高中生数学抽象素养培养策略研究

【作者】 沈艺；

【导师】 李善良；

【作者基本信息】 南京师范大学 ， 学科教学（数学）（专业学位）， 2021， 硕士

【摘要】 数学抽象素养作为培养学生适应未来发展、适应终身学习的数学学科核心素养之一,已经成为社会关注的热点。函数教学是高中数学教学的一大核心,通过函数教学有利于培养学生的数学抽象素养。因此,本文的研究重点是在函数教学中研究培养学生的数学抽象素养。本文在文献分析基础之上,通过调查分析现阶段在函数教学中培养高中生数学抽象素养的现状和存在的问题,在此基础之上提出一些有针对性的培养策略。通过实验数据来分析和验证以上培养策略对于不同组别、不同层次学生数学抽象素养产生的影响。问卷调查归纳出以下四种不利于学生数学抽象素养培养的主要问题:(1)学生普遍存在函数概念、本质理解不够的问题;(2)学生不能有效抽象与应用具体函数模型;(3)学生不能感悟函数的思维方法;(4)不能够理解和建构函数知识之间的联系和高度概括的函数知识体系。通过对比实验研究验证在函数教学中的培养数学抽象素养的有效性,得到了以下几点结论:(1)通过在函数教学中实施数学抽象素养培养策略对于学生发展数学抽象素养具有显著作用;(2)实验组的学生在函数概念、函数思想、函数体系维度上的平均得分表现高于对照组的学生;(3)学生数学学业成绩与数学抽象素养的发展存在显著的相关性,主要影响中、低水平层次成绩的学生数学抽象素养的发展。通过文献提出、调查研究调整和实验验证归纳总结了以下五条在函数教学中的数学抽象素养培养策略:(1)关注直观素材创设现实情境,实现函数知识建构;(2)借助问题串反思函数生成与应用过程,理解函数本质;(3)充分利用变式归纳函数本质特征,感悟函数思想;(4)以信息技术为基础实施函数活动,探究函数本质;(5)将函数历史融入教学,激发学生兴趣。更多还原

【Abstract】 Mathematical abstract literacy,as one of the core literacy of mathematics subject to cultivate students to adapt to the future development and lifelong learning,has become the focus of social attention.Function teaching is one of the core of high school mathematics teaching.It is conducive to cultivate students’ mathematical abstract quality through function teaching.Therefore,the focus of this paper is to cultivate students’ mathematical abstract literacy in function teaching.In this paper,based on the literature analysis,through the investigation and analysis of the current situation and problems of cultivating high school students’ mathematical abstract literacy in function teaching,some targeted training strategies are put forward on this basis.Through the experimental data to analyze and verify the above training strategies for different groups,different levels of students’ mathematical abstract literacy.The questionnaire survey summed up the following four main problems that are not conducive to the cultivation of students’ mathematical abstract literacy:(1)students generally do not understand the concept and essence of function;(2)students can not effectively abstract and apply specific function models;(3)students can not understand the thinking method of function;(4)they can not understand and construct the connection and highly generalized function between function knowledge and the number of knowledge system.Through the comparative experimental study,the effectiveness of cultivating mathematical abstract literacy in function teaching is verified,and the following conclusions are obtained:(1)the implementation of mathematical abstract literacy training strategy in function teaching has a significant effect on the development of students’ mathematical abstract literacy;(2)the average score of students in the experimental group is high in the dimension of function concept,function thought and function system(3)there is a significant correlation between students’ mathematics academic performance and the development of mathematical abstract literacy.It mainly affects the development of students’ mathematical abstract literacy in middle and low level.Through literature review,investigation,adjustment and experimental verification,this paper summarizes the following five strategies for cultivating mathematical abstract literacy in function teaching:(1)pay attention to intuitive materials,create realistic situations,and realize the construction of function knowledge;(2)reflect on the generation and application process of function with the help of question string,and understand the essence of function;(3)make full use of the essential characteristics of variable induction function,and comprehend the function;(4)to implement function activities based on information technology and explore the essence of function;(5)to integrate function history into teaching and stimulate students’ interest.更多还原