Linking language, visual-spatial, and executive function skills to number competence in very young Chinese children

Highlights

• The study examines how language, visual-spatial, and executive function skills together contribute to number competence among very young children.

• It uses a sample of 109 Chinese three-year-olds tested individually on their number competence, oral and written language, spatial perception, and behavioral executive skills.

• Receptive vocabulary, print knowledge, spatial perception, and executive skills all make a unique contribution to early number competence.

• Findings the highlight importance of considering fundamental domain-general factors that may be crucial for early number learning.

Abstract

Early number competence is highly predictive of later mathematics achievement. The present study aims to examine how fundamental domain-general skills, including language, visual-spatial, and executive functions, together relate to early acquisition of numbers among very young children. A total of 109 Chinese children, aged approximately three years, in Hong Kong were tested individually on their number competence, receptive vocabulary, knowledge of written letters, rapid automatized naming, spatial perception, and behavioral executive skills. The results showed that vocabulary, letter knowledge, spatial perception, and executive skills all made a unique contribution to number competence. The findings add to the literature by documenting the critical importance of spatial perception and written language for early number learning. They also suggest that language, visual-spatial, and executive skills provide the building blocks for children’s number acquisition at a very young age.

Introduction

Children vary substantially in their understanding of numbers and number relations at very young ages (Starkey & Klein, 2008). Because this early number competence is highly predictive of later academic achievement (Duncan et al., 2007; Jordan, Kaplan, Ramineni, & Locuniak, 2009), it is vital to identify factors associated with number learning. A growing body of studies suggests that basic domain-general skills, such as language, visual-spatial, and executive functions, provide the building blocks for this process (LeFevre et al., 2010, Noël, 2009, Purpura and Ganley, 2014; Verdine, Irwin, Golinkoff, & Hirsh-Pasek, 2014). Little research, however, has examined how these skills together relate to number competence, especially among very young children. Furthermore, most prior work has been carried out in Euro-American settings, with only limited research in Chinese societies. In the present study, we assess the relations of oral and written language, visual-spatial, and executive function skills with number competence among 3-year-old Chinese children.

Research over the past three decades suggests that preschoolers have a considerable body of number competencies (Fuson, 1988, Gelman and Gallistel, 1978, Ginsburg, 1977). Number competencies refer to ability to count numbers in the correct order, grasp counting principles (e.g., cardinality: the last number of a set indicates the total number of objects), apprehend the relations between numbers (e.g., 7 is more than 5), and join and separate sets (e.g., 1 and 3 makes 4, and 4 take away 1 is 3). These competencies are in contrast to the abstract concepts (e.g., commutative law of addition: m + n = n + m) and calculations that children acquire primarily through formal teaching (Jordan et al., 2009).

Aspects of number competencies develop over time. Oral counting begins at around two years of age and evolves from an initial acquisition phase of learning the conventional number word sequence to an elaboration phase of decomposing this sequence into separate words (Fuson, 1988). Different parts of the number sequence (e.g., “one, two, three” versus “eight, nine, ten”) may be in different phases of development at the same time, and it takes several years to acquire and elaborate the sequence. During the acquisition phase, children begin to use the number sequence to count objects (Fuson, 1988). As early as two and a half years of age, children can discover the cardinality principle (Gelman & Gallistel, 1978). The counting principles are acquired over several years, such that most six-year-olds apply these principles when they enumerate a set of objects.

Children can understand numerical relations, such as the precedence relation between number words, as they learn the number sequence at very young ages (Fuson, 1988). For example, when asked what comes after a number such as five, some two-year-olds can start with one and count up to the number: “one, two, three, four, five—oh, six.” By six years of age, children typically can automatically state the number after a given number without counting from one (Baroody & Wilkins, 1999).

