What is a math problem?From the point of view of systems theory, if for a person all the properties of the elements of a system and the relationships between the elements are known to him, then the system is a stable system for him. If there is at least one element, nature, and relationship in the system that he is not aware of, then the system is a problem.
Whether a system can count as a question is related to the people who come into contact with it. A system may be a problem for student A, but it may not be a problem for student B. If the elements, properties, and relations of the problem system are all mathematical, then it is a mathematical problem. For example, the famous Königsberg Seven Bridges problem;It wasn't originally a mathematical problem, it became a mathematical problem when Euler abstracted it into a "one-stroke" problem.
Mathematical problems in mathematics education refer to problems that can be understood and solved in multiple ways within the scope of students' existing knowledge and abilities;It is unconventional, open-ended, and unconventional, for example, the conditions are not sufficient, and the conclusion is not unique. Students can use the existing knowledge and methods to generalize the problem to a variety of situations.
Math problems include not only textbook Xi problems, but also those from practical problems;It should include not only questions in the form of simple practice Xi Xi, but also questions in the form of questions that are not simply practicedIt should include not only questions that are sufficiently conclusive, but also open-ended questions that are exploratory.
Problem solving is a series of purposeful cognitive processes, and for students, problem solving refers to the comprehensive and creative use of previously acquired mathematical knowledge and methods to solve problems that are not simply practiced Xi problems, including practical problems and problems that originate from within mathematics.
In the process of problem solving, a variety of intellectual activities such as analysis, synthesis, abstraction, generalization, and imagination are needed, which provides an environment and opportunity for students to discover and innovate, and provides a way for teachers to cultivate students' problem-solving ability, self-control ability and ability to apply mathematical knowledge. It not only focuses on the general process of problem solving, the result of problem solving, and the answer to problem solving, but also pays more attention to the process of problem solving, strategies and methods of thinking, and the metacognitive experience of problem solving. Its teaching process is a process of discovery, a process of exploration, and a process of innovation, and its purpose is to train students not only to learn mathematical problem solving;And should have the ability to apply mathematical methods to solve practical problems, especially the ability to think innovatively.