1, thinking in images.
Thinking in images means that people use thinking in images to understand and solve problems. Its thinking foundation is concrete image, and its thinking process is developed from concrete image.
The main means of thinking in images are objects, figures, tables and typical image materials. Its cognitive feature is that it is average in individual performance and always retains its intuition about things.
Its thinking process is represented by representation, analogy, association and imagination. Its thinking quality is manifested in actively imagining intuitive materials, processing and refining representations, and then revealing the essence, laws, or looking for objects. Its thinking goal is to solve practical problems and improve thinking ability in solving problems.
2. Abstract thinking method.
The thinking process of reflecting reality with concepts, judgments and reasoning is called abstract thinking, also called logical thinking.
Abstract thinking is divided into formal thinking and dialectical thinking. Objective reality has its relatively stable side, and it can adopt the form of thinking; Objective existence also has its constantly developing and changing side, and we can adopt dialectical thinking. Formal thinking is the basis of dialectical thinking.
Formal thinking ability: analysis, synthesis, comparison, abstraction, generalization, judgment and reasoning.
Dialectical thinking ability: contact development and change, law of unity of opposites, law of mutual change of quality, law of negation of negation.
Mathematics in primary and secondary schools should cultivate students' preliminary abstract thinking ability, focusing on:
(1) The thinking quality should be agile, flexible, connected and creative.
(2) In the way of thinking, we should learn to think methodically and systematically.
(3) in terms of thinking requirements, the thinking is clear, the cause and effect are clear, the words must be reasonable, and the reasoning is strict.
(4) In thinking training, we should require correct application of concepts, proper judgment and logical reasoning.