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

doi:10.16382/j.cnki.1000-5560.2021.08.006

Abstract

Abstract:

“Computational thinking” has been an important indicator for evaluating students’ high-order thinking in K-12 education in recent years. It has common thinking modes with mathematics thinking in many fields such as problem-solving. Therefore, developing computational thinking in mathematics has become a global trend. A three-layer “PBL+CT” theoretical model in primary school mathematics to develop students’ computational thinking is built. In the model, the content layer is PISA-oriented and drives teaching through the problem, the teaching layer is the mathematical model of non-programming plugged that integrates with computational thinking elements and constructs the problem-solving teaching procedure, and the goal layer is of computational thinking in relevant to the six core skills of decomposition, abstraction, algorithmic thinking, critical thinking, problem-solving, and collaborative learning. The course How to Enclose the Largest Area in primary mathematics was taken as an example, specific teaching designs and implementations in terms of the theoretical model were conducted, and the effectiveness of the model was verified in this research. Classroom observations, questionnaires, self-assessments, and interviews were used to verify the effectiveness of the model in promoting the development of computational thinking in primary students. It is found that the “PBL+CT” teaching model in primary school mathematics can significantly cultivate students’ computational thinking, especially in the fields of decomposition, algorithmic thinking, and collaborative learning. Based on the results, the research further summarizes and reflects on the mathematics teaching of “PBL+CT” to promote the development of students’ computational thinking in primary school.

Key words: primary school, mathematics, PBL, computational thinking (CT)

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.

Figures/Tables 9

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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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
任意周长值	长（正）方形		多个组块的长、宽与面积组合	不完全归纳	周长在一定的范围内（如不超过20 M）	“GeoGebra” APP、几何画板课件
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
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		不完全归纳	图形从正多边形到圆的迭代变化	几何画板课件

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^**
整体维度	后测	4.31	0.57	?3.12	0.002^**
分解	前测	4.03	0.74	?2.62	0.009^**
分解	后测	4.36	0.66	?2.62	0.009^**
抽象	前测	4.10	0.73	?1.26	0.208
抽象	后测	4.25	0.77	?1.26	0.208
算法思维	前测	4.11	0.68	?2.04	0.042^*
算法思维	后测	4.35	0.62	?2.04	0.042^*
问题解决	前测	4.09	0.82	?1.38	0.167
问题解决	后测	4.26	0.64	?1.38	0.167
批判性思维	前测	4.07	0.67	?1.31	0.190
批判性思维	后测	4.22	0.84	?1.31	0.190
协作学习	前测	3.88	1.03	?3.64	0.000^***
协作学习	后测	4.44	0.66	?3.64	0.000^***

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