Conditional inquiry, conclusion inquiry and legal inquiry
Existential inquiry, strategic inquiry and comprehensive inquiry
This paper summarizes the types of inquiry questions and problem-solving strategies in Qin Zhen's "Guide to Senior High School Entrance Examination" and "Types of Open Inquiry Questions and Problem-solving Strategies in Junior Middle School Mathematics".
There is a problematic conclusion, and the conditions are insufficient. Supplementary conditions make the conclusion valid.
Solution: the reason for holding the fruit
① Starting from the conclusion, consider the conditions that need to be met when the conclusion is established.
(2) Combined with the diagram and its properties, the possible situations are listed one by one.
③ Find out the required conditions.
① Given conditions, explore the corresponding conclusions (diversity of conclusions)
② There are corresponding conclusions to be inferred.
③ Explore the conclusion of changing conditions.
Solution: Cause leads to result.
Starting with the analysis of the meaning of the problem, we can draw a conclusion through observation, calculation, association, induction and reasonable reasoning.
Give some numbers, formulas, functions or graphs, and their changing characteristics.
Explore conclusions about the regularity or invariance of objects.
Solution: Based on what is known, observation, induction, analogy and analysis.
Explore more general conclusions from special to general, and then give proof.
Judge whether a mathematical object has a problem under certain conditions.
Problems such as "existence", "existence" and "change" often appear.
Solution:
(1) Assume that the object exists first.
(2) Operate and reason according to conditions and assumptions.
(3) there is a contradiction, it does not exist; If there is no contradiction, there is.
Know all/part of the conditions and conclusions, explore solutions or design solutions.
Solution: imitation, analogy, experiment and innovation.
Comprehensive use of the learned knowledge, reasonable transformation, the establishment of mathematical models, to solve problems.
Conditions, conclusions and methods of solving problems are incomplete or unknown.
Solution:
① Start with basic knowledge and skills.
② Characteristics of multi-angle and multi-level analysis problems.
(3) pay attention to exploring one cause and many fruits, and one cause and many fruits.
(4) Explore the necessary conditions for the establishment of the problem, or draw conclusions from specific conditions.