Visuo-spatial abilities are key for young children’s verbal number skills

Abstract

Children’s development of verbal number skills (i.e., counting abilities and knowledge of the number names) presents a milestone in mathematical development. Different factors such as visuo-spatial and verbal abilities have been discussed as contributing to the development of these foundational skills. To understand the cognitive nature of verbal number skills in young children, the current study assessed the relation of preschoolers’ verbal and visuo-spatial abilities to their verbal number skills. In total, 141 children aged 5 or 6 years participated in the current study. Verbal number skills were regressed on vocabulary, phonological awareness and visuo-spatial abilities, and verbal and visuo-spatial working memory in a structural equation model. Only visuo-spatial abilities emerged as a significant predictor of verbal number skills in the estimated model. Our results suggest that visuo-spatial abilities contribute to a larger extent to children’s verbal number skills than verbal abilities. From a theoretical point of view, these results suggest a visuo-spatial, rather than a verbal, grounding of verbal number skills. These results are potentially informative for the conception of early mathematics assessments and interventions.

Introduction

Poor mathematical skills are associated with adverse life outcomes, such as lower qualification and socioeconomic attainment, highlighting the importance of mathematical abilities in numerate societies (Duncan et al., 2007, Ritchie and Bates, 2013). The development of mathematical abilities sets off during infant years and continues along a learning trajectory (Clements & Sarama, 2010). Development along a learning trajectory implies that more complex skills build on more basic skills. In other words, basic skills lay the foundation for later achievement in mathematics and are crucially important for scholastic achievement (Claessens et al., 2009, Duncan et al., 2007, Jordan et al., 2009).

The development of mathematical abilities occurs in a quasi-hierarchical manner (Von Aster & Shalev, 2007). A first grasp of mathematical understanding is already present during infancy, allowing infants, for example, to discriminate the numerosity of two sets (Hyde, 2011, Izard et al., 2009, Starr et al., 2013, Xu et al., 2005). This inherited core representation of magnitude is preverbal and nonsymbolic. The first step toward a symbolic notion of numbers is the acquisition of verbal number knowledge. The development of symbolic knowledge starts during the preschool years by learning the number words. During these preschool years, children learn more than simply reciting the number chain. They learn to use these number words in a meaningful way and map them onto the corresponding representations of quantity and Arabic numerals (Benoit et al., 2013, Gunderson et al., 2015, Mundy and Gilmore, 2009). The knowledge of Arabic numerals marks the second milestone in the development of symbolic number knowledge (Von Aster & Shalev, 2007). In the current study, we use the term verbal number skills to refer to the knowledge about number words and their meaningful use (e.g., ascribing the correct number word to a number of items or an Arabic numeral). Hence, verbal number skills critically influence the processes of (verbal and Arabic) number symbolization (see quasi-hierarchical structure of the developmental model of numerical cognition; Von Aster & Shalev, 2007). The current study aimed at investigating the cognitive basis of these verbal number skills. It asked whether verbal number skills are relying primarily on verbal or nonverbal (i.e., visuo-spatial) processes. The first assumption may appear obvious. However, considering that children’s earliest mathematical knowledge is nonsymbolic and preverbal, it is also possible that verbal number skills have a visuo-spatial basis. Before tackling the above question, we provide a brief overview of the literature on the respective contributions of verbal and visuo-spatial abilities (VSAs) for mathematical development.

Verbal abilities have been related to math development and achievement in multiple studies (Kleemans et al., 2012, LeFevre et al., 2010, Purpura and Ganley, 2014, Purpura et al., 2011, Toll and Van Luit, 2014, Vukovic and Lesaux, 2013b). Various types of verbal and linguistic abilities have been investigated in this context such as vocabulary (Purpura & Ganley, 2014), phonological awareness (Kleemans et al., 2011, Krajewski and Schneider, 2009, Simmons et al., 2008), and verbal working memory (Bull et al., 2008, De Smedt et al., 2009, Hornung et al., 2014, Noël, 2009, Passolunghi et al., 2008). Among the many facets of mathematical abilities, the focus of the current research lies on young children’s verbal number skills. The verbal nature of these skills makes them particularly susceptible to relying on verbal abilities. LeFevre et al. (2010) reported, for instance, that children’s general vocabulary is tied to their ability to acquire number-specific vocabulary (see also Vukovic & Lesaux, 2013a). Other researchers emphasize the role of phonological awareness (i.e., the awareness of sounds in spoken language; see, e.g., Stahl & Murray, 1994, for a more precise definition) for mathematics (De Smedt et al., 2010, Hecht et al., 2001, Krajewski and Schneider, 2009, Lopes-Silva et al., 2014, Simmons et al., 2008). Simmons and Singleton (2008) formulated the weak phonological hypothesis. According to this hypothesis, children with weak phonological skills should encounter difficulties in the domains of mathematics that involve manipulations of verbal codes such as verbal number skills. Overall, during the preschool years, a general relation between language and a wide range of early numeracy measures can be observed (Purpura & Ganley, 2014).

