Development of spatial representation of numbers: A study of the SNARC effect in Chinese children

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Highlights

  • Participants were 314 Chinese children (from kindergartens to 6th grades) and adults.

  • All age groups showed a significant (marginally for 1st graders) SNARC effect.

  • It mean that China preschoolers already developed spatial representations of numbers.

  • However, the size of the SNARC effect did not show much developmental change.

  • These results are discussed in the cross-cultural differences in early development.

Abstract

Using the standard parity judgment task, this study investigated the development of numerical–spatial representation. Participants were 314 healthy right-handed Chinese children (from kindergarteners to sixth graders) and adults. The results revealed that all age groups showed a significant (or marginally significant in the case of first graders) SNARC (spatial–numerical association of response codes) effect, indicating that Chinese children as young as kindergarteners already had developed automatic spatial representations of numbers (or the mental number line). Surprisingly, however, the size of the SNARC effect did not show much developmental change. These results are discussed in the context of the literature on spatial representations of numbers and on cross-cultural differences in early development of number cognition.

Introduction

Systematic research over the last century has demonstrated a close relation between numbers and space (Dehaene et al., 1993, Galton, 1880a, Galton, 1880b, Smith, 1964). One of the important findings during the past two decades is the SNARC (spatial–numerical association of response codes) effect, which refers to the finding that numbers are associated with left–right response coordinates (Dehaene et al., 1993). Using a typical parity judgment task (i.e., judging whether a number is odd or even), researchers have found that the left hand has an advantage in reaction times over the right hand when responding to small numbers, whereas the right hand has an advantage when responding to large numbers (Dehaene et al., 1993). The SNARC effect has been replicated in a wide variety of experimental settings with different numerical materials such as single digits, two-digit numbers, negative numbers, number words (e.g., one, two, three), numbers in different languages (e.g., Chinese, English, French), dot patterns, counting fingers, and auditory or tactile magnitude information (Berch et al., 1999, Fias, 1996, Fischer and Rottmann, 2005, Gevers and Lammertyn, 2005, Shaki et al., 2009, Zhou et al., 2008).

Research has also shown that the SNARC effect is dependent on cultural and experiential factors. For example, Dehaene and colleagues (1993) found that Arabic readers, who read from right to left, showed a reversed SNARC effect. Furthermore, the reversed SNARC effect was weakened in Arabic readers who learned English as a second language (and hence learned to read from left to right). Interestingly, in a study of Chinese readers in Taiwan (Hung, Hung, Tzeng, & Wu, 2008), the direction of the SNARC effect varied within the same participants, depending on the writing system used in the task; Arabic numbers were mentally aligned with a horizontal left-to-right direction, whereas Chinese number words were aligned vertically with a top-to-bottom direction. The different orientations are due to the dominant context in which the numerical materials are often encountered because in Taiwan Arabic numbers are printed left to right, but Chinese number words are sometimes printed top to bottom. In sum, cultural factors such as the layout of printed words and daily experience with numbers may influence the SNARC effect.

Although the SNARC effect has been consistently demonstrated among adults, little is known about its onset and early development. In their meta-analysis, Wood, Willmes, Nuerk, and Fischer (2008) found 108 empirical experiments of the SNARC effect with participants ranging in age from 9 to 66 years. Based on a subset (n = 17) of these experiments, they concluded that the SNARC effect increased with age from childhood to elderly age. Wood and colleagues’ review did not include any earlier age groups, perhaps because Berch and colleagues’ (1999) original study of the SNARC effect among young children showed that the SNARC effect did not emerge until Grade 3 (mean age = 9.2 years; but see Schweiter, Weinhold Zulauf, & von Aster, 2005, for evidence that one third of second graders in Switzerland showed the SNARC effect). Since Wood and colleagues’ (2008) meta-analysis, however, there is more evidence of an earlier onset of the SNARC effect. Van Galen and Reitsma (2008) tested 7-, 8-, and 9-year-olds (corresponding to first, second, and third graders) and adults in The Netherlands with two different tasks: a magnitude judgment task (in which number magnitude is essential) and a gray box detection task (in which number magnitude is irrelevant because participants were asked to respond to the box on the right or the left of the number that may turn gray). Results showed that the SNARC effect was evident in all age groups for the magnitude judgment task, but it did not appear until third grade for the gray box detection task. These results suggest that the onset of the SNARC effect depends on whether numerical magnitude information is explicitly processed. When it is not explicitly processed, as in the gray box detection task in van Galen and Reitsma (2008) and the parity judgment task in Berch and colleagues (1999) and Schweiter and colleagues (2005), the SNARC effect does not appear until 8 or 9 years of age. When numerical magnitude is explicitly processed, the SNARC effect appears earlier (7 years of age in van Galen & Reitsma, 2008).

