A Textbook Strategy Study Of The Primary School’s Numbers And Operation Directed Toward Understanding

In the new version of Mathematics Curriculum Standard for Compulsory Education, Basic knowledge, Basic skill, Basic idea and Basic activity experience, so-called Four Basic. It’s pay much attention to the process and put forward as the curriculum goals, which embody Freudenthal’s process of mathematicilization-from mastering the knowledge and skill to understanding and applying mathematics conceptions. Moreover, creativity awareness was adopted as the key word in this new standard. Creativity is developed on the bases of deep understanding and divergent thinking. Thus, instead of the traditional idea of "algorithm oriented" in textbooks compilation,"understanding’" has being the crucial goal in elementary mathematics textbooks compilation. Researcher find many puzzles when take part in the textbooks writing such as what mathematics idea of writing is, how textbooks writing develop students the understanding of mathematics knowledge, and what aspects textbooks develop students number sense. How to combine Explore the Law and Understanding Number and Numbers? And what is the essence of About, Estimation, Estimation Contents? Moreover how to carry out the overall arrangement in textbooks? In order to solve the confusion in the textbook revision, we need a clear understanding as follows:what is understands? How to promote the students’ understanding of mathematics? Textbooks could take what strategies to promote the students’understand?The study is choosing the Number and operations for carrier, because this is a content of the connections, and this is also is the abstract content of Quantity, and this is the basic of algebraic content too. On the other hand, number and operation content accounts for a large proportion in the primary school. It is worth studying compared with the corresponding traditional content, because it’s not only added the estimated, estimation, but also emphasizes the calculation algorithm. Natural numbers is a basic content into the research vision, the fraction has also become the object of study with its rich connotation. This study takes the Number and Operation content as the carrier, in order to promote the students’ understanding and search strategy of textbook compiling, and test the feasibility verification strategy through textbook compiling and teaching experiment, and then to solve various puzzles in the process of textbooks compiling. So, this study mainly focuses these following questions.(1)The aim of textbooks compiling is to promote students’ mathematics understanding, so Understanding is embodied in which aspects? That is to say it’s needed to confirm an operational definition of understanding.(2) There are always some core concepts and basic mathematical thought in one knowledge module. These core concepts are other knowledge sources and have hair growth and fecundity. Then how to confirm the content of core concepts of Number and Operations?(3)How to structure the operational definition of Understanding combined with the characteristics of Numbers and Operation content, and how to establish the teaching material compiling strategy?(4) Is the establishment of strategy for the textbook compiling is feasible? And how to confirm?Main research methods are documentary method, comparison method and interview method and classroom observation method. It clears the outline of definition of understanding aim according to the known study, and gives the expressive words, which gives clear teaching targets. The same approach applies to numbers and operations content in the establishment of the core concepts. Comparison method mainly used in global comparison of textbooks, and choose the CM textbook in USA and Maths in Singapore as the reference group. Interview method and classroom observation method are mainly used in teaching experiment, to verify the feasibility of the strategy through the teaching experiment and the suitability of the teaching material.Study finds the conclusion as follows:(1) Understanding as the orientation and goal in textbook compilation, mathematics can be recognized as a part of human culture, is variable, error-prone and multiple comprehension. Mathematics culture in mathematics textbooks, is to enable the students to experience the spirit of mathematics, mathematical thinking, mathematical aesthetic experience, enjoy the power of mathematics application.(2) We defined operational definition Understanding based on the "the verbs of curriculum goal" in curriculum standard, Bloom’s and Anderson’s understanding level, Tao’s two-way understanding framework, and Pier Jelon’s super-regression understanding model. Understanding was structured from three levels: self-understanding, related understanding, and complex understanding. We put forward behavioral verbs for each level. For example, behavioral verbs for self-understanding include describe, interpret, multi-represent, exemplify, classify, and so on.(3) Core concepts are the center part of textbook compilation through the theoretical research and textbooks international comparison Core concepts are the strong mathematics knowledge and mathematics basic idea. According to the analysis of keywords in mathematics curriculum standard, number sense and functional idea can be two cardinals of knowing and calculating numbers in primary. And then according some study, show the operational definition of number sense and functional idea. The number cognition includes number meaning, mmultiple representation, absolute size, relative size, estimation and so on. Functional idea includes the meaning of the operation, rrelationships between operational, the influence of the operation to number, estimation and so on. Patten research is the mainly representation. At the same time, number come from the quantity, the content of number should be related to the quantity.(4) The operational definition for construction and Understanding strategy to understand written materials echoes, implies three perspectives, firstly is the structural mathematical knowledge of the whole, secondly is knowledge of learners of are diversity, thirdly is the constructive learning process. The concept of anchor is to tap the essence of mathematics, mathematical association pursuit knowledge "fecundity". The two is structural mathematics in the strategy of performance overall. The multiple representation is various forms of concept, principle of algebraic model, numbers, graphics, multiple strategies is much perspective and strategy of problem solving, make students understand the two rich knowledge ". This is the learner’s understanding of diversity in strategy performance. Anchor is the knowledge embedded in the context of situation, causes the student to obtain knowledge,"elastic" situational embedded knowledge more easy migration. From the concrete to the abstract strategy is to let the students experience the abstract knowledge "Mathematics" of the process, conforms to the cognitive rules. The two strategy reflects the constructive learning process(5) First of all, the content of Number in textbook compiling shows of the overall framework design, The overall framework design uses ideas broke down and mathematics connection strategy, which is essentially Bruner "basic structure" and "spiral" textbook philosophy essence. In the preparation of the specific knowledge in textbooks, the idea of anchor, knowledge association, situational mosaic strategy. With traditional point to "algorithm" skilled teaching material writing ideas, corresponding to "understand" the teaching material write operational definition of understanding,"number and operation" in elementary school phase content, gives the corresponding coding strategy, and the writing practice. Enrich the theory of teaching writing, and for the decimal textbooks in our country provides reference of another round of revisions. Due to time constraints, this article lack of written content reality adaptability, it became the subject of further research later.The strategy guide teaching experimental textbooks, found in the classroom observation, good strategy teaching fragments can achieve better teaching effect, for the students’ enthusiasm, to understand the profound, often appear in a creative way to solve the problem. While the students’ thinking teaching, blocking time is often because of teaching without the use of good construction strategy (increase).This paper contains eight chapters, the first chapter is the introduction, introduces the research question, research significance and content source, structure, emphasizes the study of the origin of practice. The second chapter is the literature review, at home and abroad on the "understanding" and "research and operation" were discussed. The third chapter is the research design and methods, discusses the research and implementation of the design process. The Fourth chapter, fifth chapter the sixth chapter and the seventh chapter is the main content of this research, is the development trend of linear. An operational definition of the fourth chapter in view of mathematics, mathematical cognitive psychology and curriculum research is given on the basis of understanding. The fifth chapter based on theoretical analysis and teaching materials at home and abroad on the core concept of "number and operations." On the basis of the sixth chapter in front of the building the strategy for the preparation of decimal materials. The seventh chapter textbook compilation practice and experimental teaching, writing strategies are effective to verify the textbook. The eighth chapter is review and Prospect of the eighth chapter.The study tries to innovate as follows:the source of confusion in the revision of teaching materials and textbooks, teaching materials based on theoretical analysis and international comparison, clearance Understanding concept, given the compiling strategy, then applied to the textbook compilation practice and teaching experiment, is a process of "practice-Theory-practice". For a new round of decimal materials provide reference revision, also contributed to the rich may Theory Textbooks.As my limited capability and green of understanding and number sense concept definition, there may be some mistake or error. Please experts and scholars criticized the correction.