Even before schooling, many children are interested in how to read numerals (Baroody & Wilkins, 1999). This is the first step toward formal mathematical knowledge. Learning to read numerals depends on how often children are exposed to them in the environment, but it also requires children’s ability to construct mental images of the symbols and distinguish among them (Baroody & Wilkins, 1999). Preschoolers also have some calculation abilities before they comprehend formal expressions such as 2 + 3 = ?. As early as two years of age, children can solve addition problems involving sums of three or less (Klein & Starkey, 1988), and preschoolers as young as three years of age can perform simple addition and subtraction involving larger numbers when both verbal labels and physical referents are provided (Starkey & Gelman, 1982).

The acquisition of number competencies involving words and symbols at a young age provides a foundation for later academic achievement (Duncan et al., 2007, Jordan et al., 2009). Thus, it is warranted to examine the factors associated with number competence. Most researchers agree that early number learning relies heavily upon basic domain-general processes such as visual-spatial and language (Dehaene, 2011, Mix and Sandhofer, 2007). Dehaene posits that a language-dominant area (the left angular gyrus) and a space-dominant area (the posterior superior parietal lobule) in the brain, alongside a quantity-dominant area (the intraparietal sulcus), are involved in numerical processing. Mix and Sandhofer even argue that number development can be explained solely in terms of domain-general processes such as visual-spatial (e.g., processing contour length) and language (e.g., naming). Finally, executive functions, which include a variety of top–down mental processes that help children focus attention, resist distractions, and follow directions, are another general skill set that is often highlighted in relation to number competence in the literature (Bull & Lee, 2014). Consequently, the focus of the present study is on three sets of domain-general skills, namely language, visual-spatial, and executive functions, that may be crucial for number learning. Before the details of the study are described, a review of studies of the relations from these domain-general skills to number competence will be considered.

Language skills refer to the ability to understand and use an acquired oral and written language. In the literature, language-impaired children are found to be at particular risk for difficulties with basic numeracy (Koponen, Mononen, Räsänen, & Ahonen, 2006). For example, Fazio (1994) showed that 4–5-year-old children with specific language impairment had difficulties with rote counting, displayed a limited repertoire of number terms, and miscounted sets of objects. These findings suggest that language skills may play an important role in numerical development.

Because vocabulary deficits are a defining characteristic of language impairment, some investigators are interested in the relation of vocabulary with number competence. LeFevre et al. (2010) posit that receptive vocabulary reflects children’s ability to acquire vocabulary in the number system (i.e., word names for numbers). They found that receptive vocabulary at ages 4–5 years was associated with a variety of number competencies, including number recognition, order, and magnitude comparison, measured concurrently or two years later. Negen and Sarnecka (2012) propose that children’s development of general vocabulary (e.g., nouns) helps them pick out the referents of number words (e.g., children hearing “two rabbits” are better able to figure out what “two” means if they already understand the word rabbit(s)). They further showed that both receptive and expressive vocabulary was related to number–word knowledge in children aged between 30 and 60 months.

Prior studies linking language to numerical development focused almost exclusively on children’s ability to understand oral language. To understand the Arabic number system, children must have the ability to map oral sounds to the written symbols (Brizuela, 2004; Neumann, Hood, Ford, & Neumann, 2013). It is possible that children’s early exposure to written language symbols (letters, characters etc.), where they are provided with experience of mapping sounds to the symbols, facilitates their ability to use and manipulate other written symbols, such as Arabic digits. In support of this notion, Purpura, Hume, Sims, and Lonigan (2011) showed that 3- to 5-year-old children’s print knowledge was associated with their numeracy competence one year later. Zhang et al. (2014) found that children’s knowledge of Finnish written letters at age six predicted their growth trajectory of competence in written arithmetic from ages 7 to 10. More recently, both oral and written language skills were found to have distinct relations with young children’s acquisition of numbers (Purpura & Napoli, 2015) and arithmetic calculations (Zhang & Lin, 2015). Indeed, neuroimaging research has shown that the left mid-fusiform area, often referred to as ‘the visual word form area’ (VWFA) and located in the language-dominant cortex, is involved in processing Arabic digits (Arsalidou & Taylor, 2011). From an evolutionary perspective, the VWFA is initially involved in object recognition and later on evolves and is recruited to serve an analogous function in recognizing written symbols (e.g., letters, numbers; Lervåg & Hulme, 2009). Hence, there is good reason to believe that written symbolic skills are crucial for learning Arabic digits and acquiring number competence.

