Application of theories on thinking to build the theory of mathematical thinking in teaching high school mathematics

Abstract

The paper explores the development of a theory on mathematical thinking in the teaching of Mathematics at the high school level (HSL). The first part of the paper presents characteristics of thinking, including problem-solving, direct and indirect aspects, abstraction, generalization, and its close relationship with language. The process of thinking formation is described through various stages, where direct and indirect thinking holds a significant position. The following section classifies types of thinking such as logical thinking, imaginative thinking, and argumentative thinking. Additionally, it categorizes thinking into different levels of independence. Thinking is classified based on the object, the field of perception, and the thinking method. The crucial part of the paper focuses on mathematical thinking, describing it as a creative process applying mathematical methods, concepts, and procedures to solve problems. In conclusion, the paper constructs a theory of mathematical thinking in teaching Mathematics at HSL, aiming to develop and enhance mathematical capabilities in students by grasping fundamental knowledge and skills. It encourages core mathematical abilities such as thinking, modeling and problem-solving.