Chapter 2. Predictors of arithmetic
2.4 Spatial abilities
Spatial abilities are cognitive skills involving the ability to mentally manipulate spatial information and use visual imagery (Uttal et al., 2013). From a young age, children will play with blocks and other physical objects that involve spatial skills (Rittle- Johnson et al., 2018). These skills will improve over time and can be improved through increased play with toys, shapes and objects (Jirout & Newcombe, 2015; Levine, Huttenlocher, Taylor, & Langrock, 1999).
Children are typically assessed on a range of spatial skills involving spatial visualization (imaging and transforming mental information), form perception (copying and distinguishing different shapes or symbols) and visual-spatial working memory (holding locations in working memory). As with executive function, there are different tasks used to measure these spatial skills. Spatial visualisation involves manipulating objects within space and is commonly assessed using tasks such as a mental rotation task (e.g. which of these images is a rotation of the first) or the block design task which uses physical items (e.g. WISC-IV: Wechsler, 2008). Form perception is the ability to recognise and distinguish different shapes from one another and can be measured with tasks requiring a child to separate a shape into different components (e.g. hidden shapes task; Smith & Lord, 2002). Visuospatial working memory tasks may involve holding shapes in memory, for instance copying a figure or line drawing (e.g. Beery & Beery, 2010) or remembering where an item last appeared on a screen (e.g. Kaufman & Kaufman, 1983).
An important area of investigation, as with executive function tasks, is how different types of spatial skills are related and whether they form one factor or several separate
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factors. Hambrick, Kane and Engle (2005) argue that spatial abilities reflect separate components involving executive control, verbal and visual abilities. On the other hand researchers have examined a range of spatial skills and found that these can form one unitary factor, suggesting any difference with previous evidence may be related to the ages of children measured or types of tasks used (e.g. Mix et al., 2016). As with executive function, there is mixed evidence regarding the nature and relationship between different spatial skills, with debate surrounding the extent to which these skills can be called one factor.
2.4.1 Spatial skills and arithmetic
Spatial skills have been linked with mathematical abilities in a range of studies examining children and adults (see Mix & Cheng, 2012 for a review). Additionally, children with mathematics disorder perform significantly worse on visual-perceptual skills (Geary, 1993). Verdine, Irwin, Golinkoff, & Hirsh-Pasek (2014) show that spatial skills remain a unique and significant longitudinal predictor of mathematical abilities (R2 = .15, p < .001) after controlling for executive function and verbal abilities (N = 44). Gunderson, Ramirez, Beilock, & Levine (2012) provide evidence that spatial skills in Grade 1 predict number line estimations and approximate calculations one year later. This suggests that the ability to spatially represent digits may help in the development of later numerical abilities.
This finding has also been reported for exact calculation skills (Mix & Cheng, 2012). Other studies examining this relationship have reported strong and unique correlations between arithmetic and various spatial abilities, including visuomotor skills, mental rotation and figure copying (Ansari et al., 2003; Gunderson et al., 2012; Rittle-Johnson et al., 2018). Additionally, there is evidence for transfer to arithmetic after training in spatial skills (Cheng & Mix, 2014; Hawes, Moss, Caswell, & Poliszczuk, 2015; Lowrie, Logan, & Ramful, 2017).
Spatial skills are linked to arithmetic and numerical abilities for a number of potential reasons. A dominant theoretical perspective is that numerical and mathematical thinking is governed by spatial representations, for example storing information via a mental number line or holding information about locations and quantities in space (e.g. Lakoff & Núñez, 2000). Children and adults appear to represent smaller numbers on the left side and larger numbers on the right with robust evidence from studies
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examining the SNARC effect; people are quicker to identify a smaller number with their left hand and larger number with their right (Berch, Foley, Hill, & Ryan, 1999). In development, a child who is able to associate numbers to a mental number line in this way may develop stronger associations between numbers and their associated magnitudes; a critical component of numerical development (Mix & Cheng, 2012). Additionally, studies have shown that manipulating the spatial configuration of a calculation (e.g. distance between the Arabic digits in 3+4 x 2) can affect the way people will complete the sum (Fisher, Borchert, & Bassok, 2011; Landy & Goldstone, 2007). Evidence examining the use of a mental abacus has shown that children who employ this technique are able to perform complicated calculations more rapidly than children who have no formal training (Uttal, 2000). This suggests that providing a mental model for the calculation is beneficial for strong maths performance. A second theoretical (although not mutually exclusive) proposal is that spatial skills activate the same neural regions as numerical abilities, with a particular focus on the parietal cortex with evidence supporting brain activation in these regions in functional imaging studies (see Hubbard, Piazza, Pinel, & Dehaene, 2005)
Overall, there appears to be strong evidence for a relationship between spatial skills and numerical development, and it is worth considering these within studies examining arithmetic outcomes. We included spatial abilities as a control measure in our study examining patterning skills (presented in Chapter 5). This was a particularly important control measure for this study as our pattern stimuli include some spatial information within the rotating items.
2.5 Summary
This chapter has outlined some important numerical and domain-general skills which may be important in arithmetic development. Each of these skills are presented in some way in the three studies that were conducted for the purpose of this thesis to examine arithmetic development in children. Each study is now presented in turn including a detailed introduction which evaluates evidence related to the study in question. After the method and results section a discussion outlines these findings in relation to previous evidence with a general discussion presented in the final chapter (Chapter 6).
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