Advanced Study On The Concept Of Middle School Function Based On APOS Theory

In middle school mathematics knowledge system,function knowledge is a main line throughout.But because of the abstractness and complexity of the function concept itself,plus the abstract concept which is also the general meaning first encountered by the students in the process of learning mathematics,it is difficult for the students to understand it.In this way,function becomes one of the most difficult and difficult concepts in middle school mathematics.Advanced learning is a kind of thinking change process that describes the students' initial understanding of a certain core concept in different learning stages.The construction of advanced learning can clearly reflect the students' understanding of the concept of function Thinking changes.So,it is of theoretical and practical significance to apply the advanced learning to the field of mathematics subject and develop the advanced learning with the concept of middle school mathematics function as the content.First of all,by reading and sorting out the relevant literature of advanced learning,we deeply understand the concept,characteristics and research steps of advanced learning,and then summarize some research on advanced learning in mathematics field.Based on the analysis of mathematics curriculum standards and corresponding mathematics teaching materials,we construct a hypothetical learning model based on APOS theory based on APOS theory and the characteristics of operation stage,process stage,object stage and schema.After that,to junior high A student as a sample,through the single-dimensional Rasch model developed by the test tool to test it,and then analyze the data obtained,so as to verify and revise the hypothetical learning advanced model;finally,the constructed learning advanced model of middle school function concept is composed of the following eight levels:Level 1:a preliminary understanding of constants,variables,knowing that the value of one variable is determined by the value of another variable;Level 2:Understand the changing relationship between two variables;Level 3:Recognition and understanding of the "image method" and “analytic method” of the two representation functions;Level 4:Identify and understand the “list method”as a way to represent functions;Level 5:Understand the connotation of three elements of function;Level 6:Understand the meaning of the function symbol and understand the intrinsic relation of the three elements of the function;Level 7: Form a complete functional definition;Level 8:Establish a link with other knowledge and form a comprehensive scheme of knowledge.In addition,based on the findings of the study,the following recommendations are made for teaching:(1)To guide students to study actively and stimulate their enthusiasm;(2)Strengthen students' understanding of the "list method" to represent functions;(3)Implement the core quality of mathematics in function teaching.