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中文题名:

 小学数学教材早期代数思维的国际比较研究—以中、美、新三国为例    

姓名:

 王晨曦    

保密级别:

 公开    

论文语种:

 chi    

学科代码:

 040102    

学科专业:

 课程与教学论    

学生类型:

 硕士    

学位:

 教育学硕士    

学位类型:

 学术学位    

学位年度:

 2024    

校区:

 北京校区培养    

学院:

 数学科学学院    

研究方向:

 数学教材比较    

第一导师姓名:

 郭衎    

第一导师单位:

 数学科学学院    

提交日期:

 2024-06-11    

答辩日期:

 2024-05-27    

外文题名:

 An International Comparative Study of Early Algebraic Thinking in Elementary Mathematics Textbooks: A Case Study of China, the United States, and Singapore    

中文关键词:

 小学 ; 数学 ; 教材 ; 早期代数思维 ; 国际比较    

外文关键词:

 elementary school ; mathematics ; textbooks ; early algebraic thinking ; international comparison    

中文摘要:

代数是中小学数学学习的重要内容,小学阶段培养学生早期代数思维能够为中学学习正式代数奠定基础。国际上越来越多的数学研究者开始关注在小学阶段培养学生的早期代数思维。教材作为是教师教学和学生学习的依托,在教材中如何呈现早期代数思维是需要探讨的问题。研究选取中国、美国和新加坡三个国家三个版本的小学数学教科书早期代数思维内容,比较年级覆盖小学学段的六个学年。提出以下研究问题:三个版本教材中早期代数思维内容有什么特点?三个版本教材中早期代数思维水平有什么特点?对我国的教材编写有何建议?本研究从代数思维的核心思想出发,以Kaput早期代数思维三个核心概念为理论基础,结合他人研究,构建早期代数思维内容理论框架,将早期代数思维划分为三个内容领域以及九个子维度;早期代数思维水平以SOLO分类评价理论为基础,结合他人研究,构建早期代数思维水平理论框架,将早期代数思维思维水平划分为四个水平。根据以上理论框架对三个版本教材中的早期代数思维内容进行统计、编码、分析,并选取三个版本教材中典型案例进行比较分析,得到以下结论:构建了早期代数思维的理论框架;中国教材中强调抽象算术内容领域的结论概括,但早期代数思维整体所占比重偏小;美国教材中早期代数思维内容更加丰富,更加注重函数思维;新加坡教材中强调用线段图来进行数量推理,美国教材中注重对等号概念的理解。通过比较研究,借鉴国外教材中的典型案例,为我国教材编写提供建议。

外文摘要:

Algebra is a significant component of mathematics education at the elementary level, and nurturing students' early algebraic thinking during primary school lays the groundwork for formal algebraic learning in secondary education. Internationally, an increasing number of mathematics researchers are focusing on cultivating early algebraic thinking in primary school students. As textbooks serve as the backbone of teaching and learning, it is essential to explore how early algebraic thinking is presented in textbooks. This study selects early algebraic thinking exercises from elementary mathematics textbooks in China, the United States, and Singapore, covering six grades of primary education. The following research questions are proposed: What are the characteristics of early algebraic thinking content in the textbooks of the three countries? What are the characteristics of early algebraic thinking levels in the textbooks of the three countries? What recommendations can be made for the development of Chinese textbooks? Grounded in the core ideas of algebraic thinking and the three core concepts of early algebraic thinking proposed by Kaput, this study divides early algebraic thinking into three content domains and nine subdomains. Early algebraic thinking levels are categorized based on the SOLO taxonomy theory into four levels, in conjunction with existing research. The main research findings are as follows: Constructing a theoretical framework of early algebraic thinking. The proportion of early algebraic thinking content in Chinese textbooks is relatively small, emphasizing conclusions and generalizations in the domain of abstract arithmetic. American textbooks contain more diverse early algebraic thinking content, with an emphasis on functional thinking and higher-level problem-solving tasks. Singaporean textbooks emphasize complex quantitative reasoning using line diagrams. American textbooks focus on understanding the concept of equality. Insights gained from the comparative study include the need to increase the proportion of early algebraic thinking content in Chinese elementary mathematics textbooks, enrich the content of early algebraic thinking, deepen understanding of equality relations, emphasize understanding of the concept of equality, integrate functional thinking from lower grades, emphasize procedural problem-solving, and enhance the application of information technology. By comparing Chinese textbooks with those from other countries and drawing inspiration from typical examples in foreign textbooks, recommendations can be made for textbook development in China.

参考文献总数:

 52    

馆藏号:

 硕040102/24026    

开放日期:

 2025-06-14    

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