【作者】 李巍；

【导师】 秦德生；

【作者基本信息】 东北师范大学 ， 学科教学， 2011， 硕士

【摘要】 随着信息技术的不断发展以及计算机和我们生活的联系越来越密切,作为计算科学重要基础的算法越来越受到重视。过去算法只是针对数学专业开设,但很多国家早已意识到算法知识的重要性,将算法编入中学课程,把算法作为一种基本的数学素养来培养。我国教育部也在2003年4月出台了《普通高中数学课程标准(实验)》(以下称为《课程标准》),在本次高中的新课程改革中一个极其重要的部分就是将“算法初步”作为必修内容被列入必修模块的必修3中,并且用独立的一个章节来介绍算法,可见重视程度。“算法初步”对于老师和学生来说都是一个崭新的内容,以前并没有接触过,也就是并没成型的经验可以借鉴。随着新课程的施行,虽然教师对于算法知识的了解逐步加深,但是很多教师还是对这部分的内容的设置有很多质疑。本文试图通过量化的方法来分析中学生算法的理解水平的差异,并通过难度模型来对高中数学教材与信息技术课教材中的算法课程的难度进行对比,希望能对奋斗在一线的教育工作者一些帮助,也希望给教材的编写者提供一些依据。本文主要结论:(一)中学生算法理解水平的差异性1.所研究的四个年级学生对“直接运算”和“抽象概括”水平上没有差异。2.初二与高一、高二年级之间,初三与高一、高二年级在“表示”水平上差异十分显著,对于处在这一水平的算法理解初中学生明显低于高中学生。其中在用自然语言来表示和分析算法,以及程序框图分析和表示顺序结构上四个年级学生之间并没有差异,而在程序框图分析和表示条件结构和循环结构以及分析和表示算法的程序语言上高中和初中学生之间是有差异的。3.初二与高一、高二年级之间是存在显著性差异的,即相邻的两个年级之间的对于分析和建立模型的理解水平相差不多,但是隔年级的学生还是有明显差异的。(二)算法教材难度的对比研究1.对于“算法概念”这部分内容,数学课难度略低于信息技术课,这是由于这两门课中平均课时的内容量相同但是平均课时的目标要求信息技术课要稍高一些。2.在“算法程序框图和自然语言表示算法”方面数学课中的总体难度稍小,这主要是由于虽然数学课中目标要求(课程深度)较高,但是课时安排的稍多,可比深度就相对信息技术课略低,从而降低了这部分内容数学课中的难度。3.在“算法程序语言”方面数学课中的难度高于信息技术课,因为虽然知识点(课程广度)涉及的并不多,目标要求(课程深度)也并不高,但由于课时安排比较紧造成了这部分内容的难度较大。4.对于“算法案例”这部分内容,数学课难度略低于信息技术课,平均课时知识点要求(可比广度)上两门课基本上相同,平均课时目标要求(可比深度)数学课较低,但如果数学教师不能详细准确解读《课程标准》,就会给这部分内容加大难度。更多还原

【Abstract】 As information technology continues to evolve and to calculate the total and our lives are becoming increasingly close, as an important foundation for computer science algorithms and more attention. Knowledge of the past algorithm is set up for mathematics, but many countries have already realized the importance of knowledge, algorithms, and algorithms into the secondary school curriculum, as a basic mathematical literacy to develop. China’s Ministry of Education was in April 2003 issued a "high school mathematics curriculum standards (Experimental)" (hereinafter referred to as "Curriculum Standards"), in this new high school curriculum reform is an extremely important part of the "Algorithm in "As required content is included in the compulsory module in the required 3, and used a chapter to introduce an independent algorithm, showing emphasis."Algorithm in" for both teachers and students for a new content and has not been contacted, that is, no experience can learn from forming. With the implementation of the new curriculum, although teachers gradually deepen knowledge about algorithms, but many teachers still part of the contents of this set have many questions. This article attempts to analyze the quantitative understanding of the level of secondary school students between the algorithm and by the difficulty of high school mathematics textbook model of teaching materials and information technology courses in the difficulty compared algorithms, hoping to fight in the forefront of a number of educators help, I hope to provide some basis for textbook writers.The main conclusions:(A) The level of students understanding of the difference algorithm1. The four grade students study the "direct operation" and "abstraction" no difference in the level.2. Two days and the high one, between the senior grade, and high for a third day, senior grade in the "means" very significant differences in the level, for understanding the algorithm at this level was significantly lower than junior high school students. Which in natural language to representation and analysis algorithms, as well as analysis and presentation of the order of the block diagram structure of the four students was no difference between, and in the conditions of the block diagram analysis and presentation of the structure and circulation structures and algorithms for analysis and programming language between high school and junior high school students there is a difference.3. The first two days and the high one, between the sophomore year there was significant difference, that is, between two adjacent grades for the analysis and modeling almost the same level of understanding, but every year there are significant differences between students .(B) Comparison of the difficulty of teaching method1. For the "algorithm the concept of" this part of the difficulty slightly lower than the information technology, math class, this is due to an average of two hours of course content in the same amount but the average hours of objectives and requirements of information technology courses to be slightly higher.2. In "algorithm that the block diagram and algorithm for natural language" of the overall difficulty of math class in the smaller, mainly due to the depth required (target request) is relatively high, but the arrangement a little more class, than the depth of information technology than lower classes.3. In the "algorithm programming language" of mathematics classes in information technology courses more difficult than, for while knowledge points (namely, curriculum breadth) is not much involved, the objectives and requirements (ie courses depth) is not high, but because of class tight arrangement resulted in this part of the more difficult.4. For the "case method" this part of the difficulty slightly lower than the information technology, math classes, the average hours required knowledge points (comparable breadth) essentially the same on the two classes, the average hours of objectives and requirements (comparable depth) low math But if math teachers are not more accurate interpretation of "Curriculum Standards", will give this part of the increased difficulty.更多还原