本文選題：數(shù)學(xué)建模思想 + 函數(shù)教學(xué)　； 參考：《陜西師范大學(xué)》2015年碩士論文

【摘要】：本文通過理論和實(shí)踐兩方面的共同研究,采用文獻(xiàn)綜述的方法了解了數(shù)學(xué)建模在國(guó)內(nèi)以及國(guó)外的發(fā)展概況,進(jìn)而探討了將數(shù)學(xué)建模思想融入函數(shù)教學(xué)的作用、步驟及方法。數(shù)學(xué)建模在學(xué)生學(xué)習(xí)數(shù)學(xué)的興趣、數(shù)學(xué)的學(xué)習(xí)方法、數(shù)學(xué)解題思想以及綜合實(shí)踐能力等方面發(fā)揮了巨大作用。同時(shí)又對(duì)影響中學(xué)數(shù)學(xué)建模開展的各種因素進(jìn)行了分析,了解到在中學(xué)中阻礙數(shù)學(xué)建模發(fā)展的主要因素大致來源于四個(gè)方面：教師、學(xué)生、家長(zhǎng)、社會(huì)。在研究方式上本人采取了問卷調(diào)查、訪談及實(shí)驗(yàn)驗(yàn)證等措施,主要針對(duì)學(xué)生學(xué)習(xí)數(shù)學(xué)的興趣、數(shù)學(xué)學(xué)業(yè)成績(jī)、數(shù)學(xué)學(xué)習(xí)能力展開調(diào)查。調(diào)查結(jié)果與本人所設(shè)想的基本上一致,總體來看,學(xué)生對(duì)數(shù)學(xué)建模還是很感興趣的,而數(shù)學(xué)建模對(duì)學(xué)生的學(xué)業(yè)成績(jī)也有所幫助,不僅如此,在數(shù)學(xué)學(xué)習(xí)能力方面學(xué)生也有了明顯的提高。以此為基礎(chǔ),本文特別之處在于結(jié)合教材開發(fā)案例,本人特采取改編課本上原有例題和習(xí)題的方式作為數(shù)學(xué)建模的案例給學(xué)生講解,一方面使學(xué)生比較容易接受,另一方面也使學(xué)生親身感受到數(shù)學(xué)建模與實(shí)際生活的聯(lián)系,使他們切身感受到數(shù)學(xué)建模的神奇之處,進(jìn)而感受到數(shù)學(xué)的美。在融入方式上本人提出了“分步切入”思想,即縱向思維上分為三步,主要以年級(jí)作為區(qū)分標(biāo)準(zhǔn),而橫向思維上采取漸進(jìn)式切入的方式,以學(xué)生的數(shù)學(xué)思維程度來劃分,這個(gè)需要教師來把握。除此之外本文還討論了有關(guān)開發(fā)數(shù)學(xué)建模第二課堂的觀點(diǎn)。這一內(nèi)容主要在高二和高三來進(jìn)行,利用學(xué)生寒暑假的時(shí)間,通過學(xué)生自由組隊(duì)的方式開展數(shù)學(xué)建模課外活動(dòng),題目由老師提供或者學(xué)生自擬。總之,一切論證都說明了在中學(xué)開展數(shù)學(xué)建模教學(xué)是必要的,更是可行的。而中學(xué)內(nèi)容錯(cuò)綜復(fù)雜,所以本人特選取函數(shù)作為研究?jī)?nèi)容,加之?dāng)?shù)學(xué)建模所含內(nèi)容也是一個(gè)龐大的體系,本文以其思想的融入為主,大大簡(jiǎn)化了這一過程,僅僅探究了數(shù)學(xué)建模思想在函數(shù)教學(xué)當(dāng)中的融入,希望對(duì)數(shù)學(xué)建模融入中學(xué)教學(xué)提供少許推動(dòng)力,使更多的人認(rèn)識(shí)到數(shù)學(xué)建模,體會(huì)到數(shù)學(xué)建模的優(yōu)勢(shì),進(jìn)而主動(dòng)學(xué)習(xí)它,這樣數(shù)學(xué)建模才能真正進(jìn)軍中學(xué)并占有一席之地。雖然對(duì)于融入方式已有一些人提出了很多,但本人認(rèn)為最行之有效的方式就是寓數(shù)學(xué)建模思想于函數(shù)教學(xué)之中。
[Abstract]:Through the research of theory and practice, this paper uses the method of literature review to understand the development of mathematical modeling both at home and abroad, and then discusses the function, steps and methods of integrating mathematical modeling ideas into function teaching. Mathematical modeling plays an important role in students' interest in learning mathematics, mathematical learning methods, mathematical problem solving ideas and comprehensive practical ability. At the same time, it analyzes the factors that affect the development of mathematical modeling in middle schools, and finds out that the main factors that hinder the development of mathematical modeling in middle schools come from four aspects: teachers, students, parents, and society. In the way of research, I have taken measures such as questionnaire, interview and experimental verification, mainly aimed at students' interest in learning mathematics, mathematics academic achievement and mathematics learning ability. The results of the survey are basically consistent with what I have imagined. In general, students are very interested in mathematical modeling, and mathematical modeling is also helpful to students' academic performance, not only that. In mathematics study ability aspect student also has the obvious enhancement. On the basis of this, the special point of this paper is that combining with the case of textbook development, I take the way of adapting the original examples and exercises from the textbook to explain to the students as a case of mathematical modeling. On the one hand, I make it easier for the students to accept it. On the other hand, it also makes students feel the relationship between mathematical modeling and real life, makes them feel the magic of mathematical modeling, and then feel the beauty of mathematics. In the way of integration, I put forward the idea of "step by step", that is, the longitudinal thinking is divided into three steps, which mainly takes grade as the criterion of differentiation, while the horizontal thinking adopts a progressive approach, which is divided by the degree of students' mathematical thinking. This needs to be grasped by the teacher. In addition, this paper also discusses the development of mathematical modeling the second classroom views. This content is mainly carried out in the second and third year of senior high school. Using the time of the students' summer and winter, the extracurricular activities of mathematical modeling are carried out through the way of the students forming teams freely. The subjects are provided by the teachers or written by the students themselves. In a word, all the argumentation shows that it is necessary and feasible to carry out mathematical modeling teaching in middle school. And the content of middle school is complicated, so I select function as the research content, and the content of mathematical modeling is also a huge system, this paper, mainly with the integration of its ideas, greatly simplifies this process. It only explores the integration of mathematical modeling idea in function teaching, hoping to provide a little impetus for mathematics modeling to be integrated into middle school teaching, so that more people can realize mathematical modeling, understand the advantages of mathematical modeling, and learn it actively. In this way, mathematical modeling can really enter the middle school and have a place. Although some people have put forward many methods of integration, I think the most effective way is to incorporate mathematical modeling ideas into function teaching.
【學(xué)位授予單位】：陜西師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：G633.6

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本文編號(hào)：2055455