节点文献
在函数教学中培养学生数学抽象素养的研究
A Study on Cultivating Students Mathematics Abstract Literacy in Function Teaching
【作者】 陈星宇;
【导师】 崔登兰;
【作者基本信息】 湖南师范大学 , 学科教学(数学)(专业学位), 2020, 硕士
【摘要】 新一轮以核心素养为中心的课程改革已然开始,培养学生的数学核心素养是数学教育工作者不容忽视的责任。数学抽象素养作为首要的数学核心素养,基于课堂教学培养学生的数学抽象素养具有重大意义。本研究通过测试调查的方法,利用SPSS25.0和Excel分析测试卷,得到高一学生的数学抽象素养现状,在相应的数学抽象素养水平上,分别有73%、62%、29%的学生达到了水平一、水平二、水平三,达到相应水平的学生人数比例随着数学抽象素养水平的升高而不断降低。在四个数学活动的数学抽象素养水平上,学生数学抽象素养现状表现为情境与问题>思维与表达>知识与技能>交流与反思。根据调查得到的学生数学抽象素养现状,得到了在四个数学活动中培养学生数学抽象素养的教学策略。在情境与问题维度:(1)创设有效的教学情境,使学生充分经历数学抽象的过程;(2)引导学生概括出结论,关注概括过程中学生存在的问题。在知识与技能维度:(1)设置合理的教学目标,明确对数学基础知识的认知需求;(2)建构系统的知识体系,促进学生对数学知识的理解贯通;(3)运用合理的信息技术,促进学生对相应数学内容的理解。在思维与表达维度:(1)掌握数学语言的使用,促进学生熟练表达相关数学问题;(2)注重数学思想的渗透,引导学生感悟数学的通性与通法。在交流与反思维度:(1)注重知识的实际应用,拉近数学知识与现实生活的距离;(2)开展数学交流与反思,促进学生交流与积累相应的经验。以基本初等函数(Ⅰ)的三节教学课为例,首先利用数学抽象度分析理论分析相应的教学内容,然后分析相应教学内容的课程目标,再将相应的教学策略融入到APOS教学四阶段中去,通过实验法来检验相应的培养学生数学抽象素养的教学策略和教学设计的有效性。教学实验结果表明,培养学生数学抽象素养的教学策略与教学设计有效。
【Abstract】 A new curriculum reform centered on core literacy has begun,and it is the responsibility of mathematics educators to cultivate students’ core literacy in mathematics.Mathematics abstract literacy as the primary mathematics core literacy,based on classroom teaching to cultivate students’ mathematical abstract literacy has great significance.Through the test survey method,using SPSS 25.0 and Excel to analyze the test paper,the present situation of mathematics abstract literacy of senior 1 students was obtained.In the corresponding level of mathematics abstract literacy,73%,62%and 29% of the students reached level one,level two and level three,respectively,and the proportion of the students who reached the corresponding level of abstract literacy decreased continuously with the increase of the level of mathematics abstract literacy.On the level of mathematical abstract literacy in the four mathematical activities,the present situation of students’ mathematical abstract literacy is manifested in the situation and problems>thinking and expression> knowledge and skills>communication and reflection.According to the present situation of students’ mathematics abstract literacy,the teaching strategy of cultivating students’ mathematics abstract literacy in four mathematics activities is obtained.In the dimension of situation and problem :(1)creating effective teaching situations so that students can fully experience the process of mathematical abstraction;(2)guiding students to generalize conclusions and paying attention to the problems existing in the process of generalization.In the dimension of knowledge and skills:(1)setting reasonable teaching objectives and clarifying students’ cognitive needs for basicknowledge of mathematics;(2)constructing syste matic knowledge system to promote students’ understanding and penetrating of mathematics knowledge;(3)using reasonable information technology to promote students’ understanding of corresponding mathematics contents.In the dimension of think ing and expression :(1)mastering the use of mathematical language,which promoting students to express relevant mathematical problems skillfully;(2)paying attention to the infiltration of mathematical ideas and guiding students to understand the general and general methods of mathematics.In the dimension of communication and reflection:(1)Paying attention to the practical application of knowledge,which closing the distance between mathematical knowledge and real life;(2)carrying out mathematical communication and reflection,which promoteing students to exchange and accumulate corresponding experience.Taking the three teaching classes of basic elementary function(I)as an example,Firstly,the corresponding teaching contents are analyzed by using the theory of mathematics abstractness analysis,then the course objectives of the corresponding teaching contents are analyzed,and then the corresponding teaching strategies are integrated into the four stages of APOS teaching.The results of teaching experiment show that the teaching design and teaching strategy of cultivating students’ abstract literacy in mathematics are effective.
【Key words】 Mathematics Abstract Literacy; the theory of Mathematical Abstract Analysis; APOS; Function Teaching; Teaching Strategies;
- 【网络出版投稿人】 湖南师范大学 【网络出版年期】2021年 01期
- 【分类号】G633.6
- 【被引频次】5
- 【下载频次】366