A Comparison Of Inequality Content Difficulty In Chinese And Singaporean High School Mathematics Textbooks

In order to implement the basic concepts and requirements of the new national high school mathematics curriculum standards,new textbooks based on the new curriculum standards in 2017 have been published successively.Starting from the fall semester of 2019,the first round of teaching experiments will be conducted in some provinces,autonomous regions and municipalities across the country.Whether the new textbooks conform to the requirements of the new curriculum standards ? what are the differences between the new textbooks and the old textbooks ? whether they are more conducive to the improvement of students' math core literacy and math ability ? Especially,the difficulty of the new textbooks is an urgent problem to be solved in the process of use.Moreover,it is also a hot issue in the current middle school mathematics education research.In this paper,the study on the difficulty of the new textbook is mainly carried out from two aspects: vertical and horizontal.On the one hand,it makes a longitudinal comparison with the old textbooks.On the other hand,it makes a horizontal comparison with the foreign developed countries.Therefore,in order to make an objective and comprehensive scientific assessment of the difficulty of the new edition of textbooks,this study selected three sets of representative textbooks,which included Chinese new edition and old edition as well as Singapore PM edition textbooks.And the “inequality” content of the three sets of textbooks is the research object.Then,this paper makes a comparative study on the difficulty and strength of knowledge points,the difficulty of exercises and the characteristics of textbooks,which is the innovation of this paper.Firstly,study the difficulty of knowledge points in the textbook.Based on the teaching contentand teaching experience of "inequality",this paper establishes its core concept through research.Then,it uses the Matlab software to construct the concept level directed digraph based on ISM method which referred to the Interpretative Strutural Modeling Method in the third edition.Then the knowledge structure is presented by concept level directed graph.On this basis,the concept map tool is used to analyze the depth,breadth and complexity of knowledge points in the three editions of the textbook.Further analysis of the three editions of the difficulty of knowledge points and knowledge of the degree of internal connection between similarities and differences.Secondly,study the difficulty of examples and exercises.Above all,the comprehensive difficulty model of Bao jian sheng was improved,and then the difficulty of examples and exercises in the inequality chapter of the three-edition textbook was quantitatively studied with this model.Further more,this paper analyzes the consistency of the difficulty of examples and exercise with this model.On this basis,combining with SPSS software,this paper analyzes the significant difference of between the weighted average difficulty of examples and exercises.Thirdly,study the influence of the characteristics of textbooks on the difficulty of textbooks.In this paper,the author analyzes the influence of the arrangement of textbooks,the initial height connection,the textbook column setting and the content target settings on the difficulty of the textbooks.In order to further explores the potential factors affecting the difficulty of inequality content in the third edition textbooks of China and Singapore and the characteristics of the textbooks.The results show that the Singapore edition is the most difficult and the coherence of knowledge is the strongest,while the new edition is the least difficult and the coherence of knowledge is improved on the basis of the old textbook.Then,the setting of examples and exercises in the two countries is veryprogressive,and the consistency of the exercises is good.But the mathematics situation is not rich enough,especially the textbook of Singapore edition is almost have no situation.Comparatively speaking,the new and old textbooks in China have a large number of examples and exercises,and the new textbooks are less difficult.The Singapore's examples and exercises is the most difficult,but its relevance degree is high,which reflects a practice followed by a case.Moreover,Singapore's examples and exercises pays attention to a variety of processing methods,and is better at using a graphing calculator to solve the problem.Due to the different positioning of "inequality" content,the goal setting and writing order of the three editio ns of the textbook are also different,which affects the difficulty of the textbook content to some extent.The three editions of textbooks are organized in a logical and systematic way.Among them,Chinese textbo oks are written in a "spiral" way,which reduces the content difficulty of textbooks,while the Singapore edit ion is written in a "straight line" way.The new edition of Chinese textbook takes the content of "inequality" as the preparatory knowledge,which plays a good role of the initial height connection and reduces the difficulty of the textbook.Finally,in terms of column setting,the two editions of Chinese textbooks are abundant,including chapter introduction and chapter summary,while the Singapore edition is dominated by illustrative illustrations.Through the study of the content difficulty of the inequality in high school mathematics textbooks,this paper aims to reflect the general situation of the new textbooks by the way of “to see the big by the small”.At the same time,combined with the comparative study of textbooks and the results of inte rviews with front-line teachers,this paper provides references for the subsequent adaptation and improvem ent of new senior high school mathematics textbooks,and helps teachers form the "scaffolding" for explori ng inequality teaching reform.