立体几何解题中数学思想方法的相关研究

发布时间：2018-10-15 09:53

【摘要】：一直以来,立体几何都被公认为是高中数学的重点内容之一。在我国历次数学课改中,立体几何在内容、体系和结构上都发生了诸多变化,而其在高中数学中的重要地位却自始至终保持不变。主要原因在于立体几何确有与众不同的教育价值和教育意义,对于学生数学能力的培养具有巨大作用。因此,全面掌握并深刻理解立体几何内容是高中阶段数学学习中至关重要的一个环节。而在数学学科中,知识的掌握和理解很大程度上取决于解题的训练。所以,立体几何的学习必然离不开立体几何问题的求解。数学思想方法是数学的精粹,将其运用于立体几何解题之中显然是非常重要的一个思路。在立体几何解题中合理使用数学思想方法可以将问题化繁为简,灵活克服题中的困难与障碍,从而收到事半功倍的成效。可以说,数学思想方法是立体几何解题之智慧源泉。那么,学生是否确有必要在立体几何解题中以数学思想方法为指导?教师是否必需于立体几何教学中进行数学思想方法的渗透?是否可以清晰地认识数学思想方法在立体几何解题中的显著效用,以便学生规范立体几何解题模式,教师优化立体几何教学结构。有鉴于此,本文将聚焦于阐述数学思想方法在立体几何解题中的显著性效果。首先,基于调查设计的逻辑性原则、通俗性原则、明确性原则、以及目的性原则等,设计了一份关于影响高中生立体几何解题效果的相关因素的调查问卷,并以三所学校的高中生为对象发放问卷进行调查。选取有效问卷并建立数据集。其次,完成所获数据的统计分析。利用MATLAB软件对立体几何测评考试成绩进行多元线性回归分析,同时绘制数学思想方法效用性的数据统计图。最后,根据上述统计结果可得,相比于其他立体几何解题影响因子,如知识储备量、解题经验、心理素质水平,数学思想方法是影响立体几何解题效果的最主要因素,而且在提高立体几何解题效率、准确率以及降低题目难度等方面发挥着举足轻重的作用。
[Abstract]:All along, solid geometry has been recognized as one of the key contents of high school mathematics. In the previous mathematics course reform in our country, many changes have taken place in the content, system and structure of solid geometry, but its important position in senior high school mathematics has remained unchanged from beginning to end. The main reason is that solid geometry has different educational value and educational significance, which plays an important role in the cultivation of students' mathematics ability. Therefore, mastering and deeply understanding the content of solid geometry is a crucial link in mathematics learning in senior high school. In mathematics, the mastery and understanding of knowledge depends largely on the training of problem solving. Therefore, the learning of solid geometry must be inseparable from the solution of solid geometry problems. Mathematical thought method is the essence of mathematics, it is obviously a very important train of thought to apply it to solving solid geometry problems. The rational use of mathematical thought method in solving problems in solid geometry can simplify the problems, overcome the difficulties and obstacles in the problems flexibly, and achieve twice the result with half the effort. It can be said that mathematical thinking method is the source of wisdom for solving solid geometry problems. So, is it really necessary for students to be guided by mathematical thinking methods in solving problems in solid geometry? Is it necessary for teachers to infiltrate mathematical ideas and methods in the teaching of solid geometry? Whether we can clearly understand the remarkable effect of mathematical thought method in solving solid geometry problems, so that students can standardize the model of solid geometry problem solving and teachers can optimize the teaching structure of solid geometry. In view of this, this paper will focus on the remarkable effect of mathematical thinking method in solving solid geometry problems. First of all, based on the logical principle, the general principle, the clear principle and the purpose principle of the investigation design, a questionnaire is designed about the factors that affect the effect of the high school students' three-dimensional geometric problem solving. And take three high school students as the object to issue the questionnaire to carry on the investigation. Select valid questionnaire and establish data set. Secondly, complete the statistical analysis of the obtained data. The multivariate linear regression analysis was carried out by using MATLAB software, and the data statistics of the utility of mathematical ideas and methods were plotted at the same time. Finally, according to the above statistical results, compared with other factors, such as knowledge reserve, problem solving experience, psychological quality level and mathematical thinking method, these factors are the most important factors that affect the effect of three-dimensional geometric problem solving. Moreover, it plays an important role in improving the efficiency and accuracy of solid geometry problem solving and reducing the difficulty of the problem.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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