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.

我们回顾了算术与空间之间概念关联的证据，并量化了荟萃分析中的效应大小。我们关注三个效应：（a）操作动量效应（OME），它被定义为参与者高估加法问题结果和低估减法问题结果的倾向； (b) 算术线索效应，即算术问题在目标检测或时间顺序判断任务中充当空间线索； (c) 通过眼动和手部追踪研究观察到的算术与空间之间的关联。 OME 始终存在于为参与者提供数字响应替代方案的范式中。 OME 显示出较大的效应量，这是由减法过程中的低估导致的，而加法过程是无偏的。相比之下，参与者通过将最终估计转码为空间参考框架来表明他们的估计的范式显示没有一致的 OME。算术提示研究显示出可靠的小到中等效应大小，这是由加法的向右偏差驱动的。最后，眼球和手部追踪研究指出算术与眼球或手部运动之间存在可复制的关联。为了解释观察到的模式的复杂性，我们引入了心算自适应路径（APiMA）框架。该模型容纳了数值和算术处理的核心概念，并有助于识别给定范式的运行路径。它提出 OME 和算术提示研究之间的分歧分别来自于非符号刺激与符号刺激的主要使用。总的来说，我们的评论和研究结果清楚地支持算术和空间处理之间的关联。