A positive relation between performance on tasks of VSA and mathematics has been reported for adults (Geary et al., 2000, Georges et al., in press, Thompson et al., 2013), adolescents (Casey et al., 1995, Delgado and Prieto, 2004, Reuhkala, 2001), elementary school children (Gunderson et al., 2012, Lachance and Mazzocco, 2006, Zhang et al., 2014), and preschool children (Mix et al., 2016, Verdine et al., 2014, Zhang and Lin, 2015). Even infants’ spatial processing was recently suggested to act as a precursor of later VSAs and mathematics at 4 years of age (Lauer & Lourenco, 2016). The focus of the current work lies on so-called small-scale spatial abilities (see Hegarty, Montello, Richardson, Ishikawa, & Lovelace, 2006) that require mental transformation or manipulations of visually presented shapes and objects (in contrast to large-scale spatial abilities requiring physical navigation through space). In general, different types of VSA can be distinguished. In a seminal article, Linn and Petersen (1985) distinguished among three different types of VSA: (a) spatial perception, (b) mental rotation, and (c) spatial visualization. The common feature of these visuo-spatial categories is that all of them require mental processing and/or transformation of visually presented stimuli. Furthermore, tasks of visuo-motor integration (VMI), requiring the coordination between visual input and motor output, have been consistently linked to mathematical development in children (Cameron et al., 2015, Carlson et al., 2013, Mix et al., 2016, Pieters et al., 2012, Simms et al., 2016, Sortor and Kulp, 2003). Moreover, visuo-spatial working memory (or visuo-spatial short-term memory acting as a proxy of working memory in young children; see Hornung, Brunner, Reuter, & Martin, 2011) has been related to mathematical achievement in children (Caviola et al., 2014, Holmes et al., 2008, Hornung et al., 2014, Kyttälä et al., 2003, LeFevre et al., 2010, McKenzie et al., 2003, Meyer et al., 2010, Passolunghi and Mammarella, 2012, Passolunghi et al., 2008, Rasmussen and Bisanz, 2005, Szucs et al., 2013). Summing up the current scientific literature focusing on the relation between VSAs and mathematical development during the preschool years, different types of VSA emerged as being specifically important: spatial perception (Zhang & Lin, 2015), VMI (Cameron et al., 2015, Carlson et al., 2013, Sortor and Kulp, 2003), and visuo-spatial working memory (VSWM) (Bull et al., 2008, Rasmussen and Bisanz, 2005).

Several explanations for the consistently observed relation between VSAs and math have been suggested. A predominant assumption relies on the spatial nature of numbers themselves: the mental number line (MNL). In Western cultures, small numbers/magnitudes are associated with the left side of space, whereas large numbers/magnitudes are associated with the right side of space (de Hevia et al., 2008, Fias and Fischer, 2005, Göbel et al., 2011, Hubbard et al., 2005). The systematic interaction between space and numbers is well established for healthy adults (Nuerk, Wood, & Willmes, 2005) and has recently been documented in young children (Hoffmann et al., 2013, Patro et al., 2016, Patro and Haman, 2012).

In addition, it is assumed that VSAs may benefit math performance by supporting the visualization of mathematical problems and, thus, facilitating the solution of these problems (Cheng and Mix, 2014, Skagerlund and Träff, 2016, Zhang and Lin, 2015). Furthermore, better VSAs predict the use of higher-level mental strategies in arithmetic in first grade children (Laski et al., 2013).

It is commonly reported that VSAs are substantially important for nonfamiliar mathematical tasks (Mix et al., 2016, Uttal and Cohen, 2012). From this, we can derive that VSAs should be particularly important during the preschool years. Children’s mathematical understanding is constantly developing throughout the preschool years, when children are regularly confronted with nonfamiliar tasks that would then require them to rely on VSAs to successfully solve these tasks. In this vein, studies report that VSWM is important for mathematical performance during the early school years, but its importance diminishes when different skills are mastered, and then verbal working memory becomes more important (McKenzie et al., 2003, Van de Weijer-Bergsma et al., 2015).

To the best of our knowledge, the question about the relation between VSAs and young children’s verbal number skills (defined in a broader sense, as in the current study, by integrating not only counting abilities but also, e.g., number naming) has not been addressed explicitly. One study, focusing on the contribution of VSAs to a very specific aspect of verbal number knowledge (i.e., children’s counting sequence knowledge), found that VSAs in kindergarten predicted arithmetic knowledge in Grades 1 and 3, an association that was mediated by children’s knowledge of the counting sequence (Zhang et al., 2014). A further hint for the importance of VSAs, most notably spatial perception, is provided by the results that kindergarteners’ spatial perception predicts children’s performance on arithmetic word problems, which are presented verbally (Zhang & Lin, 2015).

Considering that the first mathematical understanding in children is preverbal, and in view of the commonly reported link between VSAs and mathematics in general, it can be assumed that VSAs may also be at the basis of verbal number skills.

The current study aimed at identifying the respective roles of verbal abilities and VSAs for the development of young children’s verbal number skills. Previous research reported links between different aspects of verbal abilities and VSAs, on the one hand, and mathematics, on the other. However, much less is known about the importance of these cognitive abilities for verbal number skills in young children.

A concurrent consideration of these different abilities allows us to determine whether the considered abilities are equally important for the development of verbal number skills or whether certain abilities emerge as specifically important (Fig. 1). Second, we hypothesized that visuo-spatial aspects should be especially important for verbal number skills. Even though, at first sight, verbal number skills appear to be primarily verbal in nature, numbers are more than simple phonemes. The first numerical understanding, already observable in infants, is preverbal, giving rise to the assumption that verbal number skills should also have a nonverbal (i.e., visuo-spatial) component. We assume that the spatial nature of number is already present and critical in preschoolers’ verbal number skills.

Hence, these findings should be especially informative for the conception and development of preschool interventions fostering children’s verbal number skills.