A Comparative Study Of Examples And Exercises In The Contents Of The Pythagorean Theorem In Different Editions Of Textbooks

“Four Fundamentals” of mathematics have been one of the key and hot issues of Chinese education research.This paper selects four versions of junior high school mathematics textbooks in the stage of compulsory education(the PEP Edition,the Beijing Normal University Edition,the East China Normal University Edition,and the Shanghai Science Edition),and conducts a comparative study of the example exercises of Pythagorean Theorem from the three aspects of basic knowledge,basic skills and basic ideas,with the hope of exploring the commonalities and differences among them.The results of the research are expected to help different editions of textbooks to learn from each other and provide reference materials for the compilation of textbooks.In terms of basic knowledge: the proportion of example exercises involving single knowledge point is the highest in different versions of textbooks,while the proportion of those involving two knowledge points is slightly lower,and the proportion involving multiple knowledge points is the lowest.The proportion of example exercises involving single knowledge point in Beijing Normal University version is higher than other versions,especially the single knowledge point — “the applications of Pythagorean Theorem in real life” and “the application of Pythagorean Inverse Theorem” — having more example exercises.The proportion of the example exercises involving two or multiple knowledge points in Shanghai Science Edition is higher than other versions.In terms of cognitive level,the number of example exercises in different editions of textbooks is higher than the level of comprehension.The East China Normal University version and the People's Education version have higher proportions of example exercises at the operational memory level and conceptual memory level than other versions,and the Beijing Normal University version has a higher proportion of example exercises at the descriptive comprehension level and the exploratory comprehension level.Other editions,and the East China Normal University edition have no example exercises for the exploratory comprehension level.In terms of basic skills: In terms of the complexity of operations,the proportion of numerical operations in the Beijing Normal University textbook is higher than that in other versions.The proportions of simple operations and multi-step operations in the example exercises of the Shanghai Science Edition are higher than those of other versions.Picture recognition skills accounted for the highest proportion of the PPE version of the exercises,while drawing skills accounted for the highest proportion of the Shanghai Science version of the example exercises.Reasoning skills accounted for the highest proportion of the exercises in the Shanghai Science Edition,while the lowest in the Beijing Normal University version because it's limited by the order of content writing,and thus has a single content carrier.As for the skills of mathematical communication and the use of information technology,relevant example exercises are only found in the Beijing Normal University version.In terms of basic ideas: in each version of the textbook,the highest proportion is the combination of numbers and shapes.The proportion of examples in the Shanghai Science Edition that embodies symbolic representation,symmetry,induction,and deduction ideas is higher than that of other versions,while the proportion of exemplars embodying the ideas of transformation and reversion is lower than that of other versions,and there are no exemplars that embody optimization ideas.The Beijing Normal University version has a higher proportion of example exercises that reflect the idea of transformation,transformation and optimization than other versions,while the proportion of example exercises that reflect the idea of equations is lower than that of other versions,and there are no example exercises that involve the idea of symmetry.The East China Normal University version has a higher proportion of example exercises that reflect classification discussions and equation ideas than other versions,but there are no example exercises that reflect optimization ideas.The example exercises of the PPE version that reflect the combination of numbers and shapes are higher than those of other versions,while the proportion of examples of symbolic representation and deductive thoughts is lower than that of other versions,and there are no examples of exercises that reflect symmetrical thoughts and inductive thoughts.