Study On The Learning Difficulties And Countermeasures Of Quadratic Equations For Junior High School Students Based On APOS Theor

The unary quadratic equation plays an important role in the mathematics curriculum of junior high school.It is not only an important part of the equation part,but also contains rich mathematical ideas.It also lays the foundation of research ideas and thinking methods for further algebraic learning.However,there are many difficulties for middle school students in learning univariate quadratic equations,resulting in lower learning outcomes than expected by teachers.Therefore,analyzing the learning difficulties of univariate quadratic equations for middle school students and researching teaching strategies is of great significance for improving the teaching effectiveness of univariate quadratic equations and promoting students’ mastery of knowledge content of univariate quadratic equations.Theoretical research has found that the APOS theory and its psychological mechanisms have high application value in helping analyze students’ learning difficulties and causes of univariate quadratic equations.At the same time,teaching guided by this theory can effectively improve students’ level of mathematical concept learning.Therefore,this study is guided by the APOS theory from three aspects: types of learning difficulties,causes of learning difficulties,and teaching strategies,We have formulated three questions:what are the difficulties in learning the unary quadratic equation for junior high school students,what are the causes of the difficulties,and how to develop corresponding teaching strategies for students’ learning difficulties.In response to the research question,this study first adopted a survey research method to conduct a questionnaire survey on the learning situation of univariate quadratic equations among 200 students from four classes in the ninth grade of their school.The survey analyzed the current situation of students’ learning of univariate quadratic equations and provided a preliminary understanding of their learning difficulties.Secondly,with the help of APOS theory,a four stage test paper was developed to test students’ learning level of univariate quadratic equations,and the test results were analyzed using SPSS software.Based on the analysis results of the test paper data,combined with Morre’s concept learning hierarchy,this study delves into and summarizes the learning difficulties of middle school students in terms of concept definition,concept image,and concept application in three dimensions.Finally,through qualitative and quantitative research combined with the psychological mechanism analysis of APOS theory,it was found that obstacles in the internalization of activities,the cohesion of processes,and the construction of schemas are important reasons for students’ difficulty in learning univariate quadratic equations.Based on the analysis of junior high school students’ learning difficulties and the causes of learning unitary quadratic equation,and combined with the teaching practice,this study,from three aspects of the concept definition,concept image,and concept application of the unitary quadratic equation,combined with APOS theory,has given four stages of teaching strategies: activity,process,object,and schema,and has carried out corresponding teaching design according to the proposed teaching strategies,In order to provide certain assistance and guidance for frontline teachers’ teaching and students’ learning about onedimensional quadratic equations.