APOS理論下高中生對函數概念理解的調查研究
發(fā)布時間：2018-10-05 15:38
【摘要】：函數是高中數學的核心內容,它作為一條主線貫穿于高中數學學習的始終,在高中數學中占有很大比重,在實際教學中,函數概念又是學生理解困難的概念之一。而APOS理論在數學概念教學中有著很好的運用,其四個階段的劃分清晰地刻畫了學生函數概念認知的過程,有助于指導函數概念的教學。本文將先通過文獻研究法對函數概念及相關文獻進行梳理,為隨后的研究奠定理論基礎。其次,通過測試調查了解當前高中生函數概念的理解水平,研究結果表明:學生在各個階段的函數理解水平差異較大,對操作階段的理解水平最好,而對于圖式階段的理解水平相對較差;此外,高二學生的函數概念理解水平優(yōu)于高一學生,男生的函數概念理解水平要優(yōu)于女生,重點中學學生的函數概念理解水平要優(yōu)于普通中學。進一步,結合測試調查與訪談對學生函數概念理解四個階段中的常見錯誤進行了分析。最后,針對以上的研究對如何提高當前高中生函數理解水平提出了幾點建議:激發(fā)學生對函數學習的積極性;加強對表格形式函數的教學;重視學生對函數符號語言的理解;精心設計函數概念的變式訓練;合理運用多媒體信息技術進行教學;注重學生函數知識網絡的形成。全文共分為七個部分:第一部分為引言部分,主要介紹本文的選題緣由以及對已有研究的文獻進行綜述,從而指出本研究要解決的問題和研究意義。第二部分主要介紹了本研究的兩大理論基礎:函數概念和APOS理論。第三部分主要介紹了本研究的方法設計,主要有文獻研究法、測試調查法、訪談法。第四部分是本文重心內容,主要通過測試調查了解當前高中生函數概念的理解水平。第五部分是在結合測試調查與訪談對學生函數概念理解四個階段中的常見錯誤進行了分析。第六部分是針對以上的研究對如何提高當前高中生函數理解水平提出了幾點建議。第七部分是對本研究的主要結論進行總結,以及對本研究的不足進行反思與展望。綜上,本研究基于APOS理論了解當前高中生函數概念理解的現狀,并針對現狀提出了建議,這些工作對于開展函數概念教學具有一定的指導意義。
[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.
【學位授予單位】：揚州大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：G633.6
本文編號：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.
【學位授予單位】：揚州大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：G633.6
【參考文獻】
相關期刊論文 前10條
1 沈順發(fā);;基于APOS理論下高中函數概念的教學環(huán)節(jié)分析[J];中學數學;2015年21期
2 徐德同;;關于概念教學的幾點思考[J];數學通報;2015年03期
3 袁柳芳;黃亮;王鶴;;基于APOS理論的高中生函數概念認知調查[J];中學數學教學參考;2015年09期
4 武小鵬;;基于APOS理論的高中函數概念教學研究[J];數學教學研究;2014年03期
5 索云旺;張啟華;廖爽;張銳軍;;高效數學教學行為特征指導下的數學課堂教學設計——以“函數概念”教學設計為例[J];數學教育學報;2013年05期
6 李孟芹;;函數概念的起源、演變與發(fā)展[J];大學數學;2011年03期
7 張躍紅;;我對概念教學的實踐與認識[J];數學通報;2010年06期
8 章建躍;陶維林;;注重學生思維參與和感悟的函數概念教學[J];數學通報;2009年06期
9 徐立英;張麗娜;;APOS理論對函數概念教學的啟示和應用[J];高等教育研究(成都);2007年03期
10 李強;;高中新教材中函數概念教學思考[J];數學通報;2007年05期
相關碩士學位論文 前10條
1 陳鑫笑;高中函數學習障礙分析及教學對策研究[D];洛陽師范學院;2016年
2 周晶;高中生函數學習障礙的探究[D];華中師范大學;2015年
3 周仁哲;高中函數教學的調查研究[D];東北師范大學;2015年
4 高凌宇;基于情境認知理論的高中函數概念教學研究[D];天津師范大學;2015年
5 劉茂先;高一學生對函數概念理解的調查研究[D];貴州師范大學;2014年
6 賈艷玲;基于變式練習的函數概念的教學研究與實踐[D];河北師范大學;2013年
7 劉俠;情境創(chuàng)設在初高中函數概念教學中的應用研究[D];陜西師范大學;2013年
8 王艷輝;APOS理論下高中生對函數概念理解的差異研究[D];西南大學;2013年
9 李劍;高中與初中數學函數概念教學的銜接研究[D];重慶師范大學;2012年
10 曹麗娟;基于APOS理論下的高中函數概念教學方式探究[D];陜西師范大學;2012年
，本文編號：2253934
本文鏈接：http://sikaile.net/zhongdengjiaoyulunwen/2253934.html
