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.
Highlights
The Developmental Trajectories of Non-symbolic and Symbolic Addition CapacitiesThe capacity of non-symbolic addition is a skill of quantity calculation, which is based on the nonsymbolic representation system, such as dots
The results showed all age groups performed well above chance-level in the non-symbolic addition task
We found children were able to do non-symbolic addition at age 4 and they were able to do symbolic addition at age 5
Summary
The Developmental Trajectories of Non-symbolic and Symbolic Addition CapacitiesThe capacity of non-symbolic addition is a skill of quantity calculation, which is based on the nonsymbolic representation system, such as dots. It is widely agreed that the non-symbolic addition ability was based on the approximate number system (ANS) system (Barth et al, 2005, 2006, 2008). It is an inherent and universal system shared by animals and humans (Wynn, 1992; Flombaum et al, 2005) It is not affected by culture (Pica et al, 2004). It represents quantities in an approximate way (Feigenson et al, 2004). The range of number and the accuracy that this system is able to manipulate increase with age (Halberda et al, 2008; Praet and Desoete, 2014)
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