The Study Of Set Learning Progressions Model In The APOS Theoretical Perspective

The General High School Mathematics Curriculum Standards(2020 Revised Edition)points out that high school students learning sets can prepare them for subsequent mathematical learning in terms of learning psychology,learning styles and knowledge skills,while teaching sets is also an important way to cultivate students’ mathematical abstraction,indicating that sets have an important position in the high school mathematics knowledge system.This paper constructs a learning progressions model of set based on the study of APOS theory,analyzes the development of students’ cognitive level of sets,and provides reference for teachers to improve teaching and enhance teaching effectiveness.This study constructs a model of learning progressions of set knowledge based on APOS theory,and mainly adopts the methods of literature analysis and survey to carry out the study.Firstly,we review the related researches on sets,learning progressions and APOS theory;secondly,we construct a hypothetical learning progressions model of sets under the APOS theory by studying the General High School Mathematics Curriculum Standards(2020 Revised Edition)and analyzing the first three high school mathematics textbooks of the Humanities A edition of the Compulsory Course;thirdly,we design and develop a test instrument,and the pretest results demonstrate the reasonableness and scientific validity of the test instrument;Finally,students in the first and second years of senior high school in H city were selected for formal testing,and the learning progressions model was optimized based on the test results and the knowledge logic system to obtain an ensemble learning progressions model with four progression stages and six progression levels.In the survey,it was found that students’ overall cognition of sets was at a low level,and students’ overall cognition of sets was at the action stage,and only some of them had constructed a set knowledge schema;there were differences in the cognitive level of sets among students of different grades and genders,among which some sophomores had a decreasing trend in their understanding of sets,and most girls’ cognition of sets was at the action stage,and there were two major cognitive barriers.In view of the above problems,we propose three teaching suggestions: applying the learning progressions model to guide teaching activities;conducting timely review to penetrate the concept of sets;providing various materials to break through the cognitive barriers.By constructing a learning progressions model of students’ knowledge about sets from the perspective of APOS theory,it expands the application area of learning progressions and APOS theory in mathematics education research,and also provides reference and reference for applying the learning progressions model in basic front-line classroom teaching.