| With the continuous reform of the high school entrance examination,guangdong Provincial Examination Institute will no longer issue the outline of the Junior high School entrance Examination in 2020,and will use the current curriculum standards(2011 edition)as the basis of the proposition.In 2021,many teachers and students think the final question of quadratic function is more difficult.Under the background of the reform of the high school entrance examination,the uncertainty of the difficulty of the questions requires students to master the knowledge to a higher degree.The purpose of this study is to explore the types of errors and obstacles in solving geometric maximum value problems of grade 9 students under the background of quadratic functions,and to study the countermeasures of solving problems at students’ cognitive level.In order to study this topic,using test method,error analysis method,questionnaire survey method and interview method,based on the types of problem solving errors and students’ noncognitive level,study the weaknesses in students’ knowledge system and the obstacles in the problem solving process.Through the error statistical analysis of the test paper,it is found that the students of Level 2 mainly have the thinking obstacle in geometry and algebra transformation,while the students of Level 3 mainly have the knowledge obstacle.Combined with the characteristics of geometric maximum value problem itself,students’ thinking cognition and teachers’ problem-solving teaching under the background of quadratic function,it is concluded that junior high school students have problems in solving this kind of problem: 1.Knowledge barriers in geometry and algebra;2.Thinking disorder of transformation of figural representation;3.Psychological disorders caused by stress and anxiety.The knowledge barrier is mainly manifested in algebraic knowledge and calculation unproficiency,geometric properties and model recognition obstacle.The thinking disorder is mainly manifested in the choice of geometric solution strategy,the error transfer caused by thinking set and the weak ability of converting representation of graph and number.Psychological disorder is mainly manifested as anxiety and fear of difficulty to the calculation and thinking of the obstruction.The above obstacles can be attributed to teachers’ attention to algebraic solution and neglect of geometric intuition,students’ weak ability to transform algebra and geometry,their attention to techniques and neglect of the essence of the problem,and the negative mentality of students and teachers.In view of the obstacles and their causes,combined with students’ cognitive characteristics and teachers’ interview suggestions,the corresponding teaching suggestions and countermeasures are put forward.In addition to paying attention to the mastery of knowledge and models,the transformation of geometric and algebraic representations,the computational ability and speed of problem solving and students’ emotional factors,the teaching of solving small topics can be designed from the three aspects of skill induction,problem solving ideas and hierarchical homework. |
