百年教材几何内容中定义和定理的"编排顺序"与"呈现方式"比较研究OA

The new curriculum reform emphasizes the integrity and consistency of the content structure;however,there are differences in the arrangement and presentation of geometric content in different versions of mathematics textbooks.What are the differences in these textbooks?Why do these differences exist?A comparison of textbooks from the past century across the two dimensions of sequencing and presentation reveals that:the sequencing of the same content does not change much in different textbooks,while there are differences between different contents;definitions are predominantly presented through qualitative descriptions and quantitative characterizations,while theorems are exclusively quantitative characterization;the methods of theorem proof exhibit an evolutionary trend from"no proof → deductive reasoning → plausible reasoning to deductive reasoning";the number of corollaries is gradually decreasing,with these often being presented as theorems or basic facts.The following suggestions are provided for the compilation of teaching materials:the arrangement order should be designed flexibly in accordance with students'cognitive development,aligning with learning psychology rather than adhering rigidly to a single model;The presentation mode should favour quantitative description and essential generalization,so as to clarify the concepts and provide support for theorem exploration;The way of proof should integrate plausible reasoning and deductive reasoning to enrich the thinking process and cultivate innovative literacy.