Research On The Status Of High School Students' Mathematical Abstract Literacy Based On APOS Theory

The new curriculum standard for the 2017 edition of high school mathematics proposes six core literacy in mathematics.Mathematical abstraction is the first core literacy among them,which runs through the process of mathematics learning.Mathematical concepts,as the basic elements that constitute the structure of mathematical knowledge,are the direct products of mathematical abstraction.Research has a theoretical basis to cultivate mathematical abstract literacy in concept teaching.This research investigates the training strategy of mathematical abstract literacy by investigating the status quo of mathematical abstract literacy and APOS theory.The research object is students from a senior high school science class in a high school in Shangqiu City,Henan Province.The research methods include literature,questionnaire,test paper method and interview method.First,analyze the research background and significance of this article.Second,organize the research on the status of mathematical abstract literacy at home and abroad,define the core concepts involved in this research,and then design a questionnaire based on the APOS concept learning theory to investigate students and teachers.The questionnaire is designed to investigate students 'and teachers' understanding and practice of APOS theory applied to conceptual learning.A mathematical abstract literacy test paper is designed based on the framework of the level of mathematical abstraction proposed by the "General High School Mathematics Curriculum Standards(2017 Edition)Mathematical abstraction is divided into three dimensions vertically and horizontally into four cognitive dimensions: situation and problem,knowledge and skill,thinking and expression,communication and reflection.The new curriculum standard divides the courses taken by students into five topics: preliminary knowledge,functions,geometry and algebra,probability and statistics,mathematical modeling activities and mathematical exploration activities.Select the concept under the function theme as the content carrier of the mathematical abstract literacy test.Finally,conduct a survey,analyze the data obtained,and put forward a training strategy for mathematical abstract literacy based on the conclusions obtained.The conclusions of this study are:(1)Students can better understand the importance of APOS theory in concept learning,but the ability to apply APOS theory to concept learning is slightly inadequate,and some teachers only occasionally apply this to teaching practice.(2)From the vertical dimension,a largenumber of senior three science students can reach level one and level two,and very few students can reach level three.From the cognitive dimension,students score higher in the context and problem dimensions,but score lower in the two dimensions of knowledge and skills,communication and reflection.(3)Under the cognitive dimension of mathematical abstract literacy,girls' knowledge and skills scores are slightly higher than boys',and boys' communication and reflection dimension scores are slightly higher than girls,the difference is not significant.In the horizontal dimension,there is no significant gender difference in the math abstract literacy of senior three science students.(4)The students' APOS theory ability score has a positive correlation with the math abstract literacy test score,and the math abstract literacy score has a positive correlation with the student's usual performance.According to the APOS theory,put forward training strategies: in the activity stage,rationally create situations and guide the formation of perception concepts;in the process stage,flexibly use teaching methods to guide students to participate actively;in the object stage,consolidate concepts in time and effectively train basic knowledge and skills;At the stage,deepen the concept at the right time and build a knowledge network system.Throughout the teaching process,we must pay attention to the penetration of mathematical thinking methods,and communicate with reflection consciousness.The author analyzes the teaching case of "The Concept of Function" and discusses how to use the APOS concept learning theory to improve mathematical abstract literacy in concept teaching.