从数学建模视角对高考数学试卷中应用题的分析及建议

发布时间：2018-05-31 22:35

本文选题：数学建模 + 高考数学试卷　；参考：《西北大学》2016年硕士论文

【摘要】：近些年,高考制度不断变革,数学教育逐渐重视学生数学应用能力的培养,高考中加强了对应用题的考查力度。在实际问题背景下,利用数学建模思想处理数学问题,依此考查学生的数学应用意识以及实践创新能力成为新课程改革后最大的亮点。首先,作者通过查阅国内外书籍和相关文献,主要从高中数学新课程标准和高考数学大纲、高中师生对数学建模知识教学的情况、近十五年高考数学试卷中应用题三个角度分析并总结我国高中数学建模知识应用的情况,发现高中教学中建模知识的应用有待提高。其次,找到数学应用与数学建模的具体关系,在此基础上,对高考数学试卷中的部分应用题深层理解,建构考查知识点所对应的数学模型的雏形。然后,重新整理并分析高考试卷中的应用题,归纳出不同应用题所对应的数学模型,即：函数模型、三角模型、数列模型、几何模型、线性规划模型、概率模型等,以及模型所对应的解题策略,为高中学生解决应用题提供一点帮助。最后,通过对高考试卷中应用题和改编题分析,再通过考查创新思维和应数学的能力这两个方面进行对比,得出改编题能够更好地考查学生的思维创新和应用能力。在改编的过程中,渗透了实例引入、拟合曲线、设置隐含条件、添加参数等方法,使得改编的试题更贴近实际生活、提倡自主建模、考查学生的创新思维,从而为高考数学命题老师提供一点建议。
[Abstract]:In recent years, the college entrance examination system has been constantly changing, mathematics education has gradually attached importance to the cultivation of students' mathematical application ability, and the examination of application problems has been strengthened in the college entrance examination. Under the background of practical problems, using the idea of mathematical modeling to deal with mathematical problems, checking the students' mathematical application consciousness and practical innovation ability becomes the biggest bright spot after the new curriculum reform. First of all, by consulting domestic and foreign books and related literature, the author mainly from the high school mathematics new curriculum standards and college entrance examination mathematics outline, high school teachers and students on mathematical modeling knowledge teaching situation, In the past 15 years, the application of mathematical modeling knowledge in senior high school is analyzed and summarized from the three angles of applying questions in the college entrance examination paper, and it is found that the application of modeling knowledge in senior high school teaching needs to be improved. Secondly, it finds out the specific relationship between mathematical application and mathematical modeling, on the basis of which, some application problems in the college entrance examination paper are deeply understood, and the prototype of mathematical model corresponding to the examination of knowledge points is constructed. Then, the paper rearranges and analyzes the application questions in the college entrance examination paper, and induces the corresponding mathematical models of different application questions, that is, function model, triangle model, sequence model, geometric model, linear programming model, probability model, etc. And the corresponding problem solving strategies for senior high school students to provide a little help. Finally, through the analysis of the application problems and the adapted questions in the college entrance examination papers, and through the comparison between the innovative thinking and the ability of applying mathematics, it is concluded that the adapted questions can better examine the students' thinking innovation and applied ability. In the process of adaptation, the methods of introducing examples, fitting curves, setting hidden conditions and adding parameters are infiltrated to make the adapted questions more close to the actual life, to advocate independent modeling, and to examine the students' innovative thinking. Thus for the college entrance examination math proposition teacher to provide a little advice.
【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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