Study On Textbook Presentation Of Geometric Concept Abstract

It has not been really implemented that letting the students go through the process ofabstract concepts though it was introduced in the implementation of Mathematics CurriculumStandards for Compulsory Education (Trial Edition), long time ago. The "compulsoryeducation mathematics curriculum standards (2011edition) promulgated in2011explicitlytakes the basic ideas, basic experience and basic knowledge, basic skills as" four base ". It iswell known that the textbooks are the important resources to achieve the mathematicscurriculum goals. How to reflect the process of abstracting concept in the textbooks is veryimportant to implement the "four base". However, Most of the current domestic existingresearch appeared in the implementation of junior high school stage, almost no one involvedin elementary school.The article aims to discuss the geometrical representation and the abstract concept intextbook and reveal the concept of elementary school geometric abstraction of process.According to the elementary school mathematics in the field of graphics and geometriccharacteristics, The article takes elementary graphics and the core concept which wasregarded as the most representative concept: angle, perimeter, offset, and circle as example. Itselects12textbooks of BNUP、 PED and JSEP as comparison objects which is commonlyused in the elementary school mathematics instruction.According to the elementary school mathematics in the field of graphics and geometriccharacteristics, this study elementary graphics and geometry field generally representative ofthe four core concepts-Angle, perimeter, translation, as an example, analyzes commonlyused in current primary school mathematics teaching in the edition of BNUP、PED and JSEPthree typical version of the12textbook as the object of comparison. First analyzing the fourcore geometry concept presentation of Angle, the perimeter of the three textbooks, translationusing the content analysis and according to the three stage theory about abstract concepts putforward by Professor Shi Ningzhong, outlining their respective characteristics. Second, usingfocus interview method to make a survey among22math teachers in C city about theiridentity for the presenting ways of these four concepts in the text book. On this basic, takingthe content of angle as an example, summarizing the textbook case that will cultivatestudents’ abstract experience according to the characteristics of the elementary geometryabstract concepts which gets the recognition of backbone teachers. The paper looks forward toprovide reference for the presentation about abstract concepts of mathematics textbooks in theelementary school.It found that:First, the core of the elementary school stage geometry concepts is to help students`lifeexperiences as a geometric concept abstract material. And then use the students’ original lifeexperience and their mathematical activities experience effectively. At the same time, arrange students`hands-on hands activities among the different levels of abstraction. This way isbetter for students to experience the abstract process and understand abstract concepts.Second, compared with the previous textbooks, BNUP、PED and JSEP all begin to payattention to geometric abstraction of the concept. However, they have not yet achieve fullembodiment. For specific performance: first of all for physical level of abstraction, the threeeditions all reflected well. They can start from the material that student familiar with. But inselecting the physical life, it is not clear enough and it is easy to mislead the students. Next,for half a symbolic level of abstraction, BNUP and PED are too abstract and lack ofspecificity. On the other hand, JSUP does not well also. At last, for the abstraction of thesymbol, it’s relatively few in primary school.Through comparative analysis, we discoveredthat for the "translation" and "the circle" of learning, the elementary school stage is apreliminary understanding. While the concepts of "Angle" and "circumference"are given inPED,not clearly given in BNUP and JSEP which let the students abstract from existing lifeexperience and experience mathematical activities. After all, BNUP and JSEP’s designs aremore advantageous to cultivate students’ abstract experience.Third, through the survey of22math teachers about the abstract concept of textbookpresent situation, we can find that70%of the teachers are identify in the edition of textbookin the presentation of graphics and geometry. Their reasons are as follows: First of all, forgeometric concepts, BNUP is more of an emphasis on mathematical knowledge and students’real life. And it starts from the reality of students around which is much easier for students tounderstand. Second, hands-on activities play a very important role in understanding theconcept for students. The process of exploration is more important than to tell him the result.BNUP has more activities which leaves students a large space to explore.Fourth, take the angle for example, follow the abstract theory of different stages anddesign geometry concept abstract textbook case. Comparatively speaking, it’s more conduciveto help the students to accumulate the abstract direct experience to know well of theconcept.It got approval of top-tier research staff and primary school teacher in the interview.In order to better improve the textbook presentation of elementary geometry conceptabstract, we suggested that:1. For textbook writers, it should pay attention to the process of geometric conceptabstraction. Full and effective use of students’ existing life experiences. BNUP in theelementary school mathematics textbooks continue to combined with actual life. Thenemphasis the hands-on activities for students to understand the concept of role. What’s more,closer to the students’ real activity. We hope PED and JSEP of textbooks in the appropriateadd some schools which are linked to the actual students’ present situation.2. For teachers, teachers should fully understand the textbook by writing intention andclosely combined with the actual teaching reality.3. Strengthen the training of teachers. Through a variety of ways to make teachersunderstand and agree that the basic ideas and basic activities experiences, when improving theteachers’ ideas, to help teachers put ideas into concrete classroom behavior.