Research On The Relationship Between The Mathematical Abstraction Abilities And Mathematical Problem-posing Abilities Of Senior Two Students

Mathematical abstraction is a necessary key competence in students' development.It is one of the basic components of mathematical thinking,and it plays an integral role in students' learning of mathematical knowledge.The formulation of mathematical problems reflects the essence of mathematical thinking.At the same time,students can't learn mathematical knowledge without discovering and asking questions.The curriculum standards suggest that students should be guided to observe the world through the eyes of mathematics,thus developing the ability to identify and ask questions from a mathematical perspective.Therefore,for students' learning and teachers' teaching,there is a certain positive significance in researching the relationship between students' mathematical abstraction abilities and their problemposing abilities.This research takes 188 senior two students from two local demonstrative high schools as the research objects.Firstly,this research established the evaluation framework of mathematical abstraction ability and mathematical problem-posing ability;secondly,a test paper on mathematical abstraction ability and mathematical problem posing ability was developed based on the assessment framework;finally,this research investigated 188 senior two students' current status of mathematical abstraction abilities and mathematical problem-posing abilities,and explored the correlation between mathematical abstraction ability and mathematical problemposing ability.The following conclusions were obtained:(1)The level of mathematical abstraction abilities of senior two students are at the intermediate level.Specifically,for senior two students,there are differences in scores across course content,with mathematical abstraction abilities performing better in functions than in geometry and algebra.There are no significant differences in genders.However,there are huge differences between schools and classes.(2)The level of mathematical problem-posing abilities of senior two students are at the medium level.Specifically,students perform better in asking questions in free and semi-structured situations.However,they do not perform well in problem formulation in structured contexts.They could ask a wide range of mathematical questions and formulate them clearly,but the questions they asked are rather onedimensional or lack novelty.There are no significant differences in genders.However,there are huge differences between schools and classes.(3)There is a significant positive correlation between the mathematical abstraction abilities and the mathematical problem-posing abilities of senior two students.That is,it is moderately positive,with a correlation coefficient of 0.398.The regression analysis yielded a strong linear relationship between mathematical abstraction ability and problem-posing ability,the regression equation for mathematical abstraction ability and mathematical problem posing ability is y =0.152 x +24.313(x represents mathematical abstraction ability and y represents mathematical problem posing ability).Based on the above findings,this research proposes corresponding teaching suggestions to develop mathematical abstraction abilities.