There is mixed evidence as to whether concrete manipulatives (e.g., toy animals) are better than abstract manipulatives (e.g., counters) for teaching mathematical concepts to children. Concreteness is defined as the amount of extraneous information a manipulative provides, and in this study we aimed to unpick which dimensions of concreteness influence manipulative choice. Researchers, teachers, and parents completed a comparative judgment task comparing images of manipulatives varying in different dimensions of concreteness, selecting which they would choose to teach arithmetic to children. The findings indicated homogeneous, 3-dimensional manipulatives were the most preferred across all groups to teach arithmetic to children, regardless of more extraneous features. This contradicts research recommendations to minimize the use of concrete manipulatives due to their distractive qualities. Instead, it suggests that some concrete features may be preferred in more naturalistic contexts. More research is required to investigate how different dimensions of concreteness influence learning outcomes for children both in artificial research contexts and in practice.

中文翻译：

---

具体性对数学操作选择的影响

对于向儿童教授数学概念，具体的操作物（例如，玩具动物）是否比抽象的操作物（例如，计数器）更好，证据不一。具体性被定义为操作提供的无关信息量，在这项研究中，我们的目的是弄清楚具体性的哪些维度影响操作选择。研究人员、教师和家长完成了一项比较判断任务，比较不同具体维度的教具图像，选择他们要教孩子算术的教具。研究结果表明，无论有多少无关的特征，同质的 3 维教具是所有群体中最喜欢教儿童算术的。这与尽量减少使用具体操作物的研究建议相矛盾，因为它们会分散注意力。相反，它表明在更自然的背景下可能更喜欢一些具体的特征。需要更多的研究来调查具体性的不同维度如何影响人工研究背景和实践中儿童的学习成果。