《义务教育数学课程标准（2022年版）》指出，在小学数学阶段要求探索大单元教学，加强单元内部知识关联性。尤其是在数与代数领域，伴随着学习主题的合并，对于内容统整的要求更高，需要改变传统的教学设计以顺应内容结构化的要求。因此，学科大概念统摄下的单元教学设计应运而生。“少而精”的大概念要凸显数学课程内容是一个螺旋上升的、具有内部结构的整体。那么数学大概念的内涵和具体的表现是怎样的？在数学大概念统摄下的单元教学的流程如何制定？本研究聚焦于小学数学数与代数领域进行探究与求证。

本研究从大概念学科教学的起源与内涵演变、数学大概念的内涵与具体表现、数学大概念单元教学设计理念等角度，梳理出大概念的研究现状，重点关注国内数学大概念单元教学设计理念。文献分析后发现，相关教学理念主要集中在大概念的优势、知识建构、迁移能力三个方面。这为大概念教学意义的探寻以及单元教学流程的设计提供了研究方向。

在前人研究的基础上，本研究对数学大概念的内涵进行界定并明确数学大概念教学的意义。数学大概念是反映数学学科本质的核心概念和重要数学思想，是促进数学学科内容结构化的有力抓手，是贯穿数学大单元教学的线索。数学大概念教学促进数学的理解和学习进阶，知识迁移和方法迁移，是教师开展有效教学的关键。大概念单元教学凸显内容结构的作用，注重以理解为源，以迁移为本。

本研究基于文献研读和焦点小组访谈制定了数与代数大概念单元教学设计的流程。分为以下五个步骤：解读数学课程标准，明确核心素养和课程内容要求；对标核心素养，确立数与代数单元数学大概念；开展学情调研，合理构建大概念单元教学目标；统整课程内容，根据学习进阶安排课时课型；设计学习活动和评价，实现教学评一致性。本研究进一步阐述了与这五个步骤相对应的要素，为落实数学大概念作为线索贯穿在单元教学设计中的作用提供指导。

小学数学数与代数领域在2022新课标中被分为“数与运算”“数量关系”两个主题。研究结合大概念单元教学设计流程的五个步骤，分别选取两部分中《分数的认识》和《用字母表示数》两个典型的章节进行大概念单元教学设计，并开展课堂教学。研究者、一线教师和专家分别对四个关键课时进行反思与分析，以验证大概念单元教学设计流程的可行性，并供后续的大概念单元教学设计做参考。

The "Mathematics Curriculum Standards for Compulsory Education (2022 Edition)" clearly states that in the primary school mathematics stage, it is required to explore large unit teaching, strengthen the correlation of knowledge within units, and promote the structuring of knowledge content. Especially in the fields of numbers and algebra, with the merging of learning topics, there is a higher demand for content integration, and traditional teaching design needs to be changed to meet the requirements of content structuring. Therefore, unit teaching design under the guidance of the big ideas has emerged. The "less but more refined" big ideas make the content of mathematics courses a spiral and internally structured whole. So what is the connotation and specific expression of the mathematics big ideas? How to develop the process of unit teaching under the guidance of mathematics big ideas? This study focuses on the exploration and verification of elementary school mathematics in the fields of numbers and algebra.

This study summarizes the current research status of big ideas from the perspectives of the origin and evolution of the teaching of big ideas disciplines, the connotation and specific manifestations of mathematical big ideas, and the teaching design concept of mathematical big ideas units, with a focus on the teaching design concept of domestic mathematical big ideas units. After comparing and analyzing the literature, it was found that the relevant teaching concepts mainly focus on three aspects: the advantages of big ideas, knowledge construction, and transfer ability. This provides research direction for exploring the significance of teaching big ideas and designing unit teaching processes.

On the basis of previous research, this study once again defines the connotation of the mathematics big ideas and clarifies the significance of teaching the mathematics big ideas. The concept of mathematics reflects the essence of mathematics and should become an important clue that runs through unit teaching; The teaching of mathematical big ideas promotes the understanding and advancement of mathematics, and knowledge transfer and method transfer are the key to effective teaching by teachers; The characteristics of big ideas unit teaching: highlighting the role of content structure, emphasizing understanding as the source and transfer as the foundation.

This study developed a process for teaching design of big ideas units based on literature review and focus group interviews. It is divided into the following five steps: interpreting the curriculum standards, clarifying core competencies and course content requirements; Benchmarking core competencies and establishing the concept of unit mathematics; Conducting research on academic situation and constructing teaching objectives for large concept units in a reasonable manner; Integrating course content and arrange class hours and types based on advanced learning; Designing learning activities and evaluations to achieve consistency in teaching evaluations. This study further elaborates on the elements corresponding to these five steps, providing guidance for highlighting the role of mathematics big ideas as clues throughout unit teaching design.

The field of elementary school mathematics in numbers and algebra is divided into two themes in the 2022 new curriculum standard: "numbers and operations" and "quantitative relationships". The study combines the five steps of the teaching design process of the big concept unit, selecting two typical chapters from the two parts, "Fractions" and "Number Represented by Letters", to carry out the teaching design of the big ideas unit and carry out classroom teaching. Researchers, frontline teachers, and experts reflect and analyze the four key lesson periods respectively to verify the feasibility of the process of teaching design for big ideas units and provide reference for subsequent teaching design for big ideas units.