高中生对极限概念理解的研究
发布时间：2018-11-16 15:57
【摘要】：随着新课标的出台和实施,极限概念与极限思想的教学已经被大众所忽视,而极限理论是微积分学昀基础,“极限思想”是微积分产生和发展的最重要、最基本的数学思想。高中阶段若能较好的理解极限概念,可为后续学习微积分理论奠定重要的基础。本文利用APOS理论,通过问卷调查和访谈的方法研究高中生在极限概念的理解上的差异,探索高中生在理解中存在的问题以及理解困难的成因,以期为学生的学习和教师的有效教学提供参考和建议。得到如下结论：首先,高中生对极限概念的理解在APOS的四个阶段整体水平较低,并且没有性别差异。在得分率最高的活动阶段也仅有63.3%的学生能理解几何背景下的极限概念；其次,高中生在极限概念理解中表现出对“∞。”的理解困难,“∞。”作为一个数在学生头脑中根深蒂固的存在；高中生对极限概念的理解中表现出对极限的过程和极限结果的精确性的理解的困难,70.05%的学生认为“无限”一直在构造中,永远完成不了的；学生对“极限观”的应用意识非常薄弱,知识的联结方面的能力也较弱,很难上升到图式阶段。最后,影响学生对极限概念理解的主要原因是日常用语的干扰,难以理解极限的过程与极限的精确结果间的辩证关系和认知结构定势。基于以上发现,笔者对高中数学教师以及高中数学概念教学提出相应的建议,以期为我国数学概念教学提供一定的参考。
[Abstract]:With the introduction and implementation of the new curriculum standard, the teaching of limit concept and limit thought has been ignored by the public, and limit theory is the foundation of calculus. Limit thought is the most important and basic mathematical thought for the generation and development of calculus. If the concept of limit can be well understood in senior middle school, it can lay an important foundation for further study of calculus theory. Based on the APOS theory, this paper studies the differences in the understanding of the limit concept of senior high school students by means of questionnaires and interviews, and explores the problems existing in the understanding of senior high school students and the causes of the difficulties in understanding. In order to provide reference and suggestions for students' learning and teachers' effective teaching. The conclusions are as follows: firstly, high school students' understanding of the concept of limit is relatively low in the four stages of APOS, and there is no gender difference. Only 63.3% of the students can understand the concept of limit in the geometric background in the stage of the highest score. Secondly, the high school students show "鈭，
本文编号：2335950
[Abstract]:With the introduction and implementation of the new curriculum standard, the teaching of limit concept and limit thought has been ignored by the public, and limit theory is the foundation of calculus. Limit thought is the most important and basic mathematical thought for the generation and development of calculus. If the concept of limit can be well understood in senior middle school, it can lay an important foundation for further study of calculus theory. Based on the APOS theory, this paper studies the differences in the understanding of the limit concept of senior high school students by means of questionnaires and interviews, and explores the problems existing in the understanding of senior high school students and the causes of the difficulties in understanding. In order to provide reference and suggestions for students' learning and teachers' effective teaching. The conclusions are as follows: firstly, high school students' understanding of the concept of limit is relatively low in the four stages of APOS, and there is no gender difference. Only 63.3% of the students can understand the concept of limit in the geometric background in the stage of the highest score. Secondly, the high school students show "鈭，
本文编号：2335950
本文链接：https://www.wllwen.com/jiaoyulunwen/chuzhongjiaoyu/2335950.html
