A Comparative Study Of Natural Numbers And Fractions In Mathematics Textbooks From China,Russia And U.S.A.

The purpose of this study is:to identify the differences and similarities of Mathematics textbooks,how well the material is presented for students' understanding and to determine what methods are used in Mathematics textbooks of China,Russia and the U.S.A.to explain important concepts such as Natural Numbers and Fractions.This research is based on the construction of Mathematics Textbooks and a comparative analysis of primary and middle school Mathematics textbooks in China,Russia and the U.S.A.The study is geared at providing pertinent and useful information for the authors of Mathematics textbooks at the primary and middle school level in the countries listed above.The research demonstrates how the content of the selected topics is presented in textbooks,how the theoretical material is explained and what situations are taken into consideration during the explanation of the topics in a classroom setting.The data gathered seeks to reveal the common and distinct characteristics of the Mathematics textbooks that are used in the three countries.A preliminary study found that the content design for Natural Numbers and Fractions can be summarized into the following:In the Chinese textbooks,the learning materials are given in small portions,at first a brief explanation of the topic using an example and explanatory drawings,and then there are practice exercises based on the topic that was covered.The themes are given in accordance with the age,i.e.in the 1st and 2nd grades where greater emphasis is placed on the study of Natural Numbers and arithmetic operations on them.The students study to fluently perform operations at this stage.From grade 3,students start learning the initial concept of Fractions and Decimals.The learning materials are presented sequentially,focused on key concepts that are required to develop the mechanical ability of students to apply mathematical concepts.Although the training materials are given in small portions,the study of Numbers and Fractions progresses at the desired rate;In the Russian textbooks,the content of the textbook at the primary level is presented clearly and paragraphs are quite moderate.In middle school(5th&6th grades)the explanatory notes are very intense and have detailed explanations of complex content.The textbooks have many textual tasks,among which there are a lot of complex tasks which are not accompanied by drawings.In general,the training materials are given in a gradual and steady manner.Each topic is related to the previous one,which allows for the repetition of previously learned concepts;In the United States textbooks however,the training materials are given alternately and are interspersed with repetitions e.g.along with studying arithmetic operations on Numbers in the 2nd grade,it also introduces the initial concept of Fractions.This is continued in each new grade with the various themes in Natural Numbers and Fractions being completed gradually although it is a bit more complicated at each stage.Basically the American textbooks explain new concepts in a simplified manner with a lot of figures for easy understanding by students.