于晓雅 樊磊 | Python编程与算法教学的策略及指导原则

自信息技术新课标把语言当作核心编程语言进行推荐之后, 编程教学成为落实新课标课程目标的基础, 算法教学同样成为落实新课标课程目标的基础。在中小学编程与算法的教学里面, 要是去落实课标精神, 得围绕“算法以及基于算法的问题求解”这一核心之处, 还得按照基础教育阶段学生的特点来抓取适当深度和广度, 靠着算法学习和实践举动, 去给予深入体会并应用当作信息技术的思想、方法还有手段的计算思维帮着解决问题的坚实基础, 达成“运用计算思维解决问题”这样能力培养的课程目标, 这可是广大信息技术学科教师一块集体关注的话题, 也是主要的研究点。存在的问题和困难中小学编程与算法, 在教学里当下有着这样那样的问题以及困难, 它是普通高中信息技术新课标的关键重要内容。首先, 存在教学内容选择方面的困难。高校里计算机及其相关专业针对算法的教学已然构建起极为完备的体系, 然而因为中小学生跟大学生在年龄以及认知上有着差别, 且学科基础也是不一样的, 所以在基础教育阶段的算法以及问题求解教学, 既不能说是高校教学内容的单纯简单化, 又不可以仅仅把它当作大学算法课程的前期准备却不涉及本质问题。上述这般情况致使中小学算法教学内容在深度以及广度层面普遍呈现出“高不成、低不就”的窘迫状态。第二, 存在教学实践层次的困难。首先, 算法身为计算机科学的重要分支, 它跟数学、数据结构、编程语言特性紧密相连, 已然成为一个完备知识体系, 仅仅讲述算法自身很难得以实施。其次, 语言对很多基础算法的实现进行了封装, 并且涉及交错复杂的概念像数据类型、抽象数据类型, 到底是讲解算法的底层方面还是讲解高阶应用难以抉择。再次, 怎样去处理算法的直觉描述, 也就是非形式化描述, 还有对于流程图, 以及伪代码, 也就是半形式化描述, 和编程实现, 也就是形式化描述它们之间的关系, 这同样是教学实践的难点。这一部分, 是案例选择情形下存在的困难之处。在中小学这个教育阶段里面开展的算法教学, 它最终的目的是要为编程教学而负责的, 所以这也就必然需要服从编程教学预先设置的总的目标, 也就是运用计算思维来解决具体存在的问题。然而呢, 受到中小学生自身认知水平以及知识深度方面的限制, 教学案例当中的求解流程以及问题深度是很难去精准把握的, 所以能否选择恰当合适的案例, 就变为实施编程以及算法教学过程当中的一个关键要点了。遵循原则第一算法应该源自学生熟悉的应用情境。第二点, 于算法的挑选方面, 得把控住高阶算法跟低阶算法有关的平衡。首先, 高中涵盖小学、初中算法教学里, 算法的目标是很重要的一部分, 其次, 算法的直观思想也是重要部分, 再者, 算法逐步导致形式化描述的演化过程同样是重要部分, 并且, 教学的时候应该避免直接提出一般化的算法描述, 同时并且, 教学的时候也应该避免直接提出形式化的算法描述。其四, 算法里涉及的关键思想, 形式化或者半形式化的呈现方式法, 算法推导所关联的数学还有背景知识, 应当处于学生的知识范畴之内, 或者稍微超出学生的知识范畴。首先, 在第五点关于算法的编程实现方面, 原则上而言, 不会涉及那种比较复杂或者具有较高技巧性的编程内容。对于那些较为复杂的算法, 不一定需要进行实际的编程实现, 就算要做也只是做类似伪代码那样的实现。但是, 算法在作为教学案例的时候, 必须要先把它背后的关键思想讲解清楚。首先, 存在有第六点, 高阶算法所处理解决的问题, 应当具备典型特质, 拥有一定时代特性, 存在选择性方面的表现, 具备普适性质, 还有适用性方面的情况, 而且, 对于学生往后的学习, 或者是其他学科领域的学习, 能够产生启示方面的作用。第七, 在时间许可且条件具备情形下, 有必要针对解决同一类问题、基于不同策略达成的算法, 开展性能方面的比对, 而后挑选出更为优良的算法。实施策略1.明晰编程知识进阶合理设计教学方法在进行编程这一行为以及算法开展教学工作期间, 需要始终如一做的是, 贯彻落实“需求导向问题解决做中学”这样一种定位, 并且明确知晓, 学会对函数加以运用, 相较于掌握编程技巧而言, 更具重要性。设计编程案例之际, 需掌握输入/输出函数, 要能灵活施展非数值数据类型, 涵盖字符串、列表与字典要知晓语言异常灵活的循环以及控制结构鼓励教师把它当作实现版的“伪代码”去使用, 即便确实非得用伪代码, 也建议采用-like风格要是打算运用高级特性, 编程案例应尽可能依托语言特点, 并且依据算法实现的需求适度逐步地引入。然而笔者建议, 非必要尽量别使用的高级特性。2.熟悉算法策略找准对应求解问题算法策略, 是于算法创设里, 那被运用的问题求解之策略, 是计算思维最为笔直、最为具体的呈现样式。算法策略的视角, 在站位方面上, 要高于实现算法之际的具体编程达成办法。在中小学编程教育那里, 于算法教学当中, 常见的算法策略以及用于处理的任务主要包含: 迭代, 也就是循环, 它被用于处理重复性任务递归, 这是用于完成迭代的一种颇具效率的方法蛮力法指的是, 在没有更好解决方案且计算资源, 依据时间和空间而言, 能够允许的前提状况下可以尝试采用的求解问题的方式回溯, 用途是测试那些不可行的选择之处, 目标是尽可能排除这群选择。案例解析最关键的要点是算法教学里教学案例的挑选, 算法以及倚靠算法的问题求解属于计算机科学最为重要的构成部分, 还是信息技术新课程最基础、核心的内容。接着, 笔者以斐波那契数列的问题解决途径当作例子, 剖析在上述原则与策略的指引之下, 怎样去施行编程以及算法教学。