Effect of Non-canonical Spatial Symmetry on Subitizing

Abstract

Subitizing refers to ability of people to accurately and effortlessly enumerate a small number of items, with a capacity around four elements. Previous research showed that “canonical” organizations, such as familiar layouts on a dice, can readily improve subitizing performance of people. However, almost all canonical shapes found in the world are also highly symmetrical; therefore, it is unclear whether previously reported facilitative effect of canonical organization is really due to canonicality, or simply driven by spatial symmetry. Here, we investigated the possible effect of symmetry on subitizing by using symmetrical, yet non-canonical, shape structures. These symmetrical layouts were compared with highly controlled random patterns (Experiment 1), as well as fully random and canonical patterns (Experiment 2). Our results showed that symmetry facilitates subitizing performance, but only at set size of 6, suggesting that the effect is insufficient to improve performance of people in the lower or upper range. This was also true, although weaker, in reaction time (RT), error distance measures, and Weber Fractions. On the other hand, canonical layouts produced faster and more accurate subitizing performances across multiple set sizes. We conclude that, although previous findings mixed symmetry in their canonical shapes, their findings on shape canonicality cannot be explained by symmetry alone. We also propose that our symmetrical and canonical results are best explained by the “groupitizing” and pattern recognition accounts, respectively.

One step beyond! The conjunction-bias between non-spatial (Color) and spatial Grouping cues over approximate number perception extends to Symmetry and Connectedness.

“…Besides the ANS, it would be interesting to investigate how grouping cues such as symmetry/shape, and the effect of grouping conjunctions, impact the Groupitizing strategies, in order to increment the accuracy during Groupitizing process. For example, it is not unlikely that subsets formed by geometric/symmetrical spatial disposition (e.g., a square) of items would increase the ability to individuate and count this subset, increasing the overall accuracy in counting tasks (e.g., Gheorghiu & Goldschmitt, 2022;Hsin, Lo, & Tseng, 2021). Moreover, if the dots forming the geometrical shape are also similar in color, this conjunction of geometrical and color cues would speed up further the process (e.g., as a linear sum of the single conditions).…”

Small number enumeration processes of deaf or hard-of-hearing students: A study using eye tracking and artificial intelligence

“…In this case, the child does not need to perceive items serially but can associate the pattern to a number word (Von Glasersfeld, 1982 ). In general, the canonical representations are symmetrical and, thus, allow the use of patterns or symmetries for number enumeration (Hsin et al, 2021 ).…”