Processing the Order of Symbolic Numbers: A Reliable and Unique Predictor of Arithmetic Fluency


  • Stephan E. Vogel
  • Trent Haigh
  • Gerrit Sommerauer
  • Melanie Spindler
  • Clemens Brunner
  • Ian M. Lyons
  • Roland H. Grabner


A small but growing body of evidence suggests a link between individual differences in processing the order of numerical symbols (e.g., deciding whether a set of digits is arranged in ascending/descending order or not) and arithmetic achievement. However, the reliability of behavioral correlates measuring symbolic and non-symbolic numerical order processing and their relationship to arithmetic abilities remain poorly understood. The present study aims to fill this knowledge gap by examining the behavioral correlates of numerical and non-numerical order processing and their unique associations with arithmetic fluency at two different time points within the same sample of individuals. Thirty-two right-handed adults performed three order judgment tasks consisting of symbolic numbers (i.e., digits), non-symbolic numbers (i.e., dots), and letters of the alphabet. Specifically, participants had to judge as accurately and as quickly as possible whether stimuli were ordered correctly (in ascending/descending order, e.g., 2-3-4; ●●●●-●●●-●●; B-C-D) or not (e.g., 4-5-3; ●●●●-●●●●●-●●●; D-E-C). Results of this study demonstrate that numerical order judgments are reliable measurements (i.e., high test-retest reliability), and that the observed relationship between symbolic number processing and arithmetic fluency accounts for a unique and reliable portion of variance over and above the non-symbolic number and the letter conditions. The differential association of symbolic and non-symbolic numbers with arithmetic support the view that processing the order of symbolic and non-symbolic numbers engages different cognitive mechanisms, and that the ability to process ordinal relationships of symbolic numbers is a reliable and unique predictor of arithmetic fluency.