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The reversible thinking is the way of thinking in two opposite directions, which then support each other to help people perceive and solve problems flexibly and effectively. In this article, we mention manifestations of students'reversible thinking competence in teaching functions and graphs and propose measures to foster this ability in order to contribute to improving the quality of teaching mathematics at high schools.

Mathematical communication is one of the core competencies that needs to be formed and developed for students in the teaching of Mathematics in high schools. In this research, we have identified the manifestations of mathematical communication competence in 10th-grade students in teaching the topic “Coordinate Methods in the Plane”, based on a survey of opinions from 68 high school mathematics teachers in the provinces of Nghe An and Ha Tinh. Additionally, the research was also conducted with 32 10th-grade students who were assigned several learning tasks related to the topic “Coordinate Methods in the Plane”, with the aim of understanding the manifestations of students’ mathematical communication competence and the mistakes they made related to these manifestations. From there, propose several teaching methods to contribute to the development of mathematical communication competence in students in teaching this topic.

Competence-based teaching has been a concern of many educators in the current period. Preparing the lesson plans before classes greatly determines the success of the lessons. Applying scientific research methods such as theoretical research, investigationobservation, expert method, the article presents the structure and process of designing lesson plans for Mathematics, analyzes and clarifies the steps in the design process, thereby applying the design of specific lesson plans to facilitate teachers in the teaching process. The results published in the paper are unanimously agreed by experts.