Given the important role played by students’ spatial reasoning skills, in this paper we analyse how students use these skills to solve problems involving 2D representations of 3D geometrical shapes. Using data from in total 1357 grades 4 to 9 students, we examine how they visualise shapes in the given diagrams and make use of properties of shapes to reason. We found that using either spatial visualisation or property-based spatial analytic reasoning is not enough for the problems that required more than one step of reasoning, but also that these two skills have to be harmonised by domain-specific knowledge in order to overcome the perceptual appearance (or “look”) of the given diagram. We argue that more opportunities might be given to both primary and secondary school students in which they can exercise not only their spatial reasoning skills but also consolidate and use their existing domain-specific knowledge of geometry for productive reasoning in geometry.

中文翻译：

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关于4至9年级3D几何形状的2D表示的空间推理技巧

考虑到学生的空间推理能力所起的重要作用，本文将分析学生如何使用这些技巧来解决涉及3D几何形状的2D表示的问题。使用来自1357年级4至9年级学生的数据，我们检查了他们如何在给定的图中可视化形状并利用形状的属性进行推理。我们发现，对于需要多个步骤推理的问题，使用空间可视化或基于属性的空间分析推理是不够的，而且这两个技能还必须通过领域特定的知识来协调，以克服感知上的问题。给定图的外观（或“外观”）。