With the development and reform of education, the cultivation of core competencies for normal school students is receiving increasing attention. This article analyzes the connotation of the core literacy of preschool education teacher students, the difficulties faced in cultivating core literacy, and explores how to use flipped classrooms to enhance the core literacy of preschool education teacher students.

The six core competencies of mathematics in vocational schools are becoming increasingly important in mathematics learning. The reverse teaching design of vocational school mathematics, which focuses on core competencies, precisely grasps the internal logic of knowledge from a holistic perspective, and designs it on a unit by unit basis. The design process is to infer the starting point from the endpoint. Therefore, how to use reverse thinking in teaching design research in vocational school mathematics teaching under the background of core competencies will be the main content of this article.

The promulgation of the Curriculum Standards for ordinary high School (2017 edition, 2020 revision) has effectively promoted the reform of high school mathematics classroom. In order to cope with the change of textbook content in the new curriculum reform, it has become one of the important tasks for high school mathematics teachers to implement teaching activities better and sort out and analyze the differences between the old and new textbooks. This paper analyzes the differences between old and new textbooks from the three dimensions of system structure, course content and example exercises, and gives some reasonable teaching suggestions. Among them, the new textbook uses 2019 "Ordinary High School Textbook" person-taught A version of Compulsory Mathematics 1, and the old textbook uses 2004 "Ordinary High School Mathematics Curriculum Standard Experimental Textbook" person-taught A version of compulsory Mathematics 4. In general, the adjustment of the new teaching materials is more in line with the cognitive characteristics of students, pay attention to the penetration of mathematical culture and pay attention to the development of students' mathematical core literacy.