数学文化教学对小学生数学抽象素养的影响研究

发布时间：2018-07-05 16:10

本文选题：数学文化教学 + 小学生　；参考：《西南大学》2017年硕士论文

【摘要】：数学是一种文化,以其实用性与工具性奠基科学乃至人类社会发展的基础,以其理性价值促进人的思维发展,以其文化品格熏陶人类对真善美的追寻。数学抽象是数学学科形成与发展的基础,只有借由数学抽象舍弃事物的具体背景,抽象出数学研究对象,才能运用数学工具、理论进行探索求真。小学高段是学生由具体思维到抽象思维发展的关键期,因此,探寻行之有效的促进小学生数学抽象素养提升的教学方式尤为必要。数学文化是涵养数学学科与人类社会发展的重要源泉,与数学素养是数学“物化”与“人化”的相互转化,数学文化教学则是实现这种转化的重要途径。学界对于数学文化教学探索不断深化,然而,这种文化意义上的教学究竟追究什么、对学生数学素养有何影响,仅从理论意义上进行探讨难免纸上谈兵,这就需要从实证的角度进行探索求证。探析数学文化教学的生成与理念意蕴,构建数学文化教学模式,以数学文化教学对学生数学抽象素养的影响为切入点,从理论与实践两个层面对其进行剖析,以期填补此方面实证研究空白。从理论层面对数学文化教学的生成、理念意蕴进行了整理、分析,构建了数学文化教学的模式、分析其流程和操作要点;对于数学文化教学对小学生数学抽象素养的影响,从内涵释析、内容剖析、流程解析三个层面进行了理论论证;在借鉴国内外测评经验的基础上,结合学生认知发展规律,编制了小学生数学抽象素养认知维度测试题(前测)、小学生数学抽象素养认知维度测试题(后测)、小学数学抽象素养情意维度问卷、数学文化教学对小学生数学抽象素养影响访谈提纲,为教学实验提供测试工具支持。为探索验证数学文化教学对小学生抽象素养的影响,本研究采用2x2x3三因素实验设计,选取A小学(四年级)两个班为实验组和B小学两个班(四年级)为对照组,共197名学生。运用所建构的数学文化教学模式进行了一学期的实验。对其进行前后测测试、课堂观察与相关访谈,以获取第一手资料。对其进行数据分析,结果表明:(1)在学生数学抽象素养认知维度,数学意象抽象方面,实验组成绩高于对照组成绩,但差异不显著;在数学符号抽象、数学模式抽象方面,实验组成绩高于对照组,且差异显著。(2)在学生数学抽象素养认知维度及其各子维度方面,实验处理、性别、年级上的交互影响不显著。(3)不同数学基础的学生数学抽象素养认知维度得分存在显著差异,数学基础越好,其数学抽象素养认知维度的水平越高。(4)不同性别学生数学的抽象素养认知维度得分差异不显著。(5)在学生数学抽象素养情意维度上,实验组得分高于对照组,且差异显著。(6)在学生数学抽象素养情意维度上,实验处理、性别、年级上的交互影响不显著。(7)不同数学基础的学生数学抽象素养情意维度得分差异不显著。(8)不同性别的学生数学抽象素养情意维度得分存在显著差异,男生得分高于女生。通过理论与实践的融合,丰富与发展了数学文化教学与数学核心素养的理论与实践研究,也为教师教学提供了策略与思路,对小学生思维发展研究具有积极作用。创新之处在于构建了数学文化教学模式,并用其进行教学实践。同时编制了符合科学测量的小学生数学抽象素养的测试题及问卷。
[Abstract]:Mathematics is a kind of culture, which is based on its practical and instrumental foundation and the foundation of the development of human society. It promotes human thinking development with its rational value, and edify human's pursuit of truth, goodness and beauty with its cultural character. Mathematical abstraction is the basis for the formation and development of Mathematics, and only the concrete background of the abstraction of things by mathematical abstraction. In order to find out the object of mathematics, we can use the mathematical tools and the theory to explore the truth. The high school section is the key period for the students to develop from the concrete thinking to the abstract thinking. Therefore, it is particularly necessary to explore the effective teaching methods to promote the promotion of Mathematics abstract attainments of primary school students. The important source and mathematical literacy are the mutual transformation of mathematical "materialization" and "humanization", and the teaching of mathematics culture is an important way to realize this transformation. The exploration of mathematics culture teaching is deepened by the academic circles. However, what is the influence of teaching on the students' mathematical literacy in this cultural meaning and only from the theoretical point of view. It is necessary to probe into the paper, which needs to be explored from the perspective of empirical analysis. The formation and concept of mathematics culture teaching are discussed, and the mathematical culture teaching mode is constructed, and the influence of mathematical culture teaching on students' mathematical abstract literacy is taken as the breakthrough point, and it is analyzed from the two layers of theory and practice in order to fill this side. On the basis of the formation of the mathematical culture teaching and the idea implication, the model of mathematical culture teaching is constructed and the process and operation points are analyzed. The influence of mathematics culture teaching on mathematics Abstract literacy of primary school students is carried out from three aspects: internal and culvert analysis, content analysis and process analysis. On the basis of the domestic and foreign evaluation experience, and on the basis of the domestic and foreign evaluation experience, combined with the law of students' cognitive development, it has compiled the test questions (pre test) of primary school students' mathematical abstract literacy cognition dimension, the cognitive dimension test of primary school mathematics Abstract literacy (post test), the abstract quality of primary school mathematics, and mathematics culture teaching to primary school students. In order to test and verify the influence of mathematical culture teaching on the abstract literacy of primary school students, this study adopts the 2x2x3 three factor experimental design, selects two classes of A primary (grade four) as the experimental group and two classes of B primary school (four year grade) as the control group, with a total of 197 students. The experiment of culture teaching was carried out for one semester. The first hand information was obtained by test, classroom observation and related interviews. The results showed that: (1) the results of the students' abstract literacy cognition and mathematical image abstraction were higher than those of the control group, but the difference was not significant; in mathematics, the difference was not significant. In the aspect of symbolic abstraction and mathematical model abstraction, the results of the experimental group were higher than those of the control group, and the differences were significant. (2) there was no significant interaction between the experimental processing, gender and grade. (3) there was a significant difference in the cognitive dimension of the mathematical abstract literacy of the students with different mathematical bases. The better the basis, the higher the level of cognitive dimension of mathematical abstraction literacy. (4) there is no significant difference in the cognitive dimension of mathematics in students of different sex. (5) the score of the experimental group is higher than that of the control group, and the difference is significant. (6) in the students' mathematical abstract accomplishment emotional dimension, experimental treatment, sex, There is no significant difference in the interaction between grades. (7) there is no significant difference in the emotional dimension of mathematical abstract literacy of students with different mathematical foundations. (8) there are significant differences in the score of mathematical abstract literacy in students of different sexes, and the scores of boys are higher than those of the girls. The integration of theory and practice enriches and develops the mathematics culture teaching and mathematical core The theoretical and practical study of heart literacy also provides strategies and ideas for teachers' teaching, and has a positive effect on the study of pupils' thinking development. The innovation lies in the construction of a mathematical culture teaching model and the use of it in teaching practice. At the same time, it has compiled a test and questionnaire for the abstract accomplishment of primary school students in accordance with scientific measurement.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G623.5

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