教材作为课程的主要载体，是课程内容的具体体现，是实现课程目标，实施课堂教学的重要资源。在小学数学教材中，“数与代数”内容在几个知识领域中的占比最大，对这部分内容的研究，有助于整体把握小学数学课程内容。中美两国作为世界前两大经济体，在教育、科技等方面具有较多互补之处，对比中美两国小学数学教材有助于促进我国数学课程和教材建设的完善。我国政府和相关教育部门在教材编写、审核及使用上进行严格监管，旨在确保教材内容的科学性和时代性，为培养具备国际视野和核心素养的新时代人才提供有力保障。在此背景下，单元教学设计作为核心素养导向下的必然诉求，如何有效利用教材并创造性地使用教材，借助教材比较为单元教学设计提供指导，对于促进学生深度理解知识具有重要意义。

本研究选取了2010年获得“全球百大优秀出版物”的GO MATH版与北师大版小学数学教材做对比，结合文献分析，采用文本分析和案例设计的研究方法，比较这两版教材在数与代数领域知识组织和内容编排的共性与差异，并以小数除法单元为例，将研究结果应用于具体的单元教学设计之中。

从模块呈现与知识领域这两个方面对两版教材的整体结构进行对比分析，得出两版教材都比较重视问题对学生学习的作用、重视习题对知识的巩固作用等。同时也得出两版教材在知识组织与内容呈现等方面存在差异，且GO MATH版教材在数与代数领域的单元数与课时数远多于北师大版教材。

本研究重点对两版教材数与代数领域进行了比较研究，具体从整数、分数、小数、百分数、比与方程这五个部分进行分析。主要研究结论如下：

第一，学制差异对两版教材数与代数部分内容组织的影响较大。美国幼儿园阶段有系统的数学知识学习，而中国则是从小学一年级开始学习数的初步认识和运算。第二，文化差异对两版教材数与代数部分的知识内容有所影响。数级的不同与两国所处环境的计量单位和历史文化背景有关。第三，两版教材在数与代数领域的编排顺序有所不同，并且这种编排顺序的不同也影响了知识的学习方式。第四，两版教材在数与代数部分知识组织的侧重点有所不同。北师大版教材的知识组织更偏向学生的心理逻辑，而GO MATH版教材更偏向数学学科的知识逻辑。

最后，结合教材对比的结论，以小数除法为例，结合实习学校两个班级小数除法作业错题分析，总结了教材对比对知识编排、情境创设、活动设计等方面的启示，做出小数除法单元教学设计框架及部分教学活动，为一线数学教师整体把握教材，促进数学理解提供参考。

As the main carrier of course, teaching material is the concrete embodiment of course content, and an important resource to realize the course goal and implement classroom teaching. In primary school mathematics textbooks, the content of "number and algebra" accounts for the largest proportion in several knowledge fields. The study of this part of the content is helpful to grasp the overall content of primary school mathematics curriculum. As the world's top two economies, China and the United States have many complementary aspects in education, science and technology. The comparison of the mathematics textbooks in primary schools between China and the United States is helpful to promote the improvement of the construction of mathematics curriculum and teaching materials in China. The Chinese government and relevant education departments carry out strict supervision on the compilation, review and use of the textbooks, aiming to ensure that the content of the textbooks is scientific and contemporary, and to provide a strong guarantee for the training of talents in the new era with international vision and core qualities. In this context, unit teaching design is as the inevitable appeal under the guidance of core literacy. How to effectively use teaching materials and creatively, and provide guidance for unit teaching design with the help of teaching materials, is of great significance for promoting students' deep understanding of knowledge.

This study selected in 2010 "global hundred excellent publications" GO MATH edition and Beijing normal university edition of primary school mathematics textbooks, combined with literature analysis, text analysis and case design method, compare the two editions in the field of number and algebra knowledge organization and content arrangement and differences, and decimal division unit, for example, the research results are applied to the specific unit teaching design.

By comparative analysis of the overall structure of the two textbooks from the two aspects of module presentation and knowledge field, it is concluded that the two versions of the teaching materials attach more importance to the role of problems on students' learning and the consolidation of exercises on knowledge. At the same time, it is also concluded that the two textbooks have differences in knowledge organization and content presentation, and the number of units and class hours in the field of number and algebra is far more than that of Beijing Normal University.

This study focuses on the comparative study of the number and algebra fields of the two editions of the textbook, specifically from the five parts of integer, fraction, decimal, percentage, ratio and equation. The main study conclusions are summarized as follows:

First, the difference of schooling system has a great influence on the number of textbooks and algebra of the two editions. In the United States, there is systematic mathematical knowledge learning, while in China, I learn the preliminary understanding and operation of numbers starting from the first grade of primary school. Second, cultural differences have an influence on the knowledge content of the number and algebra parts of the two textbooks. The difference is related to the unit of measurement and the historical and cultural background of the environment of the two countries. Third, the arrangement order of the two editions is different in the field of number and algebra, and the different arrangement order also affects the way of the knowledge learning. Fourth, the two editions of the textbooks are different in the focus of knowledge organization in the number and algebra parts. The knowledge organization of the textbook of Beijing Normal University is more inclined to the students' psychological logic, while the GO MATH edition is more inclined to the knowledge logic of mathematics.

Finally, combined with the conclusion of textbook comparison, taking decimal division as an example, combined with the two classes of practice school, summarized the textbook comparison of knowledge arrangement, situation creation, activity design and other aspects of the enlightenment.