the reform of the current mathematics curriculum,the high school mathematics curriculum standard emphasizes that students should have the ability to generalize and understand the essence of mathematics.In mathematics learning,summarization is an important thinking form for students to learn mathematical knowledge,concepts and mathematical thinking methods,and is a basic activity for students to understand the essence of mathematics.At the same time,the formation stage,development level and influencing factors of mathematics generalization ability are closely related to the setting of mathematics curriculum goals,the selection and expression of teaching materials,and the design of teaching process methods.In this study,literature research method,investigation analysis,interview,educational experiment method and classroom observation method are used to explore the development status,influencing factors and teaching strategies of students’ mathematical generalization ability of senior one students in a middle school in K City,Henan Province.First of all,in order to understand the development status of senior one students’ mathematical generalization ability,based on the evaluation framework of this study,the test paper is used to effectively evaluate the performance of mathematical generalization ability from four dimensions: generalization ability of mathematical notation,generalization ability of mathematical relations,generalization ability of mathematical structure,and generalization ability of mathematical thinking methods.Secondly,in order to further explore the factors that affect the development of students’ mathematical generalization ability,a questionnaire was compiled from the four dimensions of students,teachers,families and schools.Correlation analysis was carried out to obtain the main factors affecting the four dimensions of mathematical generalization ability.Finally,combined with the analysis of the results of the test paper and the questionnaire,based on the meaningful reception learning theory and the "super regression" mathematical understanding theory,this paper proposes targeted teaching strategies,and combines the teaching strategies to carry out teaching design research with the concept of function as the foothold.Main conclusions of the current situation:(1)The analysis of the survey results shows that there is a strong positive correlation between students’ academic achievements and students’ mathematical generalization ability.(2)The overall development of students’ mathematical generalization ability is general.Among them,the generalization ability of mathematical notation and mathematical structure are poorly developed,while the generalization ability of mathematical relations and mathematical thinking methods are relatively well developed.(3)The generalization ability of mathematical notation shows gender differences,while the other three dimensions have no significant gender differences.According to the correlation study,the main influencing factors are as follows:(1)The main influencing factors of the generalization ability of mathematical notation are students’ learning motivation,self-efficacy,and the way of generalization.(2)The main influencing factors of the generalization ability of mathematical relations are students’ learning motivation and teacher-student relationship,while parents’ expectations have a negative impact on it.(3)The generalization ability of mathematical structure is mainly influenced by students’ self-efficacy,the way of generalization and teachers’ teaching methods,while parents’ expectations have a negative impact on it.(4)The generalization ability of mathematical thinking methods is mainly influenced by students’ self-efficacy,the way of generalization,teaching methods.According to the development status of each dimension of mathematical generalization ability and the main influencing factors,the following strategies can be adopted to improve students’ mathematical generalization ability:(1)clarify the teaching precautions of concept class and proposition class,and focus on improving students’ generalization ability of mathematical notation and mathematical structure through concept class and proposition class;(2)Clarify the "high-quality" indicators of situations and problems,and create problem situations to stimulate students’ self-efficacy and learning motivation;(3)Emphasize teaching methods,focus on comparative teaching,strengthen series teaching,and enable students to experience the process of summarization and master the method of summarization.Based on the cultivation strategy,the teaching case "Concept of Function" is designed.According to the classroom behavior observation table,through the comparison of the learning behaviors of students in the comparison class and the experimental class,it can be seen that the experimental class students are able to exhibit more positive learning behaviors in terms of autonomy,progressiveness,externalization,interactivity,and rigor in their general understanding of the definition of functions.The contributions of this research are as follows:(1)On the basis of the previous three levels of mathematical generalization ability and combined with the four processes of mathematical generalization,the evaluation framework of "three levels and four dimensions" of this study is obtained.(2)Take students’ performance in class as an evaluation method to evaluate teaching design,and use classroom behavior observation table to reflect the effect of teaching case implementation,so that students’ mathematical generalization ability can be visualized and controllable.(3)Provide referable teaching strategies for teachers based on specific cases and development status and influencing factors.