高年级小学生代数思维的测试与分析

发布时间：2018-05-19 02:11

本文选题：代数思维 + 水平　；参考：《华中师范大学》2017年硕士论文

【摘要】：古老传统的数学发展至今,代数仍然是至关重要的一部分.随着计算机等科学技术的普及,代数在各行各业发展中有着不可或缺的基础作用.思维的发展能够更好地培养人对事物本质的认识,而小学生正处于思维高速发展的时期,本文测试分析高年级小学生代数思维发展情况,旨在为代数思维的培养方向提供可行的数据支持.本研究分为六章:第一章引言,从代数的重要性方面来论述研究的背景、主要内容和方法.第二章研究综述,整理现有文献对代数思维的研究主要有三个方面:对代数思维核心概念的研究;对算术思维与代数思维的过渡研究;对代数思维培养的研究.在认识前人对代数思维的理解和研究成果的基础上对与代数思维相关的早期代数进行评述概括,分析出代数思维的核心特点.第三章测试量表的选取与优化,结合第二章的文献综述选取符合本文研究目的的代数思维结构模型,对模型进行改进使其更加合理,并对每个指标进行高低分层,形成测试高年级小学生代数思维的量表.第四章测试方案设计与实施,根据第三章的测试量表初步设计测试卷,再试测对测试卷进行微调,形成正式的测试卷,最后选择合适对象进行测试.第五章测试结果与分析,利用统计软件先对测试卷的信度和结构效度进行分析,得知测试卷比较可靠.再对代数思维整体水平、各因子各指标的发展水平、相关性、差异性进行分析,得到主要结果有:(1)高年级小学生已经萌发了代数思维.规律、表征、方程、函数思维基本达到低层次水平;表征、算律、方程、函数思维的高低水平得分有显著的差距,存在较大的上升空间;算律和逆算思维处在较低的水平,还需要加强.(2)代数思维发展水平受年级因素的显著影响,随着年级的上升代数思维发展水平逐渐提高;与性别、年龄无显著差异.(3)代数思维发展与数学成绩有显著的正相关关系,三个因子有较弱的正相关关系,每个因子下属两个指标之间中度相关.第六章结论与展望,叙述研究的主要成果、存在的问题和进一步的研究方向.
[Abstract]:Algebra is still a vital part of the development of ancient mathematics. With the popularization of computer science and technology, algebra plays an indispensable role in the development of various industries. The development of thinking can better train people to understand the essence of things, while the pupils are in the period of rapid development of thinking. This paper tests and analyzes the development of algebraic thinking of senior primary school students. The aim is to provide feasible data support for the cultivation of algebraic thinking. This research is divided into six chapters: the first chapter introduces the background, main contents and methods of the research from the importance of algebra. In the second chapter, there are three main aspects: the research on the core concepts of algebraic thinking; the transition between arithmetic thinking and algebraic thinking; and the research on the cultivation of algebraic thinking. On the basis of understanding the previous understanding and research achievements of algebraic thinking, the early algebraic thinking related to algebraic thinking is reviewed and summarized, and the core characteristics of algebraic thinking are analyzed. The selection and optimization of the third chapter test scale, combined with the literature review of the second chapter, select the algebraic thinking structure model which is in line with the purpose of this paper, improve the model to make it more reasonable, and layer each index. To form a scale to test the algebraic thinking of senior pupils. The fourth chapter is the design and implementation of the test scheme. According to the preliminary design of the third chapter of the test scale, the test volume is fine-tuned to form a formal test volume. Finally, the appropriate subjects are selected to test. In the fifth chapter, the reliability and structural validity of the test volume are analyzed by statistical software, and the results show that the test volume is reliable. Then it analyzes the whole level of algebraic thinking, the development level, correlation and difference of each index, and obtains the main result: 1) Algebraic thinking has been germinated in the senior primary school students. The law, representation, equation, function thought basically reached the low level; the representation, the calculation law, the equation, the function thought level score has the remarkable disparity, has the big rise space, the arithmetic law and the inverse calculation thought are in the lower level, It is also necessary to strengthen the development level of algebraic thinking. The development level of algebraic thinking is significantly affected by the factors of grade, and the level of development of algebraic thinking increases gradually with the increase of grade. There was no significant difference in age. (3) there was a significant positive correlation between the development of algebraic thinking and mathematical achievement, and there was a weak positive correlation among the three factors, and there was a moderate correlation between two indexes under each factor. In chapter 6, the conclusion and prospect, the main achievements, the existing problems and the further research direction are described.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G623.5

【参考文献】