高考中立体几何解答题的研究与思考

发布时间：2018-05-08 06:57

本文选题：立体几何 + 高考试题　；参考：《河北师范大学》2017年硕士论文

【摘要】：立体几何是高中数学知识中的重要内容之一。《普通高中数学新课程标准(实验)》中规定:学生们要用努力、积极以及敢于探索新知识的学习方法,来使自身的数学能力得到提高。在这样大的前提下,立体几何这一部分知识作为培养学生识图、画图的能力,灵活的空间想象能力,缜密的逻辑推理能力和学习类比归纳思想的载体显得十分重要。而在数学平时的学习中,除了可以不断丰富自己的认知结构以及加强数学核心素养以外,数学高考也是其中重要的一部分,高考可以直接反映数学学科课程设计和数学学科课程内容的新思想、新理念,同时高考也是评判学生是否获取数学知识甚至获取多少知识的来源。在高考中,数学的试题难易程度以及试题的质量会直接影响数学整体课程的难易程度和水平。所以说,高考就是影响今后数学教育教学趋势的一个重要因素。并且从数学高考的试卷结构上看,高考数学(新课标全国卷)立体几何试题有三种题型:解答、填空以及选择,而且高中立体几何解答题出现的规律为每年一道题,并且每年立体几何的解答题都是分为两小问,共12分。所以高考中立体几何的解答题占得比重比较大。然而,大多数的学生们在空间立体几何这部分知识的学习中感觉比较难,在空间想象、运算、逻辑推理等方面容易出现比较多的问题,尤其是在处理高考数学立体几何解答题中更加感到困难重重,分数明显偏低。因此,有必要结合历年(2007-2016)高考立体几何解答题从教学方面展开思考与研究。该论文第一部分简述了高中立体几何板块知识在数学学科中的重要性以及重要地位;第二部分本人查阅了有关于立体几何的文献资料,认真分析并研究立体几何解答题的现状,接下来笔者确定了该论文研究的一些问题以及本论文中的研究方向;第三部分是对石家庄市某重点高中高三理科学生关于立体几何知识体系的学习情况以问卷的形式进行调查,并对所调查的结果使用频率统计法,从中来了解学生在立体几何学习方面和教师在教育教学方面存在的问题,并对这些问题笔者做了相应的总结;第四部分根据所做调查问卷的结果,笔者对近十年(2007-2016)新课标数学全国卷(理科)中的立体几何解答题进行详细的统计分析,并且分析了在高考中立体几何解答题的常用知识与常用方法,之后探讨了一下新课标全国卷(理科)高考中的立体几何解答题在以后的命题趋势;然后根据以上的分析为一线教师在以后的教育教学工作中提出相关的一些教学建议。综合以上的研究结果,提出如下教学策略:(1)加深概念和命题的理解,训练严密推理能力;(2)重视通法的讲解与练习,掌握做题方法本质;(3)提升学生转化解题思路,揭示知识内在联系;(4)合理运用空间向量方法,建立坐标系是关键;(5)培养学生缜密逻辑思维,训练学生解题能力;(6)提高学生数学核心素养,更好提升创新意识。最后是笔者对本论文的一些总结和反思,总结出本论文主要研究的内容、对本论文在研究过程中不足的地方以及笔者在以后的一些展望。笔者希望这次的研究能够为一线教师在今后的教育教学实践提供一些可靠有益的参考。
[Abstract]:Stereoscopic geometry is one of the important contents of high school mathematics. "New high school mathematics new curriculum standard (Experiment)" stipulates that students should use efforts, actively and dare to explore new knowledge of learning methods, to improve their own mathematical ability. Under such a premise, the three-dimensional geometry of this part of the knowledge as the training of students' knowledge. The ability of drawing, the ability of flexible space imagination, the ability of logical reasoning and the carrier of learning analogy are very important. Besides, in the study of mathematics, in addition to enriching his own cognitive structure and strengthening the core accomplishment of mathematics, the college entrance examination is an important part of the college entrance examination. The new idea and new idea are directly reflected in the course design of mathematics subject and the course content of mathematics subject. At the same time, the college entrance examination is also the source of judging whether the students get the knowledge of mathematics or even how much knowledge. In the college entrance examination, the difficulty and the quality of the test questions will directly influence the difficulty and the level of the whole course of mathematics. It is said that the college entrance examination is an important factor affecting the trend of the teaching of mathematics in the future. And from the examination paper structure of the college entrance examination, there are three kinds of questions: the answer, the fill and the choice, and the rules of the high school geometry answer questions are one problem each year, and each year is stereoscopic. All the answers are divided into two questions, a total of 12 points. So the answer questions of the stereoscopic geometry are relatively large in the college entrance examination. However, most of the students are more difficult to learn in the knowledge of spatial geometry, and there are many problems in the space imagination, operation, logic reasoning and so on, especially in the process of dealing with the college entrance examination. There are many difficulties in the mathematical three-dimensional geometric solutions, and the scores are obviously low. Therefore, it is necessary to think and study the teaching aspects of the three dimensional geometric solutions of the college entrance examination (2007-2016). The first part of the paper briefly describes the importance and important position of the high school stereoscopic geometry plate knowledge in mathematics, and the second part of this paper. I have consulted the literature of stereoscopic geometry, carefully analyzed and studied the status of three-dimensional geometric solutions, and then I determined some problems in the study and the research direction in this thesis. The third part is the study of the three science students in a key senior high school in Shijiazhuang on the knowledge system of stereoscopic geometry. The survey was conducted in the form of a questionnaire, and the frequency statistics were used to investigate the students' problems in three-dimensional geometry learning and teachers' education and teaching, and the author made a corresponding summary of these problems. The fourth part, according to the results of the questionnaire, was new to the last ten years (2007-2016). The three-dimensional geometric solution questions in the national volume (Science) are analyzed in detail, and the common knowledge and common methods in the stereoscopic geometry answer questions in the college entrance examination are analyzed. Then the proposition trend of the three-dimensional geometric solutions in the national college entrance examination of the new curriculum standard is discussed, and then the analysis is based on the above analysis. First line teachers put forward some relevant teaching suggestions in the future education and teaching work. Combining the results of the above research, the following teaching strategies are put forward: (1) to deepen the understanding of concepts and propositions, to train strict reasoning ability; (2) to pay attention to the explanation and practice of the general law and to master the essence of the method of making a problem; (3) to improve the idea of solving the problem and to reveal the knowledge in the knowledge. In connection with; (4) the key to the rational use of space vector method, the establishment of coordinate system is the key; (5) cultivating students' careful logical thinking, training students' ability to solve problems; (6) improving students' mathematical core literacy and improving the awareness of innovation. Finally, the author summarizes and reflects on this paper, summarizes the main research content of this thesis, and studies the thesis in the research The author hopes that this study will provide some reliable and useful reference for the teaching and teaching practice of the front line teachers in the future.

【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

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