Children’s Non-symbolic, Symbolic Addition and Their Mapping Capacity at 4–7 Years Old

Abstract

The study aimed to examine the developmental trajectories of non-symbolic and symbolic addition capacities in children and the mapping ability between these two. We assessed 106 4- to 7-year-old children and found that 4-year-olds were able to do non-symbolic addition but not symbolic addition. Five-year-olds and older were able to do symbolic addition and their performance in symbolic addition exceeded non-symbolic addition in grade 1 (approximate age 7). These results suggested non-symbolic addition ability emerges earlier and is less affected by formal mathematical education than symbolic addition. Meanwhile, we tested children’s bi-directional mapping ability using a novel task and found that children were able to map between symbolic and non-symbolic representations of number at age 5. Their ability in mapping non-symbolic to symbolic number became more proficient in grade 1 (approximate age 7). This suggests children at age 7 have developed a relatively mature symbolic representation system.

Children’s Non-symbolic and Symbolic Numerical Representations and Their Associations With Mathematical Ability

“…Similarly, previous studies ( Gilmore et al, 2007 ; Kolkman et al, 2013 ) reported that children started being able to do symbolic representation task at the age of 5, before the start of formal schooling. Furthermore, researchers had found symbolic representation skills developed continuously during childhood ( Li et al, 2017 ). These results indicate the acquired nature of the symbolic comparison skills.…”

“…However, symbolic comparison ability is affected by education ( Xenidou-Dervou et al, 2015 ), and its emergence requires a certain foundation ( Kolkman et al, 2013 ). Many researchers have found that children’s symbolic representation skill will rapidly increase in the 1st grade ( Xenidou-Dervou et al, 2015 ; Li et al, 2017 ). Therefore, we observed that children could pass non-symbolic tasks at a very young age, but they were not able to pass symbolic representation tasks until 5 years old.…”

The Stability of Individual Differences in Basic Mathematics‐Related Skills in Young Children at the Start of Formal Education

“…There is evidence to suggest that a nonsymbolic addition task (e.g., Barth, La Mont, Lipton, & Spelke, ) may be a more viable alternative measure of the ANS. Several studies (Barth, Beckmann, & Spelke, ; Barth et al, ; Li et al, ) have found that young children can perform above chance on this task and show similar patterns of responding as adults. Additionally, this task appears to measure a similar underlying construct as the Dot comparison task (Gilmore, Attridge, De Smedt, & Inglis, ).…”

Validating the Early Numeracy Teacher Rating scale for Preschoolers (TRS-EN)

“…two dogs and three cats equals five animals) and symbolic addition skills (i.e. 2 + 3 = 5; Li et al 2017). They also begin to recognize that the outcome in addition tasks is larger than either one of the addends (Gelman 1972).…”

“…The reviewed longitudinal studies that covered both 3-and 4-year-olds suggested that counting (Chu et al 2019;) and understanding numerical relations (Purpura et al 2017;Scalise and Ramani 2021) were the strongest predictors of later mathematical performance in these age groups. As basic arithmetical performance is highly associated with counting skills and as research shows that children start presenting non-symbolic arithmetic skills prior to the age of 5, basic arithmetic skills were also included in the scale (Li et al 2017;Litkowski et al 2020). By this decision, a possible ceiling effect was also accounted for.…”