高中文科生立体几何推理证明能力现状调查及对策研究

发布时间：2018-06-17 23:10

本文选题：文科生 + 立体几何　；参考：《闽南师范大学》2017年硕士论文

【摘要】：立体几何是高中数学必修的课程,学习立体几何可以帮助学生更好地认识世界、发展几何思维,进而培养空间想象能力和逻辑推理能力。空间几何体和点、直线、平面之间的位置关系是高中文科立体几何学习的主要内容。其中考查重点之一是空间直线、平面位置关系特别是线面、面面的平行与垂直关系的判断及证明。由于大部分文科生数学基础较为薄弱,空间想象能力不强,对立体几何存在畏惧心理以及偏记忆不爱动笔的学习特点导致在做立体几何推理证明时束手无策,解答情况不理想。所以本文想通过对立体几何推理证明做进一步的研究来提高文科生推理证明能力和学习效率。本文采用问卷调查、测试卷和访谈的形式对福建省永安市的106名高三文科生进行调查研究,根据Biggs(1982)提出的SOLO分类评价结构对所选测试题制定出相应的SOLO水平分类评价标准,对学生的推理证明进行SOLO水平层次划分,分析结果发现:对于简单的推理证明题近70%的高三文科生推理证明的SOLO水平处于多元结构或关联结构水平;而对于稍复杂点的综合性的推理证明题学生处于关联结构和前结构均为40%左右,两极分化十分严重。分析研究结果得出影响学生推理证明能力的主要因素有:(1)非智力因素(心里惧怕、不刻苦等);(2)基础知识(定义、定理、性质)不熟悉,只是机械记忆;(3)空间想象力不足,识图、想图、画图困难;(4)逻辑推理能力差,证明方法零散;(5)语言表达能力弱,三种语言间转化难。针对以上调查得出的立体几何推理证明SOLO水平以及推理证明能力的影响要素,给出立体几何教学的相关建议:(1)树立学生学好推理证明的信心;(2)加强概念的理解与记忆;(3)加强直观感知,多画图,提高空间想象能力;(4)加强几何推理证明能力的培养。
[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.
【学位授予单位】：闽南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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