数学系大一学生对标准差的概念性理解
发布时间：2018-11-17 21:09
【摘要】：随着信息化社会的飞速发展,统计已经渗透到社会生活的各个领域。近年来,国内重视统计教育的呼声越来越高。不过,相对于国外比较成熟的统计教育研究,国内相关研究才刚刚起步,还需要相关研究人员开展大量的理论性研究。本研究的主要目的是希望通过调查数学系大一学生对于标准差概念理解的现状来呼吁教师重视标准差的概念教学。同时,对于学生理解标准差概念的困难有所发现,为改进教学提供一些理论研究的依据。 本研究主要采用定性与定量的研究方法,通过问卷调查和访谈收集数据,使用独立样本t检验和方差分析的数据分析方法。本研究主要通过以下四个方面探究数学系大一学生对于标准差的概念性理解：(1)学生对于标准差的数学内涵和统计意义的理解如何；(2)学生是否会判断不同呈现方式下的数据的标准差大小以及判断的策略有哪些；(3)学生利用标准差进行决策的水平如何；(4)学生对于标准差概念的理解水平是否存在明显的性别差异,专业差异以及生源地差异。 研究结果发现：(1)数学系大一学生对于标准差的数学内涵和统计意义综合掌握情况较好,但学生对于标准差公式内涵的理解不透彻,正确描述标准差公式的人数偏少。(2)学生对于标准差的概念性理解偏弱,综合考虑影响标准差大小的各种因素的能力欠佳。表现为判断标准差大小的有效策略偏少；学生比较标准差大小时受到数据不同呈现方式的影响,他们在判断两幅以上直方图的标准差大小时表现最差。(3)大部分学生在根据抽样信息决策时,会考虑使用标准差,并且能够正确使用标准差帮助决策。(4)学生对于标准差概念的理解水平没有表现出明显的性别差异,但存在显著的专业差异和生源地差异。具体为师范专业的学生对于标准差概念的理解水平明显低于非师范专业的学生,西部地区的学生的表现也明显弱于中部、东部地区的学生。 最后,基于本研究的发现,本文对于标准差的概念教学提出了建议。
[Abstract]:With the rapid development of information society, statistics has penetrated into all fields of social life. In recent years, the domestic attention to statistical education is getting louder and higher. However, relative to the more mature statistical education research abroad, the domestic research has just started, and a large number of theoretical research is needed. The main purpose of this study is to appeal to teachers to pay more attention to the concept teaching of standard deviation by investigating the present situation of students' understanding of standard deviation. At the same time, the difficulty of students understanding the concept of standard deviation is found, which provides some theoretical basis for improving teaching. This study mainly adopts the qualitative and quantitative research methods, collects the data through the questionnaire survey and the interview, uses the independent sample t-test and the analysis of variance data analysis method. This research mainly through the following four aspects to explore the mathematical freshmen's conceptual understanding of the standard deviation: (1) how students understand the mathematical meaning and statistical significance of the standard deviation; (2) whether the students will judge the magnitude of the standard deviation of the data under different presentation modes and what the judgment strategies are; (3) how well the students can make decisions by using the standard deviation; (4) whether there are significant gender differences, major differences and student origin differences in students' understanding of standard deviation concepts. The results are as follows: (1) the mathematics connotation and statistical meaning of the standard deviation are well grasped by the freshmen, but the students do not have a thorough understanding of the connotation of the standard deviation formula. The number of people who correctly describe the standard deviation formula is small. (2) the students' conceptual understanding of standard deviation is weak, and the ability of synthetically considering various factors affecting the standard deviation is poor. The effective strategy of judging the magnitude of standard deviation is less; Students are affected by different presentation modes of data when comparing standard deviation. They perform the worst when judging the standard deviation of more than two histograms. (3) most students consider using standard deviation when making decisions based on sampling information. And the correct use of standard deviation to help decision-making. (4) the level of understanding of standard deviation does not show significant gender differences, but there are significant differences in professional and student origin. In particular, the level of understanding of the concept of standard deviation of the students majoring in teacher training is obviously lower than that of the students of non-normal majors, and the performance of students in the western region is obviously weaker than that in the central and eastern regions. Finally, based on the findings of this study, this paper puts forward some suggestions for the concept teaching of standard deviation.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O212.1-4;G645.5
本文编号：2339042
[Abstract]:With the rapid development of information society, statistics has penetrated into all fields of social life. In recent years, the domestic attention to statistical education is getting louder and higher. However, relative to the more mature statistical education research abroad, the domestic research has just started, and a large number of theoretical research is needed. The main purpose of this study is to appeal to teachers to pay more attention to the concept teaching of standard deviation by investigating the present situation of students' understanding of standard deviation. At the same time, the difficulty of students understanding the concept of standard deviation is found, which provides some theoretical basis for improving teaching. This study mainly adopts the qualitative and quantitative research methods, collects the data through the questionnaire survey and the interview, uses the independent sample t-test and the analysis of variance data analysis method. This research mainly through the following four aspects to explore the mathematical freshmen's conceptual understanding of the standard deviation: (1) how students understand the mathematical meaning and statistical significance of the standard deviation; (2) whether the students will judge the magnitude of the standard deviation of the data under different presentation modes and what the judgment strategies are; (3) how well the students can make decisions by using the standard deviation; (4) whether there are significant gender differences, major differences and student origin differences in students' understanding of standard deviation concepts. The results are as follows: (1) the mathematics connotation and statistical meaning of the standard deviation are well grasped by the freshmen, but the students do not have a thorough understanding of the connotation of the standard deviation formula. The number of people who correctly describe the standard deviation formula is small. (2) the students' conceptual understanding of standard deviation is weak, and the ability of synthetically considering various factors affecting the standard deviation is poor. The effective strategy of judging the magnitude of standard deviation is less; Students are affected by different presentation modes of data when comparing standard deviation. They perform the worst when judging the standard deviation of more than two histograms. (3) most students consider using standard deviation when making decisions based on sampling information. And the correct use of standard deviation to help decision-making. (4) the level of understanding of standard deviation does not show significant gender differences, but there are significant differences in professional and student origin. In particular, the level of understanding of the concept of standard deviation of the students majoring in teacher training is obviously lower than that of the students of non-normal majors, and the performance of students in the western region is obviously weaker than that in the central and eastern regions. Finally, based on the findings of this study, this paper puts forward some suggestions for the concept teaching of standard deviation.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O212.1-4;G645.5
【参考文献】
相关期刊论文 前4条
1 黄敏;;构建以概念性理解为中心的课堂教学[J];北京第二外国语学院学报;2006年04期
2 史宁中,孔凡哲,秦德生,杨述春;中小学统计及其课程教学设计——数学教育热点问题系列访谈之二[J];课程.教材.教法;2005年06期
3 高潇怡;;试论“促进概念性理解”的科学课教学[J];课程.教材.教法;2009年04期
4 范宏业;统计学的现代发展[J];中学教研;2005年05期
相关硕士学位论文 前2条
1 张洁铭;学生对概率统计中变异性的认识[D];华东师范大学;2006年
2 何莎莎;9-12年级学生对标准差概念理解的调查研究[D];华东师范大学;2007年
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