Research On Learning Progression Model Of High School Sine-Type-Function Based On APOS Theory

"Learning progression" originated in the United States and is one of the emerging concepts in its science education reform.Since 2012,the academic research on learning progression has been increasing year by year,and it has become an important research topic in contemporary international science education.In recent years,in terms of the subject areas involved in this theory,most of the researches on this theory in our country are distributed in the fields of chemistry,physics,biology,etc.Relatively speaking,the related in-depth research of mathematics in this area is relatively scarce.At the same time,the trigonometric function is one of the most important mathematical concepts when students learn high school mathematical concepts.However,the concept of trigonometric function is highly abstract and general,and the concept itself is not easy to understand.Students are required to make flexible conversions.It is the first time students come into contact with the most typical type of periodic function in mathematics learning.The sine-type-function is the most representative type of trigonometric functions,and it occupies an important position in trigonometric functions.Therefore,this article takes the sine-type-function as the research content.This research applies learning progression to the learning of high school sine-type-function.It is a validated advanced research and consists of three steps.Firstly,this paper systematically sorts and analyzes high school mathematics curriculum standards,general high school mathematics textbooks,students' behavioral performance and cognitive laws,and the related teaching documents of trigonometric function to systematically sort and analyze,and determines the relevant sub-concepts,learning goals and corresponding learning performance.Secondly,combining the APOS theory,this paper tries to initially construct a hypothetical model of learning progression level of sine-type-function in high school,and compile test questions for the hypothetical model of learning progression of sine-type-function according to the characteristics and requirements of each learning progression level.This paper uses self-developed test tools to test a total of 685 students from junior grade three to senior grade three,developing test tools,and verifies the learning progression model.Lastly,this paper analyzes from the perspectives of different grades and genders,making appropriate revisions and adjustments to the learning progression model,and obtains the progression level,conceptual understanding level of the advanced sine-type-function learning progression model for students and their specific learning performances.This research aims to explore and study the laws of cognitive development in the process of students learning the concept of sine-type-function,and tries to break through this learning difficulty.This is a brand new exploration of the concept of sine-type-function in learning progression and APOS theory.