A Comparative Study Of Function Exercises Of High School Textbooks On Both Sides Of The Taiwan Straits

With the promotion and implementation of the new curriculum standard in senior high school,the new mathematics textbook in senior high school has aroused widespread concern in the educational field after being put into use.Taiwan Province officially implemented the 12-year national education system in 2018 and uniformly compiled mathematics textbooks for the basic education stage.As an important content of mathematics textbook,exercise is an important index reflecting the difficulty of mathematics curriculum.The research on the exercises of mathematics textbooks in mainland and Taiwan Province can help each other learn from each other.It not only provides reference for the future mathematics curriculum reform and examination evaluation,but also provides some practical reference value for the improvement of mathematics teaching.This paper takes the exercises of exponential function and logarithmic function in mathematics textbooks published by Hanlin Press and People's Education Press as the research object,and literature analysis,comparative research,qualitative and quantitative research methods are used.It takes the broad view to compare curriculum standards and function contents between the mainland and Taiwan Province.The surface structure(quantity,type and presentation)and the deep structure(the level of exercise,key competencies,consistency between difficulty of exercises and difficulty of examples)of function exercises are compared from the micro level.The results are as follows:Firstly,the new curriculum standard of mainland China is more detailed than the outline of Taiwan Province in terms of function content requirements.The new curriculum standard in mainland China pays attention to training students' mathematics key competencies,while the outline in Taiwan Province has overall significance.In terms of chapter arrangement and content setting of teaching materials,the design of teaching materials on both sides of the Taiwan Straits are different.Secondly,the results of the comparison of the surface structure of the high school function exercises on both sides of the strait show that the two editions of the textbook exercises show obvious differences in the number of questions,the focus of the question types and the inconsistency of the presentation methods in terms of the number,type and presentation of the mathematics questions.Thirdly,in the deep structure comparison of function exercises in high school textbooks on both sides of the Taiwan Straits,there are differences in the levels of exercises in the two editions of textbooks.In the expression of mathematics key competencies,the exercises in textbook of Hanlin version focus on the cultivation of intuitive imagination.And the exercises in textbook of the new PEP version pay more attention to mathematical operation.In the comparison of the difficulty of exercises,the difficulty factors of "background" and "knowledge synthesis" in the textbook of new PEP version are lower than those in the textbook of Hanlin version.The difficulty factors of "mathematical cognition","operation and reasoning" in the textbook of new PEP version are higher than those in the textbook of Hanlin version.In the comparison of the consistency between the difficulty of examples and exercises,the four difficulty factors of "operation and reasoning","mathematical cognition" and "knowledge synthesis" of exercise are higher than those of examples on both sides of the Taiwan Straits.According to the conclusion,the following suggestions are put forward:enriching the background of problem solving and integrating elements of real life into teaching;paying attention to the implementation of key competencies and cultivate mathematical modeling competencie;properly increasing the width and breadth of knowledge points,and paying attention to the connection of knowledge;reasonably setting the difficulty of example and exercises and attaching importance to the connection between knowledge;the setting of examples and exercises should highlight the requirements of curriculum standards and reflect consistency.