Cultivating Computational Thinking Practices and Mathematical Habits of Mind in Lattice Land
Cultivating Computational Thinking Practices and Mathematical Habits of Mind in Lattice Land
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在格域中培养计算思维实践和数学思维习惯
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
U. Wilensky
中科院分区：
文献类型：
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作者：
C. Pei;David Weintrop;U. Wilensky
摘要在“计算性思维”这一术语下收集的一系列实践与作为许多数学教学重点的数学思维习惯之间存在着大量的重叠。尽管有这种重叠，但这两种理想的教育成果之间的联系很少明确，无论是在课堂上还是在文献中。本文介绍了格子土地，计算学习环境和配套课程，旨在支持数学思维习惯的发展，促进计算思维的做法，在高中数学课堂。Lattice Land是一个数学微观世界，学习者通过操纵平面上离散点绘制的多边形来探索几何概念。使用低收入城市公立高中实施的数据，我们展示了Lattice Land的设计如何为学习者提供使用计算思维实践和培养数学思维习惯的机会，包括修修补补，实验，模式识别和常规数学符号中的形式化假设。我们提出格土地作为几何的重构，展示了这种新的和新颖的表征方法如何促进学习者发展计算思维和数学思维习惯。本文最后讨论了计算思维和数学思维习惯之间的相互作用，以及如何周到的设计计算学习环境可以支持有意义的学习，在这些学科的交叉点。
ABSTRACT There is a great deal of overlap between the set of practices collected under the term “computational thinking” and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the literature. This paper presents Lattice Land, a computational learning environment and accompanying curriculum designed to support the development of mathematical habits of mind and promote computational thinking practices in high-school mathematics classrooms. Lattice Land is a mathematical microworld where learners explore geometrical concepts by manipulating polygons drawn with discrete points on a plane. Using data from an implementation in a low-income, urban public high school, we show how the design of Lattice Land provides an opportunity for learners to use computational thinking practices and develop mathematical habits of mind, including tinkering, experimentation, pattern recognition, and formalizing hypothesis in conventional mathematical notation. We present Lattice Land as a restructuration of geometry, showing how this new and novel representational approach facilitates learners in developing computational thinking and mathematical habits of mind. The paper concludes with a discussion of the interplay between computational thinking and mathematical habits of mind, and how the thoughtful design of computational learning environments can support meaningful learning at the intersection of these disciplines.