An Assessment Research On Senior High School Students' Mathematical Abstraction Competencies

The newly revised senior high school mathematics curriculum standard puts forward six mathematical core literacy,and points out that the ultimate goal of mathematics education is to develop students' mathematical core literacy.Mathematical abstraction,as the first of six core literacy,plays a vital role in the formation and application of mathematical knowledge.Through abstraction,we obtain mathematical concepts,mathematical models,mathematical methods,and even higher levels of mathematical structure and system,all mathematical objects can be seen as the result of mathematical abstraction.Therefore,the key to improving students' mathematical competencies is to develop students' mathematical abstraction competencies.And the Assessment research on students' mathematical abstraction competencies can better promote the research in the mathematics education and guide the teaching of mathematics as well.This research mainly adopts the mixed research methods of combining qualitative and quantitative research,including literature,test and interview.Main work has been listed in the following:1.Design the assessment framework for students' mathematical abstraction competencies.First,this study uses the research method of literature analysis to define the connotation,type and main way of mathematical abstraction.And constructs the framework for students' mathematical abstraction competencies from the three dimensions of content,structure and level.The content dimension refers to the content of subject knowledge,including function,algebra and geometry,probability and statistics;structural dimension refers to competencies component,including situated abstraction and theoretical abstraction;horizontal dimension refers to the level of students' mathematical abstraction competencies,including reproduction,connection and reflection(creation).2.Compile the corresponding test tasks according to the assessment framework.This study,with the help of some mathematical education experts and front-line teachers,further refined the assessment index of mathematical abstraction ability in the revised high school mathematics curriculum standard,and used it as the evaluation standard for the test.Then,I compiled the test based on the assessment framework.According to the students' performance in the forecast,the test questions are modified and adjusted to form the test tasks which are finally used to assess the students' mathematical abstraction competencies.3.Application of the assessment framework of mathematical abstraction competencies.In this study,the whole students in senior one of Xinghai Experimental Middle School in Suzhou Industrial Park were tested.Through the analysis of the test results,the following conclusions were drawn:(1)From the percentage of the expected level of the students' abstraction competencies,the majority of the students are at level 2,which is “connection”;from the different ability components,the students' theoretical abstraction competencies is obviously higher than Situated abstraction;(2)From the gender point of view,boys' performance in the level 3 are better than girls,but the abstraction competencies of the TXTF is lower than girls;(3)From the students' specific problem solving situation,high school students in the following aspects of the abstraction competencies to be improved: First,abstraction from real-life problem to a mathematical problem;second,the abstraction of function model from the data;third,the abstraction of the TXTF;fourth,the abstraction of the mathematical concepts from the specific context.Based on the problems exposed by students in the process of mathematical abstraction,the author gives the teaching suggestions to improve senior high school students' mathematical abstraction competencies for reference.