Abstract Understanding division is critical for later mathematical achievement. Yet division concepts are difficult to grasp and are often not explicitly taught until middle childhood. Given the structural similarity between sharing and division, we investigated whether contextualizing division problems as sharing scenarios improved preschool-aged children’s abilities to solve them, as compared with other arithmetic problems which do not share structural similarities with sharing. Preschoolers (N = 113) completed an addition, subtraction, and division problem in either a sharing context that presented arithmetic via contextualized sharing scenarios, or a comparable, linguistically-matched non-social context (randomly assigned). Children were assessed on their formal, verbal responses and their informal, non-verbal, action-based responses (abilities to solve the problems using manipulatives) to these arithmetic problems. Most critically, context predicted children’s performance on the division, but not the addition or subtraction trial, supporting a structural link between sharing and division. Results also revealed that children’s action-based responses to the arithmetic problems were much more accurate than their verbal ones. Results are discussed in terms of the conceptual link between division and sharing.

中文翻译：

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分享场景促进学龄前儿童的分裂表现

摘要 理解除法对于以后的数学成就至关重要。然而，划分概念很难掌握，而且往往直到童年中期才被明确教授。鉴于共享和划分之间的结构相似性，我们研究了与其他不具有共享结构相似性的算术问题相比，将划分问题情境化为共享场景是否能提高学龄前儿童解决这些问题的能力。学龄前儿童 (N = 113) 在通过上下文共享场景呈现算术的共享上下文或可比较的语言匹配的非社会上下文（随机分配）中完成加法、减法和除法问题。评估儿童的正式、口头反应和非正式、非口头、对这些算术问题的基于动作的反应（使用操作解决问题的能力）。最关键的是，上下文预测了儿童在除法上的表现，而不是加法或减法试验，支持了分享和除法之间的结构性联系。结果还显示，儿童对算术问题的基于行动的反应比他们的口头反应要准确得多。结果是根据划分和共享之间的概念联系来讨论的。结果还显示，儿童对算术问题的基于行动的反应比他们的口头反应要准确得多。结果是根据划分和共享之间的概念联系来讨论的。结果还显示，儿童对算术问题的基于行动的反应比他们的口头反应要准确得多。结果是根据划分和共享之间的概念联系来讨论的。