An Investigation On Senior High School Students' Competence Of Mathematical Abstraction

Since 1990 s,“Key competencies” has been a hot topic discussed by educators all over the world.According to Curriculum Standard for Senior Mathematics(2017Edition),mathematical abstraction comes up as one of the six key competencies.Mathematical abstraction is a competence,with which we are able to abstract things' quantitative relations and spatial form as the objects for mathematical researches.Although the researches on mathematical abstraction are diversified,further researches are needed.In this study,I define what mathematical abstraction is with the review of relative literature firstly.Then,an evaluation framework including 4 cognitive dimensions and 3 levels for mathematical abstraction is built.At last,taking students from two senior high schools in Shenzhen as examples,I investigate senior high school students' mathematical abstraction in function and geometry&algebra.The result shows that,(1)in general,senior high school students make an average performance;(2)as for cognitive dimensions,they perform best in mathematical concepts and rules,but poorly in mathematical communication and expression;(3)senior high school students' mathematical abstraction has significant difference in different contents;(4)senior high school students' mathematical abstraction has significant difference between students of liberal arts and those of science.According to the current situation of high school students' Mathematical Abstraction,the following suggestions are put forward :(1)Adopting flipped-classroom teaching method appropriately;(2)Using Project Learning for teaching skillfully;(3)Paying attention to the connection among the mathematical knowledge;(4)Building a unified mathematics examination system for college entrance examination;(5)Improving high school students' understanding of Mathematical Abstraction.