高中生关于复数单元的概念表象之探究
发布时间：2018-08-24 12:04
【摘要】：概念表象是学生脑中关于某个数学概念的所有心理表象,包括图像、符号形式、图表、图形等等,可以说概念表象是学习者学习中最活跃的心理因素。但在数学教育的研究议题上,数学概念表象的研究仍属于待开发阶段,所以本文就以复数单元为例,探究高中生关于复数单元的概念表象,本文主要解决以下四个问题:1)学生关于“复数定义”之概念表象的具备情形与样貌为何?2)学生关于“复数的模(绝对值)”之概念表象的具备情形与样貌为何?3)学生关于“复数运算”之概念表象的具备情形与样貌为何?4)学生关于“复平面”之概念表象的具备情形与样貌为何?本文参考了复数单元错误类型的文章,经过取舍,创建了《高中生关于复数单元的概念表象探究问卷》,并以此为研究工具,对包括高程度、中程度的两个班级一共80位高二年级学生进行施测。研究结果表明:(1)与复数相关的概念中,学生面对“虚数单位”这一名称刺激时,脑中浮现的概念表象主要有虚数单位i和偏代数型,二者的比例均过半,虚数单位i的比例高达74%,偏代数型的比例为51%。(2)复数定义:有94.5%的学生能够正确的判断一个复数的实部以及虚部,仅有5.5%的学生不能准确判断复数的虚部,这部分同学认为虚部不只是实数,还带有虚数单位i,这说明仅有5.5%的学生脑中还没有牢固的复数代数定义的概念表象。(3)复数的模:从整体上看,发现有79%的学生能够准确判断复数模的几何意义,仍有21%的学生不能判断。(4)复数运算当中,最常出现的错误是实数根式乘除法过度推广。整体上看,每道题目的正确率均在70%、80%左右徘徊,说明仍让有一少部分学生对复数运算不能掌握。通过本研究,我们可以了解到高中生对复数单元的概念表象,也为中学教师了解学生提供依据。
[Abstract]:Conceptual representation is the mental representation of a mathematical concept in the student's brain, including image, symbol form, chart, graph and so on. It can be said that conceptual representation is the most active psychological factor in learners' learning. However, on the research topic of mathematics education, the research of mathematical concept representation is still in the stage of development, so this paper takes the plural unit as an example to explore the concept representation of complex unit in senior high school. This paper mainly solves the following four questions: (1) how does the student's concept representation of "complex number" exist and what it looks like? (2) the student's concept representation of "module (absolute value) of complex number"? what is the situation and appearance of the student's concept representation of "complex number"? What is the situation and appearance of students' concept representation of "complex operation"? 4) what is the situation and appearance of students' concept representation of "complex plane"? This paper, referring to the article of error type of complex unit, has created the "Inquiry questionnaire on the concept of complex Unit in Senior High School students", which is used as a research tool to include high degree. A total of 80 sophomores in two middle-level classes were tested. The results show that: (1) in the concepts related to the complex number, when students are stimulated by the name "imaginary unit", the conceptual representation in the brain mainly consists of imaginary unit I and partial algebraic type, and the proportion of both is more than half. The proportion of imaginary unit I is as high as 74 and the proportion of partial algebraic type is 51. (2) the definition of complex number: 94.5% of students can correctly judge a real part of the complex number and imaginary part, only 5.5% of the students can not accurately judge the imaginary part of the complex number. This part of the students thinks that the imaginary part is not only a real number, but also an imaginary unit I, which indicates that only 5.5% of the students do not have a solid conceptual representation of complex algebraic definition in their brains. (3) the modulus of the complex number: from the overall point of view, It is found that 79% of the students can accurately judge the geometric meaning of complex modules, while 21% can not. (4) in complex operations, the most common error is the over-generalization of the method of real root multiplication and division. On the whole, the correct rate of each question is about 80%, indicating that a small number of students still can not master the complex number of operations. Through this study, we can understand the conceptual representation of plural unit in high school students and provide basis for middle school teachers to understand students.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
本文编号：2200773
[Abstract]:Conceptual representation is the mental representation of a mathematical concept in the student's brain, including image, symbol form, chart, graph and so on. It can be said that conceptual representation is the most active psychological factor in learners' learning. However, on the research topic of mathematics education, the research of mathematical concept representation is still in the stage of development, so this paper takes the plural unit as an example to explore the concept representation of complex unit in senior high school. This paper mainly solves the following four questions: (1) how does the student's concept representation of "complex number" exist and what it looks like? (2) the student's concept representation of "module (absolute value) of complex number"? what is the situation and appearance of the student's concept representation of "complex number"? What is the situation and appearance of students' concept representation of "complex operation"? 4) what is the situation and appearance of students' concept representation of "complex plane"? This paper, referring to the article of error type of complex unit, has created the "Inquiry questionnaire on the concept of complex Unit in Senior High School students", which is used as a research tool to include high degree. A total of 80 sophomores in two middle-level classes were tested. The results show that: (1) in the concepts related to the complex number, when students are stimulated by the name "imaginary unit", the conceptual representation in the brain mainly consists of imaginary unit I and partial algebraic type, and the proportion of both is more than half. The proportion of imaginary unit I is as high as 74 and the proportion of partial algebraic type is 51. (2) the definition of complex number: 94.5% of students can correctly judge a real part of the complex number and imaginary part, only 5.5% of the students can not accurately judge the imaginary part of the complex number. This part of the students thinks that the imaginary part is not only a real number, but also an imaginary unit I, which indicates that only 5.5% of the students do not have a solid conceptual representation of complex algebraic definition in their brains. (3) the modulus of the complex number: from the overall point of view, It is found that 79% of the students can accurately judge the geometric meaning of complex modules, while 21% can not. (4) in complex operations, the most common error is the over-generalization of the method of real root multiplication and division. On the whole, the correct rate of each question is about 80%, indicating that a small number of students still can not master the complex number of operations. Through this study, we can understand the conceptual representation of plural unit in high school students and provide basis for middle school teachers to understand students.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6
【相似文献】
相关期刊论文 前10条
1 邓永奎;;(Z~m)~n=Z~(mn)成立的条件[J];教学与研究;1983年03期
2 陈斌战;;数 o,l,i,e,π间的联系[J];教学与研究;1983年04期
3 ;浏览[J];高中生学习(高二版);2012年02期
4 ;关于“复数”教学的一些看法[J];数学通报;1981年01期
5 陈湛本;关于Euler公式的证明[J];数学通报;1985年08期
6 甘志国;复数不能比大小[J];数学通讯;2005年12期
7 童永奇;;关注:函数与方程思想在解题中的应用[J];中学生数理化(高二高三版);2014年05期
8 李志边;;复数考查新靓点[J];高中数学教与学;2010年08期
9 欧阳亮;;重视基础 拿下复数[J];中学生数理化(高考版);2011年02期
10 周晓鹉;;识别题型 用对结论[J];第二课堂(高中版);2012年05期
相关硕士学位论文 前1条
1 甘经娟;高中生关于复数单元的概念表象之探究[D];上海师范大学;2016年
，本文编号：2200773
本文链接：https://www.wllwen.com/zhongdengjiaoyulunwen/2200773.html
