A Study On The Relevance Of Worked Examples In Primary School Mathematics Textbook

As an important materialized carrier for the implementation of mathematics courses,mathematics textbooks have long played an important leading role in the teaching and learning of mathematics teachers and students.The compiling quality of the former can determine the effectiveness of teaching and learning of the latter two to some extent.At the same time,the Ministry of Education will comprehensively start the revision of textbooks for various subjects in the compulsory education stage in2021.Based on this,the revision of elementary school mathematics textbooks is about to begin.As one of the main components of elementary school mathematics textbooks,worked examples will inevitably face the new task of revision in this historical period.Achieving the optimization of the function of worked examples is an important standard for the design and setting of worked example of high-quality elementary school mathematics textbooks.From the point of view of system theory,the realization of the function of worked examples must pay attention to the relationship between them and other factors that constitute the mathematics curriculum system,that is,whether the worked examples are suitable for the knowledge content of mathematics textbooks,whether they are suitable for the curriculum standard,and whether they are suitable for students learning and so on.At the same time,the curriculum standards for the compulsory education stage also clearly put forward the requirement of "relevance" in the part of compiling suggestions.To this end,it is necessary to study the actual state and the expected state of the relevance of the worked examples,build a bridge from the relevance actual state of the worked examples to the expected state,and boost the re-revision of primary school mathematics textbook examples and primary school mathematics textbooks.In view of this,the purpose of this research is to clarify what is "relevance of worked examples",and use "relevance of worked examples" as a research framework to study the worked examples in the three editions of primary school mathematics textbooks in China and Singapore.Based on this,this research intends to solve the following three main problems,namely,how to judge the relevance of the worked examples of elementary school mathematics textbooks,how relevance are the worked examples of elementary school mathematics textbooks in China and Singapore,and the future direction of the worked examples that meet the requirements of the relevance of elementary school mathematics textbooks.First of all,this research takes the relevant research results at home and abroad as the research starting point,takes "system theory" and "worked example function theory" as the theoretical basis,and extracts 2 internal relevant objects from the "primary school mathematics textbook" system,namely "textbook knowledge content" and "in-class exercises",and extract three externally relevant objects from the "primary school mathematics curriculum system",including "Curriculum Standards","Teachers","Students".Based on this,an analysis framework for the relevance of the worked examples in the primary school mathematics textbook was initially established.Then,from September 2020 to January 2021,this research was conducted on 26 primary school mathematics worked examples experts,teaching researchers and primary school mathematics teachers distributed in Jiangsu,Zhejiang,Shanghai,Anhui,Yunnan,Jilin,and Sydney Australia.Three rounds of Delphi expert consultation were conducted to optimize the preliminary analysis framework of the relevance of the worked examples.The revised worked examples relevance analysis framework is divided into two dimensions: "internal relevance" and "external relevance".There are 5 secondary indicators,10 third-level indicators,25 fourth-level indicators,22 five-level indicators.Finally,according to the constructed worked examples relevance analysis framework,this research carried out relevance text coding analysis of the worked examples in the three editions of the PEP,Jiangsu Education and Singapore MC editions of elementary school mathematics textbooks.At the same time,a total of 150 teachers and 310 students in elementary schools and educational institutions in Jiangsu,Zhejiang,Anhui and Singapore were investigated through the design of Chinese and English questionnaires.Among them,comparative worked examples groups were added to the teacher questionnaire and the student questionnaire to visually compare the differences in the relevance of different worked examples.In order to eliminate the influence of version tendency,language and other factors,a total of 21 worked examples in the 7 groups of comparative worked examples groups selected in the teacher questionnaire,and a total of 6 worked examples in the 2 groups of comparative worked examples groups selected in the student questionnaire have been processed by translation,reintegration of pictures,Localized context,removal of version identification,etc.Based on this,the last two secondary indicators in the relevance framework of the worked examples are analyzed.The main conclusions of the research are as follows:First of all,compared with the worked examples in the textbooks of the People's Education Edition,the Jiangsu Education Edition,and the Singapore MC Edition,the worked examples in the Singapore MC edition textbook are more relevant for "inside the mathematics textbook system." The number of items in the Singapore version of the worked examples relevant for the "internal relevance" indicator is more than the number of items relevant for the "external relevance" indicator.That is to say,there is a better relevance between the worked examples of the Singapore version and the "knowledge content" and "in-class exercises" within the elementary school mathematics textbook system.The worked examples in the two editions of textbooks in our country are more relevant for "outside the mathematics textbook system",in the two dimensions of "internal relevance" and "external relevance",the degree of relevance between the worked examples and the latter is higher than the degree of relevance between the worked examples and the former.In general,the worked examples of the Singapore edition are more relevant for "knowledge content",while the worked examples of the Chinese People's Education and Jiangsu Education editions are more relevant for "students' learning".A specific comparison of the two editions of our country's primary school mathematics textbook worked examples shows that the PEP version has more advantages in the “demonstration function”,while the Jiangsu version of the worked examples emphasize on the “extended educating function”.Secondly,based on the the theoretical basis and relevance judgment index of the worked examples,it is proposed to design worked examples relevant for the knowledge content,the “in-class exercises”,the curriculum standards,the students' learning,and increase the appropriate teaching auxiliary resources for teachers.This is the five development trend of the relevant worked examples in the future.Finally,it is pointed out that the future relevance development of the worked examples requires the researchers to increase their attention to the relevance of the math worked examples,worked examples compilers to improve the examination of the correlation between the math worked examples and the elements in the mathematics curriculum system,and the teachers to improve their understanding of the intention of compiling worked examples and students' mathematical thinking.The main innovations of the research are as follows:From the perspective of research,the difference between this study and previous example research is that it chooses to compare and analyze the worked examples in the primary school mathematics textbooks of China and Singapore from the perspective of relevance,and construct the relevance analysis and comparison frame of the worked examples.In terms of research methods,in addition to static text research using text analysis,this research also selected dynamic research methods such as survey methods for research,and conducted research on foreign educational institutions.In addition,the Delphi expert consultation method is used to optimize the analysis framework of the relevance of the worked examples.In terms of research content,most of the researches select the whole textbook and focus on the comparison between junior and senior middle school.This research separately compares the worked examples in the elementary school and selects the worked examples according to knowledge topics instead of directly comparing them by grade.In addition,in the version of the research object,there has not been a study that simultaneously compares the worked examples in the three editions of elementary school mathematics textbooks of the People's Education Edition,the Jiangsu Education Edition and the Singapore Edition.