有理数与无理数概念的课程与教学研究

发布时间：2018-02-05 23:27

本文关键词： 数系概念教学课程内容比较教学策略教学设计　出处：《陕西师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：在数系扩充中出现的有理数与无理数这组相对的概念是数学课程中的基础内容,但是对于这部分内容的学习,学生掌握得却并不是特别好。本文通过梳理已有的研究成果,比较相应的课程内容,从教材中分析课程内容的教学,为教师的教学活动提供教学上的策略,促使学生能够真正理解这两个概念。根据已有的研究基础与课程内容的比较研究发现：人教版在有理数概念课程内容的编排相对更为充实；在无理数课程内容上则北师版编排的更充分、更有特色。但是同时比较也反映出我们教材上的一些不足,宏观层面上有：(1)注重运算教学而轻概念教学；(2)无理数课程内容的课时量相对较少。具体层面上有：(1)在有理数概念的课程内容中不提及循环形式的小数；(2)在有理数概念的理解上未能充分表现概念里的意义；(3)在概念的过渡与接续中有理数与循环小数联系不完善；(4)教材中对于无理数概念的不可公度内容不够完全重视。针对有理数与无理数课程内容比较出现的问题,分别在教学准备阶段与教学实施阶段提出了教学策略,教学准备策略为：(1)教材知识内容的组织策略；(2)教材知识结构的分析策略。教学实施策略为：(1)引入内容全面性策略,避免认识上不完整；(2)概念内部相联系策略,具体深化概念理解；(3)遵循知识的发展策略,寻适宜的认知角度：(4)借助学科间联系策略,诠释数的概念含义：(5)多角度审视概念策略,形成数系基本结构；(6)概念图检查理解策略,完善整体概念学习。最后,依照上述各项教学策略,细化出有理数与无理数课程内容的教学思路,并提供一份具体的教学设计。
[Abstract]:In this group the relative concept of rational number and irrational number system in the extension of basic content in mathematics curriculum, but for this part of the study, students master is not particularly good. This paper reviews the existing research results, the content of the training is the analysis of the course content from textbooks in teaching, provide teaching strategies for teachers' teaching activities, students can truly understand these two concepts. According to the comparative study of basic research and curriculum content already found that PEP in the rational concept of the arrangement of curriculum content is relatively more enriched; arrangement is irrational curriculum content of textbooks in the more fully but at the same time, more features. Comparison also reflects some deficiencies of our materials on the macro level are: (1) focus on the operation instruction instead of the concept of teaching; (2) the amount of hours irrational curriculum phase For less. The specific level are: (1) the decimal circulation forms in the course content not to mention the concept of rational number; (2) in the rational understanding of the concept on the concept of the performance is not fully significance; (3) the concept of transition and connection of rational numbers and decimals (contact is not perfect; 4) textbooks for the irrational number concept of incommensurable content is not fully attention. For rational numbersirrational numbers curriculum more problems, the teaching strategies are put forward in the teaching preparation and teaching implementation, teaching preparation strategies are as follows: (1) the organization strategy of teaching material content knowledge; (2) strategic analysis of knowledge structure of teaching materials. Teaching strategies are as follows: (1) the introduction of the contents of a comprehensive strategy to avoid the recognition is not complete; (2) the concept of internal link specific strategies, deepen understanding of the concept; (3) follow the development strategy of knowledge, to find suitable cognitive perspective : (4) by discipline between strategy and concept meaning interpretation number: (5) multi angle concept strategy, form the basic structure of number system; (6) check the understanding of concept map strategy, improve the overall concept of learning. Finally, in accordance with the teaching strategy, refine teaching ideas rational numbersirrational numbers course the content, and provide a practical teaching design.

【学位授予单位】：陕西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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