Journal of East China Normal University(Educational Sciences) ›› 2021, Vol. 39 ›› Issue (8): 70-82.doi: 10.16382/j.cnki.1000-5560.2021.08.006
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Yi Zhang1, Jue Wang1, ling Xie2, Dandan Wang1, Xing Li3, Wei Mo1
Online:
2021-08-01
Published:
2021-08-04
Yi Zhang, Jue Wang, ling Xie, Dandan Wang, Xing Li, Wei Mo. An Application of a PBL+CT Teaching Model in Primary Mathematics for Cultivating Students’ Computational Thinking——Taking “How to Enclose the Largest Area” as an Example[J]. Journal of East China Normal University(Educational Sciences), 2021, 39(8): 70-82.
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条件 | 范围 | 推导思路 | 结果呈现 | 算法 | 要求 | 使用的工具 |
给定周长值 | 长(正)方形 | 周长16 M—边长 (长与宽)—面积 | 长、宽与 面积组合 | 枚举 | 不重复、不遗漏、 有序 | “GeoGebra” APP |
任意周长值 | 长(正)方形 | 1. 确定一个周长—边长 (长与宽)—面积 2. 列举一定范围内的多个周长值, 重复多次枚举算法进行面积计算 3. 根据不完全归纳算法进行推导 | 多个组块的长、 宽与面积组合 | 枚举 | 不重复、不遗漏、 有序 | “GeoGebra” APP、 几何画板课件 |
不完全归纳 | 周长在一定的范围内 (如不超过20 M) | |||||
任意周长值 | 任意图形 | 1. 根据边数确定图形 (三角形、四边形……圆) 2. 无限枚举周长—边长—面积 3. 根据不完全归纳算法进行推导 | 枚举 | 图形从正多边形到 圆的迭代变化 | 几何画板课件 | |
不完全归纳 |
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教学阶段 | 核心问题 | 设计意图 | 问题的内涵与价值 |
给定周长 (16 M)的长 (正)方形 | 周长一定的条件下,长(正)方形需要通过什么来求解面积?如何求面积问题? | 让学生明确当周长为给定值时,需要分解长与宽的中间变量进行面积求解,并运用枚举算法逐一求解面积比较大小。 | 本问题是教学的核心问题,通过这个大问题引导学生将问题分解,并且探究解决方法,这一核心问题是所有活动的核心。 |
周长一定的条件下,长(正)方形面积变化的过程中长与宽各自发生了什么变化?可以怎样调整数据? | 引导学生对长(正)方形的长与宽这一中间变量的数据进行观察,并进行有序排列。 | 这是基于大问题分解的一个小问题,通过让学生去观察这种变化引起思维活动,培养学生用变化的眼光思考问题的意识和能力。 | |
根据长、宽和面积的变化,你能发现什么规律? | 探究变量之间的关系,初步发现其中蕴含的规律。 | 将学生的推理过程引向概括从而得出规律。 | |
任意周长的长(正)方形 | 在任意周长的条件下,如何求解面积问题? | 让每个小组任意列举一个周长值,重用枚举算法进行问题求解。 | 通过问题的变式活化学生的思维,学会迁移已经掌握的方法应用于更高阶的问题解决。 |
在任意周长的条件下,什么不变?什么变化了?从这种变化中发现什么规律? | 引导学生对不完全归纳算法进行逻辑推导。 | 深入学生思维细节之处,启发学生在比较之中掌握数理变化的原因。 | |
当周长是任意值时,我们是怎样研究面积的变化规律? | 借助几何画板课件,深入验证规律的正确性。 | 由小及大,由细节到整体,再次回到问题本身,让学生不仅仅解决了一个问题,更让学生经历计算思维的过程,从而掌握解决问题的思维方法。 | |
任意周长的图形 | 周长变化的过程中,面积发生了什么变化?从这种变化中发现什么规律? | 借助几何画板课件,迁移长(正)方形面积求解的思维到其他图形面积上。理解从周长到求解面积,需要通过边长这一中间变量不断迭代、重用算法的过程,认识到计算机处理问题解决的效率。 | 通过复杂问题让学生意识到用计算机求解问题的有效性。 |
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维度 | 变量 | 均值 | 标准差 | Z | p |
整体维度 | 前测 | 4.05 | 0.65 | ?3.12 | 0.002** |
后测 | 4.31 | 0.57 | |||
分解 | 前测 | 4.03 | 0.74 | ?2.62 | 0.009** |
后测 | 4.36 | 0.66 | |||
抽象 | 前测 | 4.10 | 0.73 | ?1.26 | 0.208 |
后测 | 4.25 | 0.77 | |||
算法思维 | 前测 | 4.11 | 0.68 | ?2.04 | 0.042* |
后测 | 4.35 | 0.62 | |||
问题解决 | 前测 | 4.09 | 0.82 | ?1.38 | 0.167 |
后测 | 4.26 | 0.64 | |||
批判性思维 | 前测 | 4.07 | 0.67 | ?1.31 | 0.190 |
后测 | 4.22 | 0.84 | |||
协作学习 | 前测 | 3.88 | 1.03 | ?3.64 | 0.000*** |
后测 | 4.44 | 0.66 |
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