高中数学算法教学的调查研究

发布时间：2018-03-02 01:01

本文关键词： 高中数学算法初步算法教学　出处：《内蒙古师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：二十世纪数学科学与教育发生了巨大变革,有两个重要标志：一是数学应用领域的变革；二是数学与计算机应用技术的同步发展。计算机之父冯.诺伊曼和图灵都是著名的数学家。一个方面,不论计算机硬件发展还是计算机软件升级都离不开算法的设计,从另一个方面思考,计算机技术的高速发展也对数学的发展起到了巨大的推进作用,展了数学研究的领域,极大地丰富了数学研究的方式方法,加强了数学与其它学科领域的联系,拓宽了数学的应用领域,程序设计即算法设计已渗透到很多数学分支。“算法”是培养逻辑推理能力的非常好的载体。算法思想是初等数学学习内容的一条主线,是依据算法逻辑进行内容设计。所谓算法是指按照一些步骤,一步一步解决某一个问题的程序化或机械化思维过程；而所谓逻辑是指个体以客观真实为依据,按照一定的递推关系对问题结论做出判断的思维过程。这种一步一步地解决问题之清晰的程序化思想是每一位个体发展的现实需要。算法并非是一个很陌生的知识,虽然,有些人不太熟悉这个概念,但是,算法思想经常出现在很多的数学内容中。例如,求解方程、方程组、不等式,几何作图或证明,求解线性规划问题,等等,都可以说是算法问题。算法的特点是可操作、可检验,有一些教师在尝试把“算法”内容与计算机程序设计有机的结合起来,这对培养学生学习数学兴趣也有很好的促进作用。对于数学教师来说,难度不大,经过培训,不会有困难,有些地区采取了一些有效的措施(例如,分成小组,分工备课,集体研讨,教案共享),很好地解决了这个问题。“算法”求解或证明问题的方式是通过框图形式进行展示的,一个问题的算法框图可以把这个问题的解决过程非常清晰的、非常直观的、非常简洁的、非常准确的表示出来。基于提高算法教学实际效果和不断提高利用算法思想与方法解决实际问题的能力之观念,我们从以下几方面做了一些研究：首先,通过文献分析和课堂观察法,了解国内外算法教学研究现状和高中算法教学现实状况与存在问题,明确研究问题的目的和意义以及研究思路。其次,通过广泛详细讨论的基础上,设计了调查问卷和访谈提纲,对内蒙古地区某几所高中教师算法教学及学生学习算法的认识和态度以及存在的问题进行了调查研究,对算法教学研究找到现实依据。第三,依据文献研究和调查访谈研究结果分析,结合学科内容和学情,参照教与学相关理论,研究设计了具体的算法教学案例,并提出一些算法教学的实施建议。
[Abstract]:In 20th century, great changes have taken place in mathematics science and education, which have two important signs: one is the change in the field of mathematics application; The other is the synchronous development of mathematics and computer application technology. The father of computers, von Neumann and Turing, are both famous mathematicians. One aspect, whether the development of computer hardware or the upgrading of computer software, is inseparable from the design of algorithms. On the other hand, the rapid development of computer technology has also played a great role in promoting the development of mathematics, expanding the field of mathematical research, and greatly enriching the methods and methods of mathematical research. It strengthens the relationship between mathematics and other disciplines and widens the fields of application of mathematics. Programming, namely, algorithm design, has permeated many branches of mathematics. "algorithm" is a very good carrier to cultivate the ability of logical reasoning. The idea of algorithm is a main line of elementary mathematics learning. The so-called algorithm refers to the procedural or mechanized thinking process of solving a problem step by step according to some steps, while the so-called logic refers to the fact that the individual is based on objective reality. The thinking process of judging the conclusion of the problem according to a certain recursive relation. The clear procedure thought of solving the problem step by step is the practical need of every individual's development. The algorithm is not a very strange knowledge, although, Some people are not familiar with this concept, but the idea of algorithms often appears in a lot of mathematical content, for example, solving equations, equations, inequalities, geometric mapping or proof, solving linear programming problems, and so on. It can be said that it is an algorithm problem. The characteristic of the algorithm is that it can be operated and tested, and some teachers are trying to combine the content of "algorithm" with computer programming organically. This will also play a good role in fostering students' interest in mathematics. For mathematics teachers, it is not difficult, and after training, there are no difficulties. Some regions have taken some effective measures (for example, dividing up groups and dividing classes to prepare classes). Collective discussion, teaching plan sharing can solve this problem very well. The way of solving or proving the problem by "algorithm" is shown in the form of block diagram. The algorithm block diagram of a problem can make the process of solving this problem very clear. Very intuitive, very concise, very accurate. Based on the idea of improving the practical effect of algorithm teaching and improving the ability to use algorithm ideas and methods to solve practical problems, We have done some research from the following aspects: firstly, through literature analysis and classroom observation, we understand the current situation of algorithm teaching research at home and abroad and the current situation and existing problems in high school algorithm teaching. The purpose and significance of the research and the research ideas are clarified. Secondly, based on the extensive and detailed discussion, the questionnaire and interview outline are designed. This paper investigates the cognition, attitude and existing problems of some high school teachers' algorithm teaching and students' learning algorithm in Inner Mongolia, and finds the realistic basis for the algorithm teaching research. Based on the analysis of the results of literature research and interview, combined with the subject content and learning situation, and referring to the relevant theories of teaching and learning, this paper studies and designs specific cases of algorithmic teaching, and puts forward some suggestions for the implementation of algorithmic teaching.
【学位授予单位】：内蒙古师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

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