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高三学生微积分认知状况的思维层次研究

【作者】 陈婷

【导师】 郇中丹;

【作者基本信息】 北京师范大学, 课程与教学论, 2008, 硕士

【摘要】 微积分是高等数学的基础,导数和积分是微积分的根本概念。有关导数的部分内容已经成为高中数学的重点内容。从以往的教学实际来看,这部分内容也教学难点。对高中生学习微积分的认知过程的研究是数学教育中值得重视的问题。本文试图以导数为载体,通过对北京两所学校的普通班的测试,作者发现:(1)对导数部分内容的把握有着明显的性别差异:男生表现出比女生更多的主动性;(2)学生对于导数内容中低层次思维(运算类)部分的内容的把握是良好的,女生似乎略优于男生;(3)学生对于导数内容中高层次思维(概念和推理)部分的把握更多的依赖于低层次思维(能够根据已有经验获得结论,少有人能够给出由概念出发的证明);(4)强化学习(复习)对于学生低层次思维内容的把握的提高有明显效果,而对高层次思维内容部分效果不明显。

【Abstract】 Calculus is the foundation of high mathematics. Derivative and integral calculus are the fundamental concepts of calculus. Some contents related to derivative have become the key elements of math teaching in senior school. From the past practical teaching experience, this part is also difficult in teaching. The research of the cognitive process of high school students in learning calculus is worthy of attention in math education. This paper will view derivative as a carrier and test four ordinary classes in two high schools in Beijing. The author finds that:(1)Obvious gender differences exist in grasp of some contents of derivative: boys show more initiative than girls;(2)For students ,the grasp of the low-level thinking (operation) in derivative is good. The girls seem slightly better than boys;(3)The grasp of the high-level thinking of some contents of derivative rely much more on the low-level thinking (to get the conclusion from past experience ,few people can give proof from the concept directly).(4)Reinforcement learning(review)shows obvious effect of improvement in students’grasp of low-level thinking ,but ineffective when it comes to the high-level thinking.

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  • 【网络出版投稿人】 北京师范大学
  • 【分类号】G633.6
  • 【下载频次】610
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