1.构建问题场景斐波那契数列起始于0以及1, 此后的斐波那契数列系数是由之前的两个数相加而得。普通高中数学必修五在讲解数列前n项和的课后相关资料里提及了斐波那契数列, 将其作为数学知识能够与生活实际相联系、培养发展学生抽象思维能力的拓展内容。就斐波那契数列而言, 鉴于其相邻两项的比无限趋近于黄金比等特性, 所以又称黄金分割数列。它是由意大利数学家莱昂纳多·斐波那契, 以兔子繁殖加以例证并引入的, 因此又被叫做“兔子数列”。假设存在一对刚出生的小兔子, 一个月之后能够长成大兔子, 再过一个月就能够生下一对小兔子, 自那之后每个月都会生下一对小兔子。要是不出现死亡的情况, 那么在一年之中逐月的小兔子对数是一组极为特殊的数字, 分别是: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144……很容易就能够发觉, 从第三个数开始, 每一个数都是前两个数相加的和, 这样的数列被称作斐波那契数列。现代物理领域, 斐波那契数列有直接应用, 准晶体结构领域, 斐波那契数列有直接应用, 化学领域, 斐波那契数列也有其直接应用, 斐波那契数列的通项公式呈现为如下图所示的公式1。斐波那契数列, 是在算法教学里最简单的, 递归定义函数, 所以它非常适合, 拿去说明实现基本递归算法的方法。2.简单递归实现算法实现斐波那契数列所需的基本知识有, 借助if语句达成简单迭代或者循环, 进行自定义函数, 实现函数的递归定义。斐波那契数列是按递归形式来定义的, 它属于函数式编程语言, 这种语言支持函数的递归定义, 也就是函数体内部存在对函数自身的调用。所以, 公式1能够转化为一个合法定义的函数, 并且试着让学生输出一些能很快借由人工验证的值不要太大如下图。能留意到, 计算最后那个值之际是得花些工夫的。在上述递归调用当中, 好些中间值会被重复计算。如下方图示那般, 计算fib_14的时候, fib_12被重复计算了2回。明显地, n 的数值越大, 计算fib_1n进程里, 需重复计算fib_1kk n的次数便越多了。3.动态规划优化递归算法为了对斐波那契数列的递归实现予以优化, 一种最为简单的办法便是在每一次进行计算时, 把先前已经计算出来的值予以“记忆”留存, 使其不再重复进行计算。这样一种在计算进程当中运用记忆的机制能够切实有效地避免重复情况以及资源浪费现象, 它是所谓动态规划方法里的一个最为简单的示例, 而动态规划所指的就是资源的动态再次分配。动态规划的实现需要牵涉到如下这些知识: 字典, 的Dict内建对象这是一种特殊的字典, 针对迭代器运用if语句。如下图示的代码乃是一个带有记忆功能的版本。相对比而言, 对fib_220进行计算, 会致使fib_2出现39次自身调用要是运用fib_1运用, 那么对fib_120加以计算, 将会生成21891次调用。在其中, 但凡任意某个只要定义了某种特定的next 方法的对象, 那它就是一个迭代器。所以, 其中的那些容器类别的数据类型, 像是列表、元组、字典、集合、字符串等, 均能够用来创建迭代器。具备了迭代器的概念之后, 迭代的概念就相对比较容易去理解了: 所谓迭代其实就是从迭代器当中依照次序抽取元素的过程。4.装饰器优化递归算法存在一个内建的“装饰器”, 它能够被用来自动记忆任一函数, 借助运用此装饰器, 求得斐波那契数列的函数能得以更简化。以如下方式实现所运用的高级特性, 即装饰器语句。简单来说, 装饰器的作用是, 在不改变原本函数代码的情形下, 为其增添一些额外功能, 像上面所提到的记忆函数中间值的功能。如下的代码所实现的函数fib_3, 它和fib_1几乎是完全一样的, 只不过使用了装饰器., 当中属性是用来指示在函数的最近那种调用里应该缓冲多少次的, 设置成为None就表示对次数不做限制。5.使用元组拆包优化递归算法被分别赋给变量的是元组之中的元素, 这就是元组拆包。借助元组拆包技巧, 能够给出斐波那契函数的一个性能更高的实现, 具体情况如下所示。本事当中, 表示前次与下一个值的词, 被赋予了新的值, 前次的值被更新为下一个原先的值, 而下一个的值被更新为前次的值加上下一个原先的值, 这便是一个对于元组进行拆分赋值的操作。运用这种将元组拆分赋值的巧妙方法, 计算fib_4函数时, 只需要重复n减1次循环这样的操作就可以了6.斐波那契数列生成器-循环结构截至当前, 所撰得的函数仅能够生成特定位置处的斐波那契数之值, 要是打算一次性把直至某个值为止的整个斐波那契数列予以输出, 此时能够借助一个简单循环如下图示。Www.hgfcn.cn/Article/details/6216685.sHtMLWww.hgfcn.cn/Article/details/7884760.sHtMLWww.hgfcn.cn/Article/details/3343718.sHtMLWww.hgfcn.cn/Article/details/1524676.sHtMLWww.hgfcn.cn/Article/details/7544430.sHtMLWww.hgfcn.cn/Article/details/9854815.sHtMLWww.hgfcn.cn/Article/details/8345370.sHtMLWww.hgfcn.cn/Article/details/7605594.sHtMLWww.hgfcn.cn/Article/details/1248581.sHtMLWww.hgfcn