“脚手架”如何变成了“绊脚石”——小学数学中的图示障碍研究

How"Scaffolding"Becomes A"Stumbling Block":Research on Graphic Obstacles in Primary School Mathematics

小学数学教材和教师的教学过程中提供了大量图文与习题结合的图示,其中大部分本身是作为学生情境支架而设计的,以支撑学生跨越从生活数学到抽象符号数学之间的发展鸿沟。然而,实证调查测试表明,一些数学图示不仅没有起到“脚手架”作用,反而成了干扰学生正确理解题意的障碍。进一步分析发现,这些图示障碍内在的图文匹配度、契合学生的理解度和对学生学习的支持度之间存在正向影响关系;图示内部缺乏一致性、图像内容编排不合理以及图示信息呈现不恰当是形成6种典型图示障碍的三大主因,且通常发生在多媒体学习“选择—组织—整合”词语和画面的不同认知阶段。研究结果为设计和使用数学图示提供了有益启示:遵从多媒体学习的匹配设计、学习者中心的设计和深度学习的情境支架设计三大学习设计原则,不仅可以使图示障碍得到有效控制与消除,也是回归图示本身所赋有的“脚手架”功能的有效途径。

Primary school mathematics textbooks and teachers’ teaching processes provide a large number of graphics, most of which are designed as contextual scaffolding for students to cross the gap from life-based mathematics to abstract symbolic mathematics. However, the empirical research shows that some mathematical graphics not only fail to act as scaffolding, but also become obstacles for students’ correct understanding of the topic. Further analysis indicates that there is a positive relationship among the intrinsic matching degree of graphics and text, the understanding degree and the learning support degree of the students. The lack of consistency in graphics, the unreasonable layout of image content and the inappropriate presentation of graphics information are three main reasons for the formation of six typical graphics obstacles, which usually occur at different cognitive stages of ’selecting-organizing-integrating’words and pictures in multimedia learning. This study provides useful inspiration for designing and using those mathematical graphics: following the three learning design principles(matching principle of multimedia learning, learner-centered design principle and contextual scaffolding design principle for deeper learning) is not only an effective way to control and eliminate the graphics obstacles, but also an effective way for those graphics returning to the role of scaffolding in themselves.