Recently, rapid automatized naming (RAN) has been noted in the literature in relation to number competence. RAN is often viewed as a global measure of processing speed or a specific measure of phonological processing speed. Recent evidence suggests that RAN taps the integrity of the VWFA and the areas involved in phonological retrieval and production (Lervåg & Hulme, 2009). If this is true, RAN may capture the speed of processing both oral and written language and, consequently, should be related to number competence such as counting and number recognition. Empirically, Koponen et al. (2006) found that RAN was related to counting in preschool children, and Cirino (2011) showed that RAN was associated with number recognition in kindergarten children. Because some researchers argue that RAN and number competence are associated because numbers are used as stimuli in RAN tasks (Landerl, Bevan, & Butterworth, 2004), in this study we use objects as stimuli.

Visual-spatial skills, which refer to the ability to understand the visual-spatial relations among objects, are essential for numerical understanding. It has long been suggested that there is a spatial representation of number magnitude along a mental number line in the human mind (Dehaene, Dupoux, & Mehler, 1990). Siegler and Booth (2004) demonstrate that this spatial representation develops from a logarithmically-compressed form to a linear form; such development involves refinement of the spacing of numbers along the number line. Moreover, Siegler and Booth further found that the use of linear representation was related to children’s numerical and arithmetic acquisition, indicating that visual-spatial skills may play a crucial role in early number learning.

Visual-spatial skills are not a unitary construct. Linn and Petersen’s (1985) meta-analysis distinguishes three types, namely spatial perception (i.e., identifying spatial relations among task components in spite of distracting information), mental rotation (i.e., mentally rotating a 2-D or 3-D object), and spatial visualization (i.e., processing complicated, multi-step manipulations, often analytical, of spatial information). Recently, Uttal et al. (2013) argue for an alternative classification along two dimensions: intrinsic–extrinsic and static–dynamic. They further classify spatial perception into the extrinsic-static category, mental rotation into the intrinsic-dynamic category, and spatial visualization into the intrinsic-static or intrinsic-dynamic category (depending on the nature of the task). Earlier studies relating visual-spatial skills to number and arithmetic competence focus mainly on primary and secondary school students, revealing modest correlations between them (see Friedman, 1992; Harris, Hirsh-Pasek, & Newcombe, 2013 for meta-analyses).

In recent studies, increasing attention has been paid to younger children. These studies emphasize how sophisticated visual-spatial skills, such as mental rotation (Gunderson, Ramirez, Beilock, & Levine, 2012) and spatial visualization (Zhang et al., 2014), contribute to early grasp of numbers. For instance, Barnes et al. (2011) found that spatial visualization at age 5 was related concurrently to rote counting and nonverbal calculation. Gunderson et al. (2012) showed that mental rotation at age 5 predicted children’s linear number line knowledge at age 6 and symbolic arithmetic skills at age 8. More recently, Verdine et al. (Verdine, Golinkoff et al., 2014; Verdine, Irwin et al., 2014) developed a test of spatial assembly skills using block constructions and found that 3-year-old children’s spatial assembly was related to number competence measured concurrently and one year later. These studies, while informative, all used sophisticated visual-spatial tasks that required spatial transformation or manipulation, and largely ignored the role of basic spatial perception.

Spatial perception is a basic visual-spatial skill that does not involve transformation or manipulation. The ability to perceive visual-spatial relations can be observed in newborns and continues to develop through early childhood (Spelke, 2000). Further, children’s development of spatial perception is accompanied by substantial individual variations (McBride-Chang & Kail, 2002). Prior studies suggest that these variations can be captured easily during early childhood: unlike tests of spatial visualization and mental rotation where many 4–5-year-olds perform at chance level (Dean & Harvey, 1979), standard tests of spatial perception (see Section 2) are often simpler and can be understood more easily by them and even younger children (McBride-Chang & Kail, 2002). Recently, Zhang and Lin (2015) found that five-year-old Chinese children’s spatial perception ability was associated with their arithmetic competence one year later. Given the increasing attention devoted to the space-mathematics relation in very young children such as 3-year-olds (Verdine, Golinkoff et al., 2014; Verdine, Irwin et al., 2014), it is important to determine whether early emergent variations in basic spatial perception ability are associated with variations in number competence.

