A major challenge in the field of spatial reasoning is the translation of decades of accumulated research findings from the domain of psychology and mathematics education into the school mathematics curriculum. This study aimed to operationalise a heuristic termed visualise-predict-check (VPC) for the teaching of spatial visualisation and explore the affordances for enabling teachers to foster spatial reasoning. We conducted moment-by-moment and fine-grained analysis of teaching-learning transactions of two teachers who implemented a lesson devised on the basis of the VPC heuristic. The data sources included video-taped recordings and classroom observations. The VPC heuristic provided teaching trajectories to explicitly prompt students to engage in spatial visualisation while learning mathematics and in so doing the class routine was remarkably spatially elevated. However, subtle disparities in the implementation of the lesson lead to differences in students’ engagement. The more deliberate VPC fostered students’ spatial thinking whereas the limited application of VPC tended to inhibit opportunities for reasoning spatially. VPC offers much potential to enhance spatial skills both in classroom routine teaching and in specialised interventions.

中文翻译：

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空间可视化技能教学会带来什么：通过可视化-预测-检查启发式探索

空间推理领域的一个主要挑战是将数十年来积累的研究成果从心理学和数学教育领域转变为学校数学课程。这项研究旨在为空间可视化教学提供启发式的可视化预测检查（VPC），并探索使教师能够促进空间推理的能力。我们对两位老师的教学活动进行了逐时和细粒度的分析，这些老师实施了基于VPC启发式设计的课程。数据来源包括录像带和教室观察。VPC启发式方法提供了教学轨迹，以明确提示学生在学习数学的同时进行空间可视化，因此课堂常规在空间上得到了显着提升。但是，课程实施中的细微差异会导致学生参与度的差异。更加谨慎的VPC促进了学生的空间思维，而VPC的有限应用往往会抑制空间推理的机会。VPC在课堂常规教学和专业干预方面都具有增强空间技能的巨大潜力。更加刻意的VPC促进了学生的空间思维，而VPC的有限应用往往会抑制空间推理的机会。VPC在课堂常规教学和专业干预方面都具有增强空间技能的巨大潜力。更加刻意的VPC促进了学生的空间思维，而VPC的有限应用往往会抑制空间推理的机会。VPC在课堂常规教学和专业干预方面都具有增强空间技能的巨大潜力。