摘 要：高中数学课程增加了“算法初步”内容，并把它作为新的数学基础知识与技能.根据课程目标中具体目标对能力表现形式的描述和能力内涵，算法能力是指在解决与算法相关的问题过程中，主体表现出正确地理解题意、符号，善于将问题概括为一个算法问题，并能提炼出问题中蕴涵的“算理”，合理运用算法的知识与经验，正确地解决问题并直接影响问题解决效率高低的一种比较稳定的个性心理特征.算法能力的主要组成部分是：阅读算法能力；提炼“算理”能力；算法语言能力；应用算法能力.算法能力的主要培养途径是：通过培养阅读的深刻性、灵活性、独创性、批判性、敏捷性（五性），分析隐含条件、简缩问题、化已知为未知的能力培养阅读算法能力；通过在具体问题中，引导学生发现猜想、检验猜想、概括猜想原理的教学培养学生提炼算理能力；通过加强算法语言的语义和句法、切换、表述的教学培养算法语言能力；通过培养应用算法的意识、数学联结能力、逻辑推理能力培养应用算法能力.算法教学实验结果表明：通过培养阅读算法能力、提炼“算理”能力、算法语言能力、应用算法能力，使之形成合力，能促使算法能力的整体提高.
关键词：算法；算法能力；算理；算法语言；流程图；标准
Research on Algorithmic Ability and The Way of Its Training
ABSTRACT ：The senior middle school mathematics curriculum newly added "the algorithm to be preliminary" the content, and took it the new mathematics elementary knowledge and the skill. According to the description of the concrete goal to the ability manifestation and the ability connotation in the curriculum goal, the algorithm ability refers to in the solution to the problems related to algorithm, the main body displays correct comprehension of the meaning of the title、the mark, good at the summarizing the question into an algorithm question, and can refine the algorithmic rule contained in the question, reasonably utilizes the algorithmic knowledge and experience, correctly solves the problem and directly influences the efficiency of solving the question. It is a kind of quite stable personal psychological characteristic. The main constituent of algorithm ability is: reading algorithm ability; refining the algorithmic rule ability; algorithmic language ability; applied algorithm ability. The main training way of algorithm ability is: Through training reading profundity, flexibility, creativity, critique, agility(five natures), the ability of analyzing concealed conditions, simplifying questions, taking the known for the unknown to develop reading algorithm ability; Through in the concrete questions, the teaching of leading the students to discover ,examine and summarize the suspicions to train their refining the algorithmic rule ability；Through strengthening the teaching of the semantics and the syntax ， exchange and indication of algorithmic language to train the students’ algorithmic language ability; Through training the consciousness of applied algorithm, mathematics joint ability, logical inference ability to train their applied algorithm ability. The experiment result of algorithm teaching indicates that, Through training reading algorithm ability, refining the algorithmic rule ability, algorithmic language ability, applied algorithm ability, then these abilities form the resultant of forces to improve algorithm ability as a whole.
Key Words: Algorithm; algorithmic ability; The algorithmic Rule; Algorithmic Language; flow chart; Standard.
第一章 问题的提出
§1.1 研究的背景
算法与演算是处理计算过程—推理过程时常用的两大形式.综观数学发展史，可以发现这样一个特征：算法倾向和演绎倾向总是交替取得主体地位.随着图灵机理论的提出，第一台军用计算机 （电子数字积分计算机）的诞生，信息时代的到来，算法倾向更加明显.正如吴文俊先生在《<九章算术>及其刘徽注研究》序言中指出:“肇始于我国的这种机械化体系，在经过明代以来近几百年的相对消沉后，由于计算机的出现，已越来越为数学家所认识和重视，势必将重新登上历史舞台”.算法程序化的结构与思想，有助于人们学习和理解其他学科知识，它如处方，活动规程等正对人们生活产生广泛、积极而又深远的影响.1985年， 在斯特拉斯宝会议中，讨论“计算机和计算机科学对数学课程的冲击”时亦指出：“在中学数学课程中代数仍处于极其重要的地位.…运用公式和其他代数表达的能力将仍是必需的”， 1986年 在科威特讨论“90年代学校数学”时建议数学课程中引进离散数学概念，要重新强调算法，并让学生比较同一问题的不同算法的效率.德国 教授在 ─2002年数学教育（西藏）卫星会议所作报告“算法─数学与数学教育的基础：一个德国人关于数学教育中算法与计算机的观点”中，在当今信息时代，详述了有必要充分认识和重视算法作为数学与数学教育的基础之重要性与不可替代性.
