Research On The Relationship Between Junior High School Students' Mathematical Abstraction Ability And Mathematical Problem-making Ability

In the current research on mathematics education,the ability to pose mathematical problems has attracted more and more attention from educators and mathematicians.How to cultivate and develop the ability to pose mathematical problems is an important task for educators,and the development of students' ability to pose problems It is not only related to the teaching of teachers,but also influenced by students' own knowledge and abilities.As the first of the core qualities of mathematics,mathematical abstraction is the most basic way of thinking in mathematics.What role does mathematical abstraction play in the process of raising mathematical problems? In view of this,this paper studies the relationship between the ability of mathematical abstraction and the ability to pose mathematical problems,and provides empirical support for the development of the ability to pose mathematical problems from the perspective of mathematical abstraction.This study uses literature analysis,questionnaire survey,and statistical analysis to investigate the status quo of junior high school students' mathematical abstraction ability and mathematical problem-proposing ability,and explore the correlation between the two.Based on theoretical and empirical investigations,corresponding teaching strategies are proposed from the perspective of mathematical abstraction,with a view to cultivating students' ability to pose mathematical problems by improving students' mathematical abstraction ability.Through research,the main conclusions are as follows:(1)The level of mathematics abstraction of junior high school students is generally at the upper-middle level.Among the four dimensions of mathematical abstraction,the performance is best in the dimension of "mathematical communication and expression",and in "mathematical propositions and models","mathematical methods and ideas""Dimensional performance is poor.(2)There is no gender difference in the abstract ability of mathematics among junior high school students.The abstract ability of mathematics is positively correlated with the academic level of mathematics,that is,the higher the student's mathematics academic performance,the higher the mathematical abstract ability.(3)Junior high school students' math problem-proposing ability is generally at an intermediate level,and students have different scores in different situations.They perform well in open and semi-structured situations,and perform poorly in structured situations.The novelty of students' questions needs to be improved.(4)Junior high school students have no gender differences in the ability to pose mathematical problems.The ability to pose mathematical problems has a lower positive correlation with the academic level of mathematics,that is,the higher the student's academic performance in mathematics,the higher the ability to pose mathematical problems.(5)There is a significant relationship between the mathematics abstraction ability of the junior high school students and the mathematics problem posing ability,showing a slight correlation.Through partial correlation analysis,there is a significant correlation between the ability of mathematical abstraction and the "novelty of the problem".Through regression analysis,the equation of the regression model for mathematical abstraction ability and mathematical problem-proposing ability is:Y=6.337+0.148X(X is mathematical abstraction ability).(6)Based on the research results,corresponding teaching suggestions are put forward for the cultivation of mathematical abstraction from four aspects: concept teaching,mathematical modeling activities,formation of mathematical ideas and methods,and establishment of mathematical knowledge and systems.