Reliability and Validity of Nonsymbolic and Symbolic Comparison Tasks in School-Aged Children

Abstract

Basic numerical processing has been regularly assessed using numerical nonsymbolic and symbolic comparison tasks. It has been assumed that these tasks index similar underlying processes. However, the evidence concerning the reliability and convergent validity across different versions of these tasks is inconclusive. We explored the reliability and convergent validity between two numerical comparison tasks (nonsymbolic vs. symbolic) in school-aged children. The relations between performance in both tasks and mental arithmetic were described and a developmental trajectories' analysis was also conducted. The influence of verbal and visuospatial working memory processes and age was controlled for in the analyses. Results show significant reliability (p < .001) between Block 1 and 2 for nonsymbolic task (global adjusted RT (adjRT): r = .78, global efficiency measures (EMs): r = .74) and, for symbolic task (adjRT: r = .86, EMs: r = .86). Also, significant convergent validity between tasks (p < .001) for both adjRT (r = .71) and EMs (r = .70) were found after controlling for working memory and age. Finally, it was found the relationship between nonsymbolic and symbolic efficiencies varies across the sample's age range. Overall, these findings suggest both tasks index the same underlying cognitive architecture and are appropriate to explore the Approximate Number System (ANS) characteristics. The evidence supports the central role of ANS in arithmetic efficiency and suggests there are differences across the age range assessed, concerning the extent to which efficiency in nonsymbolic and symbolic tasks reflects ANS acuity.

Research on numerical cognition in Chile: current status, links to education and challenges (Investigación en cognición numérica en Chile: estado actual, vínculos con la educación y desafíos)

“…Research conducted in Chile has also addressed the evaluation of basic numerical skills (Castro, Estévez, Gómez, & Dartnell, 2017b; Sepúlveda, Rodríguez, & Peake, 2020), and the study of strategies and calculation errors (Cerda, Flores, & Pérez, 2015; Gálvez et al, 2011).…”

“…Similar processes have been studied with older children. Castro et al (2017b) evaluated the performance of students from grades 1 to 6 in primary school using symbolic and non-symbolic comparison tasks and their relation with mental arithmetic calculation. The results showed that both comparison tasks were highly correlated and predicted arithmetic performance, suggesting that both symbolic and non-symbolic comparison tasks evaluated the approximate representation system, while simultaneously predicting performance in arithmetic calculation.…”

“…Procesos similares han sido estudiados con niños mayores. Castro et al (2017b) evaluaron el desempeño de estudiantes desde 1° a 6° de educación básica en tareas de comparación simbólica y no simbólica y su relación con el cálculo aritmético mental. Los resultados mostraron que ambas tareas de comparación estaban altamente correlacionadas y predijeron el rendimiento aritmético, sugiriendo que tanto las tareas de comparación simbólica como no simbólica evaluaban el sistema de representación aproximado, y a la vez predecían el desempeño en cálculo aritmético.…”

“…Research conducted in Chile has also addressed the evaluation of basic numerical skills (Castro, Estévez, Gómez, & Dartnell, 2017b;Sepúlveda, Rodríguez, & Peake, 2020), and the study of strategies and calculation errors (Cerda, Flores, & Pérez, 2015;Gálvez et al, 2011). Sepúlveda et al (2020) evaluated basic numerical skills in children from different SES in their last year of early childhood education.…”

“…La investigación realizada en Chile también ha abordado las evaluación de las habilidades numéricas básicas (Castro, Estévez, Gómez, & Dartnell, 2017b;Sepúlveda, Rodríguez, & Peake, 2020) y el estudio de estrategias y errores de cálculo (Cerda, Flores, & Pérez, 2015;Gálvez et al, 2011). Sepúlveda et al (2020) evaluaron habilidades numéricas básicas en niños de último año de educación parvularia de distinto NSE.…”