Research On The Relationship Between Mathematical Metacognition And Mathematical Abstract Ability Of High School Students

Mathematical abstraction is the basic idea of mathematics and an important basis for forming rational thinking.The newly revised general high school curriculum standard lists mathematical abstraction as one of the six core mathematical literacy,which places higher requirements on students' mathematical thinking and mathematical ability.Combining mathematical metacognition theory with high school students to study the relationship between mathematical metacognition and mathematical abstraction ability has certain theoretical and practical value.The study adopts the mathematics metacognition scale for senior high school students,compiles the evaluation framework and test papers for mathematical abstract ability,grasps the intrinsic relationship between mathematical metacognition and mathematical abstract ability from a theoretical perspective,and analyzes the development status of mathematical abstract ability for high school students from a statistical perspective.Through literature analysis,survey and interview methods,the following conclusions are drawn:(1)The overall performance of mathematical abstraction is average.The mathematical abstraction ability of most students is at level two,which conforms to the normal distribution as a whole.In the four structural dimensions of mathematical abstraction,students have the best use of mathematical concepts and rules,but there are problems of insufficient understanding of thinking methods and lack of reflection and testing of problem situations.Students have the weakest performance in mathematical communication and interpretation,and lack of mathematical thinking in the face of real situations.(2)Students 'mathematical metacognition is at a medium level or above,but most students' ability to monitor mathematical metacognition is at a middle or lower level,and they generally lack the awareness of reflection testing.(3)Significant positive correlation between mathematical metacognition and mathematical abstraction.Among the three main factors of mathematical metacognition,mathematical metacognition monitoring has the greatest influence on mathematical abstraction ability,and 26% of mathematical abstraction ability is caused by mathematical metacognition monitoring.The significant correlation between mathematical metacognitive and mathematical abstraction is mainly reflected in the two structural dimensions of mathematical models and propositions,mathematical ideas and methods.(4)Students with higher mathematical metacognition ability also have higher mathematical abstraction ability.There is a significant difference in the mathematical abstraction ability of the high and low mathematics metacognition group,and the high and low mathematics abstract group has the most significant difference in the mathematical metacognition monitoring.Therefore,teaching suggestions for improving students' mathematical metacognition are put forward: 1.Accumulate mathematical metacognition knowledge and provide prerequisites for mathematical metacognition monitoring.2.Pay attention to emotional factors and mobilize mathematical metacognitive experience.3.Adopt metacognition questioning strategies to improve mathematical metacognition monitoring capabilities.