Classification idea is a mathematical idea that divides mathematical research objects into different categories according to the similarities and differences of mathematical essential attributes. The basis of classification is comparison, which is the premise and result of classification.
The idea of classified discussion runs through all the contents of middle school mathematics. The mathematical problems that need to be solved in the idea of classified discussion can be summarized as follows: (1) classifying and defining the mathematical concepts involved; The mathematical theorems, formulas, operational properties and rules used are given by classification.
There are many situations or possibilities for the conclusion of the solved math problem; There are parametric variables in mathematical problems, and their values will lead to different results. The application of classified discussion can often simplify complex problems. The process of classification can cultivate the thoroughness and orderliness of students' thinking, and classified discussion can promote students' ability to study problems and explore laws.
In teaching, students can form the positive application of classification thought from the following aspects.
1. Infiltrate the idea of classification and cultivate the consciousness of classification.
Every student has certain classification knowledge in daily life, such as the classification of people and stationery. We use this knowledge base of students to transfer the classification of life to mathematics, infiltrate the idea of mathematical classification into teaching, tap the opportunities provided by textbooks and seize the opportunities of infiltration.
2. Guide classified discussion and improve the ability to solve problems reasonably.
There are many theorems, laws, formulas and exercises in the textbook, which need to be discussed separately. When teaching these contents, students should constantly strengthen the awareness of classified discussion and make them aware of these problems. Only after classified discussion can the conclusion be complete and correct.