Research On The Measurement And Evaluation Model Of Elementary School Mathematics Textbooks' Difficulty

Textbooks are the soul and future of a nation.Textbooks pass down the most valuable essence of the nation and mankind's knowledge and experience heritage,reinvent the power of a nation,form and shape the future generations' mind,ideals,self-esteem and attitudes to live together.Because textbooks are the important parts of school education,the most consistent factors of school education in the world in addition to teachers and students,and the key factors in determining students' school opportunities to learning.Textbooks are the most important reified material entity of curriculum and instruction activities which are the core of school education.Textbooks mediate the curriculum policies and classroom teaching and learning,and interpret the curriculum policies with the specific behavior of teaching and learning.Textbooks are the de facto national intended curriculum,the important tools and resources for curriculum reform and classroom teaching and learning.The extensive use of,and even rely on textbooks is an international classroom characteristics which continuously confirmed by various kinds of studies and surveys.Particularly in the mathematics classroom,it has even become an important feature of mathematics teaching and learning distinguishing from other disciplines' teaching and learning.In other words,textbooks are the cores of school education,curriculum and instruction which defining most of the school work.In China,and even the East Asian countries,the math achievement of students in various kinds of international competition and assessment is excellent,but accompanied with relatively negative emotions,attitudes and values,and heavily burden of lessons.Reducing the heavily burden of lessons on students,especially the elementary school students,has been identified as one of the three major tasks of the Chinese compulsory education's development.The difficulty of mathematics curriculum and teaching and learning,especially mathematics textbooks,not mastered properly has been considered the most important reason for above described phenomena.Measuring and evaluating the difficulty of mathematics textbooks scientifically has been the key breakthrough in grasping the difficulty properly,scientifically designing textbooks and optimizing the quality of textbooks,and then 'reducing the heavily burden of lessons on students and improving the quality of teaching and learning'.However,the textbooks study,the 'study should not be ignored most',has not been given the due attention in the field of educational research,especially the study on the measurement and evaluation of textbooks' difficulty.In scarce related studies,(mathematics)textbooks' difficulty has been respectively interpreted as the difficulty of text reading,intended curriculum,students' learning and the overall difficulty of math problem,and then the methods and tools of the difficulty's measurement and evaluation had been explored and developed,which provides important bases and references for further explorations.But there had not studies elaborating directly the rationality and connotation of the concept of textbooks' difficulty,thus exploring and seizing the main factors and its main areas affecting the textbooks difficulty,which resulting in the related studies' partial understanding,or mingling the primary with secondary,or lack of reasons and causes,or difficulty in operating.This study,based on the needs of reality and the status of related studies,was scientifically and rationally designed to construct the measurement and evaluation model of elementary mathematics textbooks' difficulty.The study include four subject matters,such as the rationality of the concept of textbooks' difficulty,the connotation of elementary school mathematics textbooks' difficulty,the factors and its structure affecting the difficulty of elementary school mathematics textbooks,the test and verification of the measurement and evaluation model of elementary mathematics textbooks' difficulty.Theoretical and empirical research orientations are integrated in the study,and the theoretical analysis and the empirical exploration are mutually inspired and evidenced.In this dissertation,the study is divided into 10 chapters to narrate.In chapter 1,something is clarified based on existing literature,such as the'contradictory' phenomenon that refers to the coexistence of Chinese primary and secondary students' excellent mathematics achievement,relatively negative emotions,attitudes and values,and heavily lessons burden,mathematics curriculum and instruction which are identified as the most important cause for the 'contradiction',mathematics textbooks which are the most important reified material entity of mathematics curriculum and instruction,and the scientific measurement and evaluation of mathematics textbooks' difficulty as the key breakthrough in resolving the 'contradiction'.And the significance and value of this research are explained,and the relevant concepts are defined.In chapter 2,the status quo and shortcomings of related studies are cleared by combing the existing literature of the measurement and evaluation textbooks' difficulty,and the analysis and evaluation of textbook,and then the direction,specific contents and methods of this study are determined.In brief,the deficiency of existing studies,such as rationality,scientificalness and operability etc.,provides the direction and space for the theoretical analysis and empirical exploration in this research.Chapter 3 clarifies the purpose,main contents,thinking process,methods etc.of this