本文關(guān)鍵詞： 問題驅(qū)動(dòng) 復(fù)數(shù)概念 復(fù)數(shù)運(yùn)算 教學(xué)內(nèi)容重構(gòu)　出處：《廣州大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：復(fù)數(shù)不僅在數(shù)學(xué)發(fā)展史上有著重大的歷史意義,而且對科學(xué)的認(rèn)識(shí)論和方法論產(chǎn)生了深遠(yuǎn)的影響,同時(shí)它在現(xiàn)代科技中也有著廣泛的應(yīng)用.在高中數(shù)學(xué)課堂教學(xué)中,復(fù)數(shù)章節(jié)的教學(xué)是“容易教”的難點(diǎn)課.一方面教材內(nèi)容代數(shù)形式化的敘述,使學(xué)生對復(fù)數(shù)概念及其運(yùn)算可以較輕松地獲得機(jī)械的識(shí)記和應(yīng)用,這就是復(fù)數(shù)內(nèi)容表面上相對易教的原因;另一方面,正是教科書以復(fù)數(shù)產(chǎn)生的歷史結(jié)果為出發(fā)點(diǎn),以代數(shù)形式表示復(fù)數(shù)及形式化定義復(fù)數(shù)運(yùn)算,它們掩蓋了復(fù)數(shù)概念及復(fù)數(shù)運(yùn)算產(chǎn)生的本原性問題,不利于復(fù)數(shù)及其運(yùn)算的數(shù)學(xué)本質(zhì)和思想方法的揭示.本研究基于問題驅(qū)動(dòng)的數(shù)學(xué)教學(xué)理念,審視了高中復(fù)數(shù)教學(xué)的基本現(xiàn)狀:首先,剖析了現(xiàn)行中學(xué)數(shù)學(xué)教科書中有關(guān)虛數(shù)引入、數(shù)系擴(kuò)充和復(fù)數(shù)運(yùn)算等知識(shí)點(diǎn)的敘述脈絡(luò),分析了教材編寫中的存在問題;比較了主要發(fā)達(dá)國家及地區(qū)和我國有關(guān)中學(xué)復(fù)數(shù)知識(shí)的教學(xué)要求和教學(xué)內(nèi)容的差異,指出我國高中復(fù)數(shù)教學(xué)要求的差距.其次,為了掌握中學(xué)復(fù)數(shù)教學(xué)的實(shí)際現(xiàn)狀,通過聽課觀摩、教學(xué)研討,對復(fù)數(shù)章節(jié)的教學(xué)進(jìn)行調(diào)查研究,分析和尋找高中復(fù)數(shù)教學(xué)存在的問題及其根源;研究了中學(xué)一線教師有關(guān)復(fù)數(shù)教學(xué)方面的研究文獻(xiàn),考察數(shù)學(xué)教師對復(fù)數(shù)教學(xué)問題的相關(guān)認(rèn)識(shí).論文進(jìn)一步介紹了復(fù)數(shù)產(chǎn)生和發(fā)展的脈絡(luò),闡述推動(dòng)復(fù)數(shù)理論發(fā)展的深刻的物理背景,探討了復(fù)數(shù)及其運(yùn)算的重要思想和方法,并從數(shù)學(xué)思想性角度審視了高中復(fù)數(shù)內(nèi)容的教學(xué)問題,提出高中復(fù)數(shù)教學(xué)內(nèi)容重構(gòu)的建議.最后,本研究在調(diào)查和分析的基礎(chǔ)上,重構(gòu)和編寫了基于問題驅(qū)動(dòng)的高中復(fù)數(shù)教學(xué)內(nèi)容,希望能夠準(zhǔn)確把握復(fù)數(shù)產(chǎn)生與發(fā)展的本原性問題,希望能夠深度挖掘在復(fù)數(shù)認(rèn)識(shí)中起統(tǒng)帥作用的、觸及與揭示復(fù)數(shù)本質(zhì)的問題,并貫穿于問題驅(qū)動(dòng)的復(fù)數(shù)教學(xué)內(nèi)容的設(shè)計(jì)與重構(gòu).重構(gòu)方案進(jìn)行了教學(xué)試驗(yàn)和評價(jià).新教學(xué)內(nèi)容摒棄了代數(shù)視角,確立了幾何與物理視角介紹復(fù)數(shù),它能夠很好地回答:為什么要提出和引入虛數(shù)概念?如何適當(dāng)?shù)囟x復(fù)數(shù)概念和復(fù)數(shù)運(yùn)算?這些概念和運(yùn)算給我們帶來了什么?復(fù)數(shù)的重大意義和科學(xué)價(jià)值體現(xiàn)在哪里?
[Abstract]:Plural is not only of great historical significance in the history of mathematics development, but also has a profound influence on the epistemology and methodology of science. At the same time, it is also widely used in modern science and technology. In the teaching of mathematics in senior high school, the teaching of plural chapters is a difficult course which is easy to teach. On the one hand, the formal description of the content algebra of the teaching material. It is easy for students to obtain mechanical memorization and application of complex number concept and its operation, which is the reason why the complex number content is relatively easy to teach on the surface; On the other hand, the textbook takes the historical result of the complex number as the starting point, expresses the complex number and formally defines the complex number operation in the algebraic form, which cover up the original problem of the complex number concept and complex number operation. This research is based on the problem-driven mathematics teaching concept, examines the basic situation of the complex number teaching in senior high school: first of all. This paper analyzes the narrative context of the knowledge points in the current middle school mathematics textbooks, such as the introduction of imaginary numbers, the expansion of the number system and the complex number operation, and analyzes the problems existing in the compilation of the textbooks. This paper compares the differences of teaching requirements and contents of plural knowledge in middle schools between the main developed countries and regions and our country, and points out the differences in the requirements of plural teaching in senior high schools in our country. In order to grasp the actual situation of plural teaching in middle schools, through the observation of lectures, teaching discussion, the teaching of plural chapters of the investigation and research, analysis and search for the problems and root causes of plural teaching in senior high school; This paper studies the literature on the plural teaching of the first-line teachers in middle schools, and investigates the mathematics teachers' understanding of the plural teaching. The paper further introduces the context of the emergence and development of the plural. This paper expounds the profound physical background of promoting the development of plural theory, probes into the important ideas and methods of plural number and its operation, and examines the teaching problems of plural content in senior high school from the angle of mathematical thought. Finally, on the basis of investigation and analysis, this study reconstructs and compiles the plural teaching content based on problem driven. Hope to accurately grasp the origin of the emergence and development of the plural, hope to be able to dig in depth in the plural understanding of the role, touch and reveal the essence of plural problems. And the design and reconstruction of the complex teaching content which is driven by the problem. The reconstruction scheme has carried on the teaching experiment and the appraisal. The new teaching content has abandoned the algebra angle, established the geometry and the physics angle to introduce the complex number. It can answer well: why put forward and introduce the concept of imaginary number? How to define plural concepts and complex operations properly? What do these concepts and operations bring us? Where is the significance and scientific value of the plural?
【學(xué)位授予單位】：廣州大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：G633.6

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