1, construction method
For some complex problems, we can solve them by constructing appropriate models or diagrams. This method requires a deep understanding of the topic, as well as a certain degree of creativity and imagination. For example, when solving some comprehensive problems related to functions and equations, we can find solutions by constructing auxiliary functions and combining numbers and shapes.
2. Parameter method
In some problems involving variables, parameters can be introduced to simplify the problem. This method needs to find the appropriate parameters by analyzing the problem and get the answer by solving the parameters. For example, when solving some geometric problems related to triangles and quadrangles, parameters such as angle and side length can be introduced, and the answers to the questions can be obtained by solving the parameters.
Step 3 reduce to absurdity
In some cases, a proposition can be proved by reduction to absurdity. This method needs to find counterexamples or contradictions through the analysis of problems, thus proving the correctness of the original proposition. For example, when solving some geometric problems related to the congruence and similarity of triangles, two triangles can be proved to be congruent or similar by reduction to absurdity.
The role of finale in mathematics
1 to test students' comprehensive application ability.
The finale problem usually involves many knowledge points and skills, and students need to use what they have learned comprehensively to solve it. By solving the final problem, students can consolidate and deepen their understanding and mastery of mathematics knowledge and improve their comprehensive application ability.
2. Improve students' thinking ability.
The finale is usually difficult and challenging, which requires students to have certain thinking ability and problem-solving skills. By solving the final problem, students can exercise their thinking ability and problem-solving skills, and improve their mathematical literacy and problem-solving ability.
3. Promote the progress of mathematics education.
The finale is an important part of mathematics education. By designing and solving the finale problem, the progress and development of mathematics education can be promoted. The last question can also be used as an evaluation tool in mathematics education to evaluate students' mathematical ability and level.