Abstract Multiple external representations (MERs) are central to the practice and learning of science, mathematics and engineering, as the phenomena and entities investigated and controlled in these domains are often not available for perception and action. MERs therefore play a twofold constitutive role in reasoning in these domains. Firstly, MERs stand in for the phenomena and entities that are imagined, and thus make possible scientific investigations. Secondly, related to the above, sensorimotor and imagination-based interactions with the MERs make possible focused cognitive operations involving these phenomena and entities, such as mental rotation and analogical transformations. These two constitutive roles suggest that acquiring expertise in science, mathematics and engineering requires developing the ability to transform and integrate the MERs in that field, in tandem with running operations in imagination on the phenomena and entities the MERs stand for. This core ability to integrate external and internal representations and operations on them – termed representational competence (RC) – is therefore critical to learning in science, mathematics and engineering. However, no general account of this core process is currently available. We argue that, given the above two constitutive roles played by MERs, a theoretical account of representational competence requires an explicit model of how the cognitive system interacts with external representations, and how imagination abilities develop through this process. At the applied level, this account is required to develop design guidelines for new media interventions for learning science and mathematics, particularly emerging ones that are based on embodied interactions. As a first step to developing such a theoretical account, we review the literature on learning with MERs, as well as acquiring RC, in chemistry, biology, physics, mathematics and engineering, from two perspectives. First, we focus on the important theoretical accounts and related empirical studies, and examine what is common about them. Second, we summarise the major trends in each discipline, and then bring together these trends. The results show that most models and empirical studies of RC are framed within the classical information processing approach, and do not take a constitutive view of external representations. To develop an account compatible with the constitutive view of external representations, we outline an interaction-based theoretical account of RC, extending recent advances in distributed and embodied cognition.

中文翻译：

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表征能力：走向分布式和具身的认知账户

摘要 多重外部表示 (MER) 是科学、数学和工程实践和学习的核心，因为在这些领域中调查和控制的现象和实体通常无法用于感知和行动。因此，MER 在这些领域的推理中扮演着双重角色。首先，MER 代表想象中的现象和实体，从而使科学调查成为可能。其次，与上述相关，与 MER 的基于感觉运动和想象的交互使涉及这些现象和实体的集中认知操作成为可能，例如心理旋转和类比转换。这两个基本角色表明，获得科学专业知识，数学和工程需要发展在该领域转换和整合 MER 的能力，同时对 MER 所代表的现象和实体进行想象中的操作。这种整合外部和内部表示和操作的核心能力——称为表示能力 (RC)——因此对于科学、数学和工程的学习至关重要。然而，目前没有关于这个核心过程的一般说明。我们认为，鉴于 MER 所扮演的上述两个构成性角色，表征能力的理论解释需要一个明确的模型来说明认知系统如何与外部表征相互作用，以及想象能力如何在这个过程中发展。在应用层面，该帐户需要为学习科学和数学的新媒体干预制定设计指南，特别是基于具身互动的新兴媒体。作为开发这样一个理论解释的第一步，我们从两个角度回顾了化学、生物学、物理学、数学和工程学中关于使用 MER 学习以及获得 RC 的文献。首先，我们关注重要的理论解释和相关的实证研究，并研究它们的共同点。其次，我们总结了各个学科的主要趋势，然后将这些趋势汇总在一起。结果表明，大多数 RC 模型和实证研究都是在经典信息处理方法内构建的，并且不采取外部表示的本构观点。