Research On The Problem-solving Teaching Of Mathematical Circles In Junior High School Based On Polya’s Problem-solving Theory

As the key and difficult point of the geometry in junior middle schools,the knowledge of circle plays an important role in cultivating students’ geometric intuitive ability and logical thinking ability.Because of its high proportion in the middle school entrance examination,it is particularly important for the entrance examination.Because the knowledge of circle involves many contents and is closely associated with other geometric knowledge,the requirement of students’ problem-solving ability is high,which makes the scores of circle problems are not ideal.To improve teachers’ ability in teaching circle problems and students’ ability in solving circle problems,this paper carries out the research on the teaching and learning of circle knowledge based on the Polya’s problem-solving theory.First of all,based on the Polya’s problem-solving theory,we study the students’ current situation of solving circle problems in Grade 9 by using the methods of questionnaire,statistical analysis,and literature analysis.Based on the investigation and analysis,we have the following findings: the students lack the habit of mining hidden conditions and the ability to set auxiliary questions,causing the inability to formulate problem-solving plans;When writing solutions,the knowledge base is not solid enough,resulting in logical confusion;Without the habit of reviewing and reflecting,the students brush the questions blindly.At the same time,most teachers do not have a deep understanding of the Polya’s problem-solving theory and have not developed relevant problem-solving courses.On this basis,through the significant difference test,this paper explores whether the Polya’s problem-solving theory is of substantial help to students’ problem-solving.It comes to the conclusion that the hint of the Polya’s problem-solving theory is of significant help to the students in Grade 9.Finally,according to the results of the questionnaire and interview,combined with the four steps of the Polya’s problem-solving theory,this paper gives the teaching and learning suggestions of circle problems in junior middle school,which is further integrated into the example of the textbook of the People’s Education Edition.The suggestions are as follows: when examining questions,pay attention to divergent thinking;Construct clear auxiliary problems when formulating ideas;Monitor solution status when writing solution ideas;After answering,classify the solutions;When teaching new knowledge,teachers should clarify the problem setting and conclusion in order to lay a good foundation for geometric theorems.