發(fā)布時(shí)間：2018-07-05 10:03

  本文選題：初中生 + 幾何證明��； 參考：《東北師范大學(xué)》2017年碩士論文

【摘要】：幾何教學(xué)是數(shù)學(xué)教學(xué)中的一個(gè)重要組成部分,幾何內(nèi)容也是初中數(shù)學(xué)課程的主要內(nèi)容之一。幾何課程內(nèi)容的改革,歷來都是國內(nèi)外數(shù)學(xué)教育改革的熱點(diǎn)和焦點(diǎn)問題。當(dāng)前對(duì)幾何證明理解的實(shí)證研究,主要集中在學(xué)生對(duì)所給證明問題的反應(yīng)及學(xué)生依據(jù)教師或他們自己的觀點(diǎn)對(duì)不同證明方法的選擇上,而本文則是通過幾何證明的閱讀理解這一角度來研究此類問題,從中發(fā)現(xiàn)學(xué)生在幾何證明閱讀理解中存在的問題,并提出相應(yīng)的教學(xué)建議。本文利用楊凱琳教授的幾何證明閱讀理解模型,將學(xué)生的幾何證明閱讀理解劃分為四個(gè)水平,即表層理解水平、識(shí)別元素理解水平、串聯(lián)元素理解水平和綜合性理解水平,并根據(jù)各水平的標(biāo)準(zhǔn),編制測試問卷,通過對(duì)初二學(xué)生的調(diào)查問卷結(jié)果統(tǒng)計(jì)及分析,得出如下結(jié)論:1.學(xué)生的幾何證明閱讀理解水平表現(xiàn)出層級(jí)遞減趨勢。2.學(xué)生對(duì)于幾何相關(guān)知識(shí)的理解大多停留在工具性理解,只有少數(shù)學(xué)生對(duì)所學(xué)知識(shí)能達(dá)到關(guān)系性理解。3.學(xué)生在幾何證明閱讀理解中存在的問題主要有以下幾點(diǎn):(1)學(xué)生審題能力有待加強(qiáng),只能知道題目中明確給出的已知條件,而不會(huì)挖掘隱含條件;更換論題,將題目中的已知條件看成特殊條件;還有漏題的情況。(2)在學(xué)習(xí)幾何基本圖形的概念和性質(zhì)時(shí),理解不夠深刻,常停留在表面,對(duì)于一些基本圖形的性質(zhì)掌握不牢,在做題時(shí)不能做到靈活應(yīng)用,遇到基本圖形時(shí),沒有第一時(shí)間在頭腦中反映出其對(duì)應(yīng)的性質(zhì)。(3)在證明過程中犯邏輯關(guān)系錯(cuò)誤。在證明過程中應(yīng)用判定定理時(shí),易忽略其成立的條件;用未證明的論據(jù)來證明論題。(4)書寫證明過程時(shí),不完整,不能夠?qū)⒂嘘P(guān)的推理組合成一個(gè)完整的證明過程。4.針對(duì)研究中發(fā)現(xiàn)的問題,給出教師如下建議:(1)加強(qiáng)幾何基本圖形的教學(xué);(2)加強(qiáng)對(duì)學(xué)生審題、識(shí)圖和作圖能力的培養(yǎng);(3)重視對(duì)學(xué)生邏輯思維能力的培養(yǎng);(4)加強(qiáng)幾何證明過程書寫規(guī)范的教學(xué)。
[Abstract]:Geometry teaching is an important part of mathematics teaching, and geometry content is also one of the main contents of mathematics course in junior high school. The reform of geometry course content has always been the hot spot and focal point of mathematics education reform at home and abroad. The current empirical research on the understanding of geometric proof mainly focuses on the students' response to the problem of proof given and the choice of different methods of proof according to the teachers'or their own views. This paper studies this kind of problems from the angle of reading comprehension of geometric proof, finds out the problems existing in the reading comprehension of geometric proof, and puts forward corresponding teaching suggestions. In this paper, using Professor Yang Kailin's geometric proof reading comprehension model, students' geometric proof reading comprehension is divided into four levels, namely, surface level, recognition level, serial element level and comprehensive level. According to the standards of each level, the questionnaire is compiled. Through the statistics and analysis of the results of the questionnaire, the following conclusions are drawn: 1. Students' geometric proof shows that the level of reading comprehension shows a decreasing trend of hierarchy. 2. Most of the students' understanding of geometric related knowledge lies in the instrumental understanding, and only a few students can reach the relational understanding of what they have learned. The main problems in reading comprehension of students in geometric proof are as follows: (1) the students' ability to examine questions needs to be strengthened, they can only know the known conditions clearly given in the questions, not the hidden conditions, and change the topics. The known conditions in the subject are regarded as special conditions; there are also missing problems. (2) in learning the concepts and properties of basic geometric figures, the understanding is not deep enough and often stays on the surface, and the properties of some basic graphics are not well grasped. It can not be used flexibly when it comes to problems. When it comes to basic graphics, it does not reflect its corresponding properties in the mind at the first time. (3) mistakes in logic relations are made in the process of proof. It is easy to ignore the condition that the judgment theorem is applied in the process of proof, and to prove the thesis with the unproved argument. (4) when writing the proof process, it is not complete and can not combine the relevant reasoning into a complete proof process. In view of the problems found in the study, the following suggestions are given: (1) to strengthen the teaching of basic geometric graphics; (2) to strengthen the examination of students' questions. (3) pay attention to the cultivation of students' logical thinking ability; (4) strengthen the teaching of the writing criterion of geometric proof process.
【學(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：G633.6

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本文編號(hào)：2099844