study,the framework of this dissertation,and the relationship between them.The reliability and validity of the study,the tools for data collection and analysis are described briefly.The rationality of the concept of textbook difficulty is mainly analyzed theoretically.The analysis and exploration of the connotation,affecting factor and its structure of elementary school mathematics textbooks' difficulty integrate the theoretical and empirical research orientations,and comprehensively use of many research methods,including the literature research,interviews,open and close questionnaires and statistical analysis etc.the test and verification of the measurement and evaluation model is mainly empirical research,comprehensively using of various methods such as closed questionnaires,expert interviews,content analysis and comparative research.All theoretical analysis of this study is collected in chapter 4.Chapter 5 focuses on the connotation's exploration and analysis of the elementary school mathematics textbooks' difficulty in all investigations.The exploration and analysis of factors affecting elementary school mathematics textbooks' difficulty through open and close investigations correspond to chapter 6 and chapter 7 respectively.Chapter 8 focuses on the exploration and construction of the measurement and evaluation model of elementary mathematics textbooks' difficulty.The model's adaptation and validity are tested and verified in chapter 9.In chapter 10,the process and main conclusions of this research are overviewed briefly,with the reflection on the innovations and inadequacies,and the outlook for future research questions and direction.Chapter 4 to chapter 9 is the main content of the research,also the main part of this dissertation.The main conclusions are:Textbooks are the elaborated important artifacts in school education enterprise.Its production and use embody the key characteristics of school learning and knowing——indirection and sociality.Textbooks are the representational model of the human practical activities which textbooks are involved in.The dual material-conceptual feature of textbooks endows the concept of textbooks' difficulty with rationality.Textbooks' difficulty mainly refers to the difficulty of curriculum and the difficulty of teaching and learning,which is mainly represented as the difficulty of contents,working examples and exercises in elementary school mathematics textbooks.The macroscopic curriculum's difficulty and the microscopic instruction's difficulty constitute the deep difficulty of textbooks,while the instruction's difficulty is mainly made up of the difficulty of teachers' teaching with textbooks and the difficulty of students' learning with textbooks.The surface difficulty of elementary school mathematics textbooks are composed of the relative macroscopic contents' difficulty and the microscopic working examples and exercises'difficulties.The relationship between textbooks' deep and surface difficulty is similar to the'spirit' and 'shape'.Both of them are unified as the elementary school mathematics textbooks' difficulty.It can be expressed abstractly and generally as:the organically unified stipulation of the quality and quantity of the intended mathematics teaching and learning processes and results which are presented to the users by the textbooks.The measurement and evaluation model of elementary mathematics textbooks' difficulty can be described mathematically as N=0.30C+0.36W+0.34E,while C=0.45C,+0.32C2+0.23C3,W?0.40W1+0.30W2+0.30W3,E=0.34E1+0.32E2+0.34E3.In these expressions,N stands for the elementary mathematics textbooks' difficulty,C for the difficulty of contents,W for the difficulty of working examples,E for the difficulty of exercises,C1 for the quantity of contents,C2 for the expectations of contents,C3 for the means of the contents' presentation,W1 for the demands of working examples,W2 for the degree of alignment between working examples and contents,W3 for the degree of working examples' complexity,E1 for the match between working examples and exercises,E2 for the category of exercises,and E3 for the demands of exercises.The model has better adaptability and effectiveness,which is tested by empirical methods.In summary,the present study has constructed more scientifically and rationally a measurement and evaluation model of elementary mathematics textbooks' difficulty with better adaptability and effectiveness.The intended innovation in this study is to construct a measurement and evaluation model of elementary mathematics textbooks' difficulty more scientifically and rationally through integrating the theoretical and empirical researches,which refer to the relevant existing research results,such as the model of coure's difficulty of Shi ning-zhong and others,the model of curricula's composite difficulty of Bao jian-sheng,and the model of textbooks'difficulty of the study group of project "international comparative study of elementary and secondary school science textbooks"(elementary school mathematics)in Southwest University.The theoretical analysis of the rationality of the concept of textbook' difficulty,and the theoretical analysis and empirical exploration and analysis of the connotation,affecting factors and its structure of elementary school mathematics textbooks' difficulty constitute the intended innovation.Innovations and weaknesses coexist.These aspects of the intended innovation are worthy of and can be improved in further researches,in particular,the application of the model,textbooks design,the relationships between the specific factors and features of textbook and curriculum and instruction activities textbooks involved in.