Research On The Status Quo And Instructional Design Of Function Teaching In Junior High School Based On Problem Driven

The 2022 edition of the Curriculum Standards for Compulsory Education in Mathematics(2022 Edition)states that students should choose teaching methods that stimulate their thinking and focus on heuristic teaching,inquiry-based teaching,participatory teaching,and interactive teaching,etc.The 2022 edition of the standards explicitly adds the expression of reasoning,placing the strengthening of algebraic reasoning in an important position in the field of number and algebra.The reasoning needs to be established under the problem-driven,belonging to the process of analyzing the problem,and the standard emphasizes the formation of reasoning consciousness,which is also included in number and algebra in junior high school functions,so it can be seen that problem-based teaching occupies an important position in junior high school function teaching.Based on constructivism,nearest developmental zone theory,Freudenthal’s mathematics education ideas and Dewey’s "Problem-based teaching method",this paper summarizes five basic principles for designing mathematical problems,which are the principle of mapping the essence of mathematics,the principle of questions to inspire mathematical thinking,the principle of realistic mathematical situations,the principle of questioning with emotion,the principle of question presentation diversity and the principle of emotionality in questioning.Then,we investigated the current situation of problem-driven classroom teaching of middle school functions by using interview method,questionnaire survey method and case study method,and presented the teaching design of different types of classes based on problem-driven teaching of middle school functions.According to the results of teachers’ interviews,students’ questionnaires and classroom recordings,front-line teachers agree on the application of problem-driven classroom teaching to junior high school function teaching,but teachers often feel some difficulties in setting problems,and what kind of problems can guide students to discover,ask,analyze and solve problems more effectively is also the difficulty and focus of front-line teachers’ teaching.Based on a theoretical basis,the current situation of the survey and the teaching design,the following conclusions are drawn:(1)Setting problems according to different lesson types can help improve the effectiveness of classroom teaching of middle school functions;(2)The design of problem strings in the teaching of functions in junior high school should be reasonable and tightly focused on students’ thinking,and the focus of attention in the design of problem strings should be different for different types of lessons;(3)Setting appropriate and reasonable problems is the key to improving the effect of teaching function in junior high school classroom.Finally,based on the problem-driven classroom teaching of functions in junior high school,the following suggestions are given:(1)Problem design needs to restore the key points of function knowledge on the basis of students’ cognizability;(2)When designing problems,the laws and properties of function graphs should be fully considered to transform from special to general;(3)When designing problems,the function review class should pay attention to the systematic and comprehensive knowledge of functions,and in the function topic class should focus on exercising the thinking of students in solving problems.