高一学生关于对数及其运算理解水平的调查研究

发布时间：2018-07-28 11:45

【摘要】：发展学生的六大核心素养与数学核心素养对学生理解性学习提出了更高的要求.对数作为高中数学课程的基本概念,是进一步学习数学的基础,其难度不大,却是学生频繁出现问题的地方.本文主要的研究问题是刻画高一学生关于对数及对数运算的理解水平,主要进行了三个方面的工作.一是通过文献分析法构建了高一学生关于对数及其运算的理解模型:高一学生关于对数及其运算的理解可分为知其然理解、所以然理解和本然性理解.知其然理解分为知定义性质、知运算性质、知换底公式,所以然理解分为解释定义、性质公式证明、性质公式推广,本然性理解分为发明本质和数学思想.其中知定义性质与发明本质不相关,其他理解类别之间均为正相关.二是根据构建的理解模型制作调查问卷,对芜湖市第十二中学高一年级学生进行调查,运用SPSS20.0分析调查数据,发现问卷内部一致性系数为0.806,Spearman-Brown分半信度为0.813,说明问卷具有良好的信度.三是通过问卷调查法和个案访谈法比较不同性别、不同数学成绩的学生关于对数及其运算理解水平的差异性.发现男女生在知其然理解和本然性理解上没有差异,在所以然理解上男生优于女生,具体的,男生在性质公式证明与推广及数学思想领悟上比女生强,在解释定义上比女生弱;尖子生、中等生和学困生在不同理解维度上均有显著差异,且成绩越好理解水平越好,但中等生和学困生在“知运算性质”上无差异,尖子生和中等生在“知换底公式”上无差异,说明不同数学成绩的学生都存在一定程度的机械记忆现象.
[Abstract]:The development of students' six core qualities and mathematics core qualities puts forward higher requirements for students'understanding learning. Logarithm, as the basic concept of mathematics curriculum in senior high school, is the basis of further learning mathematics. The main research problem of this paper is to describe the level of understanding of logarithmic and logarithmic operations in Senior one students. The first is to construct the understanding model of logarithm and its operation by literature analysis. The understanding of logarithm and its operation can be divided into three parts: the understanding of knowledge, the understanding of reason and the understanding of nature. The understanding of knowing is divided into the nature of knowledge definition, the property of knowing operation, the formula of knowing changing the background, the interpretation definition, the proof of nature formula, the generalization of nature formula, and the understanding of nature is divided into the essence of invention and the thought of mathematics. Among them, the nature of definition is not related to the nature of invention, and the other understanding categories are all positively related. Secondly, according to the constructed understanding model, the questionnaire is made to the first grade students of Wuhu No. 12 Middle School, and the data of the survey are analyzed by SPSS20.0. It is found that the internal consistency coefficient of the questionnaire is 0.806 Spearman-Brown split-half reliability is 0.813, which indicates that the questionnaire has good reliability. The third is to compare the difference of students' understanding of logarithm and operation among different genders and different mathematics achievement by questionnaire and case interview. It is found that there is no difference between male and female students in their understanding of nature and nature, and that boys are better than girls in terms of understanding and understanding. Specifically, boys are stronger than girls in proving and popularizing their nature formulas and understanding mathematical ideas, and in terms of interpretation and definition, they are weaker than girls. There were significant differences among top students, middle students and students with learning difficulties in different understanding dimensions, and the better the achievement, the better the understanding level, but there was no difference between the middle students and the students with learning difficulties in the nature of knowledge and operation. There is no difference between the top students and the middle students in the formula of "knowing and changing the bottom", which indicates that the students with different mathematics scores all have some mechanical memory phenomenon.
【学位授予单位】：安徽师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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