Although there is only limited research on the early development of the SNARC effect, several previous studies explored early foundations of the association between numbers and space. Opfer and Furlong (2011) and Opfer, Thompson, and Furlong (2010) found that, in a spatial search task, 4-year-olds showed a bias toward left-to-right orientation. It is plausible that this bias might be extended to numerical representation. Moreover, de Hevia and Spelke (2010) showed that even preverbal infants transferred the discrimination of an ordered series of numerosities to the discrimination of an ordered series of line lengths, suggesting an early predisposition to a correspondence between representations of numerical magnitude and spatial length. This result suggests an early development of spatial representation of non-symbolic numerical magnitude, which might serve as the basis for the development of spatial representation of symbolic numbers.

Given that young children have early predisposition for associating numbers/quantities with space and that cultural factors can affect the SNARC effect, it can be speculated that the SNARC effect may appear earlier than previously documented when studied among children who show an early advantage in number cognition. Chinese children have been found to have an advantage in number-related tasks such as digit span, counting, arithmetic, number estimates, and number Stroop tasks (Chen and Stevenson, 1988, Huntsinger et al., 1997, Miller et al., 2005, Miller et al., 1995, Stevenson et al., 1993, Sy et al., 2003, Xu et al., 2013, Zhou et al., 2007). For example, Zhou and colleagues (2007) found that Chinese kindergarteners (mean age = 5.8 years) showed automatic processing of number magnitude based on a number Stroop task. This age of onset is earlier than that of children in other countries, for example, the end of the first grade (mean age = 7.32 years) in Israel (Rubinsten, Henik, Berger, & Shahar-Shalev, 2002), the third grade (mean age = 8.4 years) in Italy (Girelli, Lucangeli, & Butterworth, 2000), and the third grade (mean age = 9.2 years) in the United States (Berch et al., 1999).

In the current study, we used the standard parity judgment task (Dehaene et al., 1993) to examine the SNARC effect in eight age groups of Chinese participants: kindergarteners, first- through sixth-grade students, and adults. It should be noted that the SNARC effect obtained from the parity judgment task is likely to be based on automatic processing of magnitude because parity judgment does not involve explicit processing of magnitude information. Given the previous finding of Chinese children’s early development of automatic processing of numbers (Zhou et al., 2007), we expected to find the automatic SNARC effect among the early age groups of our Chinese participants (i.e., kindergarten or first or second grade vs. third grade for American children [Berch et al., 1999] and Dutch children [van Galen & Reitsma, 2008]). We also expected that the size of the SNARC effect would increase with age, consistent with Wood and colleagues’ (2008) meta-analysis.

Section snippets

Participants

Participants were 314 healthy right-handed children (from kindergarteners to sixth graders) and adults. The children’s handedness was assessed by asking both the teachers and the children themselves which hand the children used to hold chopsticks or a spoon for eating and a pen for writing. Children were recruited from two kindergartens and three primary schools in a middle-class neighborhood in Beijing, China. Adults were college students recruited from Beijing Normal University. Children were

Results

Table 2 shows the mean reaction times (RTs) by response hand and number size for each age group. The grand mean error rate for all participants was 6.43%, with an average error rate of 7.8% for kindergarteners, 3.5% for first graders, 6.1% for second graders, 6.6% for third graders, 6.7% for fourth graders, 6.2% for fifth graders, 6.9% for sixth graders, and 4.9% for adults. Because of the low error rates and the overall consistency in their results with the RT data based on preliminary

Discussion

The current study used the classic parity judgment task to investigate the development of numerical–spatial representations across eight age groups of Chinese participants from kindergarteners to adults. The results showed that overall error rates were very low, indicating that Chinese children as young as kindergarteners had a clear understanding of parity. Participants’ RTs decreased significantly with age, reflecting participants’ increasing efficiency in processing parity as well as overall

Acknowledgment

This research was supported by two grants from the Natural Science Foundation of China (31271187 and 31221003).

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