Teaching methods are a complex topic in mathematics education. This study aims to analyze the teaching methods of previous relevant studies and design a new lesson study on how to teach the topic of functions at the high school level in China. Lesson study focuses on the basic concepts of function and problem-solving abilities. The researcher uses the research and development method to teach the material function at the high school level. This Lesson Study is used to teach in China. The researcher explains 4 important aspects in designing a lesson study, namely the introduction or opening section, the instructional section or core section, the assessment section, and the closing section.

This study aims to develop an evaluation tool to evaluate the overall logical reasoning core literacy skill and understand the differences in logical reasoning skills between students of different classes and genders. The quality of the developed evaluation tool is tested and optimized based on the Rasch model. The measured sample data are processed and analyzed by winsteps software and SPSS software. 122 senior three students from different classes were evaluated by the developed logical reasoning literacy level evaluation tool with good reliability and validity. It was found that the overall logical reasoning skills of senior high school students was concentrated in Level II, and some students could reach Level III; there are obvious differences in the level of logical reasoning skills between the experimental class and the ordinary class. The overall level of the experimental class is higher than that of the ordinary class; there is little difference in the distribution of male and female at the low level, but compared with male, female' literacy Level Is obviously limited after reaching a certain level, so it is difficult to break through and rise to the third level.