Research On Function Teaching And Learning In Junior Middle School Based On APOS Theory

Function is an important research object in middle school mathematics learning and an important mathematical model to depict the changing law of the real world.In the compulsory education mathematics course,we should combine the specific function,do contain but not omit,to understand simple to adapt to the cognitive level and thinking level of junior high school students.As the function content has a high degree of abstraction,some students are difficult to grasp.Then,an in-depth analysis of the current situation of junior high school students’ function learning and the factors that affect their function learning is carried out to explore the effective function teaching scheme,which is not only of theoretical research value,but also of application value.APOS theory is a mathematical learning theory developed by American mathematics educators in the practice of educational research.This theory holds that students learn mathematical concepts with the help of mental construction,and explore the nature of mathematical concept learning through four stages of operation,process,object and schema.Therefore,it is feasible to use APOS theory to analyze the learning status of function concept and whether students grasp the essence of function concept.Taking PEP textbook as an example,this paper studies students’ understanding level of function based on APOS theory,and explores the strategies of function teaching based on personal practical experience,so as to solve the problems encountered by teachers and students in the process of function learning.Specific research methods and contents are as follows:1.Literature analysis: read relevant literature at home and abroad,through the screening,analysis and integration of literature,understand the status quo of function teaching and learning,and conduct research on this basis.2.Questionnaire survey method: Through the questionnaire survey of students,the functional learning of junior high school students was statistically analyzed from the five dimensions of mathematical emotion,learning habits,knowledge mastery,environmental factors and attribution of success or failure.3.Test paper analysis method: Based on the content standard of function part in the curriculum standard and the corresponding opinions of front-line teachers,this study compiled the test paper of function based on APOS theory from the aspects of function concept,image,property and application,and analyzed the status quo of students’ function learning based on the four stages of APOS theory.4.Teacher interview method: The author interviewed five front-line teachers from three aspects of the teaching theory,teaching characteristics and teaching strategies of function concept,so as to understand the teaching status quo of function.5.Case analysis: Based on the teaching strategies proposed by APOS theory,this paper analyzes teaching canonical examples and selects two key periods for teaching design.The conclusion of this study is: junior high school students in the process of functional learning,students in the operational stage and the process stage can meet the requirements;In the object stage,only some students can meet the requirements;Only a few students are able to meet the learning requirements of the schema stage.Students have not formed a complete knowledge system of functions,and cannot flexibly apply functions to solve practical problems in life.In view of the problems in teaching and learning found in the survey,the author puts forward the strategies of functional teaching :(1)At the activity stage,students’ existing experience is based on the creation of problem situations to stimulate students’ interest in learning;(2)In the process stage,teaching should be carried out step by step to effectively carry out hierarchical teaching;(3)Timely feedback in the object stage,pay attention to the communication between teachers and students in class,and exercise students’ thinking ability and expression ability;(4)Schema stage can take the form of mind mapping to establish the connection between concepts and form a complete thinking context.