【作者】 王蕾；

【导师】 王勤；

【作者基本信息】 华东师范大学 ， 教育硕士（专业学位）， 2024， 硕士

【摘要】 函数是近现代数学的基石,也是贯穿高中数学课程的三大主线之一,因此函数概念及其表示方法具有重大的奠基意义。然而由于高中函数概念内涵的丰富性、复杂性、高度抽象性以及与其他知识的紧密联系性,大量教学实践以及笔者对我校函数概念教学现状的调查表明,学生普遍在理解和掌握函数概念时存在一定困难。新课标明确指出本节教学内容应包括函数概念的形成与发展,因而我们可以从历史发生原理中得到启发,利用相应的数学史来开展函数概念教学。本文首先通过文献研究法梳理函数概念的发展历史,其次通过问卷调查法和访谈法了解师生对数学史视角下函数概念教学的看法与期望,然后通过课堂观察记录法分析函数概念的教学现状,基于上述研究设计HPM(数学史与数学教育)视角下的函数概念教学,并在实验班与对照班分别进行教学实验。最后通过试卷测试法将两班学生前测与后测成绩进行对比分析,得出如下启示与建议。后测结果表明实验班学生对函数概念及其表示方法的理解更为深刻,对“三要素”中尤其是对应关系的掌握程度更高。因此高中教师在进行函数概念及其表示法的教学时可以充分利用相关数学史,以HPM为视角开展一系列的教学活动,以促进学生对函数概念及其表示方法的理解和掌握,突破高中函数概念这一教学难点。更多还原

【Abstract】 Function is the cornerstone of modern mathematics and one of the three main threads running through the high school mathematics curriculum,so the concept of function and its representation is of great significance.However,due to the richness,complexity,high abstraction and close connection with other knowledge of the concept of function in high school,a large number of teaching practices and the author’s investigation of the current status of teaching function concepts in our school show that students generally have certain difficulties in understanding and mastering the concept of function.The new standard clearly indicates that the teaching content of this section should include the formation and development of function concepts,thus we can be inspired by the principle of historical occurrence and utilize the corresponding history of mathematics to carry out the teaching of function concepts.In this paper,we firstly sort out the development history of the function concept through the literature research method,secondly,we learn the teachers’ and students’ views and expectations on the teaching of the function concept in the perspective of the history of mathematics through the questionnaire survey method and the interview method,and then we analyze the current situation of the teaching of the function concept through the classroom observation and recording method,and based on the above research,we design the teaching of the function concept in the perspective of the HPM(History of Mathematics and Mathematics Education),and we carry out the teaching experiment in the experimental class and the control class.Finally,the pre-test and post-test results of the students in the two classes were compared and analyzed through the paper testing method,and the following insights and suggestions were drawn.The results of the post-test show that students in the experimental class have a deeper understanding of the function concept and its representation,and a higher degree of mastery of the "three elements",especially the correspondence.Therefore,teachers in high school can make full use of the relevant mathematical history when teaching function concepts and their representations,and carry out a series of teaching activities from the perspective of HPM,in order to promote students’ understanding and mastery of function concepts and their representations,and to break through the teaching difficulty of function concepts in high school.更多还原