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Edited by: Hans-Christoph Nuerk, Universität Tübingen, Germany

Reviewed by: Robert S. Siegler, Carnegie Mellon University, United States; Zachary Hawes, University of Western Ontario, Canada; Victoria Simms, Ulster University, United Kingdom

This article was submitted to Developmental Psychology, a section of the journal Frontiers in Psychology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

In this article, we review approaches to modeling a connection between spatial and mathematical thinking across development. We critically evaluate the strengths and weaknesses of factor analyses, meta-analyses, and experimental literatures. We examine those studies that set out to describe the nature and number of spatial and mathematical skills and specific connections between these abilities, especially those that included children as participants. We also find evidence of strong spatial-mathematical connections and transfer from spatial interventions to mathematical understanding. Finally, we map out the kinds of studies that could enhance our understanding of the mechanisms by which spatial and mathematical processing are connected and the principles by which mathematical outcomes could be enhanced through spatial training in educational settings.

Spatial ability contributes to performance in science, technology, engineering, and mathematics (STEM) domains even controlling for verbal and mathematical abilities (Shea et al.,

Both spatial and mathematical ability have been investigated since the early days of psychological science using factor analytical methods that sought to map the “structure of the intellect” (Spearman,

While many studies have found evidence of connections between spatial and numerical tasks in young children, only recently have studies explored the factor structure of their spatial and mathematical skills. Mix et al. (

Between kindergarten and sixth grade range, all spatial tasks loaded together on a distinctly spatial factor, and all mathematical tasks loaded on a distinctly mathematical factor (Mix et al.,

Factor analysis is a useful tool for isolating the source of correlations and removing measurement error (Bollen,

In addition to factor analyses, researchers have tackled the question of how the domains of space and math are connected through targeted experimental studies and meta-analyses. In this section, we outline prominent theories about the divisions in each domain and evidence for correlations between spatial and mathematical skills. Understanding these theories is important because they can help us to understand which particular facet or type of spatial thinking is linked to a particular type of mathematical thinking.

One comprehensive meta-analysis of spatial skills training by Uttal et al. (

The number and nature of basic mathematical skills that underlie mathematical thinking are also in question. For example, a distinction has been made between core number systems that represent exact and approximate number (Carey,

Certain connections between specific spatial skills and mathematical skills have been observed (e.g., visuospatial working memory and computation, Raghubar et al.,

Observed relations between mental rotation and mathematical skills.

Gunderson et al., |
5.4 | Children's mental transformation task, 2D figure rotation/construction (Levine et al., |
Number une estimation, appoximate calculation |

Kyttälä et al., |
6.16 | Novell “'Troll” task, 2D, same/different choice | General math skill |

Carr et al., |
7.5 | Cube rotation (Vandenberg and Kuse, |
Arithmetic |

Battista, |
12 | Purdue spatial visualizaiton Test, 3D images rotation (Guay, |
Logical reasoning, geometric knowledge and problem solving |

Hegarty and Kozhevnikov, |
12.08 | Primary mental abilities, 2D rotation/figure completion (Thurstone, |
Problem solving skill |

Delgado and Prieto, |
13 | Cube rotation (Peters, |
Geometry, word problems |

Casey et al., |
13.8 | Cube rotation (Vandenberg and Kuse, |
Geometry, SAT math |

Kyttälä and Lehto, |
15.5 | Cube rotation (Vandenberg and Kuse, |
Mental arithmetic, geometry, word problems |

Reuhkala, |
15.5 | Cube rotation (Vandenberg and Kuse, |
Math skill (mental arithmetic, algebra, geometry) |

Geary et al., |
19 | Cube rotation (Vandenberg and Kuse, |
Arithmetic |

Thompson et al., |
21.26 | Cube rotation (Peters, |
Compatibility effect of number comparison |

Moving beyond correlational studies, studies that have measured the impact of training mental rotation on specific mathematical skills, have not yielded consistent findings, with some finding evidence of transfer (e.g., Cheng and Mix,

Cognitive process models provide an account of the mental processes engaged when performing a specific task. What cognitive process or processes actually drive performance on a spatial task? Answering this question would also allow us to understand the mechanism that accounts for the connection between spatial skills, like mental rotation, and performance on mathematical tasks such as missing term problems (Cheng and Mix,

What is known about the processes used for spatial skills? Various studies have supported substantive divisions between particular kinds of spatial skills, e.g., the intrinsic-extrinsic divide separating tasks such as mental rotation from perspective taking (Huttenlocher and Presson,

Mental rotation was first described based on the finding that time to simulate the rotation of an object was related to the angle through which the object was rotated (Shepard and Metzler,

Each of these modeled components of mental rotation performance has a potential role to play in the observed relationship between mental rotation and various mathematical skills over the course of development. If spatial constructs are actually based on wide-ranging processes it opens up the hypothesis space to determine the source of connections between spatial and mathematical thinking. Rather than a simple connection between two monolithic skills, there are numerous possible connections based on the components of each, and possibly even multiple ways a spatial skill can act in a single math problem. The work of figuring out which components are critical to the observed relation between spatial and mathematical skills, while daunting, is needed in order to unpack what otherwise are opaque connections.

To take one example, Gunderson et al. (

Potential connections among spatial and mathematical skill components.

Meta-analyses provide strong evidence that training spatial skills in the laboratory result in significant improvements and transfer to other spatial skills (Uttal et al.,

One finding substantiated by factor analyses and interventions is that spatial skills are more closely related to novel mathematical and scientific content than to STEM skills that are more familiar (Stieff,

In this review, we critically evaluate the contributions of the factor analytic method to identifying and elucidating the connection between spatial and mathematical thinking across development. We highlighted a central gap in our knowledge—understanding the mechanisms connecting spatial and mathematical skills—which can be better addressed through targeted experimental studies that are informed by process models than by factor analytic studies. The findings that can emerge from this approach are important for increasing our basic understanding of why spatial and mathematical thinking are connected. They also hold promise for informing educational efforts to increase mathematical achievement by strengthening spatial thinking by training spatial skills, by encouraging the use of spatial tools, and by showing children how they can deploy these skills and tools to solve particular kind of mathematical problems.

CY wrote the original draft and led efforts to refine subsequent drafts for this article. All authors worked on a related chapter; SL and KM contributed substantially to the writing and editing of this article.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.