本文選題：幾何推理　切入點(diǎn)：代數(shù)推理　出處：《華中師范大學(xué)》2015年碩士論文

【摘要】：數(shù)學(xué)推理教育的本質(zhì)意義,在于培養(yǎng)人良好的數(shù)學(xué)思維習(xí)慣以及極強(qiáng)的反應(yīng)能力。幾何推理與代數(shù)推理貫穿整個(gè)數(shù)學(xué)學(xué)習(xí)過(guò)程,所以說(shuō)培養(yǎng)學(xué)生的幾何推理與代數(shù)推理思維對(duì)其學(xué)好數(shù)學(xué)相當(dāng)重要。學(xué)生的幾何推理與代數(shù)推理能力的培養(yǎng)逐步受到國(guó)內(nèi)外數(shù)學(xué)教育界的關(guān)注,本研究旨在討論我國(guó)各層級(jí)階段幾何推理與代數(shù)推理學(xué)習(xí)能力的表現(xiàn)情形,依據(jù)幾何推理與代數(shù)推理能力發(fā)展的認(rèn)知先后順序,指出了不同年級(jí)階段的推理形式,小學(xué)階段是對(duì)推理的初步認(rèn)知,初中階段幾何推理占主導(dǎo)地位,高中階段幾何推理與代數(shù)推理能力已趨于成熟,此階段著重培養(yǎng)對(duì)幾何推理與代數(shù)推理的靈活運(yùn)用能力,其中數(shù)形結(jié)合是連接這兩種推理的主導(dǎo)思想。本文依據(jù)教材內(nèi)容要求,階段性分析推理的不同學(xué)習(xí)形式,結(jié)合數(shù)學(xué)家們的研究成果,來(lái)區(qū)分幾何推理與代數(shù)推理之間的差異性及聯(lián)系。首先,在對(duì)推理有了初步認(rèn)識(shí)情況下,對(duì)推理能力的地位進(jìn)行分析。了解推理與證明的區(qū)分,讓學(xué)生明白推理與證明之間的關(guān)系,通過(guò)分析教材,結(jié)合教材內(nèi)容,教學(xué)目標(biāo),從宏觀上來(lái)認(rèn)識(shí)幾何推理與代數(shù)推理在數(shù)學(xué)發(fā)展中的先后順序,分析出小學(xué)階段,初中階段,高中階段幾何推理與代數(shù)推理引入及著重引用的推理方式。其次,由于此方面的研究甚少,幾何推理與代數(shù)推理并沒(méi)有嚴(yán)格的概念性語(yǔ)言。筆者通過(guò)文獻(xiàn)分析總結(jié)出幾何推理與代數(shù)推理的概念及其特征,通過(guò)查閱期刊文獻(xiàn)等等,了解到幾何推理與代數(shù)推理的發(fā)展歷程,結(jié)合教學(xué)實(shí)踐了解推理在數(shù)學(xué)各內(nèi)容方面的運(yùn)用及其之間的關(guān)聯(lián)。分析出哪些題目類型適合于幾何推理,哪些類型必須用代數(shù)推理,又有哪些題目幾何與代數(shù)推理結(jié)合起來(lái)更易于題目的解決。再次,指出只要有數(shù)學(xué)存在,就會(huì)有幾何與代數(shù),幾何推理與代數(shù)推理能夠很好的培養(yǎng)數(shù)學(xué)思維,是數(shù)學(xué)發(fā)展的推進(jìn)劑。處理好兩者之間的關(guān)系,能夠幫助學(xué)生更好的學(xué)習(xí)數(shù)學(xué)。本研究獲得的結(jié)論是： (1)促進(jìn)幾何與代數(shù)之間的聯(lián)系,能夠引導(dǎo)學(xué)生對(duì)推理能力進(jìn)行順利地轉(zhuǎn)換； (2)關(guān)注學(xué)生推理能力的發(fā)展,注重推理之間的差異性,具體情況具體分析。為了之后能夠更好的進(jìn)行推理知識(shí)的傳授,推理能力的培養(yǎng),及時(shí)的發(fā)現(xiàn)它們之間更多的聯(lián)系是相當(dāng)有必要的； (3)教師自身的數(shù)學(xué)推理素養(yǎng)首先要得以提升,在對(duì)推理進(jìn)行深刻理解的基礎(chǔ)之上將推理知識(shí)滲透于教學(xué)中,因材施教； (4)要促進(jìn)國(guó)內(nèi)外數(shù)學(xué)知識(shí)之間的及時(shí)交流,教師之間的交流尤為重要,知識(shí)上的溝通融匯,能夠促進(jìn)教師及學(xué)生的專業(yè)性發(fā)展。
[Abstract]:The essential meaning of mathematical reasoning education lies in the cultivation of good mathematical thinking habits and strong reaction ability.Geometric reasoning and algebraic reasoning run through the whole process of mathematics learning, so it is very important to cultivate students' thinking of geometric reasoning and algebraic reasoning for them to learn mathematics well.The cultivation of students' ability of geometric reasoning and algebraic reasoning has been paid more and more attention to in the field of mathematics education at home and abroad. The purpose of this study is to discuss the performance of the learning ability of geometric reasoning and algebraic reasoning at different stages in China.According to the cognitive sequence of the development of geometric reasoning and algebraic reasoning, this paper points out the reasoning forms in different grades. The primary stage is the primary cognition of reasoning, and the junior middle school stage is dominated by geometric reasoning.The ability of geometric reasoning and algebraic reasoning has matured in senior middle school. In this stage, the flexible application of geometric reasoning and algebraic reasoning is emphasized, among which the combination of number and form is the leading idea linking the two reasoning.According to the content requirements of the textbook, this paper analyzes the different learning forms of reasoning by stages, and combines the research results of mathematicians to distinguish the differences and relations between geometric reasoning and algebraic reasoning.First of all, the status of reasoning ability is analyzed with a preliminary understanding of reasoning.The methods of introduction and citation of geometric reasoning and algebraic reasoning in primary, junior and senior middle school are analyzed.Secondly, there is no strict conceptual language for geometric reasoning and algebraic reasoning due to the lack of research in this field.The author summarizes the concepts and characteristics of geometric reasoning and algebraic reasoning through literature analysis, and finds out the development course of geometric reasoning and algebraic reasoning by consulting the periodical literature, etc.Combined with teaching practice to understand the application of reasoning in various aspects of mathematics and the relationship between them.It is found out which problem types are suitable for geometric reasoning, which types must be algebraic reasoning, and which problems can be solved more easily by combining geometry with algebraic reasoning.Thirdly, it is pointed out that as long as mathematics exists, there will be geometry and algebra, geometric reasoning and algebraic reasoning can train mathematical thinking very well and are propellants of mathematics development.Dealing with the relationship between the two can help students learn math better.The conclusions of this study are as follows: 1) promoting the relationship between geometry and algebra, which can guide students to transfer their reasoning ability smoothly; 2) paying attention to the development of students' reasoning ability, paying attention to the difference between reasoning and concrete analysis.In order to teach reasoning knowledge, cultivate reasoning ability, and find more connections between them in time, it is necessary to improve teachers' mathematical reasoning literacy.On the basis of deep understanding of reasoning, the reasoning knowledge is permeated into teaching and teaching in accordance with students' aptitude. (4) to promote the timely exchange of mathematics knowledge at home and abroad, the communication among teachers is particularly important.Can promote the professional development of teachers and students.
【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】：2015
【分類號(hào)】：G633.6

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本文編號(hào)：1691400