發(fā)布時(shí)間：2018-05-19 02:11

  本文選題：代數(shù)思維 + 水平　； 參考：《華中師范大學(xué)》2017年碩士論文

【摘要】：古老傳統(tǒng)的數(shù)學(xué)發(fā)展至今,代數(shù)仍然是至關(guān)重要的一部分.隨著計(jì)算機(jī)等科學(xué)技術(shù)的普及,代數(shù)在各行各業(yè)發(fā)展中有著不可或缺的基礎(chǔ)作用.思維的發(fā)展能夠更好地培養(yǎng)人對(duì)事物本質(zhì)的認(rèn)識(shí),而小學(xué)生正處于思維高速發(fā)展的時(shí)期,本文測(cè)試分析高年級(jí)小學(xué)生代數(shù)思維發(fā)展情況,旨在為代數(shù)思維的培養(yǎng)方向提供可行的數(shù)據(jù)支持.本研究分為六章:第一章引言,從代數(shù)的重要性方面來(lái)論述研究的背景、主要內(nèi)容和方法.第二章研究綜述,整理現(xiàn)有文獻(xiàn)對(duì)代數(shù)思維的研究主要有三個(gè)方面:對(duì)代數(shù)思維核心概念的研究;對(duì)算術(shù)思維與代數(shù)思維的過(guò)渡研究;對(duì)代數(shù)思維培養(yǎng)的研究.在認(rèn)識(shí)前人對(duì)代數(shù)思維的理解和研究成果的基礎(chǔ)上對(duì)與代數(shù)思維相關(guān)的早期代數(shù)進(jìn)行評(píng)述概括,分析出代數(shù)思維的核心特點(diǎn).第三章測(cè)試量表的選取與優(yōu)化,結(jié)合第二章的文獻(xiàn)綜述選取符合本文研究目的的代數(shù)思維結(jié)構(gòu)模型,對(duì)模型進(jìn)行改進(jìn)使其更加合理,并對(duì)每個(gè)指標(biāo)進(jìn)行高低分層,形成測(cè)試高年級(jí)小學(xué)生代數(shù)思維的量表.第四章測(cè)試方案設(shè)計(jì)與實(shí)施,根據(jù)第三章的測(cè)試量表初步設(shè)計(jì)測(cè)試卷,再試測(cè)對(duì)測(cè)試卷進(jìn)行微調(diào),形成正式的測(cè)試卷,最后選擇合適對(duì)象進(jìn)行測(cè)試.第五章測(cè)試結(jié)果與分析,利用統(tǒng)計(jì)軟件先對(duì)測(cè)試卷的信度和結(jié)構(gòu)效度進(jìn)行分析,得知測(cè)試卷比較可靠.再對(duì)代數(shù)思維整體水平、各因子各指標(biāo)的發(fā)展水平、相關(guān)性、差異性進(jìn)行分析,得到主要結(jié)果有:(1)高年級(jí)小學(xué)生已經(jīng)萌發(fā)了代數(shù)思維.規(guī)律、表征、方程、函數(shù)思維基本達(dá)到低層次水平;表征、算律、方程、函數(shù)思維的高低水平得分有顯著的差距,存在較大的上升空間;算律和逆算思維處在較低的水平,還需要加強(qiáng).(2)代數(shù)思維發(fā)展水平受年級(jí)因素的顯著影響,隨著年級(jí)的上升代數(shù)思維發(fā)展水平逐漸提高;與性別、年齡無(wú)顯著差異.(3)代數(shù)思維發(fā)展與數(shù)學(xué)成績(jī)有顯著的正相關(guān)關(guān)系,三個(gè)因子有較弱的正相關(guān)關(guān)系,每個(gè)因子下屬兩個(gè)指標(biāo)之間中度相關(guān).第六章結(jié)論與展望,敘述研究的主要成果、存在的問(wèn)題和進(jìn)一步的研究方向.
[Abstract]:Algebra is still a vital part of the development of ancient mathematics. With the popularization of computer science and technology, algebra plays an indispensable role in the development of various industries. The development of thinking can better train people to understand the essence of things, while the pupils are in the period of rapid development of thinking. This paper tests and analyzes the development of algebraic thinking of senior primary school students. The aim is to provide feasible data support for the cultivation of algebraic thinking. This research is divided into six chapters: the first chapter introduces the background, main contents and methods of the research from the importance of algebra. In the second chapter, there are three main aspects: the research on the core concepts of algebraic thinking; the transition between arithmetic thinking and algebraic thinking; and the research on the cultivation of algebraic thinking. On the basis of understanding the previous understanding and research achievements of algebraic thinking, the early algebraic thinking related to algebraic thinking is reviewed and summarized, and the core characteristics of algebraic thinking are analyzed. The selection and optimization of the third chapter test scale, combined with the literature review of the second chapter, select the algebraic thinking structure model which is in line with the purpose of this paper, improve the model to make it more reasonable, and layer each index. To form a scale to test the algebraic thinking of senior pupils. The fourth chapter is the design and implementation of the test scheme. According to the preliminary design of the third chapter of the test scale, the test volume is fine-tuned to form a formal test volume. Finally, the appropriate subjects are selected to test. In the fifth chapter, the reliability and structural validity of the test volume are analyzed by statistical software, and the results show that the test volume is reliable. Then it analyzes the whole level of algebraic thinking, the development level, correlation and difference of each index, and obtains the main result: 1) Algebraic thinking has been germinated in the senior primary school students. The law, representation, equation, function thought basically reached the low level; the representation, the calculation law, the equation, the function thought level score has the remarkable disparity, has the big rise space, the arithmetic law and the inverse calculation thought are in the lower level, It is also necessary to strengthen the development level of algebraic thinking. The development level of algebraic thinking is significantly affected by the factors of grade, and the level of development of algebraic thinking increases gradually with the increase of grade. There was no significant difference in age. (3) there was a significant positive correlation between the development of algebraic thinking and mathematical achievement, and there was a weak positive correlation among the three factors, and there was a moderate correlation between two indexes under each factor. In chapter 6, the conclusion and prospect, the main achievements, the existing problems and the further research direction are described.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：G623.5

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