A Survey Of Mathematical Abstract Forms Of Expression And Their Teaching And Learning

In 2011, the "compulsory education mathematics curriculum standards (2011 Edition)" promulgated the basic idea, the basic activity experience, the basic knowledge and the basic skills as "four base", so the study of mathematics abstract is very meaningful. As we all know, textbook is an important resource for students to achieve the purposes of mathematics courses. How to embody in the process of Mathematics Textbooks in the abstract is very important for the implementation of the "four base".Based on the "mathematical abstraction in the textbook" graphics and geometry "in the present--a case study of junior mathematics as an example", aims to reveal the importance of mathematics in junior middle school abstract. First of all, to the junior six textbooks as the object for analysis, the statistics of the "graphics and geometry" in the field of mathematics, four forms of abstract (material, semi abstract symbols, symbols of abstract and abstract form) in the context of the text, numbers, and mathematical activities in practice. Secondly, based on the analysis of the textbook, for "this section details the Pythagorean theorem" of teachers knowledge survey. Furthermore, based on the analysis of the textbook, making use of mathematical abstraction thinking to solve problems, and strive to show the students of Mathematics Textbooks "graphics and geometry" in the abstract way of presenting knowledge. Finally, the "Pythagorean theorem" and "graphic translation" as an example, the design for the mathematical abstract thinking training presentation case.The study found that:First, Jiangsu Science version textbooks began to pay attention to mathematical abstraction, but do not reflect the full;Second, all the teachers are aware of the importance of mathematical abstraction, but the degree is not enough;Third, teacher of the textbook presentation of the high degree of recognition, but there is still much room for improvement;Fourth, the students understanding of abstract mathematical thought and textbook writers are expected to master degree is inconsistentAccording to the above research conclusion, the thesis puts forward the following suggestions:1. For the textbook writers, the most important is to understand the students demand for textbooks, full and effective use of the existing student life experience, emphasis on hands-on activities to understand the important role of knowledge to the students, pay attention to the integrity of the process of mathematical abstraction, comprehensive and balanced development of all aspects of students’ ability.2. For the teachers, first of all have to pay full attention to mathematical abstraction, and through a variety of ways to understand the textbook compilation purpose, closely combined with the actual situation of the students’ creative teaching.3. The students should be the rational use of the textbook, to actively participate in classroom teaching, and cherish the accumulation of experience in mathematics activities in the classroom, pay attention to the cultivation of the ability of mathematical abstraction.