A Comparative Study On The Cognitive Complexity Of Geometry Textbooks For Junior High School In China,Singapore And Britain

In this study,we take the mathematical problems of triangle,quadrangle and circle in junior middle school geometry teaching materials in China,Singapore and Britain as the research object,and compare the following two questions:(1)A comparative study of the cognitive complexity of junior high school geometry textbooks in China,Singapore and Britain;(2)A comparative study of the cognitive depth of junior high school geometry textbooks in China,Singapore and Britain.This study found that there are some similarities between the three sets of textbooks through the comparison of the cognitive complexity of the exercises for the triangle,quadrilateral and circle related cases of the junior middle school mathematics textbooks in China,Singapore and Britain:(1)In terms of breadth,the geometry of the three textbooks takes more attention to the use of the rules or procedures to solve the problem.In addition,the cognitive breadth of the species are not rich enough.(2)In terms of depth,the geometric part of the three textbooks requires relatively less tasks about doing mathematics which need high demand.high level of mathematical tasks,and the diagram complexity on the whole is also not highIn addition to the similarities,the cognitive complexity of the three textbooks has some differences,mainly presented in:(1)In terms of breadth,Chinese textbook is more focused on the settings for mathematical problems about reasoning and problem solving and has more rich andbalanced knowledge and skills than others.Singapore textbook takes more attention to the use of the rules or procedures to solve the problem than others.Britain textbook takes more attention to settings for representation knowledge for tasks than the other two.(2)In terms of depth,for cognitive demand,Chinese textbooks have the highest level of cognitive demand,followed by Singapore textbook,level of English textbook is lowest.For diagram complexity,on the whole the number of point line changes need in Chinese textbook geometry problem was the highest,followed by Singapore textbook,the number for English textbooks is the lowest.For problem solving complexity,Chinese textbook degree is the highest,followed by Singapore textbook,the degree of English textbooks is the lowest.According to the conclusion,here are some advice for textbook writers and teachers: strengthen the representation of knowledge for students to understand the nature of geometric properties better.Increase the settings for doing mathematics task(C4)to meet the high level requirements.Strengthen the diagram complexity of problems with diagrams.Teachers should provide supplementary materials to meet the needs of different levels of cognitive level of students.teachers should allocate the time reasonably to meet the different cognitive complexity of mathematical problems.