Analysis And Research On Learning Condition Of Primary Function Based On APOS Theory

As an important knowledge penetrating middle school mathematics,the concept of function plays a vital role in the development of mathematics teaching.First-order function is the first specific function that students contact,is the simplest function,and is also the basis for learning other specific functions.At the same time," function" is a brand-new concept for students.Due to the abstract feature of function,students have difficulty in understanding function.Therefore,primary function is not only the important content of junior high school mathematics,but also the key and difficult point of eighth grade mathematics teaching.It is also the turning point for students to learn mathematics and the key to the development of students' abstract thinking and logical thinking.In recent years,Jinzhou city's examination questions about primary function can be seen that the focus of examination for primary function is on function image,undetermined coefficient method and determination of primary function expression according to known conditions,supplemented by calculation of function value,meaning of point on image and positive proportion function expression,etc.It mainly embodies the ideas of function and equation,combination of number and form,classification and discussion,etc.Pay attention to the connection between mathematical thinking methods and knowledge points,and pay attention to students' understanding of knowledge from mathematical thinking methods.APOS theory,as a theory related to constructivism,points out that students should actively construct mathematics concepts in the process of learning,and further indicates the level of concept construction,which makes our learning not only stay at the visual learning stage,but also integrate knowledge through continuous sublimation,reflection and abstraction.In this study,students in grade 2 of a junior high school in Jinzhou city and a junior high school nearby Jinzhou city were selected as the research objects.taking the mathematics textbook published by Beijing normal university as an example,a questionnaire survey was conducted among the students at first,the aim is to understand the current situation of students' learning and teachers' teaching,then the test paper is designed based on the four stages of " activities"," procedures"," objects" and " schemata" of APOS theory,taking the test paper as a research tool,this paper conducts a test survey on students and evaluates and analyzes their understanding of the primary function in the four stages of APOS theory.According to the results of the questionnaire,in the teaching process,teachers attach importance to the explanation of the laws of primary function images and the combination of old and new knowledge,but they do not attach importance to the initiative of students in learning.They give priority to teaching.Instillation teaching is easy to make students feel tired,has less contact with real life,and has no obvious penetration of mathematical thinking methods.In the study of students,students are not good at summarizing knowledge,they do not pay enough attention to mathematical thinking methods,they cannot combine primary function with daily life closely,and their learning initiative is not strong.The author found that from the perspective of APOS theory,the students' understanding of the knowledge of the primary function activity stage is the best of the four stages in terms of both the average score and the stability of standard deviation.The overall performance of the students in the program stage is also relatively ideal.At the same time,the existing problems should not be underestimated.The students' understanding of the primary function object stage is not as good as that of the activity and program stage.The average score is low and the existing problems are obvious.The average score of the students in the schema stage is obviously low and the standard deviation is obviously large,indicating that the two stages are seriously divided.The specific problems of students reflected in the test paper mainly include the confusion of independent variables,dependent variables and constant items.Ignore the value range of independent variables;It is not flexible enough to master the expression and image of primary function.At the same time,several teaching Suggestions are obtained:(1)In the activity stage,pay attention to the inspiration before class and perceive the meaning of the primary function;(2)Through situational variation,repeat activities continuously to promote positive transfer of learning;(3)Knowledge and thought are combined to help students form a whole body of knowledge;(4)Following the three stages of schema,construct the cognitive structure of primary function.