Executive functions refer to a family of top–down mental capacities, including working memory, inhibitory control, and cognitive flexibility, that originate from the dynamics of prefrontal cortex and enhance children’s goal-orientated exploration, reasoning, and problem solving (Diamond, 2013). Although it is theoretically important to examine whether certain components of executive functions relate differentially to number competence (Bull & Lee, 2014), prior evidence suggests that the three components cannot be distinguished among preschool children (Clark, Sheffield, Wiebe, & Espy, 2013; Willoughby, Wirth, & Blair, 2012). Therefore, in this study we opt to assess the integration of executive functions by using a behavioral executive function task, namely the head–toes–knees–shoulders (HTKS) task.

Executive functions enable children to be better able to successfully regulate their behavior (e.g., inhibiting automatic impulses), focus their attention, monitor their progress, and shift to more appropriate task strategies. Hence, executive functions are foundational for learning in many domains. It is found that the relation of executive functions with academic outcomes is especially strong for mathematics (Bull & Lee, 2014). Until recently, most studies linking executive skills to mathematics were confined to older children. However, as Noël (2009) suggests, there is good reason to believe that executive functions play a vital role in early number learning. To count, for example, a child has to hold sequential information in working memory while simultaneously processing it by suppressing the counted items and numbers and updating them with the items and numbers that come next. In support of this hypothesis, recent studies have shown that executive functions are a strong predictor of number competence among young children (Verdine, Irwin et al., 2014). In a study of 2- to 6-year-olds, for instance, Bull, Espy, Wiebe, Sheffield, and Nelson (2011) found that executive function skills were strongly associated with number and arithmetic competence.

Behavioral executive skills, which involve multiple cognitive components including working memory, inhibitory control, and cognitive flexibility, may be especially important for developing number competence (McClelland et al., 2007). Studies of 3–6 year-olds have shown that behavioral executive skills were associated with number competence both concurrently and longitudinally between prekindergarten and kindergarten (McClelland et al., 2014), even after controlling for the cognitive components (Becker, Miao, Duncan, & McClelland, 2014; Clark, Pritchard, & Woodward, 2010).

Cross-cultural studies have documented that Chinese children seem to have better executive skills than Western children (Lan, Legare, Ponitz, Li, & Morrison, 2011; Sabbagh, Xu, Carlson, Moses, & Lee, 2006). Nevertheless, individual variations in executive functions have been observed in Chinese children, and have been associated with their arithmetic competence in primary school (Lan et al., 2011). These studies, however, have not examined the relation of executive functions with Chinese younger children’s number competence, leaving unclear what role executive skills play in their early numerical learning.

Oral and written language, visual-spatial, and executive skills are domain-general predictors of individual differences in number competence. Neuroimaging evidence has also linked the brain areas involved in each of these skills (the left angular gyrus for oral language, the VWFA for written language, the posterior superior parietal lobule for visual-spatial, and the prefrontal cortex for executive skills) to number processing (Arsalidou and Taylor, 2011, Dehaene, 2011). However, executive skills have been ignored in the main theories of number learning, such as McCloskey’s (1992) abstract code model and Dehaene’s (1992) triple-code model. Recently, Geary (2013) proposed a model of young children’s numerical development, where intelligence (language and visual-spatial ability) and executive functions make independent contributions to the learning of numbers and arithmetic. Whereas intelligence can facilitate understanding of the abstract information in mathematics (e.g., the logical and systematic relations among numerals), executive functions help children stay focused and organized and maintain goal-relevant information in mind while processing other information. Hence, there is a good reason to assume that language, visual-spatial, and executive function skills all have a unique role in children’s numerical development.

