【摘要】：函數(shù)是高中數(shù)學(xué)的核心內(nèi)容,它作為一條主線貫穿于高中數(shù)學(xué)學(xué)習(xí)的始終,在高中數(shù)學(xué)中占有很大比重,在實(shí)際教學(xué)中,函數(shù)概念又是學(xué)生理解困難的概念之一。而APOS理論在數(shù)學(xué)概念教學(xué)中有著很好的運(yùn)用,其四個(gè)階段的劃分清晰地刻畫了學(xué)生函數(shù)概念認(rèn)知的過(guò)程,有助于指導(dǎo)函數(shù)概念的教學(xué)。本文將先通過(guò)文獻(xiàn)研究法對(duì)函數(shù)概念及相關(guān)文獻(xiàn)進(jìn)行梳理,為隨后的研究奠定理論基礎(chǔ)。其次,通過(guò)測(cè)試調(diào)查了解當(dāng)前高中生函數(shù)概念的理解水平,研究結(jié)果表明:學(xué)生在各個(gè)階段的函數(shù)理解水平差異較大,對(duì)操作階段的理解水平最好,而對(duì)于圖式階段的理解水平相對(duì)較差;此外,高二學(xué)生的函數(shù)概念理解水平優(yōu)于高一學(xué)生,男生的函數(shù)概念理解水平要優(yōu)于女生,重點(diǎn)中學(xué)學(xué)生的函數(shù)概念理解水平要優(yōu)于普通中學(xué)。進(jìn)一步,結(jié)合測(cè)試調(diào)查與訪談對(duì)學(xué)生函數(shù)概念理解四個(gè)階段中的常見錯(cuò)誤進(jìn)行了分析。最后,針對(duì)以上的研究對(duì)如何提高當(dāng)前高中生函數(shù)理解水平提出了幾點(diǎn)建議:激發(fā)學(xué)生對(duì)函數(shù)學(xué)習(xí)的積極性;加強(qiáng)對(duì)表格形式函數(shù)的教學(xué);重視學(xué)生對(duì)函數(shù)符號(hào)語(yǔ)言的理解;精心設(shè)計(jì)函數(shù)概念的變式訓(xùn)練;合理運(yùn)用多媒體信息技術(shù)進(jìn)行教學(xué);注重學(xué)生函數(shù)知識(shí)網(wǎng)絡(luò)的形成。全文共分為七個(gè)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(duì)已有研究的文獻(xiàn)進(jìn)行綜述,從而指出本研究要解決的問(wèn)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(chǔ):函數(shù)概念和APOS理論。第三部分主要介紹了本研究的方法設(shè)計(jì),主要有文獻(xiàn)研究法、測(cè)試調(diào)查法、訪談法。第四部分是本文重心內(nèi)容,主要通過(guò)測(cè)試調(diào)查了解當(dāng)前高中生函數(shù)概念的理解水平。第五部分是在結(jié)合測(cè)試調(diào)查與訪談對(duì)學(xué)生函數(shù)概念理解四個(gè)階段中的常見錯(cuò)誤進(jìn)行了分析。第六部分是針對(duì)以上的研究對(duì)如何提高當(dāng)前高中生函數(shù)理解水平提出了幾點(diǎn)建議。第七部分是對(duì)本研究的主要結(jié)論進(jìn)行總結(jié),以及對(duì)本研究的不足進(jìn)行反思與展望。綜上,本研究基于APOS理論了解當(dāng)前高中生函數(shù)概念理解的現(xiàn)狀,并針對(duì)現(xiàn)狀提出了建議,這些工作對(duì)于開展函數(shù)概念教學(xué)具有一定的指導(dǎo)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(xué)位授予單位】：揚(yáng)州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：G633.6

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 沈順發(fā);;基于APOS理論下高中函數(shù)概念的教學(xué)環(huán)節(jié)分析[J];中學(xué)數(shù)學(xué);2015年21期

2 徐德同;;關(guān)于概念教學(xué)的幾點(diǎn)思考[J];數(shù)學(xué)通報(bào);2015年03期

3 袁柳芳;黃亮;王鶴;;基于APOS理論的高中生函數(shù)概念認(rèn)知調(diào)查[J];中學(xué)數(shù)學(xué)教學(xué)參考;2015年09期

4 武小鵬;;基于APOS理論的高中函數(shù)概念教學(xué)研究[J];數(shù)學(xué)教學(xué)研究;2014年03期

5 索云旺;張啟華;廖爽;張銳軍;;高效數(shù)學(xué)教學(xué)行為特征指導(dǎo)下的數(shù)學(xué)課堂教學(xué)設(shè)計(jì)——以“函數(shù)概念”教學(xué)設(shè)計(jì)為例[J];數(shù)學(xué)教育學(xué)報(bào);2013年05期

6 李孟芹;;函數(shù)概念的起源、演變與發(fā)展[J];大學(xué)數(shù)學(xué);2011年03期

7 張躍紅;;我對(duì)概念教學(xué)的實(shí)踐與認(rèn)識(shí)[J];數(shù)學(xué)通報(bào);2010年06期

8 章建躍;陶維林;;注重學(xué)生思維參與和感悟的函數(shù)概念教學(xué)[J];數(shù)學(xué)通報(bào);2009年06期

9 徐立英;張麗娜;;APOS理論對(duì)函數(shù)概念教學(xué)的啟示和應(yīng)用[J];高等教育研究(成都);2007年03期

10 李強(qiáng);;高中新教材中函數(shù)概念教學(xué)思考[J];數(shù)學(xué)通報(bào);2007年05期

相關(guān)碩士學(xué)位論文 前10條

1 陳鑫笑;高中函數(shù)學(xué)習(xí)障礙分析及教學(xué)對(duì)策研究[D];洛陽(yáng)師范學(xué)院;2016年

2 周晶;高中生函數(shù)學(xué)習(xí)障礙的探究[D];華中師范大學(xué);2015年

3 周仁哲;高中函數(shù)教學(xué)的調(diào)查研究[D];東北師范大學(xué);2015年

4 高凌宇;基于情境認(rèn)知理論的高中函數(shù)概念教學(xué)研究[D];天津師范大學(xué);2015年

5 劉茂先;高一學(xué)生對(duì)函數(shù)概念理解的調(diào)查研究[D];貴州師范大學(xué);2014年

6 賈艷玲;基于變式練習(xí)的函數(shù)概念的教學(xué)研究與實(shí)踐[D];河北師范大學(xué);2013年

7 劉俠;情境創(chuàng)設(shè)在初高中函數(shù)概念教學(xué)中的應(yīng)用研究[D];陜西師范大學(xué);2013年

8 王艷輝;APOS理論下高中生對(duì)函數(shù)概念理解的差異研究[D];西南大學(xué);2013年

9 李劍;高中與初中數(shù)學(xué)函數(shù)概念教學(xué)的銜接研究[D];重慶師范大學(xué);2012年

10 曹麗娟;基于APOS理論下的高中函數(shù)概念教學(xué)方式探究[D];陜西師范大學(xué);2012年

，

本文編號(hào)：2253934