Functions are the core of algebra, and the teaching of function concepts is also the main task of high school mathematics Students' learning of functions and their concepts shifts from understanding specific quantitative relationships to understanding abstract quantitative relationships The monotonicity of functions, as the property of the first function that students learn in high school, lays a certain foundation for learning function related knowledge in the future.

The curriculum reform in 2022 puts forward new requirements for the professional literacy cultivation of primary science teachers, and the cultivation of primary science classroom teaching skills is an important aspect of the professional literacy cultivation of science education teachers, mainly including subject knowledge and teaching theory, teaching design and preparation, teaching methods and strategies. On the basis of following the principle of combining theory and practice, diversified teaching and student subjectivity, the training strategies of group cooperative learning, observing the teaching process of excellent teachers, and strengthening the effect of micro-grid teaching are proposed, and in addition to the expected evaluation, it provides a certain theoretical basis for the cultivation of normal students in science education.

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.