There is an emerging consensus that spatial thinking plays a fundamental role in how people conceive, express, and perform mathematics. However, the underlying nature of this relationship remains elusive. Questions remain as to how, why, and under what conditions spatial skills and mathematics are linked. This review paper addresses this gap. Through a review and synthesis of research in psychology, neuroscience, and education, we examine plausible mechanistic accounts for the oft-reported close, and potentially causal, relations between spatial and mathematical thought. More specifically, this review targets candidate mechanisms that link spatial visualization skills and basic numerical competencies. The four explanatory accounts we describe and critique include the: (1) Spatial representation of numbers account, (2) shared neural processing account, (3) spatial modelling account, and (4) working memory account. We propose that these mechanisms do not operate in isolation from one another, but in concert with one another to give rise to spatial-numerical associations. Moving from the theoretical to the practical, we end our review by considering the extent to which spatial visualization abilities are malleable and transferrable to numerical reasoning. Ultimately, this paper aims to provide a more coherent and mechanistic account of spatial-numerical relations in the hope that this information may (1) afford new insights into the uniquely human ability to learn, perform, and invent abstract mathematics, and (2) on a more practical level, prove useful in the assessment and design of effective mathematics curricula and intervention moving forward.

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Prior research has revealed robust and consistent relations between spatial and mathematical skills. Yet, establishing a causal relation has been met with mixed effects. To better understand whether, to what extent, and under what conditions mathematics performance can be improved through spatial training, we conducted a systematic meta-analysis of the extant literature. Our analysis included 29 studies that used controlled pre-post study designs to test the effects of spatial training on mathematics (N = 3,765; k = 89). The average effect size (Hedges's g) of training relative to control conditions was .28 (SE = .07). Critically, there was also evidence that spatial training improved individuals' spatial thinking (g = .49, SE = .09). Follow-up analyses revealed that age, use of concrete manipulatives, and type of transfer ("near" vs. "far") moderated the effects of spatial training on mathematics. As the age of participants increased from 3 to 20 years, the effects of spatial training also increased in size. Spatial training paradigms that used concrete materials (e.g., manipulatives) were more effective than those that did not (e.g., computerized training). Larger transfer effects were observed for mathematics outcomes more closely aligned to the spatial training delivered compared to outcomes more distally related. None of the other variables examined (training dosage, spatial gains, posttest timing, type of control group, experimental design, publication status) moderated the effects. Additionally, analyses of publication bias and selective outcome reporting were nonsignificant. Overall, our results support prior research and theoretical claims that spatial training is an effective means for enhancing mathematical understanding and performance. However, our meta-analysis also highlights a poor understanding of the mechanisms that support transfer. To fully realize the potential benefits of spatial training on mathematics achievement, more theoretically guided studies are needed.

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