Interplay between paper-and-pencil activity and dynamic-geometry-environment use during generalisation and proving
Interplay between paper-and-pencil activity and dynamic-geometry-environment use during generalisation and proving
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泛化和证明过程中纸笔活动与动态几何环境使用之间的相互作用
DOI：
10.1007/s40751-020-00067-3
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
K.
中科院分区：
文献类型：
--
作者：
Komatsu;K.;& Jones;K.
研究表明，与纸笔环境等物理工具相比，数字工具有可能显着改变课堂上数学学习的形式。然而，很少有研究深入研究这两类工具在数学学习中所发挥的相互关联的作用。这个相互关联的角色问题很重要，因为当数字工具被纳入课堂时，学生通常还会有笔记本和工作表，他们可以在其中执行与数字工具的使用相补充的操作。在本文中，我们重点关注动态几何环境 (DGE) 在猜想和证明中的使用，特别是，我们研究了学生的纸笔活动与他们在生成和证明陈述的概括过程中使用 DGE 之间的相互作用。我们分析了涉及中学生（14-15 岁，9 年级）的一系列课程，结果表明，虽然 DGE 的使用支持学生概括一个陈述，但他们最初无法在使用 DGE 时证明概括，但随后通过纸笔活动成功了。我们的研究说明了纸笔环境可以支持学生进行不同的表示，从而强调纸笔活动和 DGE 使用之间的相互作用对于推测和证明的进展非常重要。我们还展示了教师在支持学生作业中所扮演的角色，并指出需要进一步研究数字和物理工具的来回使用。
Digital tools have a potential to change significantly the form of mathematical learning taking place in classrooms, with research pointing to various affordances in comparison with physical tools such as paper-and-pencil environments. Nevertheless, there is a scarcity of research that has examined in-depth the interrelated roles these two types of tools fulfil in mathematics learning. This issue of inter-related roles is important because, when digital tools are incorporated into classrooms, students usually also have notebooks and worksheets within which they carry out actions complementary to their use of digital tools. In this article, we focus on the use of dynamic geometry environments (DGEs) in conjecturing and proving, and, in particular, we examine the interplay between students’ paper-and-pencil activity and their use of a DGE during the producing and proving of a generalisation of a statement. We analyse a series of lessons involving secondary school students (aged 14–15, Grade 9) and show that, while DGE use supported the students in generalising a statement, they were initially unable to prove the generalisation while using the DGE, but subsequently succeeded through their paper-and-pencil activity. Our research illustrates the affordance of paper-and-pencil environments to support students in working on different representations, and thus highlights how the interplay between paper-and-pencil activity and DGE use can be important for the progress of conjecturing and proving. We also show the roles taken by the teacher in supporting the students’ work, and point to the need for further research into the back-and-forth use of digital and physical tools.