Prior studies relating multiple domain-general skills to numerical development focused almost exclusively on only two skill sets. They provided support for the differential roles of language versus visual-spatial (Krajewski & Schneider, 2009), language versus executive (Purpura & Ganley, 2014), and visual-spatial versus executive skills (Verdine, Irwin et al., 2014) in number competence. However, it is unclear whether the observed relations persist when all three skill sets are considered simultaneously. In several studies, RAN was a stronger predictor of number and arithmetic competence than executive functions, with the former almost fully accounting for the effect of the latter (van der Sluis, de Jong, & van der Leij, 2004, 2007). Likewise, there is evidence showing that the relation of vocabulary with number competence disappeared when executive or written language skills was controlled (Clark et al., 2013, Zhang et al., 2014). Finally, some studies found that the relation of visual-spatial skills to number and arithmetic competence was weakened or disappeared after taking into account language or executive skills (Assel, Landry, Swank, Smith, & Steelman, 2003; Fuchs et al., 2006), possibly because performing most visual-spatial tasks requires language and executive skills. Hence, it is essential to evaluate whether oral and written language, visual-spatial, and executive skills contribute independently to early number competence.

Chinese children generally have higher mathematical competence than their Western peers (Geary, Fan, & Bow-Thomas, 1992; Stevenson et al., 1990). This is even true for some basic number competencies, including counting, cardinal understanding, and place value enumeration, that were measured before formal schooling (Ho and Fuson, 1998, Miller and Stigler, 1987). For example, Miller, Smith, Zhu, and Zhang (1995) administered a series of monthly counting tasks in a longitudinal sample of Chinese and American children. They found that it was equally difficult for two-year-olds in both countries to recite a list of ten items. From three to four years, however, children’s performance began to diverge. Whereas American children progressed steadily but slowly in learning the teen numbers, Chinese children made much more rapid progress. By age four, Chinese children made very rapid progress in generalizing number names up to 100 after being able to count to approximately 40, while fewer American children could do so.

The superiority of Chinese children’s mathematical competence has been attributed to a number of factors, including, but not limited to, the linguistic features of the Chinese number word system (brief number names: e.g., all single syllables for 0–10; highly clear base-ten structure: e.g., “ten–one” for 11; Miller & Stigler, 1987), Chinese cultural value on academic skills (Needham, 1959), parental expectations and practices (Stevenson et al., 1990), and Chinese children’s advantage in executive functions (Ng, Tamis-LeMonda, Yoshikawa, & Sze, 2015). So far only a few attempts have been made to examine the cognitive foundations of Chinese children’s mathematical competence, and those on young children are even rarer.

In the present study, we examine the extent to which oral and written language (i.e., receptive vocabulary, knowledge of written letters, and RAN), visual-spatial (i.e., spatial perception), and executive skills are associated with number competence among Chinese children aged approximately three years. Based on the literature reviewed above, we expect that language (oral and written), visual-spatial, and executive functions constitute three basic domain-general skill sets that contribute independently to children’s overall number competence. We also explore how these domain-general skills together contribute to each of the individual number competencies that are tested in this study. Specific hypotheses are not drawn, and we do not want to assume that all domain-general skills have independent relations to all individual number competencies, because these relations have rarely been investigated in very young children.

This study extends prior work by considering a larger pool of domain-general skills that encompass three different skill sets in a single framework. It further adds to the literature by examining the relations of written language and spatial perception, two important yet understudied domain-general skills, with number competence. Moreover, these relations are evaluated in children at three years of age, which may be the earliest age at which individual differences in written language and visual-spatial skills can be measured. Finally, this study was conducted in Hong Kong, where Cantonese (a dialect of Chinese, which almost 90% of the population uses as their daily language) and English are the official languages and people are exposed to two scripts (Chinese characters and Roman alphabet) in their daily life. Data from the present sample would be valuable to determine whether a model of number learning derived mainly from studies of Euro-American number and language systems is unique to Euro-American settings or can likewise be applied to understanding number and language systems elsewhere. The present study will facilitate our understanding of the very early sources of individual differences in number competence.