Using Auxiliary Diagrams To Solve "Number And Algebra" Application Problems And Case Study

The Mathematics Curriculum Standards for Compulsory Education(2022 Edition)makes problem solving an important curriculum goal and states that students should be able to use mathematical knowledge and mathematical methods to try to solve "number and algebra" application problems from a mathematical point of view.Students should not only learn how to solve problems in middle school mathematics "number and algebra" application problems,but should also update their problem solving methods.The content of "Number and Algebra" is a vital part of middle school mathematics,and an important tool for students to solve problems.The use of auxiliary diagrams in the classroom is a good way to solve problems,and is a necessary problem solving skill for students.It is also a very common type of problem in Chinese exams,where the graph is given directly or the student is asked to make a diagram.The research method used is literature research,interview survey,questionnaire survey,classroom observation,and case study.According to the interview and questionnaire survey,the use of auxiliary diagrams in "Number and Algebra" application problems is very high,the most used in the function application problems,followed by the use of the number axis diagram.Not all types of problems are suitable for auxiliary diagrams,and it is important to use them correctly in the appropriate problems.Teachers and students need to pay attention to the simplicity and standardization of auxiliary diagrams in teaching.Through classroom observation and case studies,it was found that auxiliary diagrams allow students to clearly see the quantitative relationships and facilitate knowing the meaning of the problem,and auxiliary diagrams can also be used in future learning as well as to increase interest in learning mathematics.The problems found in the study are:(1)the auxiliary diagrams drawn do not fit the meaning of the question,not paying attention to the range of values;(2)the appropriate use of auxiliary diagrams,some problems can be solved without drawing a diagram;(3)the auxiliary diagrams drawn are not concise enough,not enough standard,pay attention to the diversity of auxiliary diagrams.According to the above problems,the following teaching suggestions are made:(1)the standardization and simplicity of auxiliary diagrams must be paid attention to;(2)the optimal solution is selected according to the meaning of the problem,not only the drawing can solve the problem,but also the reasonable use of auxiliary diagrams;(3)the auxiliary diagrams drawn are closely related to the meaning of the problem;(4)attention is paid to the cultivation of students’ ideas of combining numbers and shapes.