A Study On The Correlation Between Mathematics Abstract Ability And The New Definition Problem Solving Level Of Senior Three Students

The ability to abstract mathematics is an important foundation for the formation of mathematical thinking and an indispensable key ability in the development process of high school students.The new definition question tests the comprehensive qualities and abilities of high school students,including their mathematical abstraction ability,reading ability,and reasoning ability.So,what role does high school students’mathematical abstraction ability play in solving new definition problems?Conversely,how much help does high school students have in solving new definition problems as their mathematical abstraction ability improves.Based on this,the author has decided to conduct research on the current situation and correlation between mathematical abstract ability and the level of problem-solving in newly defined problems,in order to provide front-line teachers with a theoretical and practical foundation for teaching.This study divides mathematical abstraction into empirical abstraction and theoretical abstraction through literature analysis,and divides new definition problems into three categories:new concepts,new relationships,and new properties.According to the established evaluation framework,compile a test paper for mathematical abstraction ability and problem-solving proficiency in new definition problems;Adopting empirical research,conducting trial and actual measurements.In addition,high school students in their third year have significantly improved their mathematical abstraction ability through training in their first and second years of high school.However,the knowledge tested in the newly defined questions is relatively comprehensive,and high school students have already learned all mathematical knowledge.Therefore,this study focuses on high school students as the research object;Further utilizing statistical analysis methods,the obtained data was entered into Excel,and the following conclusions were ultimately obtained using software such as SPSS:1.The overall level of mathematical abstraction ability and problem-solving skills of senior high school students is above average.Empirical abstraction ability is slightly better than theoretical abstraction ability.Among the three types of new definition questions,the mastery of new relationships is relatively good.In terms of difference analysis,gender differences are not significant.The overall level of male students is slightly better than that of female students.There is a significant difference in the humanities and science classes,and the science class is better than the humanities class;2.The correlation between mathematical abstraction ability and problem-solving level of newly defined problems:There is a significant correlation between the two,with a correlation coefficient of 0.708.Among them,the relationship between empirical abstraction and new definition questions is more closely related than that between theoretical abstraction and new definition questions;3.The mutual influence between the mathematical abstraction ability and the level of problem-solving for newly defined problems of senior high school students:The mathematical abstraction ability will increase with the increase of problem-solving level for newly defined problems,and in turn,the increase of problem-solving level for newly defined problems will also promote the improvement of mathematical abstraction ability.It is worth noting that when one of the two rises to a certain level,the other will sharply increase;4.Mathematical abstraction ability has predictive value for the level of problem-solving in newly defined problems:using mathematical abstraction ability as the independent variable x and the level of problem-solving in newly defined problems as the dependent variable y for univariate regression analysis,the linear equation obtained is y=4.004+0.626x.Using theoretical abstraction as the independent variable x₁,empirical abstraction as the independent variable x₂,and the newly defined problem-solving level as the dependent variable y for multiple regression analysis,the linear equation obtained is y=0.539x₁+0.705x₂+4.044.Based on the research findings,the following teaching suggestions are proposed:1.Suggestions for using mathematical abstraction to improve the problem-solving level of high school students’new definition problems:（1）Accumulate students’experience of abstraction and enhance their ability to transfer knowledge.（2）Strengthen the assimilation of students’knowledge and enhance their ability to abstract theories.2.Suggestions for improving high school students’mathematical abstraction ability in the process of solving new definition problems:（1）Strengthen the training of conventional and exploratory problem-solving to improve the flexibility of abstract thinking;（2）Mobilize cognitive foundation,utilize information technology,and enhance the creativity of abstract thinking.Finally,there are still some shortcomings in this study,such as subjectivity in the development of research tools and insufficient comprehensiveness of research objects.It also proposes some future directions worth studying.