Dynamic Geometry Contribution in the Introduction to the Perspective Study for High School Students

Abstract The objective was to investigate contributions of an interventional proposal using perspective initial ideas for Geometry teaching, in order to expand the repertoire of plane representations and spatial visualization abilities for ten Brazilian High School students. Based on the historical development of techniques for bidimensional representations of spatial figures and methodologically oriented by Design Experiment procedures, activities have been developed in three meetings, at first to analyze paintings and images from various times and, afterwards, using the Dynamic Geometry environment to explore techniques for constructing images in perspective. We sought theoretical support in Parzysz and Gutiérrez's studies on bidimensional representations of spatial figures, particularly on the ideas of "seeing" and "knowing" poles. Qualitative data analysis showed that using a software may provoke interest on geometric constructions and Geometry study, although there were limitations in learning new concepts, especially those based on those participants previous ones. On the other hand, using the software has allowed some participants to become aware of the importance of knowing the representation rules for the interpretation of images in perspective, which shows that a long-term work of this nature can promote learning and visualization in Geometry.

摘要 本研究旨在探究以透视初始理念开展的几何教学干预方案的教学成效，以期扩充10名巴西高中生的平面表征技能储备，提升其空间可视化能力。本研究基于空间图形二维表征技术的历史发展脉络，以设计实验（Design Experiment）为方法论框架，开展了三次主题教学活动：首先分析不同时代的绘画与图像，随后借助动态几何环境（Dynamic Geometry environment）探索透视图像的构建技法。本研究的理论支撑源自Parzysz与Gutiérrez关于空间图形二维表征的研究，尤其是其提出的“视觉”与“认知”两极理念。质性数据分析结果显示，尽管在学习新概念（尤其是基于参与者既有知识储备的概念）时存在一定局限，但借助该软件可激发学生对几何作图与几何学习的兴趣。另一方面，借助该软件可使部分参与者意识到掌握透视图像解读所需的表征规则的重要性，这表明此类长期教学实践可有效促进几何学习与空间可视化能力的提升。