Research On The Investigation And Cultivation Of Mathematics Generalization Ability Of Senior First-year Students

Mathematical generalization is an important mathematical skill that plays an important role in students’ learning of mathematical concepts,mathematical problem solving and mathematical thinking,and is a factor that promotes the development of mathematical abstraction.The "abstraction" of functions in senior secondary school is the key point that students need to break through in learning senior secondary mathematics.By developing students’ mathematical generalization skills in the teaching of functions,students can enhance their mathematical generalization ability and develop their core literacy in mathematical abstraction.Based on this,this study takes two parallel classes of senior secondary students as the research objects,and uses "functions" as the research theme.Through the investigation and cultivation of mathematical generalization ability of 110 senior secondary students in a secondary school in Nanning,we understand the specific status and performance of senior secondary students’ mathematical generalization ability,and conduct experimental cultivation for students.This paper uses literature analysis,tests,and the development of mathematical generalization skills.This paper uses documentary analysis,test paper surveys,statistical analysis,interviews and teaching experiments to address the following four main questions:(1)How to establish a framework for mathematical generalization levels?(2)What is the current status of the mathematical generalization level of senior secondary students,and are there certain differences among students of different genders and levels?(3)How can strategies for developing mathematical generalization skills be constructed?(4)Did students’ mathematical generalization skills improve through the experimental development of teaching and learning,and did their performance show any significant differences? How did the levels change between the two classes?To address the above four questions,the study was divided into the following stages: firstly,a framework of mathematical generalization levels was identified by sorting out relevant research on mathematical generalization levels and mathematical generalization ability,and test questions corresponding to the levels were developed according to the framework.Secondly,two classes of students in the senior class of a secondary school in Nanning were selected for the test,and the current situation of the mathematical generalization level of the senior class was obtained through data analysis and student interviews.Again,strategies related to developing students’ mathematical generalization skills were summarized based on their level of performance.Following the development of the strategies,an eight-week experimental teaching period was conducted using the mathematical generalization model proposed in the development strategies.Finally,the results of the teaching experiment and post-test are analyzed and appropriate teaching suggestions are made.Combining the results of the survey,the interviews and the results of the development and testing of senior students’ mathematical generalization skills,the paper draws the following key conclusions:(1)The mathematical generalization level of Upper Class 1 students basically reaches Level 1 and Level 2,over 60% reach Level 3,and about 20% can reach Level4.Fewer students can reach Level 4,and there is a need to strengthen students’ mathematical generalization level.(2)The analysis of gender differences shows that there is no significant difference in the overall mathematical generalization ability of male and female students.(3)From the different levels,there were significant differences between students at the high,middle and low levels,with a larger gap between students at the middle and low levels.(4)According to students’ performance in answering questions,students appeared to be confused about similar concepts,and students were weak in generalizing about concepts.(5)Students did not perform very well in generalizing knowledge systematically,and there was a lack of close linkage of knowledge points.(6)Students’ poor performance in generalizing problem examination and problem solving methods affects the development of their mathematical generalization skills.(7)Teacher guidance and the teaching model of mathematical generalization affect the development of students’ mathematical generalization skills.Teaching using the teaching model of mathematical generalization skills improves students’ mathematical generalization skills to a certain extent,and students’ generalization of concepts,problem solving methods and knowledge systems improves and their understanding of the nature of knowledge becomes more profound.(8)After the teaching experiment,there was a significant improvement in the mathematical generalization ability of the students in the experimental class,with significant differences in the test scores between the control class and the experimental class;in terms of levels,the difference between Level 1 of the two classes was not significant,and there were significant differences between Level2,Level 3 and Level 4,with the gap between Level 3 and Level 4 of the students in the experimental class narrowing significantly and Level 4 of the experimental class improving significantly.