APOS理论下高中生对函数概念理解的调查研究
发布时间：2018-10-05 15:38
【摘要】：函数是高中数学的核心内容,它作为一条主线贯穿于高中数学学习的始终,在高中数学中占有很大比重,在实际教学中,函数概念又是学生理解困难的概念之一。而APOS理论在数学概念教学中有着很好的运用,其四个阶段的划分清晰地刻画了学生函数概念认知的过程,有助于指导函数概念的教学。本文将先通过文献研究法对函数概念及相关文献进行梳理,为随后的研究奠定理论基础。其次,通过测试调查了解当前高中生函数概念的理解水平,研究结果表明:学生在各个阶段的函数理解水平差异较大,对操作阶段的理解水平最好,而对于图式阶段的理解水平相对较差;此外,高二学生的函数概念理解水平优于高一学生,男生的函数概念理解水平要优于女生,重点中学学生的函数概念理解水平要优于普通中学。进一步,结合测试调查与访谈对学生函数概念理解四个阶段中的常见错误进行了分析。最后,针对以上的研究对如何提高当前高中生函数理解水平提出了几点建议:激发学生对函数学习的积极性;加强对表格形式函数的教学;重视学生对函数符号语言的理解;精心设计函数概念的变式训练;合理运用多媒体信息技术进行教学;注重学生函数知识网络的形成。全文共分为七个部分:第一部分为引言部分,主要介绍本文的选题缘由以及对已有研究的文献进行综述,从而指出本研究要解决的问题和研究意义。第二部分主要介绍了本研究的两大理论基础:函数概念和APOS理论。第三部分主要介绍了本研究的方法设计,主要有文献研究法、测试调查法、访谈法。第四部分是本文重心内容,主要通过测试调查了解当前高中生函数概念的理解水平。第五部分是在结合测试调查与访谈对学生函数概念理解四个阶段中的常见错误进行了分析。第六部分是针对以上的研究对如何提高当前高中生函数理解水平提出了几点建议。第七部分是对本研究的主要结论进行总结,以及对本研究的不足进行反思与展望。综上,本研究基于APOS理论了解当前高中生函数概念理解的现状,并针对现状提出了建议,这些工作对于开展函数概念教学具有一定的指导意义。
[Abstract]:Function is the core content of senior high school mathematics. As a main line, it runs through the study of high school mathematics all the time and occupies a large proportion in senior high school mathematics. In practical teaching, the concept of function is one of the difficult concepts for students to understand. The APOS theory is well applied in the teaching of mathematical concepts. The division of the four stages clearly depicts the process of students' cognition of the concept of function, which is helpful to guide the teaching of the concept of function. In this paper, the concept of function and related literature will be combed through the literature research method, which will lay a theoretical foundation for the subsequent research. Secondly, through the test investigation to understand the current high school student function concept understanding level, the research result shows: the student's function understanding level in each stage is quite different, the understanding level of the operation stage is the best. In addition, the level of functional concept understanding of senior two students is better than that of senior one students, and that of male students is better than that of female students. The understanding level of function concept of key middle school students is better than that of ordinary middle school. Furthermore, the common mistakes in the four stages of understanding the concept of student function are analyzed by means of test investigation and interview. Finally, in view of the above research, some suggestions are put forward on how to improve the functional understanding of senior high school students: to stimulate students' enthusiasm in learning function, to strengthen the teaching of tabular form functions, to attach importance to students' understanding of functional symbolic language; The concept of function is carefully designed for variant training, multimedia information technology is used reasonably for teaching, and attention is paid to the formation of students' functional knowledge network. The full text is divided into seven parts: the first part is the introduction part, mainly introduces the reason of this paper and the literature review, and points out the problems to be solved and the significance of the research. The second part mainly introduces the two theoretical bases of this study: the concept of function and the theory of APOS. The third part mainly introduces the method design of this research, including literature research, test investigation and interview. The fourth part is the focus of this paper, mainly through the test investigation to understand the current high school students understanding of the concept of function. In the fifth part, the common mistakes in the four stages of understanding the concept of student function are analyzed in combination with test investigation and interview. The sixth part puts forward some suggestions on how to improve the function comprehension of senior high school students. The seventh part is a summary of the main conclusions of this study, as well as the shortcomings of this study reflection and prospects. In summary, based on the APOS theory, this study understands the current situation of high school students' function concept understanding, and puts forward some suggestions for the current situation, which has certain guiding significance for the development of function concept teaching.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
本文编号：2253934
[Abstract]:Function is the core content of senior high school mathematics. As a main line, it runs through the study of high school mathematics all the time and occupies a large proportion in senior high school mathematics. In practical teaching, the concept of function is one of the difficult concepts for students to understand. The APOS theory is well applied in the teaching of mathematical concepts. The division of the four stages clearly depicts the process of students' cognition of the concept of function, which is helpful to guide the teaching of the concept of function. In this paper, the concept of function and related literature will be combed through the literature research method, which will lay a theoretical foundation for the subsequent research. Secondly, through the test investigation to understand the current high school student function concept understanding level, the research result shows: the student's function understanding level in each stage is quite different, the understanding level of the operation stage is the best. In addition, the level of functional concept understanding of senior two students is better than that of senior one students, and that of male students is better than that of female students. The understanding level of function concept of key middle school students is better than that of ordinary middle school. Furthermore, the common mistakes in the four stages of understanding the concept of student function are analyzed by means of test investigation and interview. Finally, in view of the above research, some suggestions are put forward on how to improve the functional understanding of senior high school students: to stimulate students' enthusiasm in learning function, to strengthen the teaching of tabular form functions, to attach importance to students' understanding of functional symbolic language; The concept of function is carefully designed for variant training, multimedia information technology is used reasonably for teaching, and attention is paid to the formation of students' functional knowledge network. The full text is divided into seven parts: the first part is the introduction part, mainly introduces the reason of this paper and the literature review, and points out the problems to be solved and the significance of the research. The second part mainly introduces the two theoretical bases of this study: the concept of function and the theory of APOS. The third part mainly introduces the method design of this research, including literature research, test investigation and interview. The fourth part is the focus of this paper, mainly through the test investigation to understand the current high school students understanding of the concept of function. In the fifth part, the common mistakes in the four stages of understanding the concept of student function are analyzed in combination with test investigation and interview. The sixth part puts forward some suggestions on how to improve the function comprehension of senior high school students. The seventh part is a summary of the main conclusions of this study, as well as the shortcomings of this study reflection and prospects. In summary, based on the APOS theory, this study understands the current situation of high school students' function concept understanding, and puts forward some suggestions for the current situation, which has certain guiding significance for the development of function concept teaching.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
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