Abstract
The nature of the relation between non-symbolic and symbolic magnitude processing in the prediction of arithmetic remains a hotly debated subject. This longitudinal study examined whether the influence of non-symbolic magnitude processing on arithmetic is mediated by symbolic processing skills. A sample of 130 children with age-adequate (N = 73) or below-average (N = 57) achievement in early arithmetic was followed from the end of Grade 1 (mean age: 86.9 months) through the beginning of Grade 4. Symbolic comparison of one- and two-digit numbers serially mediated the effect of non-symbolic comparison on later arithmetic. These results support a developmental model in which non-symbolic processing provides a scaffold for single-digit processing, which in turn influences multi-digit processing and arithmetic. In conclusion, both non-symbolic and symbolic processing play an important role in the development of arithmetic during primary school and might be valuable long-term indicators for the early identification of children at risk for low achievement in arithmetic.
Highlights
The development of arithmetic skills in primary school is of fundamental importance in modernday societies: already at the age of seven, arithmetic abilities predict adult socio-economic status over and above the effects of intelligence and socio-economic status at birth (Ritchie and Bates, 2013)
In the non-symbolic comparison task the correlation between median RTs and response accuracy was only moderate, r = 0.324, p < 0.001 and response accuracy was close to ceiling in both symbolic comparison tasks
One extreme outlier score in the non-symbolic comparison task was moved to the tail of the distribution to the second highest score to avoid overemphasizing its effect on the results
Summary
The development of arithmetic skills in primary school is of fundamental importance in modernday societies: already at the age of seven, arithmetic abilities predict adult socio-economic status over and above the effects of intelligence and socio-economic status at birth (Ritchie and Bates, 2013). Children’s arithmetic development has often been linked to their “number sense,” meaning the ability to deal with non-symbolic magnitudes, for example dots or other concrete objects. Typical tasks involve choosing the numerically larger of two sets of objects (e.g., or ). This ability has been proposed to reflect the acuity of the supposedly innate approximate number system (ANS). Numerical Processing and Arithmetic non-symbolic skills are steadily refined, until young adults can successfully discriminate between sets with a ratio of 10:11 (Halberda and Feigenson, 2008)
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