.cn/Article/details/8773207.sHtMLWww.hgfcn.cn/Article/details/1211352.sHtMLWww.hgfcn.cn/Article/details/2007221.sHtMLWww.hgfcn.cn/Article/details/7664883.sHtMLWww.hgfcn.cn/Article/details/4006379.sHtMLWww.hgfcn.cn/Article/details/6126403.sHtMLWww.hgfcn.cn/Article/details/3314292.sHtMLWww.hgfcn.cn/Article/details/8203600.sHtMLWww.hgfcn.cn/Article/details/3557689.sHtMLWww.hgfcn.cn/Article/details/6401320.sHtMLWww.hgfcn.cn/Article/details/7718221.sHtMLWww.hgfcn.cn/Article/details/3689580.sHtMLWww.hgfcn.cn/Article/details/2331222.sHtMLWww.hgfcn.cn/Article/details/5097786.sHtMLWww.hgfcn.cn/Article/details/7863406.sHtMLWww.hgfcn.cn/Article/details/2522585.sHtMLWww.hgfcn.cn/Article/details/6820630.sHtMLWww.hgfcn.cn/Article/details/7243730.sHtMLWww.hgfcn.cn/Article/details/7523310.sHtMLWww.hgfcn.cn/Article/details/3675754.sHtMLWww.hgfcn.cn/Article/details/7086926.sHtMLWww.hgfcn.cn/Article/details/1591009.sHtMLWww.hgfcn.cn/Article/details/1376259.sHtMLWww.hgfcn.cn/Article/details/5693466.sHtMLWww.hgfcn.cn/Article/details/6606392.sHtMLWww.hgfcn.cn/Article/details/3127650.sHtMLWww.hgfcn.cn/Article/details/6006886.sHtMLWww.hgfcn.cn/Article/details/1668480.sHtMLWww.hgfcn.cn/Article/details/4217491.sHtMLWww.hgfcn.cn/Article/details/3233125.sHtMLWww.hgfcn.cn/Article/details/3088203.sHtMLWww.hgfcn.cn/Article/details/5435506.sHtMLWww.hgfcn.cn/Article/details/4501505.sHtMLWww.hgfcn.cn/Article/details/7104340.sHtMLWww.hgfcn.cn/Article/details/1853259.sHtMLWww.hgfcn.cn/Article/details/2944167.sHtMLWww.hgfcn.cn/Article/details/7817937.sHtMLWww.hgfcn.cn/Article/details/3726869.sHtMLWww.hgfcn.cn/Article/details/7813577.sHtMLWww.hgfcn.cn/Article/details/3272168.sHtMLWww.hgfcn.cn/Article/details/7640954.sHtMLWww.hgfcn.cn/Article/details/8683980.sHtMLWww.hgfcn.cn/Article/details/9007917.sHtMLWww.hgfcn.cn/Article/details/3031858.sHtMLWww.hgfcn.cn/Article/details/7938581.sHtMLWww.hgfcn.cn/Article/details/8455546.sHtMLWww.hgfcn.cn/Article/details/6606378.sHtMLWww.hgfcn.cn/Article/details/1057510.sHtMLWww.hgfcn.cn/Article/details/4921505.sHtMLWww.hgfcn.cn/Article/details/2442376.sHtMLWww.hgfcn.cn/Article/details/6094936.sHtMLWww.hgfcn.cn/Article/details/8589515.sHtMLWww.hgfcn.cn/Article/details/6134448.sHtMLWww.hgfcn.cn/Article/details/4184807.sHtMLWww.hgfcn.cn/Article/details/7207034.sHtMLWww.hgfcn.cn/Article/details