HPM视角下的概率教学研究
发布时间：2018-11-04 21:40
【摘要】：概率论的诞生被誉为是划时代的数学成就。进入21世纪以来,概率教学进入了一个新时代,世界各国基本上都把概率引入高中数学课程,我国教育部2003年颁发的《普通高中数学课程标准(实验)》也将概率的内容加入其中,作为必修和选修的课程内容。HPM主要研究的内容是数学史如何激励数学教育,是数学教育研究的重要组成部分,当前数学教育研究者都认识到数学史融入数学教育的重要性,不仅有效地促进学生的课堂学习效率,还能增加学生的数学史与数学文化知识,也是对数学课程标准的有效实践。本文以HPM理论为基础,探究融入数学史的高中概率的教学设计。首先对概率的历史发展进行了梳理,从近半个世纪的酝酿时期到雅各布·伯努利创立概率论以及18世纪数学家对概率论的发展直到柯尔莫哥洛夫等人将概率论严格化的发展过程。其次依据研究设计了融入数学史的概率教学设计并在课堂中实施。然后对实施结果分析。最后,对高一学生《概率》这部分知识的学习情况进行了调查,研究新课程标准下的课程设计是否有利于学生对概率思想的深刻理解。对高中数学老师进行了访谈,了解教师在讲授概率内容时存在的问题,并和教师探讨符合学生认知的教学方法。虽然实验组和对照组两组学生在答题的正确率方面没有太大的差异,但是通过访谈可以了解到实验组的学生对概率论这部分内容比较感兴趣,不仅仅只是为了高考而学习,他们愿意将来继续深入学习。教师们反映将数学史融入到教学中能够激发学生的兴趣,课堂气氛更加活跃。教师们总结了教学方法,符合学生认知的教学方法是将数学史融入到数学教育中。
[Abstract]:The birth of probability theory is regarded as an epoch-making achievement in mathematics. Since entering the 21st century, probabilistic teaching has entered a new era. All countries in the world have basically introduced probability into the mathematics curriculum of senior high schools. The Mathematics Curriculum Standard (experiment) issued by the Ministry of Education in 2003 also includes the content of probability as a compulsory and optional course. The main research content of HPM is how to stimulate mathematics education in mathematics history. It is an important part of mathematics education research. At present, the researchers of mathematics education all realize the importance of integrating mathematics history into mathematics education, which can not only effectively promote the efficiency of students' classroom learning, but also increase the students' knowledge of mathematics history and mathematics culture. It is also an effective practice of mathematics curriculum standards. On the basis of HPM theory, this paper explores the teaching design of high school probability which is integrated into the history of mathematics. First of all, the historical development of probability is combed. From the brewing period of nearly half a century to the creation of probability theory by Jacob Bernoulli and the development of probability theory by mathematicians in the 18th century to the development of probability theory by Colmogorov and others. Secondly, the probabilistic teaching design is designed based on the research and implemented in the classroom. Then the implementation results are analyzed. Finally, this part of the knowledge of senior high school students "probability" is investigated to find out whether the curriculum design under the new curriculum standards is conducive to the students' profound understanding of probability thought. The high school mathematics teachers were interviewed to find out the problems existing in the teaching of probability content and to discuss the teaching methods which accord with the students' cognition. Although the two groups of students in the experimental group and the control group have no significant difference in the correct rate of answering questions, it can be learned from the interviews that the students in the experimental group are more interested in this part of probability theory, not only for the purpose of the college entrance examination, but also for the purpose of studying. They are willing to continue their further study in the future. Teachers report that integrating the history of mathematics into the teaching can stimulate students' interest and make the classroom atmosphere more active. Teachers summed up the teaching methods, which accord with the students' cognition is to integrate the history of mathematics into mathematics education.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
本文编号：2311218
[Abstract]:The birth of probability theory is regarded as an epoch-making achievement in mathematics. Since entering the 21st century, probabilistic teaching has entered a new era. All countries in the world have basically introduced probability into the mathematics curriculum of senior high schools. The Mathematics Curriculum Standard (experiment) issued by the Ministry of Education in 2003 also includes the content of probability as a compulsory and optional course. The main research content of HPM is how to stimulate mathematics education in mathematics history. It is an important part of mathematics education research. At present, the researchers of mathematics education all realize the importance of integrating mathematics history into mathematics education, which can not only effectively promote the efficiency of students' classroom learning, but also increase the students' knowledge of mathematics history and mathematics culture. It is also an effective practice of mathematics curriculum standards. On the basis of HPM theory, this paper explores the teaching design of high school probability which is integrated into the history of mathematics. First of all, the historical development of probability is combed. From the brewing period of nearly half a century to the creation of probability theory by Jacob Bernoulli and the development of probability theory by mathematicians in the 18th century to the development of probability theory by Colmogorov and others. Secondly, the probabilistic teaching design is designed based on the research and implemented in the classroom. Then the implementation results are analyzed. Finally, this part of the knowledge of senior high school students "probability" is investigated to find out whether the curriculum design under the new curriculum standards is conducive to the students' profound understanding of probability thought. The high school mathematics teachers were interviewed to find out the problems existing in the teaching of probability content and to discuss the teaching methods which accord with the students' cognition. Although the two groups of students in the experimental group and the control group have no significant difference in the correct rate of answering questions, it can be learned from the interviews that the students in the experimental group are more interested in this part of probability theory, not only for the purpose of the college entrance examination, but also for the purpose of studying. They are willing to continue their further study in the future. Teachers report that integrating the history of mathematics into the teaching can stimulate students' interest and make the classroom atmosphere more active. Teachers summed up the teaching methods, which accord with the students' cognition is to integrate the history of mathematics into mathematics education.
【学位授予单位】：曲阜师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
【参考文献】
相关期刊论文 前3条
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2 王丽霞;杨静;;人类对于随机性认识的四个阶段[J];自然辩证法通讯;2006年03期
3 汪晓勤;张小明;;HPM研究的内容与方法[J];数学教育学报;2006年01期
，本文编号：2311218
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