本文選題：文科生 + 立體幾何　； 參考：《閩南師范大學(xué)》2017年碩士論文

【摘要】：立體幾何是高中數(shù)學(xué)必修的課程,學(xué)習(xí)立體幾何可以幫助學(xué)生更好地認(rèn)識世界、發(fā)展幾何思維,進(jìn)而培養(yǎng)空間想象能力和邏輯推理能力。空間幾何體和點(diǎn)、直線、平面之間的位置關(guān)系是高中文科立體幾何學(xué)習(xí)的主要內(nèi)容。其中考查重點(diǎn)之一是空間直線、平面位置關(guān)系特別是線面、面面的平行與垂直關(guān)系的判斷及證明。由于大部分文科生數(shù)學(xué)基礎(chǔ)較為薄弱,空間想象能力不強(qiáng),對立體幾何存在畏懼心理以及偏記憶不愛動筆的學(xué)習(xí)特點(diǎn)導(dǎo)致在做立體幾何推理證明時束手無策,解答情況不理想。所以本文想通過對立體幾何推理證明做進(jìn)一步的研究來提高文科生推理證明能力和學(xué)習(xí)效率。本文采用問卷調(diào)查、測試卷和訪談的形式對福建省永安市的106名高三文科生進(jìn)行調(diào)查研究,根據(jù)Biggs(1982)提出的SOLO分類評價結(jié)構(gòu)對所選測試題制定出相應(yīng)的SOLO水平分類評價標(biāo)準(zhǔn),對學(xué)生的推理證明進(jìn)行SOLO水平層次劃分,分析結(jié)果發(fā)現(xiàn):對于簡單的推理證明題近70%的高三文科生推理證明的SOLO水平處于多元結(jié)構(gòu)或關(guān)聯(lián)結(jié)構(gòu)水平;而對于稍復(fù)雜點(diǎn)的綜合性的推理證明題學(xué)生處于關(guān)聯(lián)結(jié)構(gòu)和前結(jié)構(gòu)均為40%左右,兩極分化十分嚴(yán)重。分析研究結(jié)果得出影響學(xué)生推理證明能力的主要因素有:(1)非智力因素(心里懼怕、不刻苦等);(2)基礎(chǔ)知識(定義、定理、性質(zhì))不熟悉,只是機(jī)械記憶;(3)空間想象力不足,識圖、想圖、畫圖困難;(4)邏輯推理能力差,證明方法零散;(5)語言表達(dá)能力弱,三種語言間轉(zhuǎn)化難。針對以上調(diào)查得出的立體幾何推理證明SOLO水平以及推理證明能力的影響要素,給出立體幾何教學(xué)的相關(guān)建議:(1)樹立學(xué)生學(xué)好推理證明的信心;(2)加強(qiáng)概念的理解與記憶;(3)加強(qiáng)直觀感知,多畫圖,提高空間想象能力;(4)加強(qiáng)幾何推理證明能力的培養(yǎng)。
[Abstract]:Solid geometry is a compulsory course in high school mathematics. Learning solid geometry can help students understand the world better, develop geometric thinking, and then cultivate the ability of spatial imagination and logical reasoning. The spatial geometry, point, line and plane are the main contents of the high school liberal arts solid geometry learning. One of the key points is the judgment and proof of the parallel and vertical relationship between space line, plane position, especially line and surface. Because the mathematics foundation of most arts students is relatively weak, the ability of space imagination is not strong, the learning characteristics of fear to solid geometry and partial memory do not like to start writing lead to be unable to do the proof of solid geometry reasoning, and the solution is not ideal. Therefore, this paper aims to improve the reasoning proof ability and learning efficiency of arts students through further research on solid geometric reasoning proof. In this paper, 106 senior high school students in Yongan City, Fujian Province were investigated by questionnaire, test paper and interview. According to the classification and evaluation structure of Solo proposed by Biggsfen (1982), the corresponding SOLO level classification and evaluation criteria were worked out for the selected test questions. According to the level of SOLO, the results show that the level of Solo for the simple reasoning proof is at the level of multiple structure or correlation structure for 70% of the senior high school students; The comprehensive reasoning of the more complex points proves that the students are about 40% in the relation structure and the front structure, and the polarization is very serious. The results show that the main factors influencing students' reasoning and proof ability are: 1) Non-intelligence factors (fear in mind, not hard working, etc.) basic knowledge (definition, theorem, nature) is not familiar, but mechanical memory is 3%) space imagination is insufficient, map recognition, etc. (4) the ability of logical reasoning is poor, and the ability of language expression is weak, and the transformation of the three languages is difficult. According to the results of the above investigation, the level of Solo and the factors influencing the ability of reasoning proof are proved by solid geometric reasoning. This paper gives some suggestions on the teaching of solid geometry: 1) establishing the confidence of students to learn reasoning and proving well) strengthening the understanding and memory of concepts, strengthening intuitionistic perception, drawing more pictures, and improving the ability of spatial imagination. 4) strengthening the cultivation of the ability of geometric reasoning proof.
【學(xué)位授予單位】：閩南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：G633.6

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