A Comparative Study On The Content Of "Series" In The Old And New Textbooks Of People’s Education Press A

As the new textbooks come into use in all provinces and cities,the differences between the old and new textbooks and how to grasp the changes and make appropriate instructional adaptations have become a major concern.The series is closely related to real life and contains rich mathematical ideas.It is an important part of high school mathematics and also occupies a place in the college entrance examination.In this study,the chapters of "Series" in Compulsory 5,published in 2007,and Compulsory 2,published in 2020,were selected as the subjects of the study.By using the methods of literature analysis,content analysis,comparative analysis and quantitative analysis of mathematical models,a comparative analysis of the curriculum standards and the content of the two textbooks was conducted,which was mainly from the perspectives of the content of the curriculum standards,the difficulty of the curriculum,the cognitive level of the curriculum,the structure of the textbook,the illustrations of the textbook,the penetration of mathematical culture and the setting of examples and exercises in the textbook.With regard to the curriculum standards,the new textbook has been restructured to include mathematical induction as an optional component under the topic of Functions in the optional Compulsory 2,which emphasizes the link between series and functions.In this paper,a quantitative model of curriculum difficulty is developed to analyse the curriculum standards of the old and new textbooks,shows that the new textbook is higher than the old one in three dimensions: curriculum breadth,curriculum depth and curriculum difficulty,with the old textbook having a curriculum difficulty of 1.9167 and the new textbook having a curriculum difficulty of 2.With regard to the structure of the textbook,both the old and new textbooks contain four basic sections: chapter headings,sections,summaries and revision questions;the marginal notes in the new textbook are more comprehensive and effective,and the end-of-chapter summaries are logical and highlight important and difficult points.With regard to textbook illustrations,the old and the new textbooks have fewer illustrations for "Mathematics" and "Science",with the new textbook focusing on "History".With regard to the infiltration of mathematical culture,the number and proportion of cultural objects in mathematics in the old and new textbooks are basically the same,but the new textbook has a balanced distribution of different types of mathematical cultural objects,making cultural infiltration more effective.With regard to the setting of examples and exercise,the proportion of examples,in terms of quantity,the new textbook has a balanced distribution of different types of examples and exercise.In this paper,a "five-factor,multi-level" model of the difficulty of mathematical problems was developed to quantify the difficulty of the sample exercises,resulting in a difficulty of 2.31 and 2.23 for the old and new textbooks respectively;the difficulty of the exercises in the new textbook was 2.64,higher than that of the old textbook,which was 2.32.The difficulty of the new textbook is higher than that of the old textbook,except for the situational factor,in which the arithmetic factor and the cognitive factor are significantly higher than that of the old textbook.Based on the research results,the author puts forward some suggestions on the compilation of series contents and some inspirations for teachers in teaching:Suggestions for the compilation of textbooks: refine the curriculum objectives and balance the target cognitive levels;increase the number of example solutions to broaden students’ mathematical thinking;increase the reading materials in the textbooks to enhance the cultural infiltration of mathematics;enrich the problem situations in the textbooks to improve the ability to solve practical problems;and strengthen the integration of mathematics curriculum with information technology to cultivate comprehensive talents.Implications for teachers’ teaching: increase the series situational questions appropriately;make good use of classroom practice questions for accurate teaching through timely feedback;increase the number of moderately difficult questions appropriately to help students cross the cognitive level;guide students to draw concept maps and develop the ability to summarize and generalize on their own.