Supporting dynamic conceptions of area and its measure
Supporting dynamic conceptions of area and its measure
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支持面积及其测量的动态概念
DOI：
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发表时间：
2019
影响因子：
1.6
通讯作者：
R. Lehrer
中科院分区：
文献类型：
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作者：
Marta Kobiela;R. Lehrer
摘要设计研究旨在探讨动态区域概念的发展。学生们使用简单的物理工具，挤压器和油漆，以连续产生矩形区域作为一个扫过另一个长度的运动。然后，他们通过协调边的长度测量，包括以不同单位测量的边长，如“英寸”和“英寸”，将产生的扫描空间分解为离散的测量单位。教学后2个月的课堂话语分析、形成性评估和灵活的访谈表明，学生发展了区域及其测量的动态图像和意义。这些扩展了他们对乘法乘积的理解，使其包括了参照变换量，并为重新设想乘法的交换和分配性质的意义提供了手段。学生们利用这些性质来联系分数和整数面积积。动态生成和解剖串联帮助学生桥梁离散和连续的面积及其测量的概念。
ABSTRACT Design research was conducted to investigate the development of dynamic conceptions of area. Students used simple physical instruments, squeegees, and paint, to generate rectangular areas continuously as a sweeping motion of one length through another. Then, they dissected the resulting swept space into discrete units of measure by coordinating measures of the lengths of the sides, including side lengths measured in different units, such as “squeegee” and inch. Analysis of classroom discourse, formative assessments, and flexible interviews conducted 2 months after instruction illustrated that students developed dynamic images and meanings of area and its measure. These expanded their understanding of multiplicative product to include referent-transforming quantity and provided means for re-envisioning the meaning of the commutative and distributive properties of multiplication. Students employed these properties to relate fractional and whole number area products. Dynamic generation and dissection in tandem helped students bridge discrete and continuous conceptions of area and its measure.