Centre de Recherche en Neurosciences de Lyon (CRNL), INSERM U1028 - CNRS UMR5292, Université de Lyon, Lyon, France.
Université Paris Cité, LaPsyDÉ, CNRS, F-75005, Paris, France.
Psychon Bull Rev. 2024 Oct;31(5):2036-2057. doi: 10.3758/s13423-024-02499-z. Epub 2024 Apr 2.
We review the evidence for the conceptual association between arithmetic and space and quantify the effect size in meta-analyses. We focus on three effects: (a) the operational momentum effect (OME), which has been defined as participants' tendency to overestimate results of addition problems and underestimate results of subtraction problems; (b) the arithmetic cueing effect, in which arithmetic problems serve as spatial cues in target detection or temporal order judgment tasks; and (c) the associations between arithmetic and space observed with eye- and hand-tracking studies. The OME was consistently found in paradigms that provided the participants with numerical response alternatives. The OME shows a large effect size, driven by an underestimation during subtraction while addition was unbiased. In contrast, paradigms in which participants indicated their estimate by transcoding their final estimate to a spatial reference frame revealed no consistent OME. Arithmetic cueing studies show a reliable small to medium effect size, driven by a rightward bias for addition. Finally, eye- and hand-tracking studies point to replicable associations between arithmetic and eye or hand movements. To account for the complexity of the observed pattern, we introduce the Adaptive Pathways in Mental Arithmetic (APiMA) framework. The model accommodates central notions of numerical and arithmetic processing and helps identifying which pathway a given paradigm operates on. It proposes that the divergence between OME and arithmetic cueing studies comes from the predominant use of non-symbolic versus symbolic stimuli, respectively. Overall, our review and findings clearly support an association between arithmetic and spatial processing.
我们回顾了算术和空间之间概念关联的证据，并在荟萃分析中量化了效应大小。我们关注三个效应：（a）操作动量效应（OME），其被定义为参与者倾向于高估加法问题的结果而低估减法问题的结果；（b）算术提示效应，其中算术问题在目标检测或时间顺序判断任务中充当空间提示；（c）眼动和手动追踪研究中观察到的算术和空间之间的关联。OME 在为参与者提供数值反应选择的范式中始终得到一致发现。OME 表现出较大的效应大小，由减法时的低估而加法时的无偏性驱动。相比之下，在参与者通过将其最终估计值转换为空间参考框架来表示其估计值的范式中，没有一致的 OME。算术提示研究显示出可靠的小到中等效应大小，由加法的右偏驱动。最后，眼动和手动追踪研究表明算术和眼动或手动运动之间存在可复制的关联。为了说明所观察到的模式的复杂性，我们引入了心理算术的自适应途径（APiMA）框架。该模型包含了数值和算术处理的核心概念，并有助于确定给定范式所采用的途径。它提出，OME 和算术提示研究之间的分歧来自于分别主要使用非符号和符号刺激。总的来说，我们的综述和发现清楚地支持了算术和空间处理之间的关联。
