本文選題：歷史發(fā)生原理 + 三角函數(shù)��； 參考：《新疆師范大學(xué)》2015年碩士論文

【摘要】：隨著新課程改革的深入推進(jìn),新課程改革也開(kāi)始從理念上進(jìn)行突破,將學(xué)生的被動(dòng)學(xué)習(xí)向主動(dòng)學(xué)習(xí)轉(zhuǎn)變作為新課程改革的一個(gè)重要目標(biāo)。新課程中,三角函數(shù)的學(xué)習(xí)有利于提高學(xué)生的思維能力,培養(yǎng)學(xué)生的分析問(wèn)題和解決問(wèn)題的能力,使學(xué)生感受數(shù)學(xué)建模的思想。但是本人在實(shí)際的三角函數(shù)教學(xué)中發(fā)現(xiàn),教師的教存在著許多困難,同時(shí)學(xué)生學(xué)習(xí)時(shí)也常感到困惑。主要由于在初中階段的三角比是以角度為自變量,但是到了高中三角函數(shù)的角是用任意實(shí)數(shù)表示;其次,三角函數(shù)是學(xué)生在高中階段唯一進(jìn)行全面研究的周期函數(shù),這對(duì)于學(xué)生而言是一個(gè)難點(diǎn);第三,學(xué)生在學(xué)習(xí)三角函數(shù)的時(shí)候,需要熟練掌握和運(yùn)用大量的公式;第四,高中階段,函數(shù)的概念開(kāi)始逐漸地向集合與集合間的“對(duì)應(yīng)說(shuō)”過(guò)渡,面對(duì)如此多的抽象概念復(fù)合在一起,能夠讓學(xué)生真正地理解和消化掉這些內(nèi)容是有一定難度的。因此,為了解決三角函數(shù)教與學(xué)中的一些困難,對(duì)基于歷史發(fā)生原理的三角函數(shù)教學(xué)展開(kāi)研究。首先對(duì)歷史發(fā)生原理的文獻(xiàn)資料和三角函數(shù)教與學(xué)的已有研究做了一定的研究和分析,在此基礎(chǔ)上,對(duì)三角函數(shù)的歷史發(fā)展過(guò)程進(jìn)行了較為詳盡的梳理,并收集總結(jié)了歷史中出現(xiàn)過(guò)的一些不同的兩角三角函數(shù)關(guān)系的推導(dǎo)方法。其次是結(jié)合高中數(shù)學(xué)教材中三角函數(shù)的教與學(xué)的現(xiàn)狀情況,以兩角和與差的正弦公式作為教學(xué)設(shè)計(jì)的切入點(diǎn),對(duì)兩角的三角函數(shù)關(guān)系的推導(dǎo)進(jìn)行了歷史重構(gòu),從而設(shè)計(jì)出基于歷史發(fā)生原理的兩角和(差)公式的教學(xué)。并根據(jù)課堂實(shí)踐法將教學(xué)設(shè)計(jì)付諸實(shí)踐,然后與接受依據(jù)教材設(shè)計(jì)的教學(xué)方案的班級(jí)進(jìn)行測(cè)驗(yàn)比較,并對(duì)教師進(jìn)行問(wèn)卷調(diào)查和訪談,最后對(duì)得到的結(jié)果進(jìn)行分析,對(duì)之前的教學(xué)設(shè)計(jì)進(jìn)行了修改和完善。通過(guò)對(duì)學(xué)生測(cè)驗(yàn)結(jié)果的比較分析,得到了基于歷史發(fā)生原理的教學(xué)設(shè)計(jì)較基于教材的教學(xué)設(shè)計(jì)在解決學(xué)生的學(xué)習(xí)困難上更為有效,使學(xué)生可以經(jīng)歷知識(shí)的發(fā)生發(fā)展過(guò)程,提高了學(xué)生的學(xué)習(xí)興趣,促進(jìn)了學(xué)生對(duì)知識(shí)的掌握和理解。對(duì)教師進(jìn)行問(wèn)卷調(diào)查和訪談中發(fā)現(xiàn),教師傾向于使用基于歷史發(fā)生原理的兩角和(差)公式的教學(xué)設(shè)計(jì)。最后,結(jié)合訪談的一些結(jié)果對(duì)研究的過(guò)程進(jìn)行反思,探究了歷史發(fā)生原理應(yīng)用于中學(xué)數(shù)學(xué)教學(xué)存在的困難,并根據(jù)已有的教學(xué)工作經(jīng)驗(yàn)提出一些解決策略,以促進(jìn)歷史發(fā)生原理在中學(xué)數(shù)學(xué)教學(xué)中能夠有更為廣泛地應(yīng)用。
[Abstract]:With the deepening of the new curriculum reform, the new curriculum reform has begun to break through from the concept of passive learning to active learning as an important goal of the new curriculum reform. In the new curriculum, the study of trigonometric function is helpful to improve students' thinking ability, to cultivate their ability to analyze and solve problems, and to make students feel the idea of mathematical modeling. However, in the teaching of trigonometric functions, I find that there are many difficulties in the teaching of teachers, and students often feel confused when they study. The main reason is that the trigonometric ratio in junior middle school is dependent on angle, but the angle of trigonometric function in senior high school is expressed as arbitrary real number. Secondly, trigonometric function is the only periodic function that students study comprehensively in senior high school. This is a difficult point for students; third, students need to master and use a large number of formulas skillfully in learning trigonometric functions; and fourth, in high school, The concept of function begins