The Study Of High School Students' Learning Progress For The Concept Of Function Based On Core Literacy And APOS Theory

The theory of learning progression originating from the United States.,is currently in the initial research stage in China.In this paper,the theory is applied to the study of the concept of function,and the first learning progression of the concept of function is constructed with the core literacy of mathematics as the horizontal research dimension,and the APOS theory as the vertical level division basis.The study in the paper is not only an innovative attempt of the application of learning progression in the field of mathematics education,but also a new exploration of the concept of function in the theory of core literacy and construction.In the paper the top-down verification research method is adopted,which is divided into three research stages.In the first stage,the advanced model is constructed by text analysis.Through the analysis of mathematics curriculum standards,the learning objectives of the concept of function in each stage are clarified.By analyzing the four versions of textbooks,the relevant sub concepts are determined to get,the necessary operation skills and learning performance in each core literacy.In the second stage,the advanced model is tested by testing method.781 students of 4 differnet grades ranging from junior 3 to senior 3 are experimented with self-developed measurement tools and therefore,the learning progression is tested from the single dimension,item fit and internal consistency reliability of data.In the third stage,In the third stage,the advanced model is modified by data analysis,content analysis and interview.Based on the test data,relevant literature and in-depth interviews with teachers and students,students' academic performance in each advanced level is revised and common difficulties and mistakes are collected,so as to depict the obstacles and key points of promotion of each advanced level.According to the requirements of learning objectives and students' specific learning performance,the advanced learning stage of the concept of function constructed in this paper consists of five stages: preparation,operation,process,object and diagrams.Each stage is divided into two levels.Longitudinal analysis show that the difficulty of the 10 advanced levels gradually increased,among which the learning performance level of the preparatory stage and the graphic stage is significantly different from that of the adjacent stage.The overall learning performance of the students in different grades shows less difference.The senior students have better performance in the content integration and comprehensive application of the function concept,but they forget the essence of the concept to varying degrees.The influence of gender on the concept of learning function is negligible.Horizontal comparison of core literacy,logical reasoning and intuitive imagination are the key to cognitive obstacles,mathematical abstraction is the basis of conceptual cognition,and mathematical operation is the tool of transformation analysis.Data analysis and mathematical modeling are the embodiment of concept application.In the process of advanced development,there are corresponding key points and obstacles in each stage.The key points include: understanding the corresponding essence,judging the function relationship,image analysis and application,and grasping the function tool.The main obstacles are: the distinction between dependency and function,the understanding and application of symbolic language,the transformation between number and shape,the analysis of composite function and abstract function and the application of mathematical modeling.