摘    要：数学概念课的教学研究一直是数学教学研究中的核心，数学概念的学习影响着学生的数学思维与创新能力的发展。概念课的教学设计优化有助于提升教师认知水平，提高教学质量。

新课程标准把初中数学分成包括数与代数在内的四个板块。数与代数是学生学习数学的基础。数与代数板块中的基础内容就是实数，学生掌握实数的概念是从具体情境中抽象出数学符号语言的过程。

本文是在新课改下对历史发展原理应用于教学的理论研究。基于历史发展原理，针对传统教学模式的不足，优化了教学设计。将历史上数学家在研究实数遇到的问题重现在课堂上, 使学生直接参与概念的形成过程，加深学生对于概念的本质理解。通过对比传统教学设计，验证了历史发展原理应用于概念课教学的可行性。希望本文的研究，对教师在做概念课的教学设计有一定帮助。

关键词：数学概念；教学设计；实数教学；历史发展原理

Abstract：The teaching research of mathematics concept course is always the core of mathematics teaching research. The learning of mathematical concept influences the development of students' mathematical thinking and innovation ability. The optimization of teaching design of concept class helps to improve teachers' cognitive level and improve teaching quality.

The new curriculum standard pides junior middle school mathematics into four parts, including numbers and algebra. Numbers and algebra are the basis for students to learn mathematics. The basic content in number and algebraic plate is real number. The concept of real number is the process of abstracting mathematical symbolic language from specific situations.

This paper is a theoretical research on the application of historical development principles to teaching under the new curriculum reform. Based on the historical-genetic- principle, aiming at the shortcomings of traditional teaching mode, the teaching design is optimized. The problems encountered by the mathematicians in the history are reproduced in the classroom, and the students are involved in the concept, then deepen the student's understanding of the essence of the concept. By comparing the traditional teaching design, it verifies the feasibility of applying the principle of historical development to the teaching of concept class. I hope this research is helpful for teachers in teaching design of concept class.

Keyword: Mathematical concept; teaching design; Teaching of Real Numbers; historical-genetic- principle

目录

一、绪论 3

（一）研究背景 3

（二）研究意义 3

（三）研究内容与方法 3

二、文献综述 4

（一）数学概念教学的相关研究 4

（二）数学概念教学设计的研究 4

（三）实数的发展历史研究 5

三、历史发展原理对实数教学的意义 6

  （一）历史发展原理的相关研究 6

  （二）历史发展原理对于实数概念教学的可行性分析 7

四、基于“历史发展原理”的实数教学设计 8

（一）基于“历史发展原理”的实数教学设计 8

      （二）与传统概念课教学设计进行比较