to transition gradually to the "correspondence" between the set and the set. It is difficult for students to truly understand and digest these contents when they are combined with so many abstract concepts. Therefore, in order to solve some difficulties in the teaching and learning of trigonometric functions, the teaching of trigonometric functions based on the principle of historical occurrence is studied. First of all, it makes a certain research and analysis on the literature of historical occurrence principle and the existing research on trigonometric function teaching and learning. On this basis, the historical development process of trigonometric function is sorted out in detail. The derivation methods of some different trigonometric function relations in history are also collected and summarized. Secondly, according to the current situation of trigonometric function teaching and learning in senior high school mathematics teaching materials, this paper takes the sinusoidal formula of two-angle sum and difference as the starting point of teaching design, and reconstructs the derivation of trigonometric function relationship between two angles. Thus, the teaching of biangular and (differential) formula based on the principle of historical occurrence is designed. According to the classroom practice method, the teaching design is put into practice, and then compared with the class which accepts the teaching plan according to the teaching material design, and the teachers are surveyed and interviewed, and the results obtained are analyzed. The former teaching design has been modified and perfected. Through the comparative analysis of the students' test results, it is concluded that the teaching design based on the principle of historical occurrence is more effective in solving the students' learning difficulties than the teaching design based on the textbook, so that the students can experience the process of the development of knowledge. Improve the students' interest in learning, and promote the students to master and understand knowledge. Through the questionnaire survey and interview, it is found that teachers tend to use the two-angle (poor) formula based on the principle of historical occurrence in the teaching design. Finally, based on the results of the interview, this paper reflects on the process of the research, explores the difficulties of applying the principle of historical occurrence to mathematics teaching in middle schools, and puts forward some solving strategies according to the existing teaching experience. In order to promote the principle of historical occurrence in middle school mathematics teaching can be applied more widely.
【學(xué)位授予單位】：新疆師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：G633.6

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 任明俊;汪曉勤;;中學(xué)生對(duì)函數(shù)概念的理解——?dú)v史相似性初探[J];數(shù)學(xué)教育學(xué)報(bào);2007年04期

2 陳婷;詹紫浪;;托勒密定理的向量證明[J];數(shù)學(xué)教學(xué)研究;2009年11期

相關(guān)碩士學(xué)位論文 前1條

1 蘇醒;基于歷史發(fā)生原理的新課程高中概率教學(xué)研究[D];浙江師范大學(xué);2008年

，

本文編號(hào)：2039661