/4022167.sHtMLWww.hgfcn.cn/Article/details/2840093.sHtMLWww.hgfcn.cn/Article/details/2491845.sHtMLWww.hgfcn.cn/Article/details/5278556.sHtMLWww.hgfcn.cn/Article/details/9831308.sHtMLWww.hgfcn.cn/Article/details/2731773.sHtMLWww.hgfcn.cn/Article/details/6521856.sHtMLWww.hgfcn.cn/Article/details/2439778.sHtMLWww.hgfcn.cn/Article/details/7082000.sHtMLWww.hgfcn.cn/Article/details/9581771.sHtMLWww.hgfcn.cn/Article/details/4592222.sHtMLWww.hgfcn.cn/Article/details/2664274.sHtMLWww.hgfcn.cn/Article/details/3571280.sHtMLWww.hgfcn.cn/Article/details/2808937.sHtMLWww.hgfcn.cn/Article/details/4076145.sHtMLWww.hgfcn.cn/Article/details/9184083.sHtMLWww.hgfcn.cn/Article/details/8951983.sHtMLWww.hgfcn.cn/Article/details/8288941.sHtMLWww.hgfcn.cn/Article/details/2218247.sHtMLWww.hgfcn.cn/Article/details/2693494.sHtMLWww.hgfcn.cn/Article/details/3669121.sHtMLWww.hgfcn.cn/Article/details/7425435.sHtMLWww.hgfcn.cn/Article/details/5285582.sHtMLWww.hgfcn.cn/Article/details/7972281.sHtMLWww.hgfcn.cn/Article/details/5001963.sHtMLWww.hgfcn.cn/Article/details/1876670.sHtMLWww.hgfcn.cn/Article/details/9017165.sHtMLWww.hgfcn.cn/Article/details/2365112.sHtMLWww.hgfcn.cn/Article/details/5434662.sHtMLWww.hgfcn.cn/Article/details/8555850.sHtMLWww.hgfcn.cn/Article/details/5388719.sHtMLWww.hgfcn.cn/Article/details/4675303.sHtMLWww.hgfcn.cn/Article/details/4458137.sHtMLWww.hgfcn.cn/Article/details/8551709.sHtMLWww.hgfcn.cn/Article/details/3721349.sHtMLWww.hgfcn.cn/Article/details/1659799.sHtMLWww.hgfcn.cn/Article/details/1674674.sHtMLWww.hgfcn.cn/Article/details/2357806.sHtMLWww.hgfcn.cn/Article/details/1839174.sHtMLWww.hgfcn.cn/Article/details/6329239.sHtMLWww.hgfcn.cn/Article/details/1448568.sHtMLWww.hgfcn.cn/Article/details/5059539.sHtMLWww.hgfcn.cn/Article/details/4827213.sHtMLWww.hgfcn.cn/Article/details/6997514.sHtMLWww.hgfcn.cn/Article/details/3918590.sHtMLWww.hgfcn.cn/Article/details/1427982.sHtMLWww.hgfcn.cn/Article/details/5178097.sHtMLWww.hgfcn.cn/Article/details/9098129.sHtMLWww.hgfcn.cn/Article/details/9604799.sHtMLWww.hgfcn.cn/Article/details/8760482.sHtMLWww.hgfcn.cn/Article/details/4423824.sHtMLWww.hgfcn.cn/Article/details/1911601.sHtMLWww.hgfcn.cn/Article/details/9547274.sHtMLWww.hgfcn.cn/Article/details/5893587.sHtMLWww.hgfcn.cn/Article/detail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