Investigation And Research On The Current Situation Of Equation Learning For Junior High School Students Based On APOS Theory

Every study of mathematical knowledge has important significance and value,and it is the foundation of the construction of students' knowledge system.Quadratic equation with one variable is an important learning content of Grade 9.Students at this stage have a basic understanding of equation knowledge,but the understanding degree of students varies in the whole knowledge content.APOS theory is divided into four stages,each stage corresponds to a different learning content.On the one hand,the test can comprehend the difference and understanding level of students in studying knowledge content of quadratic equation with one variable.The survey method,which is primary based on tests and auxiliary by interviews,can comprehend the studying course and learning psychology of students and analyze the reasons for their cognitive difficulties.On the other hand,teachers' teaching steps and means have a straightforward impress on students' learning effects.Through case analysis combined with teacher interviews to understand the current situation and deficiencies of teachers' teaching,the corresponding teaching implementation suggestions are given to improve the learning efficiency of quadratic equation with one variable.Based on APOS theory,this paper divides the content of quadratic equation with one variable into whole parts,investigates the learning status of quadratic equation with one variable of Grade 9 students by preparing test questions,and collates the collected data,and draws the following conclusions after analysis:(1)Most of Grade nine students' understanding of quadratic equation with one variable can reach the activity stage and the process stage;(2)Grade nine students' understanding of quadratic equation with one variable varies greatly in the object stage;(3)Grade nine students' overall performance in understanding quadratic equation with one variable is not ideal in the graphical stage.Based on the summary of the teaching cases and after-class interviews at the present stage,the existing problems are as follows: First,the creation of problem situations in the activity stage is not sufficient;Secondly,students spend less time communicating in exploring new knowledge.Finally,in the diagram stage,the teacher discussed the topic without establishing the connection between knowledge and so on.Depending on the investigation results and reason analysis of the present stage of ninth-grade students' studying of quadratic equation with one variable,the following teaching inspirations are incorporated:(1)Carry out teaching step by step according to the arrangement of textbooks to ensure the play of students' subjectivity(2)Establish the connection between knowledge and help students build a complete knowledge structure(3)According to the four stages of APOS theory,the teaching of equation-related concepts was conducted.